DISS. ETH NO. 23499
W I T H I N - H O S T P O P U L AT I O N D Y N A M I C S A N D T H E E V O L U T I O N
O F D R U G R E S I S TA N C E I N B A C T E R I A L I N F E C T I O N S
A thesis submitted to attain the degree of
DOCTOR OF SCIENCES of ETH ZÜRICH
(Dr. sc. ETH Zürich)
presented by
DOMINIQUE RICHARD CADOSCH
M.Sc. ETH Zürich, Switzerland
born on 30.05.1984
citizen of Vaz/Obervaz GR, Switzerland
accepted on the recommendation by
Prof. Dr. Sebastian Bonhoeffer, examiner
Prof. Dr. Theodore H. Cohen, co-examiner
PD Dr. Roland Regoes, co-examiner
2016
To my parents, Ruth and Edgar Cadosch,
for their sedulous support and guidance.
“I have a friend who’s an artist and has sometimes taken a view which I don’t
agree with very well. He’ll hold up a flower and say "look how beautiful it is,"
and I’ll agree. Then he says "I as an artist can see how beautiful this is but you
as a scientist take this all apart and it becomes a dull thing," and I think that
he’s kind of nutty. First of all, the beauty that he sees is available to other people
and to me too, I believe. Although I may not be quite as refined aesthetically
as he is ... I can appreciate the beauty of a flower. At the same time, I see
much more about the flower than he sees. I could imagine the cells in there, the
complicated actions inside, which also have a beauty. I mean it’s not just beauty
at this dimension, at one centimeter; there’s also beauty at smaller dimensions,
the inner structure, also the processes. The fact that the colors in the flower
evolved in order to attract insects to pollinate it is interesting; it means that
insects can see the color. It adds a question: does this aesthetic sense also exist
in the lower forms? Why is it aesthetic? All kinds of interesting questions
which the science knowledge only adds to the excitement, the mystery and the
awe of a flower. It only adds. I don’t understand how it subtracts.”
Richard Feynman
v
CONTENTS
summary
1
zusammenfassung
3
1
2
general introduction
5
the role of adherence and retreatment in de novo emergence of mdr-tb
11
3 alternative treatment strategies for tuberculosis
39
4 considering antibiotic stress-induced mutagenesis
61
5 general discussion
77
acknowledgements
103
curriculum vitae
105
vii
S U M M A RY
This thesis investigates the influence of population dynamics of bacterial infections
and their treatment on the probability of the emergence of drug resistance. In particular the study of the effects of suboptimal patient compliance, various treatment regimens and the possibility of antibiotic stress-induced mutagenesis call for a deeper
understanding of the mechanisms at play. The work presented in this study uses
mathematical models that incorporate pharmacokinetics and -dynamics, as well as
the effect of bacterial traits to make predictions about the evolution of drug resistance.
All dynamics are being simulated at the within-host level.
Chapter 1 is a general introduction of the central themes of this thesis. It gives
a short overview over the advent of the study of population dynamics as a field of
research. The global significance of tuberculosis and the problems that arise due to
the frequent occurrence of drug resistance are being explained. I also address the
issue of suboptimal treatment adherence and rationalize the value of mathematical
modeling to tackle the questions in the following chapters.
In Chapter 2, we investigate how adherence to the treatment regimen and the
use of a standard retreatment regimen are involved in the emergence of multidrugresistant tuberculosis (MDR-TB). MDR-TB is characterized by its resistance against
isoniazid and rifampicin, two important first-line drugs. To answer the question
whether there is a considerable probability for the de novo emergence of MDR-TB we
simulate patients with various degrees of adherence to a standard treatment regimen
containing a combination of four drugs. Patients who do not achieve complete clearance of the infection undergo a prolonged retreatment regimen with an additional
fifth drug.
Chapter 3 explores proposed alternative strategies for the treatment of pulmonary
tuberculosis. We extend the previously established model and introduce more detailed absorption pharmacokinetics. This extension of the model enables us to investigate the potential benefit and effects of extended-release formulations of rifampicin.
Extended-release formulations show a much lower absorption and thus exhibit a
lower but longer time-concentration profile. Such formulations are compared in
daily or intermittent treatment regimens with conventional rifampicin formulations
and their influence on the probability of treatment failure and the emergence of
drug resistance are recorded. Furthermore, we also tested the advantage and risks
involved with increased rifampicin doses.
Chapter 4 then deals with the concept of antibiotic stress-induced mutagenesis
(ASIM). The concept of stress-induced mutagenesis describes the increase of the
bacterial mutation rate in response to a stress, such as the exposure to certain antibiotics. We propose a model to simulate the increase of the mutation rate in a
drug concentration-dependent manner. With this ASIM model we then investigate
how much a model with a fixed mutation rate would underestimate the risk for the
emergence of a drug resistance mutation. Lastly, we study whether the regimen of
administering a stress-inducing drug and a non-stress-inducing drug has an influence on the emergence of resistance if we consider ASIM.
1
2
summary
Finally, in Chapter 5 I put the results and conclusions from the preceding chapters
in a bigger perspective. Furthermore, I present some future directions that could be
explored with further research.
Z U S A M M E N FA S S U N G
Diese Dissertation untersucht den Einfluss von Populationsdynamik in bakteriellen Infektionen und deren Behandlung auf die Wahrscheinlichkeit des Auftretens
von Medikamentenresistenz. Im Besonderen die Analyse der Effekte suboptimaler
Patienten-Adhärenz, die Anwendung unterschiedlicher Behandlungsstrategien und
die Möglichkeit stress-bedingter Mutagenese durch Antibiotika verlangen nach einem tiefgreifenderem Verständnis für die zugrundeliegenden Wirkmechanismen. Die
Arbeit, welche in dieser Dissertation vorgestellt wird nutzt mathematische Modelle, welche Pharmakokinetik und Pharmakodynamik, sowie Effekte von bakteriellen
Merkmalen beinhalten, um Prognosen in Bezug auf die Evolution von Medikamentenresistenz aufstellen zu können. Alle Dynamiken werden dabei jeweils auf der
Ebene eines einzelnen Patienten simuliert.
Kapitel 1 ist eine allgemeine Einführung in die zentralen Themen dieser Dissertation. Das Kapitel gibt einen kurzen Überblick über die Ursprünge der Erforschung
von Populationsdynamiken. Die globale Bedeutung von Tuberkulose sowie die Probleme, welche durch das häufige Auftreten von Medikamentenresistenz entstehen,
werden erklärt. Ich spreche auch die Thematik von suboptimaler Adhärenz an sowie
den Wert von mathematischer Modellierung, um die Fragestellungen der folgenden
Kapitel anzupacken.
In Kapitel 2 untersuchen wir, wie Adhärenz während der Behandlung und die Anwendung einer standardisierten Nachbehandlung involviert sind in das Auftreten
von multiresistenter Tuberkulose (engl. multi-drugresistant tuberculosis; MDR-TB).
MDR-TB ist gekennzeichnet durch die Resistenz gegenüber Isoniazid und Rifampicin, zwei wichtigen standardmässig eingesetzten Antibiotika. Um die Frage zu beantworten, ob es eine nennenswerte Wahrscheinlichkeit gibt für das Auftreten de novo
MDR-TB, simulieren wir Patienten mit unterschiedlichen Adhärenzen gegenüber einer Behandlungsstrategie mit einer Kombination von vier Medikamenten. Patienten,
in denen die Infektion nicht vollständig sterilisiert wurde, werden einer längeren
Nachbehandlung mit einem zusätzlichen fünften Medikament unterzogen.
Kapitel 3 erforscht alternative Behandlungsvorschläge für Lungentuberkulose. Wir
erweitern das zuvor etablierte Modell und führen eine detailiertere AbsorptionsPharmakokinetik ein. Diese Erweiterung des Modells ermöglicht es uns, die potentiellen Vorteile und Auswirkungen eines Retard-Präparats von Rifampicin zu untersuchen. Retardarzneiformen zeichnen sich durch eine verlangsamte Absorption
aus und weisen deshalb eine niedrigeres aber gestrecktes Konzentrationsprofil. Solche Arzeneiformen werden in täglichen und intermittierenden Behandlungsregimes
verglichen mit konventionellen Rifampicin-Präparaten und die Wahrscheinlichkeiten
für ein Behandlungsversagen sowie das Auftreten von Medikamentenresistenz werden ermittelt. Des Weiteren testen wir ebenfalls die Vorteile und Risiken die mit
erhöhten Rifampicindosen verbunden sind.
Kapitel 4 behandelt das Konzept von stressbedingter Mutagenese durch Antibiotika (engl. antibiotic stress-induced mutagenesis; ASIM). Das Konzept von stressbedingter Mutagenese beschreibt den Anstieg der bakteriellen Mutationsrate als Reakti3
4
zusammenfassung
on auf einen äusseren Stressreiz, wie die Exposition gegenüber gewissen Antibiotika.
Wir stellen ein Modell vor, um den Anstieg der Mutationsrate in Abhängigkeit zur
Medikamentenkonzentration zu simulieren. Mit diesem ASIM-Modell untersuchen
wir dann, wie stark ein Modell mit einer festen Mutationsrate das Risiko für das
Auftreten von einer Mutation, die zu Medikamentenresistenz führt, unterschätzen
würde. Schliesslich studieren wir ob ein Behandlungsregime, in dem ein stressauslösendes mit einem nicht-stressauslösenden Medikament kombiniert wird, einen Einfluss auf die Auftrittswahrscheinlichkeit von Medikamentenresistenz hat, wenn wir
ASIM in Betracht ziehen.
Zuletzt stelle ich in Kapitel 5 die Resultate und Schlussfolgerungen der vorangegangenen Kapitel in einen grösseren Kontext. Des Weiteren stelle ich mögliche
Richtungen vor, welche zukünftige Studien erforschen könnten.
1
GENERAL INTRODUCTION
The advent of the scientific discussion of population dynamics is probably An Essay on the Principle of Population [1] by Thomas Robert Malthus. In this book Malthus
introduces the Malthusian growth model, which describes the exponential growth of
a population over time. This growth is governed by the population growth rate r,
sometimes called Malthusian parameter. While this model may seem rather simple
it is still a basic component for most population dynamics models today. It is applicable to all scales of life - from large animals and plants down to tumor cells and
bacteria.
Since Thomas Robert Malthus the modeling of populations evolved further to reflect
more complex relationships. The influence of density dependence on population
growth can be achieved by introducing a carrying capacity parameter that turns the
exponential growth model into a logistic function [2]. Further one could consider
the mutual influence of two distinct populations that are either competing over the
same resource or that are in a predator-prey relationship [3]. The complexity may
increase even more if we consider migration and mutation as well as temporal and
spatial dependencies of parameters.
Particularly in the case of infectious diseases the study of population dynamics
can be of great value. Historically this has been done predominantly on an epidemiological scale but scientific progress provided a more detailed picture of intra-host
dynamics, which enables the development of models dealing with viral and bacterial
populations. Among pathogens viruses represent a special case because they depend
on the replication machinery of other living cells to proliferate. Bacteria on the other
hand usually reproduce through binary fission.
The study of population dynamics is of particular interest when we try to understand the underlying mechanisms of the emergence of drug resistance in bacterial
infections. Here we can examine on an epidemiological scale the population dynamics of patients who are at risk of being infected, actually infected or who have
recovered from an infection [4] or we can study the population dynamics of bacteria (or viruses) inside a patient. In the first case we are interested in the relative
spread of susceptible and resistant pathogens in a host population and in the later
case we focus on the spread of individual bacteria and the evolution of drug resistant
subgroups of the overall bacterial population within a single host.
This thesis concentrates on the study of the within-host population dynamics of
a bacterial infection with a particular interest in the corresponding mechanisms that
may lead to drug resistance. These studies are performed with the help of stochastic computer simulations. Two chapters of this thesis deal with the influence of
treatment and retreatment strategies on the emergence of drug resistance in pulmonary tuberculosis infections. The last chapter is a more conceptual work that
investigates the impact of antibiotic stress-induced mutagenesis in any bacterial infection in which this may occur.
5
6
general introduction
1.1
tuberculosis
Two chapters of this thesis focus on the population dynamics and the treatment of
pulmonary tuberculosis. For years the research funding for tuberculosis has only
been a fraction of what is spent on HIV/AIDS [5]. Concerns about tuberculosis
may be often less acute due to a reduced awareness among the population in developed countries where incidence rates of TB are mostly rather low [6]. However,
there are still about 2 billion people worldwide who are latently infected with TB
[7], 9.6 million people have fallen ill and 1.5 million people died in 2014 due to a
TB infection [6]. When in the middle of the 20th century effective antibiotics like
streptomycin, isoniazid and rifampicin were discovered tuberculosis was thought to
be under control [8]. Today we have to acknowledge that TB remains a global health
problem. Even though the global incidence rates of TB started to decline the frequency of multidrug-resistant TB (MDR-TB) cases did not decline despite increased
efforts for specialized MDR-TB treatments [6]. MDR-TB is characterized by its resistance against at least isoniazid and rifampicin, two important first-line drugs [6]. In
some countries MDR-TB and extensively drug-resistant TB (XDR-TB) have become
a growing epidemic [9; 10; 11]. Besides resistance against isoniazid and rifampicin
XDR-TB is also resistant against at least one fluoroquinolone and either kanamycin,
amikacin or capreomycin [12].
The standard short-course therapy for TB lasts six months. During the intensive
phase of the first two months isoniazid, rifampicin, pyrazinamide and ethambutol
are administered as a combination therapy. In the following two months of the continuation phase only isoniazid and rifampicin are given [13]. The reasoning behind
the application of a combination therapy is based on concerns regarding the loss of
efficacy due to the pre-existence or de novo emergence of mono-resistant subpopulations [13]. During monotherapy it could be possible for bacteria that already carry a
corresponding resistance mutation to gain a selective advantage, eventually replace
the susceptible bacteria and render the therapy ineffective. In combination therapy
there should always be another drug against which mono-resistant bacteria are still
susceptible and are subsequently eradicated.
1.2
adherence
Non-adherence to treatment has always been considered a major risk factor for the
emergence of de novo drug resistance [14; 15]. One of the main goals of the directly
observed treatment, short course strategy (DOTS) by the WHO is to ensure a sufficiently high level of adherence to ensure treatment success [16]. The actual monitoring of DOTS in resource-limited settings is often provided by community members
[17]. However, the actual degree of adherence by patients under such communitybase programs has not been assessed [17] and these programs are often beyond direct
control of health care providers. It is generally often difficult to obtain accurate estimates of patient adherence. Patients may not truthfully answer in a survey and
more sophisticated measures like a Medication Event Monitoring System (MEMS)
[17] may only be conducted on a small scale. It is also imaginable that it not necessarily patient compliance that jeopardizes treatment success, discontinuous drug
1.3 methodology
supply or other factors that may occasionally prevent physical access to drugs (e.g.
unreliable means of transport, armed conflicts etc.) and influence overall adherence
negatively.
Problems that may arise due to suboptimal patient adherence can be relatively
conveniently examined with the help of mathematical models. Mathematical models
allow us to assess the implications of reduced adherence. We are able to gather
estimates about what levels of adherence are still reasonably safe and when do we
face serious consequences. When we assume suboptimal adherence and simulate
the corresponding population dynamics we get predictions about possible negative
treatment outcomes like treatment failure and the emergence of resistance and we
also gather estimates about the strength of association between different adherence
levels and those outcomes.
1.3
methodology
In all chapters of this thesis we are applying mathematical models that are being
simulated in silico. Mathematical models in evolutionary biology serve generally two
purposes that are also relevant for the conclusions of this thesis. Firstly, mathematical
models can be used to do "proof-of-concept" tests [18]. Verbal or theoretical concepts
can be translated into a mathematical model and it can be assessed whether the
hypothesized results of the theory coincide with the predictions of the model. This
is particularly useful for concepts that are difficult to prove in vivo or in vitro because
of experimental constraints or because of ethical reasons.
The second purpose of mathematical models becomes evident when their validity
has been confirmed by real-life observations. Then they can be used to explore new
directions and make predictions about the natural world. The two purposes of computational modeling therefore engage in an ideally mutually stimulating interaction
with empirical sciences: The theory about empirical observations can be tested in
computational models, which then again may extend the currently existing theory
and inspire new empirical investigations.
A crucial point of contact between empiricism and modeling are assumptions. A
hypothesis that is verbalized to explain an empirically observed phenomenon contains specific assumptions. These assumptions also have to be the foundation of a
mathematical model. If the model is then not able to corroborate the hypothesis without violating the basic assumptions the hypothesis may have to be reconsidered or
reformulated. The reformulation of the hypothesis may be supported by the model
because the model allows to test whether changing one or a few assumptions might
be sufficient to explain the observed phenomenon.
In this thesis we use computational modeling for both scopes. On one hand, the
mathematical model with which we simulate the course of infection and treatment
of pulmonary tuberculosis is able to replicate patient outcomes that other studies
observed previously. It is further able to confirm hypotheses about the progression to
higher levels of drug resistance and the risks and chances involved with suboptimal
and alternative treatment strategies. On the other hand, our mathematical model
allows us to make qualitative predictions about the potential benefits of retreatment
7
8
general introduction
regimens and alternative treatment strategies. These results hopefully fuel further
research in these directions.
1.4
overview of chapters
This thesis contains three studies that I conducted during my doctoral studies (Chapters 2–4). Chapters 2 and 3 explore how treatment of a pulmonary tuberculosis
infection affects the probabilities for the emergence of drug resistance. Chapter 4 is
a more conceptual work and examines how increased mutation rates due to stress
elicited by the exposure to antibiotics changes the risk for the emergence of drug
resistance. The thesis then concludes with a general Discussion (Chapter 5).
In Chapter 2 we present a model framework that simulates the intra-host pathogenesis during an acute pulmonary tuberculosis (TB) infection and its treatment. The
population dynamics of M. tuberculosis is modeled in three distinct compartments
within the lung: macrophages, granulomas and open cavities [19]. The treatment
that we apply and the retreatment, in case the first treatment is not able to clear
the infection, correspond to standard regimens recommended by the WHO [20; 21].
The stochastic model simulates patient that differ in several pharmacodynamic and
pharmacokinetic parameters and they adhere to the treatment regimen to various
degrees. Eventually after treatment and retreatment, patients are diagnosed as either
successfully treated, if they do not harbor any M. tuberculosis bacteria anymore, failed
patients, if there are any bacteria left, failed patients with multi-drug resistant TB, if
10% or more of the remaining bacteria are at least resistant against isoniazid and
rifampicin, or failed patients with fully resistant TB, if 10% or more of the remaining
bacterial population is resistant against all drugs that have been applied.
Chapter 3 considers alternative treatment strategies for pulmonary tuberculosis.
To study these strategies we extend the model framework that we used in Chapter
2 with a more detailed pharmacokinetic model. Besides the elimination of the drug
in the patient due to excretion the pharmacokinetics model now also simulates the
absorption of the drugs after administration. This enables us to test the efficacy of
drug formulations that have lower absorption rate constants. Low absorption rate
constants are a characteristic feature of extended-release formulations [22]. In patient simulations we examine how combinations of intermittent and daily treatment
regimens with and without the use of extended-release formulations of rifampicin
influence the probabilities for a successful treatment outcome and for the emergence
of resistance. Lastly, we also test what the effect of a net increase of the rifampicin
dosage yields for the patient [23].
In Chapter 4 we then explore the influence of antibiotic stress-induced mutagenesis (ASIM) on the probability for the emergence of resistance. In the model that we
present the mutation rate of bacteria increases in a concentration-dependent manner
when the bacteria are exposed to a drug that triggers a specific stress response [24].
We compare the ASIM model with a model that does not consider a change of the
mutation rate and show the relative differences regarding the probabilities for the
occurrence of resistance mutations. We also show the relative dependence of the
observed effects on the underlying parameters. Eventually, we test whether the in-
1.4 overview of chapters
clusion of ASIM causes a difference in the effectiveness of combination therapy or a
cycling regimen for a single patient.
Chapter 5 is a general discussion of this thesis. There I explore possible future
directions in which research could expand. I also put the results and observations
that have been made in this thesis in a bigger perspective.
9
T H E R O L E O F A D H E R E N C E A N D R E T R E AT M E N T I N D E N O V O
EMERGENCE OF MDR-TB
Published as:
D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (2016). The Role of Adherence and Retreatment in De Novo Emergence of MDR-TB. PLOS Computational
Biology 12(3):e1004749.
abstract
Treatment failure after therapy of pulmonary tuberculosis (TB) infections is an important challenge, especially when it coincides with de novo emergence of multi-drugresistant TB (MDR-TB).We seek to explore possible causes why MDR-TB has been
found to occur much more often in patients with a history of previous treatment.We
develop a mathematical model of the replication of Mycobacterium tuberculosis within
a patient reflecting the compartments of macrophages, granulomas, and open cavities as well as parameterizing the effects of drugs on the pathogen dynamics in these
compartments. We use this model to study the influence of patient adherence to therapy and of common retreatment regimens on treatment outcome. As expected, the
simulations show that treatment success increases with increasing adherence. However, treatment occasionally fails even under perfect adherence due to interpatient
variability in pharmacological parameters. The risk of generating MDR de novo is
highest between 40% and 80% adherence. Importantly, our simulations highlight the
double-edged effect of retreatment: On the one hand, the recommended retreatment
regimen increases the overall success rate compared to re-treating with the initial
regimen. On the other hand, it increases the probability to accumulate more resistant genotypes. We conclude that treatment adherence is a key factor for a positive
outcome, and that screening for resistant strains is advisable after treatment failure
or relapse.
11
2
12
the role of adherence and retreatment in de novo emergence of mdr-tb
2.1
author summary
Our ability to treat and control acute pulmonary tuberculosis (TB) is threatened by
the increasing occurrence of multi-drug-resistant tuberculosis (MDR-TB) in many
countries around the globe. It is not clear whether MDR-TB occurs predominantly
due to transmission, or whether there is a substantial contribution due to de novo
emergence during treatment. Understanding the underlying mechanisms that are
involved in the emergence of MDR-TB is important to develop countermeasures. We
use a computational model of within-host TB infection and its subsequent treatment
to qualitatively assess the risks of treatment failure and resistance emergence under
various standard therapy regimes. The results show that especially patients with a
history of previous TB treatment are at risk of developing MDR-TB. We conclude that
de novo emergence of MDR-TB is a considerable risk during treatment. Based on our
findings, we strongly recommend widespread implementation of drug sensitivity
tests prior to the initiation of TB treatment.
2.2
introduction
Tuberculosis (TB) is a key challenge for global health [25; 26]. At present about
one third of the global population is latently infected [27] and every year about 1.7
million people die of tuberculosis. A large number of patients live in resource-limited
settings with restricted access to health-care. It is imperative that standard treatment
measures are assessed for their efficacy and reliability.
Understanding the driving forces behind therapy failures is challenging. This is to
a large extent the case because of the complex life cycle and population structure of
TB: The typical sequence of events leading to acute pulmonary tuberculosis occurs
as follows [25; 28; 19; 29; 30]. Upon inhalation, TB bacilli reach the pulmonary alveoli
of the lung. There they are assimilated by phagocytic macrophages. In most cases
the bacteria are being killed continuously by phagocytosis while the cell-mediated
immunity develops. More rarely, they may persist in an inactive state, which is
considered a latent infection. Infected macrophages may aggregate and form granulomas by recruiting more macrophages and other cell types. Inside granulomas,
increased necrosis of macrophages can lead to the formation of a caseous core. In latently infected hosts, an equilibrium establishes where the immune system prevents
further growth but the bacteria persist in a dormant state [31; 32]. However, especially in patients with a compromised immune system, the bacteria may continue
or resume growth [28; 29]. In this case, the bacterial population steadily increases
until the granuloma bursts into the bronchus forming an open cavity. Mycobacterium
tuberculosis is an aerobic organism and depends on the availability of oxygen to promote its growth. Because the oxygen levels inside macrophages and granulomas are
low, the growth rate is reduced [29; 32; 33; 34; 35]. In open cavities, oxygen supply
is not limiting anymore and the population size increases rapidly. The extracellular
bacteria in the cavities may also spread to other locations in the lung where they are
again combated by the dendritic cells of the immune system. Some bacteria can be
expelled with sputum and be transmitted to other individuals or they may enter a
blood vessel and cause lesions in other organs.
2.2 introduction
The standard treatment is a six-month short-course regimen [25; 36; 37; 38; 13],
consisting of two months of combination therapy with isoniazid, rifampicin, pyrazinamide and ethambutol followed by a continuation phase of four months with isoniazid and rifampicin only [39]. According to tuberculosis treatment guidelines all
drugs are taken daily during the first two months. During the following four months
isoniazid and rifampicin are administered three times a week with a 3-fold increased
isoniazid dose [37]. For patients with previous TB treatments the WHO recommends
a 8-month retreatment regimen containing additionally streptomycin [13].
In recent years, the problem of drug resistance has increased in severity due to the
emergence and spread of multi-drug-resistant tuberculosis (MDR-TB) [40; 41; 42],
where MDR-TB is defined as infection by M. tuberculosis strains conferring resistance
to at least isoniazid and rifampicin. Resistant TB is assumed to emerge at least
in part due to inappropriate treatment or suboptimal adherence to the treatment
regimen [43]. Poor compliance has been associated with treatment failure and the
emergence of resistance in previous studies [44; 45; 46; 47; 48]. Multi-drug-resistance
usually develops in a step-wise manner. These steps are thought to include functional monotherapy; either due to different drug efficacies among certain bacterial
populations or due to different pharmacokinetics [49; 50]. Prevalence data of MDRTB in Europe (see Fig 2.1) show that patients who have previously received treatment
are on average six times more likely to suffer from MDR-TB than patients who are
newly diagnosed. There are several possible explanations for this observation. Individuals who are infected with MDR-TB are more likely to have a treatment failure or
a later relapse [51; 20; 52; 53], especially if they are not properly diagnosed. These patients could then come under more accurate scrutiny and eventually be reported as
MDR-TB patients with previous treatment history. Another more direct possibility is
that a considerable fraction of patients who have contracted susceptible TB develop
de novo MDR-TB during the first therapy [54].
The goal of this study is to assess the factors that determine the de novo acquisition
of drug resistance and to get a better insight in the underlying dynamics. Specifically, we want to study the contribution of imperfect compliance and retreatment
regimens. In some areas, second-line drugs are not easily accessible. Moreover,
drug-susceptibility tests may not be performed due to the lack of required infrastructure or questionable reliability of patient treatment history [55]. Hence, we assess the
impact of a retreatment that is identical to the first therapy as well as a retreatment
that follows the WHO recommendation [13]. To achieve this goal we develop a computational model of a within-host TB infection and its consecutive treatment with
currently recommended first-line regimens. The model framework encompasses the
population dynamics of various M. tuberculosis genotypes with different resistance
patterns in three pulmonary compartments as well as the pharmacodynamics and
the pharmacokinetics of the drugs that are used for treatment. The aim is to provide
qualitative insights into the infection dynamics of tuberculosis. The parameterization
is based on the most recent concepts and individual experimental results found in
the literature. Given the current lack of a good animal or in vitro model for TB, a
computational model,may help to bridge the gaps arising from the inaccessibility of
TB in experimental model systems and allow the hypothetical assessment of treatment scenarios, which would be otherwise ethically inadmissible in patient trials.
13
14
the role of adherence and retreatment in de novo emergence of mdr-tb
Figure 2.1: The prevalence of multidrug-resistant tuberculosis (MDR-TB) in most European countries is higher among previously treated patients than among newly
diagnosed patients. The data on the percentage of newly diagnosed and previously treated patients with MDR-TB where taken from reference [56] for 2009 and
from reference [57] for 2010. Countries with incomplete data were omitted.
In particular, problems resulting from imperfect therapy adherence can be usefully
addressed with a computational model.
2.3
methods
In the following section we present the basic framework of the computational model,
the parameterization and key aspects of our simulations. In essence, our model
consists of coupled logistic-growth models that are connected such that they capture
the basic population structure (compartments) of TB (see Fig 2.2). The action of TBdrugs is included in this model via realistic pharmacokinetics / pharmacodynamics
functions. Resistance to these drugs is modelled by distinguishing between up to 32
genotypes (all combinations of 5 mutations) with varying resistance patterns. Since
mutations are generated at low frequencies and numbers (due to the low bacterial
mutation rate), chance events are essential in the dynamics of this system and hence
we consider a stochastic version of the model. In the following we provide a detailed
2.3 methods
description of the model; the model equations and further details can be found in S1
Text.
2.3.1
Model
Our model describes pulmonary tuberculosis and assesses the emergence of resistance during multi-drug therapy. A graphical illustration of the model is provided
in Fig 2.2. The model reflects the compartmentalization of the bacteria into three
distinct subpopulations as described by Grosset [19] intracellular bacteria within
macrophages (M), bacteria within the caseating tissue of granulomas (G) and extracellular bacteria which mostly reside in open cavities (OC). The compartments
differ in their maximum population sizes as well as the bacterial replication rates
that they allow. The base replication rate r is modified by a factor γ, which reflects
the compartment specific conditions that influence the replication rate. Bacteria have
a natural density-dependent death rate in each compartment. The constant replication rate and the density-dependent death rate constitute a logistic growth model
that was assumed to describe the basic population dynamics. Bacteria also migrate
unidirectionally at a rate m from one compartment to another. Offspring bacteria
have a certain chance to acquire or lose a mutation that confers resistance to one
out of up to five drugs that may be administered during treatment. Every resistance
mutation confers a fitness cost which affects the reproductive success of its carrier.
This means that the bacterial population inside a compartment comprises of up to
32 genotypes, which differ in their drug resistance pattern as well as their relative
fitness.
To outline the population dynamics within a single compartment we describe them
first in the form of a deterministic differential equation. The dynamical equation is
given by
dNc,g
Nc
N 0
= r · γc · ωg · Nc,g − mc ·
· Nc,g + mc 0 · c · Nc 0 ,g − (dc + κc,g ) · Nc,g (2.1)
dt
Kc
Kc 0
Here Nc,g is the number of bacteria of a specific genotype g in a specific compartment c. The parameter r is the base replication rate of M. tuberculosis and γc is a factor,
which modifies the replication rate according to the different metabolic activities in
each compartment. ωg represents the relative fitness of the specific genotype. mc is
the rate with which bacteria migrate to the subsequent compartment. The migration
rate is multiplied by the ratio between the total population size Nc and the carrying
capacity Kc . This reflects the increased migratory activity that takes place during
an acute infection. Nc 0 , Kc 0 and mc 0 correspond to the overall bacterial population
including all genotypes of the supplying compartment, its carrying capacity and its
migration rate, respectively. The last term reflects the density-dependent death rate
dc and the drug induced genotype specific killing rate κc,g . The bactericidal effects
of the drugs contribute additively to the killing rate κc,g (see 2.A for further details).
The dynamics of the bacterial population in the model are actually simulated as
stochastic processes. For this reason we translated the underlying deterministic differential equations into a corresponding stochastic framework by applying Gillespie's
τ -leap method [58].
15
16
the role of adherence and retreatment in de novo emergence of mdr-tb
Figure 2.2: Diagram of model for the pathogenesis during acute pulmonary tuberculosis
infection. We consider three different physiological compartments for the location of TB bacteria: host macrophages (M), granulomas (G) and open cavities
(OC). The base replication rate r of the bacteria is modified by a compartment specific parameter γ. The bacteria die with a density-dependent rate d and migrate
from one compartment to another at a rate m.
2.3 methods
2.3.2
Parameterization
The parameter estimates used in this model are whenever possible drawn or derived
from experimental results in the literature. To account for the diversity of infection
and treatment courses in different patients we allow some parameters to vary within
a certain range. Parameters are summarized in Table 2.1.
The basic growth dynamics rest upon the replication rate and the carrying capacity of the compartments. Based on recent studies [59; 60; 61] we assume a maximum
bacterial load between 105 and 107 bacteria each for the macrophage and the granuloma compartment and 108 to 1010 bacteria for the extracellular compartment. Under
optimal conditions M. tuberculosis has a replication time of 20 h, hence we set the
maximum replication rate in the model to 0.8 d−1 [19].
Every new bacteria cell has at birth the chance to acquire or lose one or multiple resistance mutations and therefore get a genotype, which is different from the
mother cell. The frequency of specific resistance mutations and therefore the mutation rate for the main first-line drugs have been first estimated by David in 1970
[62] to be around 10−7 –10−10 . However, more recent observations suggest considerably higher frequencies in the order of 10−6 to 10−8 [29; 63]. A possible reason
for this discrepancy between these estimates are varying mutation rates in in vitro
experiments compared to the conditions encountered in vivo due to stress-induced
mutagenesis mechanisms or variations among strains [64; 65; 66]. Furthermore, we
assume that mutations only occur during proliferation while mutations during the
stationary phase could serve as an additional source of resistance mutations [67].
Therefore, we choose to allow for patients with the more recent higher mutation
rates because this will yield more conservative estimates (see 2.2). Our model incorporates backwards mutations from the resistant to the sensitive phenotype, which
also restore the reproductive fitness. However, we consider a reversion to be ten
times less likely than the original forward mutation because the occurrence of any
additional mutation within a gene to be an exact reversion is more infrequent.
When assessing the prevalence of certain genotypes, fitness costs that come with
resistance mutations have to be considered. The cost of resistance against antituberculosis drugs appears generally to be low [88; 84; 85; 86]. Drug-resistant mutants isolated in patients have even been found to be on par with susceptible wild
type strains regarding their infectivity and replicative potential. Since cost-free resistance mutations are rather rare, the high fitness of resistant strains that have been
found in clinical isolates [48,49] is assumed to arise due to the acquisition of secondary site mutations which minimize the fitness costs (so-called compensatory mutations) [85]. However, there is evidence that at least initially newly acquired drug
resistance confers some physiological cost [89]. Because our model simulates the
de novo acquisition of resistance mutations and because the time frame of a single
patient treatment is rather short we assign a small fitness cost to every possible mutation and neglect the counterbalance of fitness costs by compensatory mutations.
The effect of administered drugs depends on the pharmacokinetics and pharmacodynamics of these drugs (see Table 1). Both influence the killing rate κc,g at any
given time point during treatment. While pharmacokinetic parameters describe the
course of the drug concentration in the target tissue, pharmacodynamic parame-
17
18
the role of adherence and retreatment in de novo emergence of mdr-tb
Table 2.1: Compartment characteristics
Macrophages
Granulomas
Open cavities
Compartmental characteristics
Carrying capacity (Kc )
105 –107
105 –107
108 –1010
Growth modifier (γc )
0.5
0.1
1
Migration rate (mc
,m’,d−1 )
0–0.1
a
0–0.1
a
0–0.1 a
Relative drug efficacies
Isoniazid
0–1 [68; 69; 70] 0.01 [71]
1
Rifampicin
0.01 [69]
0.01 [29]
1
Pyrazinamide
0 [72; 73]
1 [29]
0 [74]
Ethambutol
1 [69]
0–1 [29; 75; 76] 1
Streptomycin
0.1 [77; 68]
0.01 [29]
1
The provided references support the order of magnitude of the parameters,
not the exact value.
a
estimation
ters characterize the effect the drugs have at a given concentration. The minimal
inhibitory concentration (MIC) describes the minimal drug concentration at which
bacterial growth is reduced by at least 99%. Additionally, the EC50 describes at which
drug concentration the half-maximal effect (commonly, bacterial killing) is observed,
while the Emax indicates the maximal effect of the drug. These pharmacodynamic
parameters are obtained by fitting the drug action model to killing curves found in
the literature [90; 82] (see S1 Text). The specific efficacy of most drugs in the different compartments is typically not quantified. There are several studies that tried to
assess the bactericidal activity inside macro- phages [77; 68; 72; 69]. Unfortunately,
these estimates are highly variable and sometimes even contradictory [91; 72]. In
addition to these experimental difficulties, it is possible that the pharmacodynamics
of anti-tuberculosis drugs are again different in the human body [92; 93; 94; 95; 96].
To reflect this uncertainty we assign compartment efficacies from a range of values
which cor- responds to the most recent estimates [77; 68; 72; 69; 75; 73; 74; 70; 71; 76].
2.3.3
Simulations
To investigate the role of treatment adherence on patient outcome, we followed disease progression starting with the infection of macrophages until all compartments
approximately reached their maximum bacterial load. For each parameter set, we
simulate the outcome of 10,000 patients who vary both in their pharmacokinetic and
-dynamic characteristics as well as compartmental attributes. Parameters are generally picked from a normal distribution. If only a range is known the parameters are
chosen from a uniform distribution. To measure the actual treatment efficacy we let
every patient develop an acute tuberculosis infection during 360 days. This allows
1.31 d
0.32 d
0.5 [82; 77]
35–45 [36; 81]
3 [80; 81]
Streptomycin
2.95 · 10−8 –10−7 [62], c
0.1 [84; 85]
10−7 [62]
0.1 c
0.92–1.13 [83] 1 c
0.96 d
0.20 d
1.0 [68]
FA = fast acetylators, SA = fast acetylators
If isoniazid is administered three times a week instead of daily the dosage is three times higher [36; 87]
estimation
see text
ELF = epithelial lining fluid
a
b
c
d
e
Some of the provided references support the order of magnitude of the parameters, not the exact value.
0.1 [84]
0.1 [85; 86]
0.1 [84]
Resistance cost
13.60–24.76 [83]
1.94 d
40 d
28 [74]
2.25 · 10−10 –10−8 [62; 63] 10−9 –10−8
0.34 [83]
2.6 [79]
Ethambutol
29.21 ± 4.35 [81] 5.0 [79]
9.6 ± 1.8 [78]
Pyrazinamide
Resistance frequency 2.56 · 10−8 –10−7 [62; 63]
SA a : 1.37–5.69[83]
FA a : 1.74–5.88 [83]
1.82 d
1.86 d
Emax
e
0.51 d
0.033 d
EC50 (mg/L)
CELF /CSerum (ρ)
0.4 [68]
13.61 ± 3.96 [81]
2.46 [78]
0.025 [68]
SA a : 4.26 ± 0.94 b [81]
FA a : 2.80 ± 0.71 b [81]
SA a : 3.68 ± 0.59[78]
FA a : 1.54 ± 0.30 [78]
Rifampicin
MIC (mg/L)
Dose (mg/L)
Half-life (h−1 )
Isoniazod
Table 2.2: Model parameters
2.3 methods
19
20
the role of adherence and retreatment in de novo emergence of mdr-tb
for the emergence of mutants prior to treatment initiation and provides enough time
for the establishment of an equilibrium in the bacterial population composition. After this period we start the standard short course therapy regimen with four drugs
being taken daily for two months followed by four months in which just isoniazid
and rifampicin are taken three times per week. If the infection is not completely sterilized after the first treatment we schedule a retreatment. Since the model does not
cover the possibility of dormant bacteria the population recovers rather quickly after
an unsuccessful treatment. Hence, we begin the retreatment 30 days after completion
of the previous treatment. After such a time span the population reaches a bacterial
load where acute symptoms would be again suspected. If not stated otherwise the
retreatment corresponds to the WHO recommendation for retreatments [20; 21]. The
WHO recommendations include streptomycin, which is used together with the original four first-line drugs during the first two months. Afterwards the therapy is being
continued for another month without streptomycin and during the last five months
only isoniazid, rifampicin and ethambutol are administered. All drugs are being
taken daily during the whole retreatment.
The 95% confidence intervals (CI) of patient outcomes in the figures is calculated
by picking the value for a two-sided 95% confidence limit with n − 1 degrees of
freedom from a t-distribution table where n is the number of patients. This value
is then multiplied with the standard deviation σ and divided by the square root of
n. The resulting value is then added and subtracted from the mean to get the actual
confidence interval.
t95%
·σ
√
CI = n−1
n
2.4
2.4.1
(2.2)
results
Treatment efficacy in single compartments against wild-type TB and MDR-TB
The impact of treatment on the net growth rate of wild-type or MDR bacteria differs strongly between compartments (Fig 2.3): Before treatment starts, the growth
rates in macrophages and granulomas are lower than in the open lung cavities due
to hypoxia and a generally adverse environment for bacterial growth in these compartments. Since we assume that the drug concentration immediately reaches the
maximum the impact of combination therapy on growth rate is immediately apparent after the administration of the first dose of drugs. In all compartments the drugs
are able to keep the wild-type populations from regrowth during the following days.
Especially in granulomas pyrazinamide is able to diminish the population over a
long period due to its relatively long half-life. MDR-TB is substantially less affected
by the combination therapy because only pyrazinamide and ethambutol are effective. This means that in macrophages or open lung cavities the multi-drug-resistant
population remains constant at best or is even able to slowly grow. Only in the granulomas where mostly pyrazinamide is active (see Table 1) the loss of effectiveness of
isoniazid and rifampicin is less prominent.
2.4 results
Macrophages
8
Log CFU
Growth rate [d−1]
10
0
−2
−4
4
wild type
MDR−TB
−6
6
wild type
MDR−TB
2
0.0
1.0
2.0
Days
3.0
0.0
1.0
2.0
Days
3.0
Granulomas
8
Log CFU
Growth rate [d−1]
10
0
−2
−4
4
wild type
MDR−TB
−6
6
wild type
MDR−TB
2
0.0
1.0
2.0
Days
3.0
0.0
1.0
2.0
Days
3.0
Open cavities
8
Log CFU
Growth rate [d−1]
10
0
−2
−4
4
wild type
MDR−TB
−6
6
wild type
MDR−TB
2
0.0
1.0
2.0
Days
3.0
0.0
1.0
2.0
Days
3.0
Figure 2.3: Net growth rates and population dynamics of wild-type and MDR bacteria in
the modeled compartments after two days of treatment with the four first line
drugs. All parameters for which a range of values exist have been set to the
median value. On day 1 and day 2 all four drugs are applied simultaneously.
21
22
the role of adherence and retreatment in de novo emergence of mdr-tb
2.4.2
The role of adherence
The compliance of a patient with the prescribed drug regimen is a key factor for
a successful treatment outcome. For the assessment of treatment success we monitor for every patient three different nested treatment outcomes. Firstly, we define
treatment failure as the incomplete sterilization of the lung at the end of the therapy. Secondly, the emergence of MDR-TB is defined in our simulations as 10% or
more [97] of the remaining bacterial population after treatment failure being resistant against at least isoniazid and rifampicin. Finally, emergence of full resistance
(FR) is defined as 10% or more of the population being resistant against all drugs
that were used in the treatment regimen (either 4 drugs for first treatment or up to 5
drugs for retreatment).
Adherence in our simulations refers to the probability with which the patient takes
the prescribed drugs at any given day. We assume that failure to take drugs on a
given day always affects all drugs of the prescribed regimen.
In our simulations, the level of adherence has a strong but complex impact on
treatment success (Fig 2.4 A). Under perfect adherence the model shows a very low
failure rate. However, if adherence decreases the probability for treatment failure
increases rapidly. Between 40% and 80% adherence there is also a small fraction of
patients that fail treatment due to the emergence of MDR-TB. Furthermore, at these
adherence levels the model also shows only limited treatment success. Thus, failure
decreases monotonically with adherence while MDR is maximized at intermediate
levels. Patients who fail on the first treatment and who undergo retreatment (Fig
2.4 B) have a failure rate of 20% at 80% adherence. However, the probability for
treatment failure increases to about 50% under perfect adherence. Patients who fail
the first treatment despite high adherence may often have disadvantageous combinations of PK/PD parameters, which also decrease their success probabilities during
the retreatment. In Fig 2.4 B, 2.4C and 2.4 D the number of patients per adherence
level undergoing retreatment decreases strongly as can be seen from the frequency
of treatment failure in Fig 2.4 A. When comparing Fig 2.4 A and 2.4 E, which shows
the combined outcome probabilities for both treatments, we see that the retreatment
reduces the probability of failure over the upper half of the adherence spectrum.
2.4.3
The role of retreatment
The additional treatment success of retreatment regimens depends on adherence
and the addition of streptomycin to the regimen (Fig 2.4 B). In our model, even
under perfect adherence the chance of treatment failure remains substantial, and
in the majority of patients who fail under retreatment MDR-TB emerged de novo.
Furthermore, at suboptimal adherence levels a considerable proportion of patients
even carry strains that are not susceptible to any of the five administered drugs. The
outcome of retreatment depends crucially on whether MDR was acquired during
initial treatment: Because the majority of patients who fail the first treatment do not
carry MDR-TB their outcome probabilities for the retreatment are almost identical
to the overall cohort of failed patients (Fig 2.4 C). Even though the vast majority of
patients who failed the first treatment did not develop MDR-TB, a substantial fraction
2.5 discussion
of patients who also failed the second treatment harbor MDR or FR strains. This
occurs due to increased subpopulations of monoresistant bacteria that accumulate
during the first treatment and that are by itself not sufficient to be diagnosed as
MDR-TB. When comparing patients who are diagnosed with MDR-TB after the first
treatment (Fig 2.4 D) and those who are not (Fig 2.4 C) we see that patients who
develop MDR-TB are very likely to fail the retreatment as well. At higher adherence
levels the majority of those patients develops full resistance against all five drugs
(Fig 2.4 D). When considering the outcome for both treatments combined (Fig 2.4
E) it becomes more evident that the addition of streptomycin and the more intense
retreatment has a beneficial effect on the overall success rate but patients who also
fail the retreatment are more likely to carry multi-drug-resistant TB strains.
When second-line drugs are not available or susceptibility test are not performed,
it may occur frequently that a previously treated patient is retreated with the first line
treatment. Our results in Fig 2.5 show that such a retreatment with the first line drugs
has almost no additional treatment success beyond the initial treatment. Patients all
across the spectrum of adherence experience treatment failure. The identical firstline retreament only increases the chances for the bacteria to accumulate resistance
mutations and leads between 50% to 100% adherence to nearly all uncleared patients
harboring MDR-TB or worse. This outcome is standing out when comparing the
cumulative treatment success in Fig 2.5 D with the results after the first treatment.
While the overall success curve did not change the fraction of MDR-TB patients over
a large adherence range increased substantially.
2.5
discussion
The aim of this study is to elucidate the effects of treatment adherence and retreatment on the emergence of resistance in TB. The model explicitly incorporates the
pharmacodynamics and pharmacokinetics of all drugs that are used for standard
therapy and the WHO retreatment recommendation. Depending on the compartment in the lung in which the bacteria reside (macrophages, caseous centers of
granulomas or open cavities), M. tuberculosis has different stages of infection and
drug-susceptibilities. Therefore, we explicitly include these different compartments
to be able capture the effect of heterogeneous selection pressure. Because not all
of the parameters used in our model have been quantified with high accuracy, we
do not claim that the model has quantitative predictive power. Rather, it aims to
qualitatively demonstrate the underlying dynamics of a tuberculosis infection.
Our results suggest that poor adherence is a major cause for treatment failure.When
considering the predicted rates of treatment failure one also has to take into account
that our definition of treatment failure is probably rather conservative. We do not
include the possibility of remaining dormant bacteria, which might increase the likelihood of treatment failure or relapse. On the other hand, we also neglect the possibility of the infection being contained at a later time point by the immune system,
thus probably underestimating the chance of success. It is also noteworthy that even
at perfect adherence some patientsmay have a negative treatment outcome. This is
most likely due to a random aggregation of very adverse pharmacokinetic parameters and unfavorable infection attributes in some patients. Such outcomes due to
23
the role of adherence and retreatment in de novo emergence of mdr-tb
B
Treatment outcome after
first treatment
Treatment outcome after retreatment
among failed patients
1.0
1.0
0.8
0.8
0.6
Treatment failure
Emergence of MDR
Emergence of FR
0.4
Probability
Probability
A
0.2
0.6
0.4
0.2
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.4
0.6
0.8
1.0
Adherence
D
Treatment outcome after retreatment
among failed patients with MDR
1.0
1.0
0.8
0.8
0.6
0.4
0.2
no data
Treatment outcome after retreatment
among failed patients without MDR
Probability
Probability
C
0.6
0.4
0.2
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
E
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Adherence
Treatment outcome for
both treatments combined
1.0
0.8
Probability
24
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Figure 2.4: Probabilities for treatment failure (blue), emergence of MDR-TB (green) and
the emergence of a fully resistant strain (FR, red). (A) Treatment outcome probabilities based on the assessment of 10,000 simulated patients undergoing six
month short course therapy at different levels of adherence. (B) Outcome probabilities of the standard retreatment regimen containing streptomycin for patients
failing the previous treatment. (C and D) Retreatment outcome probabilities for
patients failing the first treatment without or with MDR-TB respectively. (E) The
overall probabilities for treatment outcome when both treatment regimens are
considered. The width of the dark colored areas indicate the 95% confidence interval. Please note that the colored areas overlap and share a common baseline.
Therefore, FR is a subcategory of MDR and FR and MDR are subcategories of
treatment failure. The confidence intervals for the retreatment tend to widen at
higher adherence levels due to the lower number of patients failing the previous
treatment. The area with no data in panel (D) arises because patients with low
adherence do not harbor MDR-TB after the first treatment.
2.5 discussion
B
Treatment outcome after retreatment
among failed patients
Treatment outcome after retreatment
among failed patients without MDR
1.0
1.0
0.8
0.8
0.6
Treatment failure
Emergence of MDR
Emergence of FR
0.4
Probability
Probability
A
0.2
0.6
0.4
0.2
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
Treatment outcome after retreatment
among failed patients with MDR
D
0.8
0.8
Probability
1.0
0.4
0.8
1.0
Treatment outcome for
both treatments combined
1.0
0.6
0.6
Adherence
no data
Probability
C
0.4
0.2
0.6
0.4
0.2
0.0
0.0
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Figure 2.5: Corresponding treatment outcomes after two rounds of identical six-month
short course therapy. (A) Treatment outcome probabilities after two rounds of
identical first line therapy for treatment failure (blue), the emergence of MDR-TB
(green) and the emergence of a fully resistant strain (FR, red). (B) Probabilities for
patients who did not complete the first therapy successfully but who also did not
harbor MDR-TB. (C) Treatment outcome probabilities for patients who failed the
first treatment with MDR-TB. (D) The overall probabilities for treatment outcome
when both treatment regimens are considered. There is no data available in panel
(C) for patients with a lower adherence than 25% because such patients did not
harbor MDR-TB after the first treatment.
25
26
the role of adherence and retreatment in de novo emergence of mdr-tb
pharmacokinetic variability and despite good adherence have been predicted in an
in vitro study [98]. Furthermore, our results show that over a certain range of adherence a small fraction of patients develop MDR-TB. At intermediate adherence
these patients also have a low likelihood of being treated successfully. Thus, good
adherence to therapy is crucial: Not only does it increase treatment success, it also
decreases the probability for the emergence of MDR-TB.
According to our model, the WHO recommendation for retreatment is somewhat
of a double-edged sword. While at high adherence levels the recommended treatment is able to cure the majority of patients who failed the first line therapy, it also
increases the fraction of patients harboring drug resistant strains across almost the
whole spectrum of adherence. Previous studies already raised concerns about the
possible amplification of resistance [21; 99; 100; 101; 102]. In the WHO treatment
guidelines it is recommended that drug susceptibility test results should be taken
into account when deciding upon the retreatment regimen [17]. However, the vast
majority of patients in our model would probably not have been diagnosed with
MDR-TB after the first regimen even though they may still harbor increased subpopulations of monoresistant bacteria. Therefore it is conceivable that many would have
been treated with the WHO recommended regimen. A large fraction of patients who
failed this retreatment eventually developed MDR-TB. Considering the results from
our model further clinical studies are needed which analyze the treatment success
rates and the accompanying risks of the standard retreatment regimen.
Retreating failed patients with an identical short course therapy leads to poor outcome in our simulations. A lower success rate for MDR-TB patients treated with the
standard short- course therapy has been confirmed in a large cohort study [55]. In
our simulations it is rare that patients who failed the previous treatment are cured after undergoing the same therapy again provided that adherence remains unchanged.
Retreatment with the same regimen only generates more opportunities for single
resistant mutants that emerged during the first treatment to accumulate further mutations, thus minimizing the number of future treatment options.
These findings are in accordance with previous studies which found a positive
correlation between previous treatment and the occurrence of resistance [103; 104;
105; 106]. This might be an indicator that de novo resistance on an epidemiological
scale occurs at a significant frequency and that the main contributor to the frequency
of MDR-TB is not necessarily the mere transmission of such strains.
In summary our data show that patient adherence is a crucial component of treatment success. The probably cheapest and most effective way to ensure a positive
treatment outcome while also minimizing the risk for the emergence of MDR-TB is
to maintain proper patient compliance with the treatment. This supports the Directly
Observed Treatment, Short-Course (DOTS) strategy of the WHO, which includes
healthcare workers or community health workers who directly monitor patient medication. If treatment fails, thorough tests of drug susceptibility of the remaining
infecting population, would be of considerable value. According to our results a
retreatment regimen including streptomycin has the potential to increase the overall
cure rate, but also increases the fraction of patients who carry drug-resistant strains.
A common principle of physicians is to “never add a single drug to a failing regime”
[107] this principle is often not followed in retreatment. A preceding drug sensitiv-
2.6 acknowledgments
ity test might show existing drug resistances and the retreatment regimen could be
adapted accordingly. Nonetheless the standard retreatment regimen is still superior
to a retreatment with the identical first-line drugs. Such a retreatment is unlikely
to achieve a higher overall cure rate and dramatically increases the probability for
the emergence of MDR-TB, which reduces further treatment options. This shows
that a dependable patient treatment history that is available to the responsible health
professional is also important before initiating a treatment regimen.
2.6
acknowledgments
We thank Florian Marx and Ted Cohen for reviewing the manuscript and stimulating
discussions.
2.7
author contributions
Conceived and designed the experiments: DC PAzW RK SB. Performed the experiments: DC. Analyzed the data: DC PAzW. Contributed reagents/materials/analysis
tools: SB. Wrote the paper: DC PAzW RK SB.
27
APPENDIX
2.a
2.a.1
supplementary material
Model equations
The following descriptions contain further details about the model mechanics and
specifications of the equations that comprise the mathematical basis in addition to
the explanations in the main article (see 2.3.1).
The model is based on the τ-leap approximation [58]. In our case we do the simulations with a temporal resolution of 10−2 d. If in a time step a new bacterium is born
it mutates and gains or loses resistance to one or several drugs with a likelihood that
is equal to the corresponding mutation rate. For every patient and every drug we
initially randomly pick a rate from a uniform distribution with the indicated minimum and maximum values in Table 2.1. The probability for a backward mutation is
ten times lower than the corresponding picked rate.
We assume that (uncompensated) resistance alleles confer a fitness disadvantage
in the absence of drugs. In our model we restrict the effect of resistance costs cl to the
reduction of the reproductive success. If multiple alleles involve a cost, the fitness of
the corresponding genotype is given by
n
Y
(1 − cl )
wg =
(2.3)
l=1
where cl is the cost of a resistance allele at the locus l and n is the number of
resistance loci. The susceptible wild-type alleles have no cost and therefore the fully
susceptible strain has a fitness of 1. The death rate dc of the bacterial population
depends on the population density in the compartment among all genotypes.
dc = r · γc
Nc
Kc
(2.4)
where r is the maximal replication rate of M. tuberculosis and γc is a factor, which
modifies the maximal growth rate according to the different metabolic activities in
each compartment. Nc is the combined population size of all genotypes in the compartment and Kc is the carrying capacity of that specific compartment. The higher
the population density is, the more increases the death rate. Together with the basic
growth function this results in the conventional model for logistic growth:
dNc,g
Nc
= r · Nc,g · 1 −
dt
Kc
(2.5)
The bactericidal activity of the antituberculosis drugs is accounted for by the sigmoid Emax model [108]. This leads to an adapted version of the enhanced death model
29
30
the role of adherence and retreatment in de novo emergence of mdr-tb
by Czock et al. [108] which we extend to reflect the use of multiple distinct drugs .
The bactericidal effects of the drugs in a compartment are reflected in the killing rate
variable κc,g .
κc,g =
n
X
d=1


Emax,d · 1 −
1
Cd ·δc,d ·ρd
EC50,d
+1
· νg,d 
(2.6)
The killing rate depends on the genotype. Here we assume that a resistant mutant
allele confers full resistance to the bactericidal activity of the corresponding drug.
The resistance of a given genotype against an antibiotic drug is represented by the
boolean variable νg,d with νg,d = 0 indicating resistance.
For simplicity we assumed that the drug effects are additive. n is the number of
drugs and EC50,d describes the concentration at which the half-maximal kill rate of
a specific drug is reached. Emax is the maximal death rate. Together with the MIC
and the EC50 it determines the antibacterial potency of a drug. Cd is the current
drug concentration while δc,d and ρd are the efficacy of the drug in the specific
compartment and the ratio between plasma and epithelial lining fluid concentration,
respectively.
We assume that immediately after the uptake of a drug the concentration increases
instantaneously by an amount Cmax,d , followed by a exponential decay according to
the following function,
Cd (t) = Cd (t0 ) · e−a(t−t0 )
(2.7)
where t0 is the last time point where the drug has been taken and
a=
ln(2)
td1/2
(2.8)
where td1/2 is the half-life of drug d within the patient.
For simplicity we assume that if the patient is non-adherent on a specific day
all due drugs are missed simultaneously. Allowing the drugs to be missed independently caused only a marginally lower chance of a treatment failure (data not
shown).
2.a.2
Fitting of anti-tuberculosis drug action
The Emax and EC50 values as we use them in our model were not readily available in
the literature. In order to obtain them we use again an equation from the enhanceddeath constant-replication model [108].
dN
C
= r · N − Emax ·
·N
dt
EC50 + C
(2.9)
2.A supplementary material
If we assume that the population has no net growth and therefore the drug concentration C is equal to the MIC we get the following relation
Emax =
r · (MIC + EC50 )
MIC
(2.10)
The different Emax and EC50 values are collected by fitting equation 2.10 to the kill
curves that were recorded in vitro by de Steenwinkel et al. and Marcel et al. [90; 82].
These papers report the in vitro effects of constant drug concentrations of isoniazid, rifampicin, ethambutol and streptomycin on the density of a M. tuberculosis suspension
over the course of six or seven days, respectively. In Figure 2.6 we show simulations
of this experimental setup using our model by assuming a single compartment in
which all four available drugs have unimpaired efficacy. The data points were extracted from the original figures as far as the data points were distinguishable. In
order to prevent the unpredictable stochastic influence of rescue mutations we remove the possibility of emerging resistance from the model. From the growth curves
in the absence of any drug we estimate the average growth rate to be 1.95. This
comparably high growth rate is likely due to the adapted phenotypes of regular lab
strains of M. tuberculosis. The carrying capacity in the assays of de Steenwinkel et al.
[90] we estimated to be 108.5 and 1013 in the assay of Marcel et al. [82].
The MIC concentrations from the literature [82; 77; 68] which are also confirmed in
the experimental kill curves serve as reference points at which the bacterial growth
and the bactericidal activity of the drug would cancel each other out and the population would stay constant. The EC50 concentrations and the interdependent Emax
values are derived by linear least-square fitting. The best fit values are calculated by
averaging over all the available concentrations. The experimental data for isoniazid
shows a recovery of population growth after day 2. The authors claim that this effect
appears due to the development of a isoniazid-resistant subpopulation [90]. Because
we do not consider such rescue mutations we decide to include only the first two
days for the fitting of the bactericidal activity of isoniazid.
To validate the quality of the fitting we calculate the average coefficient of determination R2 for every drug. Isoniazid and ethambutol show a satisfactory R2 of 0.67 and
0.70 respectively and a very good 0.90 for streptomycin. The coefficient of determination for the fitting of rifampicin is rather low with 0.36. Our model overestimates
the bactericidal activity of rifampicin at high concentrations and underestimates the
activity at low concentrations. Apparently a single drug action model as we use it
does not provide the same descriptive quality for every first line drug. No kill curves
were available for pyrazinamide hence we estimate an appropriate EC50 value from
other studies [74; 109].
2.a.3 Robustness analysis
In order to obtain a better understanding of the influences of different parameter estimates in the model we performed a robustness analysis in which we vary them and
looked at their impact on the treatment outcome. In the following results we monitor the likelihood of treatment failure and the emergence of MDR-TB after a single
31
32
the role of adherence and retreatment in de novo emergence of mdr-tb
treatment with the four standard first-line drugs. As in the main text treatment failure is again defined as incomplete sterilization after the completion of therapy and
emergence of MDR-TB is defined as 10% or more [97] of the remaining population
being resistant against at least isoniazid and rifampicin.
2.a.3.1
Carrying capacity
There is a large variance in reports about the maximum population size of M. tuberculosis in a human lung during acute infection. This is also based on the fact that
this number depends on the host immune defense and the course of infection. Many
studies report 109 bacilli per open cavity and therefore an overall population size of
1010 or above. Thus, to study the effect of varying carrying capacity we ran simulations with compartmental carrying capacities that are 10-fold higher or lower for
every compartment (see Figure 2.7 A and B). With 10-fold higher carrying capacities
the probability for treatment failure increases substantially. The increased number
of bacilli in each compartment also increases the standing variation in the bacterial
population. This means that there are more bacteria that carry single or even double resistance mutations. Therefore, an increased carrying capacity also favors the
emergence of MDR-TB.
2.a.3.2
Resistance costs
The cost of resistance in M. tuberculosis is generally assumed to be low [88; 84; 85; 86].
However, those estimates are mostly based on observations of clinically isolated
strains. It is possible that these fitness costs are alleviated by compensatory mutations, which occur later during a chronic infection or during the chain of transmission events. Since we assumed de novo emergence of resistance we assigned a 10%
fitness cost on reproductive success for every mutation.
We ran simulations in which we increased as well as decreased the fitness costs per
resistance mutations. As we can see in Figure 2.7 C and D the results with slightly
lower fitness costs still provide reasonable results. Although, if the costs are lower
than 5% the probability of treatment failure and the likelihood of MDR emergence
are unrealistically high. Thus, we conclude that resistance mutations are do very
likely carry some fitness costs. Otherwise treatment outcomes would be expected
to be much worse than what is generally observed in studies. This conclusion is
partially confirmed in a previous study [89].
2.a.3.3
Migration rates
The rate with which M. tuberculosis migrates among the three compartments has to
our knowledge not been quantified. We follow the assumptions made by Lipsitch
and Levin [50]. The migration has only a pronounced influence if it increases (see
Figure 2.7 C and D). This is most likely due to the increased density-dependent
bacterial killing in the small compartments of macrophages and granulomas. With
higher migration rates these compartments are flooded with bacteria from the open
cavities. However, the influence on the emergence of MDR-TB is still small. Even
though our estimates for the migration rate are not well established and we consider
2.A supplementary material
them to be already rather high we think that its minor influence does not severely
affect the validity of our model.
2.a.3.4
EC50
We also investigate the influence of the EC50 parameter, i.e. the efficiency of the
drug. In Figure 2.7 G and H we vary the EC50 values of every drug simultaneously
between 1/10, 5/10 and the five- and tenfold of the standard parameter setting. An
increased EC50 is predicted to cause a guaranteed treatment failure even at perfect
adherence. On the other hand a decreased EC50 may dramatically improve the likelihood of a successful treatment at adherence levels, which are far below the optimum.
Figure 7 F indicates that an elevated EC50 only promotes the selection of MDR-TB at
intermediate levels of adherence, i.e. if the drugs are able to exert a certain selective
pressure.
2.a.3.5
Missing drugs
In resource-limited settings, the drug supply is not always guaranteed, such that
therapy might only comprise a subset of the four drugs. To investigate the impact
of a missing drug, we test all four possible standard treatments that each lack one of
the first-line drugs and assess the effect (see Figure 2.7 I and J). The lack of isoniazid,
rifampicin or ethambutol always leads to treatment failure irrespective of the level
of adherence. The explanation for this is as follows: The extracellular compartment
harbors the largest number of bacteria. Here, isoniazid rifampicin and ethambutol
most efficiently reduce bacterial load. Because of the high bacterial load we would
expect that mutants resistant to either of these drugs pre-exist at treatment initiation.
However, double-resistant mutants that could evade two drugs are expected to preexist only in a small fraction of drug-naive patients. If one of these main drugs is
missing the mutants that are resistant against the remaining drug immediately take
over and spread. Compared to isoniazid, rifampicin and ethambutol pyrazinamide
is less essential for treatment success. This is probably because it does not affect the
large extracellular compartment. However, it is important for clearing bacteria residing in the caseous centers of granulomas, where it is the most active drug. Therefore,
its usage favors a positive treatment outcome. However, its absence does not affect
the outcome as much as the other drugs.
Because the lack of isoniazid and rifampicin does not select for resistance against
these drugs it is also unlikely that MDR occurs at a substantial frequency. The previously observed minor influence of pyrazinamide is also evident as its absence
does not substantially increase the risk of MDR emergence. Only a regimen without ethambutol drastically increases the probability for MDR to occur. This shows
how important the role of ethambutol as a third extensively effective bactericidal
drug is. Ethambutol is needed to prevent widespread treatment failure due to the
development of MDR-TB.
2.a.3.6
Transmitted resistance
In Figure 2.8 we examine the possible effect of an infection with an M. tuberculosis
strain that is already resistant at transmission. To model this, we exchange the bacte-
33
34
the role of adherence and retreatment in de novo emergence of mdr-tb
rial inoculum at the beginning of the infection with a strain that is resistant to one or
two drugs. It is known that patients with active TB are highly infectious and even a
small inoculum of one hundred bacilli or less that comprises primarily resistant mutants might establish an infection in a susceptible host. As in every simulation the
infection is simulated for one year to reach its full potential and equilibrate. During
this year random reversion mutations may occur which give rise to sensitive strains.
These strains may slowly outcompete resistant strains and become more frequent
due to their higher fitness in absence of drugs.
The pre-existence of rifampicin or isoniazid resistance increases the risk of treatment failure the most among the single mutants at perfect adherence. This could be
due to the potency of these drugs and the competitive advantage that such resistance
mutations grant. Not surprisingly, a isoniazid- or rifampicin-resistant inoculum also
increases the risk of MDR-TB. Pre-existing pyrazinamide or ethambutol-resistance
has almost no effect on treatment outcome. Most likely due to their minor bactericidal effectivity during the therapy. A double-resistant inoculum as in Figure 2.8 C
and D has a fatal impact. Treatment failure is almost inevitable and MDR-TB occurs
especially at higher levels of adherence.
2.A supplementary material
Experimental data
Fitted model
Isoniazid
8
Log CFU/ml
7
6
5
4
3
2
1
0
0
1
2
3
Isoniazid
9
4
5
6
Control
0.015 mg/L
0.031 mg/L
0.062 mg/L
0.125 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
4 mg/L
8 mg/L
16 mg/L
32 mg/L
64 mg/L
128 mg/L
256 mg/L
R2: 0.67
8
7
Log CFU
9
6
5
4
3
2
1
0
0
1
2
3
8
6
5
4
3
2
1
0
1
2
3
4
5
6
Time (days)
R : 0.36
7
6
5
4
3
2
1
0
0
1
2
3
7
6
5
4
3
2
1
5
6
Control
0.0005 mg/L
0.001 mg/L
0.0019 mg/L
0.0038 mg/L
0.0075 mg/L
0.015 mg/L
0.031 mg/L
0.062 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
8 mg/L
16 mg/L
32 mg/L
64 mg/L
128 mg/L
256 mg/L
Ethambutol
Control
0.125 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
4 mg/L
8 mg/L
16 mg/L
32 mg/L
64 mg/L
128 mg/L
256 mg/L
2
8
R : 0.70
7
6
5
4
3
2
1
0
0
0
1
2
3
4
5
6
0
1
2
3
Streptomycin
11
4
5
6
Time (days)
Time (days)
Streptomycin
11
10
10
8
7
6
5
4
3
2
1
R2: 0.90
9
0.01 mg/L
0.125 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
4 mg/L
8 mg/L
16 mg/L
32 mg/L
8
Log CFU
0.01 mg/L
0.125 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
4 mg/L
8 mg/L
16 mg/L
32 mg/L
9
Log CFU/ml
4
Time (days)
9
Control
0.125 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
4 mg/L
8 mg/L
16 mg/L
32 mg/L
64 mg/L
128 mg/L
256 mg/L
8
Log CFU/ml
2
8
Ethambutol
9
6
Rifampicin
9
Log CFU
Log CFU/ml
7
Control
0.0005 mg/L
0.001 mg/L
0.0019 mg/L
0.0038 mg/L
0.0075 mg/L
0.015 mg/L
0.031 mg/L
0.062 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
8 mg/L
16 mg/L
32 mg/L
64 mg/L
128 mg/L
256 mg/L
Log CFU
Rifampicin
0
5
Time (days)
Time (days)
9
4
Control
0.015 mg/L
0.031 mg/L
0.062 mg/L
0.125 mg/L
0.25 mg/L
0.5 mg/L
1 mg/L
2 mg/L
4 mg/L
8 mg/L
16 mg/L
32 mg/L
64 mg/L
128 mg/L
256 mg/L
7
6
5
4
3
2
1
0
0
0
1
2
3
4
Time (days)
5
6
7
0
1
2
3
4
5
6
7
Time (days)
Figure 2.6: Comparison of the concentration- and time-dependent effects of isoniazid, rifampicin, ethambutol and streptomycin on sensitive M. tuberculosis. The plots
in the left column are experimentally obtained killing curves for anti-tuberculosis
drugs by de Steenwinkel et al. [90] and Marcel et al. [82] and originate from a
metabolically highly active strain of Mtb H37Rv cultured in vitro at 37°C [90]. The
plots on the right show the simulated killing curves that were calculated by fitting
the pharmacodynamic model to the experimental data. The fitting was done by
minimizing the sum of least squares over all curves. The coefficient of determination (R2 ) indicates the average goodness of fit for each drug. Greyed out lines
were not used for fitting. Modified from [90].
35
the role of adherence and retreatment in de novo emergence of mdr-tb
B
1.0
0.8
0.6
0.4
0.0
0.2
0.4
Standard
10−fold decreased
10−fold increased
0.2
Probability of MDR Strain
1.0
0.8
0.6
Carrying Capacity
0.0
Probability of Treatment Failure
A
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.8
1.0
0.8
1.0
0.8
1.0
0.8
1.0
0.8
1.0
1.0
0.8
0.6
0.4
0.0
0.2
0.4
0.6
0.00
0.02
0.05
0.08
0.10
0.15
0.2
Probability of MDR Strain
1.0
0.8
Resistance Costs
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.4
0.6
Adherence
F
1.0
0.8
0.6
0.0
0.0
0.2
0.4
10%
50%
100%
500%
1000%
0.4
0.6
Migration Rates
0.2
0.8
Probability of MDR Strain
1.0
E
Probability of Treatment Failure
0.6
D
0.0
Probability of Treatment Failure
C
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.4
0.6
Adherence
H
1.0
0.8
0.6
0.0
0.0
0.2
0.4
10%
50%
100%
500%
1000%
0.4
0.6
EC50
0.2
0.8
Probability of MDR Strain
1.0
G
Probability of Treatment Failure
0.4
Adherence
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.4
0.6
Adherence
J
1.0
0.8
0.6
0.4
0.4
0.6
no drug missing
Isoniazid
Rifampicin
Pyrazinamide
Ethambutol
0.0
0.2
Probability of MDR Strain
1.0
0.8
Missing Drug
0.2
Probability of Treatment Failure
I
0.0
36
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
Adherence
Figure 2.7: Sensitivity analysis of the probability of treatment failure and emergence of
resistance. In the left column are the plots for the probability of treatment failure
due to incomplete clearance and in the right column are the plots for the probability of the emergence of an MDR-TB strain, which accounts for at least 10% of
the overall population. (A and B) Effect of different carrying capacities. (C and
D) Effect of different fitness costs per resistance mutation. (E and F) Effect of different migration rates among compartments. (G and H) Effect of lower or higher
EC50 values. (I and J) Effect of treatment consisting of only three drugs.
2.A supplementary material
1.0
0.8
0.6
0.0
0.2
0.4
0.6
wt
INH
RMP
PZM
EMB
0.4
Single Mutants
0.2
Probability of MDR Strain
0.8
1.0
B
0.0
Probability of Treatment Failure
A
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.6
0.8
1.0
0.8
1.0
Adherence
D
1.0
0.8
0.6
0.0
0.0
0.2
0.4
0.6
wt
INH + RMP
INH + PZM
RMP + PZM
INH + EMB
RMP + EMB
PZM + EMB
0.4
Double Mutants
0.2
Probability of MDR Strain
0.8
1.0
C
Probability of Treatment Failure
0.4
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
Adherence
Figure 2.8: Influence of pre-existing resistance mutations on treatment outcome after a regular six-month therapy. In the left column are the plots for the probability of
treatment failure due to incomplete clearance and in the right column are the
plots for the probability of the emergence of an MDR-TB strain, which accounts
for at least 10% of the overall population. (A and B) Effect of a homogeneous
inoculum consisting of genotypes resistant to one drug. (C and D) Effect of a
homogeneous inoculum consisting of genotypes resistant to two drugs.
37
A LT E R N AT I V E T R E AT M E N T S T R AT E G I E S F O R T U B E R C U L O S I S
D Cadosch, P Abel zur Wiesch, S Bonhoeffer
abstract
The standard six-month short-course therapy for pulmonary tuberculosis has been
established in the 1970s. Since then there have not been major changes in the regimen that still requires considerable effort and dedication from the patient as well
as from the health care system. In this study we explore the potential benefits and
disadvantages of intermittent therapy as well as extended-release formulations and
dose escalations of rifampicin. These alternative treatment strategies are tested for
varying levels of patient adherence. Intermittent therapy is shown to have a reduced
probability for a positive treatment outcome as well as a lower risk for the emergence of de novo MDR-TB. Extended-release formulations of rifampicin can mitigate
the lower chances of successful treatment associated with intermittency but they also
increase the probability for the emergence of resistance at suboptimal adherence levels. In contrast to the other strategies the absolute drug exposure is increased when
we test for the effects of dose escalation of rifampicin. Dose escalation of rifampicin
shows the same or lower probabilities for treatment failure at equal adherence levels
but the probability of de novo MDR-TB increases for intermediate levels of adherence. We conclude that intermittent regimens could potentially lower the time and
organizational burden for patients and the health care system but they show lower
success rates. Extended-release formulations of rifampicin are a feasible strategy to
mitigate the potential weaknesses of intermittent regimens. Dose escalation is also a
promising alternative strategy. However, dose escalation as well as extended-release
formulations of rifampicin depend on a very good patient compliance to be effective,
otherwise the risks associated with the stronger selection for resistant genotypes may
outweigh the benefits.
39
3
40
alternative treatment strategies for tuberculosis
3.1
introduction
The treatment of pulmonary tuberculosis (TB) with a six-month short-course chemotherapy was developed in the 1970s by the British Medical Research Council
and its partners [110; 111]. This treatment regimen containing four antituberculosis drugs is still the current standard recommended by the WHO [13]. Adherence
to the treatment regimen is considered to be a crucial factor influencing the successful completion of treatment and for preventing emergence of drug-resistant TB. The
improvement of adherence was one of the goals of the directly observed treatment,
short course (DOTS) strategy launched in the mid-90s. Since then, the case detection increased and case prevalence decreased in countries where DOTS was applied
[27]. However, the effort and organization that is needed to maintain a successful
TB control program is substantial. TB patients are usually administered their drugs
on a daily basis by a local health care worker during at least the first two months of
the treatment. Also the long treatment period and the effort of the patient who in
some countries has to travel long distances to see his supervising health worker may
prevent him or her from uninterrupted attendance [13]. Another reason for patients
to discontinue therapy may be the high pill burden or uncomfortable side effects
[13; 112].
Given the difficulties with the current treatment strategy possible improvements
of the standards could be of interest. In this study we are discussing three alternative strategies that address the problems outlined above: intermittent treatment, extended-release drug formulations and dose escalation. Intermittent regimens could facilitate the task of treatment supervision. Some studies found intermittent regimens to have equally good success rates when compared to daily treatment
[21; 38]. Large-scale tuberculosis control programs that used simplified intermittent
treatment regimes were considered to be sufficiently successful [113; 114]. However,
intermittent treatment has also been found to be associated with a greater risk of
acquired drug resistance [21] and with higher incidence rates of side effects from
isoniazid and rifampicin [13; 38; 115; 116], the two most important first-line drugs.
Another possible concern in intermittent treatment regimens is the possible pharmacokinetic mismatch that could lead to prolonged phases of mono-therapy [117].
Because the concerns of intermittent therapy are thought to outweigh the potential
benefits the WHO recommends daily administration of antituberculosis drugs if possible [13].
However, some of the issues mentioned with intermittent regimens could be alleviated with the use of extended-release formulations. Such formulations cause a
slower absorption of the drug and consequentially provide a more steady suppressive drug concentration over time [22]. Intermittently extended-release formulations
should keep the antibiotic concentration above the minimum inhibitory concentration (MIC) long enough to prevent a substantial regrowth of the bacterial population.
The more long-lasting presence of rifampicin for example could decrease the probability for side effects such as flu-like symptoms. These symptoms are assumed to
be at least partially caused by the formation of anti-rifampicin antibodies and the
development of a more potent immune reaction which may be triggered during alternating prolonged phases of high and low rifampicin concentrations that occur
3.2 methods
with intermittent therapy and standard rifampicin formulations [115; 116; 81; 92].
The benefits of an intermittent regimen with extended release drugs could prove to
be at least as successful as daily treatment, decrease the work effort and operating
expenses for monitoring programs as well as lower the pill burden and incidence of
side effects for the patient and hence increase adherence and herewith the probability
for a positive treatment outcome.
Another point of improvement of the conventional treatment strategy would be the
increase of the rifampicin dose (dose escalation). An increase of the rifampicin dose
has been considered a promising direction because rifampicin is known to cause side
effects less frequently than other first-line drugs [115; 63]. Furthermore, higher doses
are more likely to prevent sub-target plasma concentrations due to malabsorption or
reduced bioavailability in certain patients [115; 118; 119]. A study looked at the
early bactericidal activity of an increased rifampicin dose in 14 patients and found
promising results but concluded that further studies are warranted [120]. A more
extensive clinical study that looked at increasing rifampicin doses found that higher
doses were well tolerated and had a stronger bactericidal effect while also reducing
resistance [23].
In this study we investigate the possible benefits of extended-release formulations
in a daily or intermittent treatment regimen by means of extending a mathematical
model used in a previous study [121]. We further test how big the impact of increased
rifampicin doses is on treatment outcome. We evaluate the effects of these regimens
over a range of patient adherence. We focus here exclusively on rifampicin since it
is considered to have the biggest untapped potential in terms of sterilizing capacity
[115; 63].
3.2
3.2.1
methods
Model
Our model is based on the extension of a framework of an acute pulmonary TB
infection from an earlier study [121]. The mathematical model of the population
dynamics of Mycobacterium tuberculosis considers three different compartments:
macrophages, granulomas and open cavities. The compartments differ in their size,
which limits the maximal population size and in the growth rate at which bacteria
may replicate. Bacteria may migrate from macrophages to granulomas, from granulomas to open cavities and from there again to macrophages. This represents an
abstraction of the pathogenic cycle during an acute pulmonary TB outbreak in a patient. The bacterial populations are assumed to consist of up to 16 genotypes, which
represent all possible combinations of the four considered resistance mutations – one
for each first-line drug. During replication bacteria may acquire resistance mutations
with a certain probability. To reflect variations in the phenotype of bacteria as well as
in the physiology of patients parameters are picked randomly from a specified range
of values. Bacteria differ in their migration rates, maximal population densities and
mutation rates for resistances against each drug. Patients may absorb and excrete
drugs at variable rates, vary in their efficacy to absorb drugs, have different ratios
between the blood serum drug concentration and the concentration in the epithelial
41
42
alternative treatment strategies for tuberculosis
lining fluid inside the lungs as well as varying drug penetrations for the three compartments. The precise description of the model as well as its parametrization can
be found in the previous study by Cadosch et al. [121]. Newly introduced parameters
and parameter values that differ from the previous study are in Table 3.1. Beyond
the previously established model framework we extended the pharmacokinetics to
also include a first order absorption reaction. All simulations are stochastic and use
the τ-leap method by Gillespie [58].
3.2.2
Pharmacokinetics
In the model the blood serum drug concentration in a patient is governed by a first
order absorption reaction and a first-order excretion reaction. The first order absorption reaction in our case reflects the uptake of drug from the digestive tract to the
blood stream while the first order excretion reaction reflects the elimination of drug
primarily by the kidneys or the biliary tract [126]. Upon drug administration the
amount of unabsorbed drug U in the digestive tract instantaneously increases by the
administered dose D. The amount of unabsorbed drug U then decreases according
to the following differential equation:
dU
= −ka · U
dt
(3.1)
where ka is absorption rate constant. Besides the absorption rate constant the drug
concentration in the blood serum C is also influenced by the excretion rate constant
ke .
dC
= ka · U − ke · C
dt
(3.2)
The absorption rate constant ka is related to the time tmax until the peak blood
serum concentration is reached on the absorption and excretion rate constant as
tmax =
ln(ka ) − ln(ke )
ka − ke
(3.3)
By transforming equation 3.3 we can calculate the absorption rate constant ka for
known tmax and ke .
ka = −
W−1 (−e−ke ·tmax · ke · tmax )
tmax
(3.4)
Here W−1 denotes the lower branch of the Lambert function. The excretion rate
constant depends on the concentration half-life t1/2 .
ke =
ln(2)
t1/2
(3.5)
0.025 [68]
MIC (mg/L)
12.5 [95; 98]
1.0 [68]
1.5–3 [115; 123; 79; 124]
20–50 [115; 122; 123; 78; 125] 1.0–5.5 [115; 123; 79; 124]
Some of the provided references support the order of magnitude of the parameters, not the exact value.
0.4 [68]
Ethambutol
5.5–9.6 [115; 122; 123; 78; 79] 2–4 [115; 124]
Pyrazinamide
1.3–3 [115; 122; 123; 79; 125] 1–2 [115; 122; 123; 79; 125]
0.75–2 [115; 122; 123; 79; 125]
tmax (h)
1.6–3 [115; 122; 123; 78; 79]
Rifampicin
1.9–7.1 [115; 122; 123; 79; 125] 6.1–9.9 [23; 122; 123]
1.5–4 [115; 122; 123; 78; 79]
Isoniazid
Cmax (mg/l)
Half-life
(h−1 )
Table 3.1: Drug parameterization
3.2 methods
43
44
alternative treatment strategies for tuberculosis
To calculate the required dose D that has to be administered in order to achieve
a maximum blood serum concentration Cmax after a time tmax we can look at the
Bateman equation [127; 128], which is used to calculate the drug concentration C at
time t depending on the underlying absorption and excretion rate constants.
C(t) =
D · ka
· (e−ke ·t − e−ka ·t )
ka − ke
(3.6)
From equation 3.6 we can then derive a formula with which we can calculate the
dose D that is needed to reach the specified concentration Cmax .
D=
Cmax · (ka − ke )
ka · (e−ke ·tmax − e−ka ·tmax )
(3.7)
The different concentration-time curves of rifampicin between the standard absorption rate constant of 16.3 d−1 and a fixed absorption rate constant of 1 d−1 , representing an extended-release formulation, can be seen in Figure 3.1. Both curves are based
on a half-life of 2.3 h [115; 122; 123; 78; 79] and the same amount of drug is administered but the fast standard absorption rate constant results from a tmax that is set to
2.15 h [10,26,27,29,30]. In the simulations involving extended-release formulations of
rifampicin the standard fast absorption rifampicin formulation with an absorption
rate constant ka that is dependent on tmax and ke is compared to an extended-release
formulation of rifampicin that has a fixed slow absorption rate constant of 1 d−1 or
an intermediate absorption rate constant of 5 d−1 .
3.2.3
Patient simulations
In order to capture a wide range of combinations of bacterial and patient parameters
we simulate every treatment scenario for 1000 independent patients. Every patient
is initially inoculated with 1000 wild-type bacteria. Because we assume that the patients are immunocompromised, we allow bacteria to replicate and mutate freely
for 360 days. During this time all three compartments harbor bacteria up to their
carrying capacity and in the compartment of open cavities small subpopulations of
monoresistant bacteria emerge and reach equilibrium sizes. The compartment of
open cavities is the only compartment that is large enough for such low frequency
genotypes to establish. The size of these subpopulations in the absence of any drug is
determined by the carrying capacity, the mutation rate and the fitness cost, which is
imposed by the de novo mutations. After the first 360 days a six months short-course
therapy starts. The treatment involves the four standard first-line drugs isoniazid,
rifampicin, pyrazinamide and ethambutol. In our standard regimen all drugs are
administered daily during the first two months (intensive phase) and during the last
four months isoniazid and rifampicin are administered three times a week (continuation phase) [13]. If the simulation involves intermittent therapy then rifampicin
is administered every second or third day during the intensive phase and 1.5 times
or once per week during the continuation phase respectively. To ensure comparable drug exposure the rifampicin doses are doubled or tripled in an intermittent
regimen.
3.2 methods
Concentration [mg/l]
Concentration [mg/l]
Rifampicin
8
6
4
2
0
0.0
1.0
2.0
Time [days]
3.0
8
6
4
2
0
0.0
1.0
2.0
3.0
Time [days]
Figure 3.1: Comparison of serum concentration profiles of rifampicin between the standard absorption rate constant and the extended-release formulation. In the left
panel are the pharmacokinetic profiles for a single administration of a rifampicin
dose with the midpoint standard absorption rate constant of 16.3 d−1 (solid line)
and with an absorption rate constant of 1 d−1 representing the extended-release
formulation (dashed red line). The dotted line is the MIC of rifampicin for M.
tuberculosis (see Table 3.1) [68]. The right panel shows the profiles for three consecutive daily administrations with the standard absorption rate constant (solid
line) or a single three-fold higher dose with the extended-release pharmacokinetics. The drug concentration profiles in each panel have within the computational
accuracy the same AUC.
45
46
alternative treatment strategies for tuberculosis
At the end of the six months of therapy a patient is diagnosed with treatment
failure if there are any Mtb bacteria left in any compartment. Among treatment
failures besides patients with predominantly drug susceptible bacteria we further
differentiate between patients with bacterial populations of which 10% or more [97]
are resistant against at least isoniazid, resistant against at least rifampicin or those
that are resistant against at least both isoniazid and rifampicin, which is the definition of MDR-TB [99; 107]. Please note that MDR-TB is a subset of our definitions
of isoniazid or rifampicin resistance and that it is the exact intersection of these two
resistance definitions.
3.2.4
Pharmacodynamics simulations
In the pharmacodynamics simulations we have four genotypically distinct subpopulations: a fully susceptible wild-type, two populations that are either isoniazid- or
rifampicin-resistant and a multidrug-resistant population that is resistant to isoniazid and rifampicin. As we are interested in the relative population dynamics of
the four genotypes, we start all populations from an arbitrary initial size that does
not necessarily reflect their size in any patient at any time point. All drugs are
administered only every second time that they are prescribed which corresponds
to an enforced adherence level of exactly 50%, which has for all considered treatment regimens a high relative probability to favor the emergence of MDR-TB (see
Results). The growth conditions and the drug efficacies are identical to the ones we
attribute to the open cavities compartment, which we consider due to its size to be
the most influential. In contrast to other simulations all patient-specific parameters
are based on the midpoint of the parameter intervals (see Table 3.1 and [121]). For
the pharmacodynamic simulations of intermittent therapy rifampicin is prescribed
to be administered every three days in a triple-dose — but effectively it is taken only
every six days due to the lowered adherence.
3.3
3.3.1
results
Treatment efficacy of an extended-release formulation of rifampicin in a daily or intermittent treatment regimen
The comparison between treatment regimens of different intermittencies with and
without extended-release rifampicin formulations reveals that intermittency generally has a negative effect on the probability of treatment failure while extendedrelease formulations have a positive effect (see Figure 3.2). We perform this comparison over the full range of patient adherence. The standard daily administration of all
drugs with rifampicin that has the standard fast absorption rate constant achieves a
successful treatment outcome in almost all patients under perfect adherence (Figure
3.2 A). The success rate drops substantially below 90% adherence and at less than
40% adherence we find that the infection is not cleared in almost all patients. If an
extended-release formulation of rifampicin is administered the curve shifts further
to the left the slower the absorption is, indicating that such formulations provide
a similar or higher likelihood of treatment success at the same adherence level. If
3.3 results
rifampicin with the standard absorption rate constant is administered at intervals
of two or even three days in a double or triple-dose respectively, a positive treatment outcome at the same adherence level becomes less likely. However, the treatment success rate of high-dose intermittent administration of rifampicin increases if
rifampicin is given as an extended-release formulation with lower absorption rate
constants. The relative increase of benefit of the extended-release formulations is
higher in high-dose intermittent regimens as is shown by the spread of the treatment
failure curves within a group of equal absorption rate constants. While the treatment
failure curves in the upper half of the adherence range between treatments with the
same standard absorption rate constant but varying intermittency differ substantially
from each other, the curves for the lowest absorption rate constant are rather close
together.
When we look at the probability for the emergence of MDR-TB we see that there
is a substantial increase in the middle of the adherence spectrum for daily treatment
regimens if we lower the absorption rate constant (Figure 3.2 B). For the intermittent regimens the probability of MDR-TB emergence is almost zero if we administer
rifampicin with the standard absorption rate. The probability of MDR emergence
when we intermittently use a rifampicin formulation with an intermediate absorption rate constant is equal or lower than the daily administration of the fast absorption formulation. When we use rifampicin formulations with the lowest absorption
rate constant the risk of MDR-TB increases substantially for both intermittent therapies.
We also compare the probabilities for the occurrence of genotypes that are at least
resistant against against isoniazid or rifampicin for the different treatment regimens
(see Figure 3.2 C and D). The slopes of all curves for isoniazid-resistance between
about 30% and 100% adherence are almost identical to the curves indicating the probability of treatment failure (Figure 3.2 C). This implies that at adherence levels above
30% treatment failure is generally due to the remaining bacterial population being
resistant to at least isoniazid. The frequency of isoniazid-resistance decreases rapidly
below 30% adherence. The probability for the occurrence of rifampicin-resistance on
the other hand almost exactly mirrors the probability for the emergence of MDR-TB
over the whole adherence spectrum (Figure 3.2 D). This indicates that rifampicinresistance almost exclusively occurs in the context of MDR-TB. These results are
confirmed when we exclusively consider isoniazid- or rifampicin-monoresistance.
The probabilities for the emergence of isoniazid-monoresistance (Figure 3.2 E) are
almost identical to Figure 3.2 C. Only when the adherence levels are low enough for
MDR-TB to occur in regimens with slowly absorbed extended-release formulations
of rifampicin does the probability for isoniazid-resistance decrease more than in Figure 3.2 C. The low probability for the emergence of rifampicin-monoresistance for all
regimens along the whole spectrum of adherence except for a narrow band between
10% and 40% adherence supports the prior observation that rifampicin-resistance is
almost exclusively associated with MDR-TB (Figure 3.2 F).
47
alternative treatment strategies for tuberculosis
Probability of treatment failure
B
Probability of MDR−TB emergence
1.0
1.0
0.8
0.8
Probability
Probability
A
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
D
Probability of isoniazid−
resistance emergence
0.6
0.8
1.0
Probability of rifampicin−
resistance emergence
1.0
1.0
0.8
0.8
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
E
0.4
Adherence
Probability
Probability
C
0.4
0.6
0.8
1.0
Adherence
Probability of isoniazid−
monoresistance emergence
F
Probability of rifampicin−
monoresistance emergence
1.0
1.0
0.8
0.8
Probability
Probability
48
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Figure 3.2: Probabilities of treatment failure and the emergence of MDR-TB, isoniazidand rifampicin-resistance with 10% fitness costs per resistance mutation for
different treatment intervals and varying absorption rate constants. We distinguish the risk of incomplete infection clearance (A), the emergence of MDR-TB
(B), the emergence of any isoniazid-resistant genotype (C), the emergence of any
rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E)
and the risk of the emergence of rifampicin-monoresistance (F). In every panel are
the probabilities for a regime with the standard dose daily administration of all
drugs (black lines), a regime where a double-dose of rifampicin is administered
only on every second occasion (blue lines) and a regime in which rifampicin is
given every third time in a triple-dose (red lines). Within a regime the pharmacokinetics of rifampicin have a standard fast absorption rate constant (solid lines),
a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed
low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low
absorption rate constants represent two different extended-release formulations
of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial
population in the open cavities compartment being resistant.
3.3 results
3.3.2
Pharmacodynamics of an extended-release formulation of rifampicin in a daily or intermittent treatment regimen at intermediate adherence
To better understand the underlying population dynamics during daily or intermittent treatment regimens with slowly absorbed extended-release formulations of rifampicin we performed additional pharmacodynamics simulations shown in Figure
3.3. Under the daily treatment regimen with the standard formulation of rifampicin
(see Figure 3.3 A) we observe that the wild-type population declines rapidly every
time after the antibiotics are being taken but the decline slows down and the population is even able to recover somewhat before the next administration every other
day. The time until extinction for this initial population size is approximately 12
days. The isoniazid-resistant subpopulation also declines after every drug administration but the regrowth of the population after the drug concentrations declined to
sub-MIC is more pronounced than the initial decline and the population is therefore
able to persist and even increases over time. The rifampicin-resistant subpopulation
on the other hand is more strongly affected by the remainder of effective drugs and
declines similar to the wild-type population — just with a slightly slower rate. Since
pyrazinamide is not expected to be effective in the pH-neutral environment of open
cavities the MDR-TB population is only influenced by ethambutol. Ethambutol is
not potent enough to control the MDR-TB population, which equally increases in all
shown scenarios.
If we administer rifampicin intermittently and in a triple-dose the picture looks
similar (see Figure 3.3 B). The rifampicin-resistant population declines at the same
rate here as well as in every other situation because the only difference between
regimens is the formulation and frequency of rifampicin administrations. The wildtype population declines at a slower rate than if it is administered daily which may
partially explain the lower success rates of intermittent therapies with standard rifampicin formulations. Isoniazid-resistant bacteria as well as the wild-type show a
more distinct drop of their population size every sixth day when rifampicin is administered. These rare events as well as the smaller declines in population size in
between rifampicin administrations are however not strong enough to diminish the
population size in the long term. The overall growth rate is even higher than with
the daily regimen.
The extended-release formulation with a lower absorption rate constant in Figure 3.3 C and D is able to suppress the isoniazid-resistant subpopulation in a daily
regimen and in an intermittent regimen with a higher dosage. Extended-release rifampicin also seems to be more effective against wild-type TB as the population goes
extinct after approximately 8 days in contrast to 12 or 15 days with the standard rifampicin formulation.
The influence of different assumptions of fitness costs for resistance mutations on
these results is described in the Supplementary Material 3.A.
3.3.3
Treatment efficacy of a regimen with increased rifampicin doses
A dose escalation of rifampicin decreases the probability for treatment failure but
increases the risk of MDR-TB (see Figure 3.4). In the clinical study [23] that we re-
49
alternative treatment strategies for tuberculosis
B
106
106
105
105
104
104
CFU
CFU
A
103
102
103
102
101
0
5
10
15
20
time [days]
C
101
wild type
rINH
rRMP
MDR−TB
0
5
10
15
20
time [days]
D
106
106
105
105
104
104
CFU
CFU
50
103
103
102
102
101
101
0
5
10
15
time [days]
20
0
5
10
15
20
time [days]
Figure 3.3: Pharmacodynamics at 50% adherence of four subpopulations with different
drug susceptibilities under treatment regimens with different rifampicin administrations. The four panels all show the bactericidal effect of the standard
regimen on four different M. tuberculosis subpopulations. The subpopulations are
either fully susceptible to all drugs (wild type), fully resistant to isoniazid (rINH ),
fully resistant to rifampicin (rRMP ) or resistant to both isoniazid and rifampicin
(MDR-TB). The environmental conditions correspond to the extracellular compartment in a patient. All patient-specific variable parameters are set to their midpoint
value. The initial population sizes are arbitrarily chosen and do not necessarily
reflect the population composition in any patient at any time point. The absorption rate constant for rifampicin in the panels A and B is at the standard midpoint
value of 16.3 d−1 . In the panels C and D rifampicin is given as an extendedrelease formulation with a slow absorption rate constant of 1 d−1 . The treatment
regimen for the panels A and C prescribes all drugs to be administered daily. The
regimen for the panels B and D prescribes a three-fold higher rifampicin dose
every third day under perfect adherence. In all panels every second prescribed
drug administration is missed corresponding to an enforced adherence level of
50%.
3.4 discussion
Probability of treatment failure
Probability of MDR−TB emergence
1.0
Rifampicin
0.8
10 mg/kg
20 mg/kg
25 mg/kg
30 mg/kg
35 mg/kg
0.6
0.4
0.2
0.0
Probability
Probability
1.0
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
0.8
Adherence
Figure 3.4: Probabilities of treatment failure and the emergence of MDR for increasing
doses of rifampicin. The parametrization of the increased rifampicin doses is
derived from a clinical study [23].
produce in our model the 10 mg/kg dose that we use as our standard dose and which
is the recommended dosage by the WHO [13] reaches a mean Cmax concentration
of 8 mg/l. For the 20 mg/kg rifampicin dose the clinical study we get a mean Cmax
of 23.95 mg/l. Therefore, unsurprisingly we find that the 20 mg/kg dose achieves
a substantially higher treatment success rate than 10 mg/kg at least for adherence
levels between 40% and 100%. The mean Cmax concentration correlates well with
the applied dosage. However, the additional benefit of an increased rifampicin dose
becomes smaller with higher doses. When we look at the probability for MDR emergence we see that 10 mg/kg bears the lowest risk at any level of adherence. This risk
increases for intermediate adherence levels with higher rifampicin dosages.
3.4
51
discussion
In this study we investigated the feasibility of applying extended-release formulations of rifampicin in daily or intermittent treatment regimens as well as increasing
the rifampicin dosing to improve TB therapies. We tested these alternative treatment
strategies in a previously established mathematical model [121]. The mathematical
model simulates the population dynamics of various genotypes with different drug
susceptibilities during an acute pulmonary tuberculosis infection within a patient.
Furthermore, the model also encompasses the pharmacodynamics and pharmacokinetics during the treatment with first-line drugs. Many parameter values that are
being used in our model have been established in in vitro studies or are based on
estimates with limited accuracy. Because of the intrinsic uncertainty with these parameter values we have to stress that the results we are presenting are of a qualitative
kind and do not provide accurate quantitative predictions.
From our results we see that in general the application of extended-release formulations increases or maintains the probability of a successful treatment for the same
dosing regimen. This is most probably attributed to the fact that slowly absorbed
extended-release formulations keep the rifampicin concentration above the growth
suppression threshold for a longer time (see Figure 3.1). Furthermore, extendedrelease formulations may maintain suppressive concentrations even if the drug is
1.0
52
alternative treatment strategies for tuberculosis
occasionally not taken. On the other hand, according to our results intermittency
is expected to work less well if formulations are used that are given at higher
doses but with the standard absorption kinetics. An intuition for this observation
can be found if we consider that the half-life of rifampicin is between 1.6 and 3 h
[115; 122; 123; 78; 79] and the bactericidal activity does not necessarily linearly correlate with the concentration [121; 90]. Therefore, even if we double or triple the
dose the rifampicin concentration stays above the MIC for only a few more hours
which is too small of a benefit if the administration interval is two or three days.
However, if we combine an intermittent treatment regimen with extended-release
formulations the negative consequences are somewhat mitigated and we see comparable or even better results than with the daily administration of the standard
rifampicin formulation. Thus, the application of extended-release formulations has
the potential to decrease the possible negative aspects of intermittent treatment and
make it a more promising strategy. An intermittent dosing strategy is attractive because it is expected to be less time-consuming for the responsible health care worker
and therefore less costly. It also decreases the pill burden for the patient and especially in combination with extended-release formulations, that induce lower peak
concentrations, may cause fewer side effects. These patient-specific benefits may increase compliance and decrease the likelihood of defaulting, which in turn makes
the whole control program more effective.
Extended-release formulations potentially have a negative effect if adherence is
suboptimal. At intermediate adherence levels our simulations showed a higher likelihood for the emergence of MDR-TB in regimens that use extended-release formulations especially for formulations with the lower absorption rate constant. To understand this phenomenon we have to look at the prevalence of subpopulations that
are resistant against either isoniazid or rifampicin. We notice that treatment failure
except for very low adherence levels (between 0% and 30%) almost always coincides
with the presence of isoniazid-resistance. The association of isoniazid-resistance and
a lower probability for a positive treatment outcome has been described previously
in epidemiological studies [55; 53]. In our simulations rifampicin-resistance is less
common and predominantly occurs in the context of MDR-TB. This confirms the
rationale for the GeneXpert MTB/RIF assay to be used to diagnose the presence
of MDR-TB [129]. The answer to the question why in our simulations isoniazidresistance correlates with treatment failure and why extended-release formulations
of rifampicin may increase the likelihood of MDR-TB to emerge can be found in the
pharmacodynamics. There we see that in regimens that do not use extended-release
formulations the isoniazid-resistant subpopulation is not sufficiently suppressed at
suboptimal adherence and can grow. In comparison a rifampicin-resistant subpopulation is expected to go extinct. The pre-existence of isoniazid-resistance even before
the treatment starts is expected in a small fraction of the overall bacterial population.
This population would be strongly selected for its competitive advantage over the
wild-type and rifampicin-resistant populations during treatment and would eventually dominate the composition of the overall population. Besides the higher frequency of isoniazid-resistance mutations relative to rifampicin-resistance mutations
[63; 62] this may also contribute to the higher prevalence of clinical isoniazid-resistant
samples among all clinically diagnosed first-line drug monoresistances [130; 105]. An
3.4 discussion
MDR subpopulation would be even less suppressed than the isoniazid-resistant one.
However, MDR-TB is not expected to be initially present in a treatment-naïve patient
who gets infected with wild-type TB. It most probably emerges from an isoniazidresistant bacterium at a later stage of treatment and due to the rather low reproductive rate of Mycobacterium tuberculosis it would need some time before it could
reach a detectable frequency. If we would continue an unsuccessful treatment that
is not able to suppress the infection but still exerts a sufficiently high selection pressure we would expect MDR-TB to eventually dominate the overall population. This
has been suggested previously in a computational model, in which unsuccessfully
treated patients underwent again the standard first-line therapy and accumulated
further resistance mutations [121]. This step-wise accumulation of resistance has
also been confirmed by clinical studies [100; 48; 131]. If we use extended-release formulations of rifampicin the isoniazid-resistant subpopulation is most probably not
able to grow even if we miss half of all prescribed doses. It will decline while MDRTB on the other hand is now at a clear competitive advantage, which means that it
will outcompete all other monoresistant subpopulations rather quickly if it can arise
in the first place. There are currently technical means developed that are able to
reduce the absorption rate constant for drugs (unpublished data). In the example of
rifampicin we see that such extended-release formulations are expected to be more
effective in treating TB patients, and it is conceivable that the extension of this to
all first-line drugs could increase the positive effects even more. However, if patient
compliance drops low enough that more resistant genotypes have sufficient time and
opportunity to arise they are more strongly selected.
The relative order of the results in terms of treatment efficacy and risk of resistance emergence is rather robust to changes of the fitness of resistant genotypes (see
Supplementary Material 3.A). Because the competitive advantage conferred by drug
resistance is so strong the comparably low imposed fitness costs of 10% per mutation
do not substantially influence the relative pharmacodynamics between genotypes.
In contrast to the previous simulations in which the total amount of drug exposure
remained constant we also tested treatment regimens in which we simply increased
the amount of rifampicin that is being administered. Unsurprisingly, this strategy
improves the success rate of treatment for intermediate to high adherence levels.
However, according to our results an increased rifampicin dose is also more likely
to promote the emergence of MDR-TB at intermediate adherence levels. This finding seems to contradict the results from a previous in vitro study [93]. In this study
Gumbo et al. discovered that suppression of resistance was associated with a higher
Cmax -to-MIC ratio. This makes sense if resistance is not absolute as in our model but
variable. If we have in a population a diversity of genotypes that vary in their extent
of resistance for a particular drug, e.g. their MIC, then it follows that higher doses
are more likely to exceed the MIC of these moderately resistant subpopulations and
are able to suppress them. For simplicity our model only considers absolute susceptibility or resistance and the level of resistance is not concentration dependent. We
also do not simulate the emergence of higher resistance through step-wise acquisition of intermediate resistance mutations for a single drug. Our model is therefore
not able to capture this aspect of partial resistance emergence or suppression and
may thus overestimate the occurrence of de novo MDR-TB. However, there are single
53
54
alternative treatment strategies for tuberculosis
point mutations that confer resistance that is high enough to enable its carrier to be
virtually unaffected by clinically achievable rifampicin concentrations [132]. Hence,
such genotypes may account for only a small fraction within the rifampicin-resistant
subpopulation but they would be more strongly selected if they could arise.
We can see that intermittent treatment could be a more feasible regimen option if
extended-release formulations of rifampicin would be available. Intermittency itself
has a number of benefits for care providers as well as for patients. Also higher
rifampicin doses are a promising alternative treatment strategy. However, those more
effective hypothetical treatment regimens might also bear an increased risk if they
are suboptimally applied. If a potentially more effective regimen is inappropriately
applied it could backfire due to its stronger selective pressure for drug resistance.
We conclude that the guideline of ’hitting hard’ does yield a positive effect in that it
is able to eradicate the infection more reliably. However, if a hard-hitting strategy
is compromised by low enough adherence so that monoresistant genotypes may
thrive it may actually increase the selective pressure on these genotypes and cause
an amplification of resistance [133; 134].
3.5
acknowledgments
We thank Balázs Bogos for reviewing the manuscript.
APPENDIX
3.a
supplementary material
In order to investigate the influence of fitness costs on the probabilities for treatment
failure and the emergence of drug resistance when testing daily and intermittent
regimens with and without extended-release formulations of rifampicin we ran additional simulations in which we varied the relative fitness of genotypes. With our
standard assumptions every mutation rate confers a fitness cost of 10% and the costs
stack in a multiplicative manner with every additional mutation. That means that
MDR-TB usually is assumed to have a relative fitness of 81% ((1 − 0.1)2 ) if it does not
carry any more resistance mutations.
Instead of 10% fitness costs per mutation we assumed 5% fitness costs and repeat
the simulation of 1’000 patients (see Figure 3.5). In comparison with Figure 3.2 we
observe slightly increased probabilities for treatment failure above 50% adherence for
all treatment regimens (Figure 3.5 A). The probability for the emergence of MDR-TB
increased substantially relative to the simulations with 10% fitness costs per mutation
(Figure 3.5 B). Even the daily treatment regimen with the standard formulations of
rifampicin now bears a considerable risk for the emergence of MDR-TB from 20%
up to 100% adherence. The occurrence of isoniazid- and rifampicin-resistance are
comparable to the pattern observed in Figure 3.2. For the upper half of the adherence
spectrum isoniazid-resistance (Figure 3.5 C) coincides with treatment failure and
rifampicin-resistance almost exclusively occurs in the context of MDR-TB (Figure 3.5
D).
If we completely neglect the any fitness costs inferred by resistance mutations the
situation appears even more serious (see Figure 3.6). There is now a substantial
chance for treatment failure even at perfect adherence and under the most effective
treatment regimen (Figure 3.6 A). The comparison of Figure 3.6 A and B shows
that treatment failure in regimens with extended-release formulations of rifampicin
occurs almost always due to the emergence of MDR-TB at adherence levels of 75%
and higher. The prevalence of isoniazid- and rifampicin-resistance are again very
similar to the previous patterns.
When we keep the fitness cost for monoresistance at 10% but increase the fitness
of MDR-TB to the same level as the fully susceptible wild type the situation changes
somewhat (see Figure 3.7). The probabilities for treatment failure are almost the
same as with the original assumptions (Figure 3.7 A). However, treatment failure
for patients with an adherence above 40% ensues almost always due to MDR-TB
(Figure 3.7 B). Monoresistances of isoniazid an rifampicin are more rare than in any
previous scenario (Figure 3.7 E and F) indicating that MDR-TB is outcompeting the
monoresistant subpopulations.
When we look at the pharmacodynamics with and without fitness costs we observe
slight increases in growth rates if we neglect the costs inferred by resistance mutations (see Figure 3.8). However, neglecting the fitness costs does not affect the relative
55
56
alternative treatment strategies for tuberculosis
selective advantage of the different genotypes granted by the resistance mutations.
Therefore, it is not surprising that we do not observe much of a change between
the order of regimens in the Figures 3.2 and 3.5 – 3.7 in regard to the probability of
treatment failure or the emergence of MDR-TB.
3.A supplementary material
Probability of treatment failure
B
Probability of MDR−TB emergence
1.0
1.0
0.8
0.8
Probability
Probability
A
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
D
Probability of isoniazid−
resistance emergence
1.0
0.8
0.8
0.6
0.4
0.2
0.0
1.0
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.4
0.6
0.8
1.0
Adherence
Probability of isoniazid−
monoresistance emergence
F
Probability of rifampicin−
monoresistance emergence
1.0
1.0
0.8
0.8
Probability
Probability
0.8
0.0
0.0
E
0.6
Probability of rifampicin−
resistance emergence
1.0
Probability
Probability
C
0.4
Adherence
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Figure 3.5: Probabilities of treatment failure and the emergence of MDR-TB, isoniazidand rifampicin-resistance with fitness costs of 5% per resistance mutation for
different treatment intervals and varying absorption rate constants. We distinguish the risk of incomplete infection clearance (A), the emergence of MDR-TB
(B), the emergence of any isoniazid-resistant genotype (C), the emergence of any
rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E)
and the risk of the emergence of rifampicin-monoresistance (F). In every panel
are the probabilities for a regime with the standard daily administration of all
drugs (black lines), a regime where a double-dose of rifampicin is administered
only on every second occasion (blue lines) and a regime in which rifampicin is
given every third time in a triple-dose (red lines). Within a regime the pharmacokinetics of rifampicin have a standard fast absorption rate constant (solid lines),
a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed
low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low
absorption rate constants represent two different extended-release formulations
of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial
population in the open cavities compartment being resistant.
57
alternative treatment strategies for tuberculosis
Probability of treatment failure
B
Probability of MDR−TB emergence
1.0
1.0
0.8
0.8
Probability
Probability
A
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
D
Probability of isoniazid−
resistance emergence
0.6
0.8
1.0
Probability of rifampicin−
resistance emergence
1.0
1.0
0.8
0.8
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
E
0.4
Adherence
Probability
Probability
C
0.4
0.6
0.8
1.0
Adherence
Probability of isoniazid−
monoresistance emergence
F
Probability of rifampicin−
monoresistance emergence
1.0
1.0
0.8
0.8
Probability
Probability
58
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Figure 3.6: Probabilities of treatment failure and the emergence of MDR-TB, isoniazidand rifampicin-resistance with no fitness costs for any resistance mutation for
different treatment intervals and varying absorption rate constants. We distinguish the risk of incomplete infection clearance (A), the emergence of MDR-TB
(B), the emergence of any isoniazid-resistant genotype (C), the emergence of any
rifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E)
and the risk of the emergence of rifampicin-monoresistance (F). In every panel
are the probabilities for a regime with the standard daily administration of all
drugs (black lines), a regime where a double-dose of rifampicin is administered
only on every second occasion (blue lines) and a regime in which rifampicin is
given every third time in a triple-dose (red lines). Within a regime the pharmacokinetics of rifampicin have a standard fast absorption rate constant (solid lines),
a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixed
low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low
absorption rate constants represent two different extended-release formulations
of rifampicin. Emergence of resistance is defined as at least 10% of the bacterial
population in the open cavities compartment being resistant.
3.A supplementary material
Probability of treatment failure
B
Probability of MDR−TB emergence
1.0
1.0
0.8
0.8
Probability
Probability
A
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
D
Probability of isoniazid−
resistance emergence
1.0
0.8
0.8
0.6
0.4
0.2
0.0
1.0
0.6
0.4
0.2
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Adherence
0.4
0.6
0.8
1.0
Adherence
Probability of isoniazid−
monoresistance emergence
F
Probability of rifampicin−
monoresistance emergence
1.0
1.0
0.8
0.8
Probability
Probability
0.8
0.0
0.0
E
0.6
Probability of rifampicin−
resistance emergence
1.0
Probability
Probability
C
0.4
Adherence
0.6
0.4
0.2
0.0
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Adherence
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Adherence
Figure 3.7: Probabilities of treatment failure and the emergence of MDR-TB, isoniazidand rifampicin-resistance with monoresistance conferring normal 10% fitness
cost and MDR-TB with the same fitness as the wild type for different treatment
intervals and varying absorption rate constants. We distinguish the risk of incomplete infection clearance (A), the emergence of MDR-TB (B), the emergence
of any isoniazid-resistant genotype (C), the emergence of any rifampicin-resistant
genotype (D), the emergence of isoniazid-monoresistance (E) and the risk of the
emergence of rifampicin-monoresistance (F). In every panel are the probabilities
for a regime with the standard daily administration of all drugs (black lines), a
regime where a double-dose of rifampicin is administered only on every second
occasion (blue lines) and a regime in which rifampicin is given every third time
in a triple-dose (red lines). Within a regime the pharmacokinetics of rifampicin
have a standard fast absorption rate constant (solid lines), a fixed intermediate
absorption rate constant of 5 d−1 (dotted lines) or a fixed low absorption rate constant of 1 d−1 (dashed lines). The intermediate and low absorption rate constants
represent two different extended-release formulations of rifampicin. Emergence
of resistance is defined as at least 10% of the bacterial population in the open
cavities compartment being resistant.
59
alternative treatment strategies for tuberculosis
B
106
106
105
105
104
104
CFU
CFU
A
103
102
103
102
101
0
5
10
15
20
time [days]
C
101
wild type
rINH
rRMP
MDR−TB
0
5
10
15
20
time [days]
D
106
106
105
105
104
104
CFU
CFU
60
103
103
102
102
101
101
0
5
10
15
time [days]
20
0
5
10
15
20
time [days]
Figure 3.8: Pharmacodynamics at 50% adherence of four subpopulations with different
drug susceptibilities, with and without fitness costs under treatment regimens
with different rifampicin administrations. The four panels all show the bactericidal effect of the standard regimen on four different M. tuberculosis subpopulations. The subpopulations are either fully susceptible to all drugs (wild type),
fully resistant to isoniazid (rINH ), fully resistant to rifampicin (rRMP ) or resistant
to both isoniazid and rifampicin (MDR-TB). Fitness costs are either 10% per resistance mutation (dashed lines) or resistance mutations do not confer any costs
at all (solid lines). The environmental conditions correspond to the extracellular
compartment in a patient. All patient-specific variable parameters are set to their
midpoint value. The initial population sizes are arbitrarily chosen and do not
necessarily reflect the population composition in any patient at any time point.
The absorption rate constant for rifampicin in the panels A and B is at the standard midpoint value of 16.3 d−1 . In the panels C and D rifampicin is given as
an extended-release formulation with a slow absorption rate constant of 1 d−1 .
The treatment regimen for the panels A and C prescribes all drugs to be administered daily. The regimen for the panels B and D prescribes a three-fold higher
rifampicin dose every third day under perfect adherence. In all panels every
second prescribed drug administration is missed corresponding to an enforced
adherence level of 50%.
C O N S I D E R I N G A N T I B I O T I C S T R E S S - I N D U C E D M U TA G E N E S I S
D Cadosch, P Abel zur Wiesch, S Bonhoeffer
abstract
The mutation rate is a key parameter in the assessment of the risk of drug resistance.
Mutation rates of resistance mutations are usually measured in absence of antibiotics
and are assumed to be constant rates. Environmental stress elicited by antibiotic exposure has been shown to transiently increase the mutation rate in pathogenic bacteria. In this study we explore the implications for the emergence of drug resistance
that arise due to antibiotic stress-induced mutagenesis (ASIM). With a computational
model we simulate the effect of ASIM on bacterial population dynamics. We show
the magnitude by which models with a constant mutation rate underestimate the
probability for the emergence of drug resistance. In a within-host model that also
incorporates pharmacokinetics we further demonstrate that a cycling regimen of two
drugs is less likely to cause multidrug-resistance compared to a combination regimen if ASIM is taken into account. We conclude that ASIM is likely to substantially
increase the risk of drug resistance and reveals drug interaction dynamics that could
improve treatment efficacy. Our study shows that the measurement of parameters
involved in ASIM is crucial for reliable estimates about the occurrence of drug resistance.
61
4
62
considering antibiotic stress-induced mutagenesis
4.1
introduction
Resistance to antibiotics has been a concern for almost as long as the history of antibiotic usage and will likely continue to be a major threat to public health in the
foreseeable future [135; 136; 137; 138]. A large body of literature describes the underlying factors that lead to drug resistance in many pathogen/drug combinations.
One of the key factors for the emergence of antibiotic resistance is the mutation rate
[139; 140; 141]. The mutation rate is typically measured by culturing bacteria in the
absence of drugs and then measuring the frequency of spontaneously emerged resistant mutants in this population on selective media [142; 143]. However, in recent
years there has been mounting evidence that phenotypic mutation rates in bacteria
are influenced by various stresses [24]. Importantly, these stresses include many antibiotics [144]. Most of the stresses are directly or indirectly linked to an increased
abundance of reactive oxygen species (ROS) [24; 145]. Higher ROS concentrations,
which can also be caused by certain antibiotics, may inflict DNA damage and lead to
a change in the regulation of genes that are involved in DNA repair and replication.
These genes control the induction of the SOS stress response, the methyl-directed
mismatch repair pathway, the activation of double-strand break repair proteins or
the expression of error-prone DNA polymerases [24; 146]. All of these responses
increase the probability of introducing mutations. It has been argued that the ability to transiently increase the mutation rate is a trait that has been established in
many bacteria due to a second-order selection for increased mutability under adverse circumstances [24; 147; 148]. The existence of stress-induced mutagenesis has
been controversially discussed [149; 150]. However, it may be still worth investigating how a phenotypic alteration of mutation rates in response to antibiotic exposure
affects resistance evolution.
Here, we focus on the transient mutagenic effect of antibiotic exposure. We expect that the resulting stress response has a positive feedback on the emergence of
resistance mutations against the drug that is mutagenic as well as other drugs. Most
mathematical models investigating the emergence of drug resistance assume stable
mutation rates [151; 152; 153; 154]. By not taking into account the possibility of changing mutation rates they may fail to describe a possible effect of pharmacokinetics on
mutation rate and misjudge the overall likelihood of the emergence of resistance, especially when more than one antibiotic is used. The aim of this study is to assess the
influence of antibiotic stress-induced mutagenesis (ASIM) on the emergence of drug
resistance. We find that ASIM does not only alter the expected frequency of de novo
emergence of resistance, but also changes our expectations regarding the success of
different treatment strategies.
4.2
4.2.1
methods
Mathematical model
The detailed description of the mathematical model is available in the Supplementary
Material 4.A. In brief, we model bacterial population biology by assuming logistic
growth and adding a drug-dependent death rate (Suppl Mat 4.A.1). The relationship
4.2 methods
between drug concentration and antibiotic-induced killing is described by a sigmoid
Emax model [108] extended to multiple drugs (Suppl Mat 4.A.2). Additionally, we
model the emergence of resistance mutations and assume that the mutation rate depends on the drug concentration (Suppl Mat 4.A.3). Pharmacokinetics are described
by translating the values of the maximally achievable peak concentration, Cmax , the
time until the peak concentration is reached, tmax , and the excretion half-life, t1/2 ,
from the literature to a time-dependent concentration profile in patients (Suppl Mat
4.A.5). The bacterial population dynamics are simulated as stochastic processes by
applying the Gillespie τ-leap method [58].
4.2.2
4.2.2.1
Assumptions and parameterization
Bacterial growth
The modeling of the bacterial growth is described in detail in Suppl Mat 4.A.1. We
assume that the bacteria have a growth rate of 2 d−1 , corresponding to a doubling
time of approximately 15.1 h. The initial population size for the simulations with
constant drug concentrations is assumed to be 107 fully susceptible bacteria. The
maximum population size (carrying capacity) is 109 bacteria.
4.2.2.2
Resistance mutations
The model assumptions for the emergence of resistance are described in detail in
Suppl Mat 4.A.4. The central part of this study is the introduction of a drug concentration dependent mutation rate. We assume that bacterial mutation rates increase
with drug concentration in a sigmoidal fashion [155]. We make this assumption because the mutagenic effect of antibiotics has been argued to arise due to the increased
expression of more error prone DNA polymerases and repair proteins [144; 156; 157].
The expression levels of such polymerases and repair proteins are likely to eventually
saturate and their error rate is expected to be constant at high drug concentrations.
The sigmoidal curve is defined by three parameters: a minimum corresponding to
the base mutation rate in absence of drugs, a maximum corresponding to the saturation of the mutation rate at high drug concentration, and a parameter termed mut50 ,
which corresponds to the drug concentration at which the mutation rate reaches the
half-point between minimum and maximum. As an estimate for the minimum mutation rate to become resistant to a single drug we conservatively assumed a rate
of 10−9 per cell doubling [62]. The maximum mutation rate varies widely between
studies [158; 159; 160; 161; 162; 163; 164; 165; 166]. The differences are probably due
to both differences between combinations of bacteria and drugs and differences in experimental designs and measuring methods. Here we assume a maximum ten-fold
increase of the mutation rate for high drug concentrations. Most of the aforementioned studies did not look at the concentration-dependent increase of the mutation
rate. The few studies that measured the increase of the mutation rate at more than
one drug concentration did this mostly at sub-MIC concentrations [158; 162; 165; 166].
Therefore, it is difficult to estimate whether and how far ASIM extends beyond the
MIC. In our default parameter setting, we assume that the turning point of the mut50
parameter coincides with the MIC.
63
64
considering antibiotic stress-induced mutagenesis
Furthermore we assume that if a resistance mutation is acquired, it grants absolute
resistance and the drug becomes completely ineffective. For every drug we assume
that there is on such resistance mutation and the corresponding allele confers a fitness cost of 10% on the growth rate. Multiple resistance mutations are assumed to
contribute multiplicatively to the overall fitness costs.
4.2.2.3
Pharmacokinetics
During the simulations the drug concentrations are either kept constant or they increase and decrease according to a pharmacokinetic model that is described in detail
in Suppl Mat 4.A.5. Firstly, we investigate the effect of ASIM in a situation where
a patient is treated with two equally bactericidal drugs, only one of which elicits
ASIM. Secondly, we explore the dosing regime and compare situations where patients are taking the two drugs combined every day (combination) and situations
where patients alternate between the drugs every day (cycling). In order to be able
to compare the two regimens the efficacy of the two regimens is equalized by adjusting the dosage of the drugs in both cases so that patient clearance is achieved on
average after 28 days. The exact dosages can be found in the Suppl Mat. Before treatment starts every patient harbors 5 × 107 fully susceptible wild-type bacteria and
the simulation is repeated 1’000 times for every treatment scenario and drug type in
Figures 4.1 and 4.2. In order to decrease the confidence intervals in the Figures 4.3
and 4.4 we performed these simulations 10’000 times each.
4.3
results
To get an overview over the basic parameters and their effects we first study a basic model of ASIM. In Figure 4.1 a homogeneous population of sensitive bacteria is
exposed to various constant drug concentrations. The net growth rate (red line), i.e.
the difference of the natural replication rate and the drug-induced bactericidal killing
rate, declines with increasing drug concentrations in a sigmoidal manner. In addition
to the drug concentration, the net growth rate is affected by the replication rate, the
KC50 , the Emax value and the MIC of the drug (see Equations 4.4–4.4 and Table 4.1).
At the MIC the drug-induced killing and the replication rate cancel each other out
and the net growth rate is zero. The mutation rate (black line) without considering
ASIM stays constant and is independent of the drug concentration (grey line). When
ASIM is taken into account the mutation rate increases sigmoidally with higher drug
concentrations (black line). The mutation rate increase depends on the mut50 and
the maximum fold change Md . Here, mut50 is set to the MIC. These parameters are
assumed constant during the simulations shown in Figure 4.1. We get three possible
treatment outcomes: (i) complete sterilization, i.e. the drug concentration is sufficient to eradicate the bacterial population and the treatment is deemed successful;
(ii) treatment failure, here defined as the treatment being unable to clear the bacterial
population after 20 days (green line); (iii) emergence of resistance, defined here as
the population containing at least 50 resistant bacteria after 20 days (dark blue line).
Emergence of resistance implies treatment failure and is therefore a subset of the previous category. We show the emergence of resistance with ASIM (dark blue line) and
without ASIM (light blue line). Unsurprisingly, the risk for treatment failure drops
4.3 results
Table 4.1: Compartment characteristics
Replication rate (r)
2 d−1
Initial population size (N0 )
5 × 107 CFU
Carrying capacity (K)
109 CFU
Drug half-life (t1/2 ) a
3h
Absorption time (tmax ) a
1h
Dosage (D0 )
3.18 / 8.80 c
MIC a
1b
a
5b
KC50
Base mutation rate (md ) a
mut50
d
10−9 per replication
0.25 b
Maximum fold increase of mutation rate (Md ) 10
Resistance cost (cl ) a
a
for all used drugs
b
arbitrary concentration unit
c
combination / cycling
d
only for mutagenic drug
0.1 b
from 100% at sub-inhibitory drug concentrations rapidly if the drug concentrations
are above the MIC. Beyond the MIC in about 5% of all simulations the bacterial population is rescued by the emergence of a resistant mutant under ASIM. Below the
MIC resistant genotypes occur in up to 60% of all populations. This is substantially
more frequent than in a model without ASIM.
Next we assess how the emergence of resistance depends on mut50 (see Figure
4.2). To do so we repeat the simulations shown above for a wide range of drug
concentrations and additionally vary the mut50 concentration. For each pair of drug
concentration and mut50 value we count the frequency of the emergence of resistant
mutants. The remaining parameters and the criteria for scoring the outcome of the
simulations are the same as above. Resistant genotypes emerge rarely if the mut50
value is high and the drug concentration is either very low or very high. The risk for
the emergence of resistance generally increases with lower mut50 . It is highest at the
lowest mut50 that we tested and at a drug concentration of 1/4 × MIC. Interestingly,
1/4 × MIC is the drug concentration at which the frequency of drug resistance is
highest for every mut50 . We conclude that the mut50 concentration has a substantial
influence on the probability of emergence of resistance.
To estimate the influence of ASIM on the emergence of resistance we repeated the
above simulations 10’000 times for each parameter set with and without ASIM (see
Figure 4.3). At low drug concentrations the frequency of emergence of resistance only
differs marginally. However, at the MIC the risk of emergence of resistance increases
about five-fold increasing to an about ten-fold risk at high drug concentrations. In
Figure 4.1 we see that a considerable fraction of bacterial populations are rescued
65
0.6
0.5
0.4
0.3
0.2
0.1
0.0
1.0
4
0.9
3
0.8
2
1
0
−1
−2
−3
0.7
0.6
0.5
0.4
0.3
Treatment failure rate
0.7
10−92 × 10−9
0.8
Mutation rate per generation
4 × 10−9
6 × 10−9
8 × 10−9
0.9
5
Net growth rate of sensitive strain
1.0
10−8
considering antibiotic stress-induced mutagenesis
Frequency of resistance emergence
66
0.2
−4
0.1
−5
0.0
IC IC IC IC IC IC IC IC IC IC IC IC
M ×M ×M ×M ×M ×M ×M ×M ×M ×M ×M ×M
×
64 32 16 1/8 1/4 1/2 1 2 4 8 16 32
1 1 1
Concentration
Figure 4.1: Antibiotic stress-induced mutagenesis (ASIM) increases the risk of drug resistance over a large concentration range. A population of 107 bacteria is exposed
to a range of constant drug concentrations. The outcome of 1000 simulations of
treatment per parameter set is collected and the lines show the average. Treatment failure (green line) is defined as incomplete clearance after 20 days. The
frequency of resistance emergence under ASIM is given in dark blue and without
ASIM in light blue. At least 50 drug resistant bacteria have to be present in the
population for a strain to be classified as resistant. Without considering ASIM
resistance evolves in fewer populations. The mutation rate per generation in presence of ASIM is given in black and increases in a sigmoidal manner with higher
drug concentrations. The base mutation rate (without ASIM) is given in grey. The
inflection point where the mutation rate reaches the half maximal increase (mut50 )
is at the MIC. The net growth rate (red line) is composed of the natural growth
rate and the killing due to the bactericidal drug activity.
8
0.8
4
2
0.6
mut50
1
0.5
0.4
0.25
0.125
0.2
1
1
1
64
32 × M
I
16 × M C
1/ × MIC
8
1/ × MIC
4
1/ × MIC
2 IC
×
1 MI
× C
2 M IC
×
4 M IC
×
8 M IC
×
16 M
IC
32 × M
× IC
M
IC
0.0625
Probability of emergence of resistance
4.3 results
Concentration
Figure 4.2: Emergence of drug resistance depends on drug concentration and mutation rate.
The mut50 concentration is the antibiotic concentration at which the half maximal
mutation rate is reached. To predict the influence of the mut50 value on the
probability of resistance emergence 107 bacteria with varying mut50 values are
exposed to a wide range of drug concentrations. The color scale indicates the
fraction of 1000 simulations per parameter set in which at least 50 drug resistant
bacteria evolved after 20 days.
67
68
considering antibiotic stress-induced mutagenesis
due to the emergence of resistance even at very high drug concentrations. This is
a much higher fraction than with a constant mutation rate. The simulations thus
suggest that the underestimation of the risk of emergence of resistance due to AISM
increases with higher drug concentrations.
Next we investigate the implications of ASIM for the treatment of patients. To this
end we are introducing a model that incorporates the pharmacokinetics as would be
observed in a human patient treated with two bactericidal drugs simultaneously (see
Figure 4.4). Four cases are studied: Patients receive both drugs either simultaneously
or alternatingly every day and the drugs either do not elicit ASIM or only one of them
elicits ASIM. The dosage of the drugs is adjusted to achieve complete clearance after
28 days on average if no double-resistance emerges. The simulation is stopped after
50 days and the frequency of patients harboring double-resistant bacteria is counted.
Thus, if the bacterial population is not eradicated after 50 days, it is always due
to the emergence of resistance. In accordance with the previous results the risk of
emergence of double-resistant genotype is substantially lower if both drugs are not
mutagenic. The two treatment strategies also do not differ from each other if no drug
elicits ASIM. However, if one drug is mutagenic combination treatment seems to be
significantly worse than an alternating regimen. The advantage of the alternating
treatment is a direct consequence of ASIM.
4.4
discussion
Mathematical models are a useful tool to investigate the expected outcome of antibiotic treatment strategies before costly and time consuming experimental and clinical
studies are performed. Moreover, they aid in identifying gaps in our current knowledge that preclude quantitative predictions of treatment success and resistance evolution. It is well known that at least some antibiotics increase bacterial mutation rates
and thereby the rate of resistance evolution in a dose-dependent fashion. In this
study we present a population dynamic model that addresses how dose-dependent
antibiotic stress induced mutagenesis (ASIM) affects the probability of emergence of
drug resistance in a single patient.
Our study indicates that ASIM changes both our quantitative expectations regarding the frequency of resistance emergence as well as our qualitative expectations
which treatment strategy is least likely to lead to treatment failure due to resistance. This is in agreement with previous expectations and results from other studies
[160; 162; 167; 168]. Previous models, which do not take ASIM into account, underestimate the probability for the emergence of resistance. The degree to which those
models underestimate resistance evolution depends on the drug concentration to
which the bacteria are exposed. High drug concentrations do not necessarily reduce
the risk of drug resistance if fully resistant mutants rescue the bacterial population
before it is completely eradicated. We find that the probability of resistance emergence peaks at approximately 1/4 × MIC independent from the exact relationship of
drug concentration and mutation rates. Sub-MIC concentrations have been demonstrated to be associated with elevated occurrences of drug resistance [164; 166]. There
are several factors which we would expect to drive resistance evolution: i) the size of
the susceptible population that gives rise to resistant mutants, ii) the number of gen-
15
10
5
1
M
1 IC
×
M
I
2 C
×
M
I
4 C
×
M
I
8 C
×
M
16 IC
×
M
32 IC
×
M
IC
×
2
1
1
8
1
4
×
×
M
IC
IC
M
IC
×
M
16
1
32
×
×
1
64
1
M
IC
0
M
IC
fold change of resistance emergence with ASIM
4.4 discussion
drug concentration
Figure 4.3: ASIM increases the emergence of drug resistance at higher drug concentrations.
A population is classified as resistant when at least 50 bacteria became drug resistant after 20 days of treatment. The panel shows the fold change in emergence
of drug resistance with ASIM compared to a model with a fixed mutation rate.
In the ASIM model the mutation rate increases with higher drug concentrations
assuming mut50 equals the MIC. The fixed mutation rate model assumes a mutation rate that is equal to that of the ASIM model at drug concentration zero.
Each data point summarizes 10’000 simulations. The error bars indicate the 95%
confidence interval. The increasing size of the confidence intervals is due to the
increasingly rare occurrence of drug resistant bacteria at high drug concentrations
without ASIM.
69
70
considering antibiotic stress-induced mutagenesis
Figure 4.4: ASIM changes theoretical predictions for optimal drug therapy. This graph
shows the emergence of drug resistance within single patients that are treated
with two bactericidal drugs, either administered every day simultaneously (combination, red bars) or given alternately on consecutive days (cycling, blue bars)
Patients harbor a homogeneous population of 5 × 107 wild-type bacteria. For the
simulations assuming fixed mutation rates neither drug is mutagenic (i.e. resistance mutations arise irrespective of the applied drug concentration), while with
ASIM one of the two drugs induces mutagenesis. The mut50 concentration for
the ASIM drug is 1/4 × MIC. Every parameter set is simulated 10’000 times and
the fraction of patients that developed multidrug-resistance is given. The drug
dosages are adjusted to achieve complete clearance after 28 days of treatment assuming no emergence of multidrug-resistant strains. The error bars indicate the
95% confidence interval. In this case, the emergence of resistance is equivalent
to treatment failure, i.e. patients who develop resistance are still infected after 28
days and all patients who fail treatment do so because of resistance evolution.
4.5 acknowledgments
erations before the population is eradicated, iii) the rate per replication with which
resistance mutations emerge and iv) the fitness difference between susceptible and
resistant bacteria. When keeping the initial population size constant, there seems to
be an optimum for the last three factors to favor a high frequency of populations
containing drug resistant bacteria.
Patients who are treated with a mixture of drugs usually receive them in combination [169; 170]. Our results show that this strategy might not be optimal in
preventing the emergence of resistance if one of the drugs elicits ASIM. This effect
probably arises due to the lower number of drug applications that is compensated
by higher doses. If a drug is less often administered the drug concentration is less often at subinhibitory concentrations, which have previously been shown to favor the
emergence of drug resistance. The advantage of a cycling regimen over combination
therapy on an epidemiological scale has previously been shown to be advantageous
in a hospital setting [168].
To the best of our knowledge, this study is the first that addresses the effects of
dose-dependent ASIM. Our main limitation is the scarcity of experimentally obtained
parameters. Depending on the study the increase of mutation rates varies widely,
from 2-fold [164; 166] up to 10’000-fold [160]. Most studies report increases in the
order of a few- up to 100-fold [158; 159; 161; 162; 163; 165]. Furthermore, most studies showed an increase of the mutation rate only qualitatively, but did not establish
a quantitative relationship between the drug concentration and the increase of the
mutation rate. Due to the insufficient data from the literature we apply conservative
parameter estimates. This also means that we are potentially over- or underestimating the magnitude of the effects that we found. We therefore have to point out that
the focus should be on the qualitative aspects of our results. We further have to point
out that we look specifically at the influence of changing probabilities on the emergence of de novo rescue mutations [171]. That means, mutations that are involved
in preventing the population from eradication and which appear when the stress is
already present. We assume that none of these mutations occur in the population
before the introduction of antibiotics and that the population is therefore genetically
homogeneous.
Here, we show that that ASIM has a profound effect on resistance evolution. One
of the main messages of this work is therefore that dose-dependent ASIM should
be investigated experimentally in more detail, especially at antibiotic concentrations
above the MIC. The negative consequences of ASIM could be prevented by the introduction of drugs that specifically inhibit the intracellular mechanisms that increase
the mutation rate of bacteria. Such drugs have been proposed previously as an effective instrument to reduce the evolvability of pathogens [161; 172; 173; 174]. We
find that ASIM increases the probability of treatment failure by up to 10-fold. Thus,
drugs that prevent stress-induced mutagenesis might have a major impact on treatment outcome and warrant further investigation.
4.5
acknowledgments
We thank Antoine Frénoy for reviewing the manuscript.
71
APPENDIX
4.a
4.a.1
supplementary material
General model
The bacterial population dynamics are simulated as stochastic processes by applying
the Gillespie τ-leap method [58] with a temporal resolution of 10−2 d. The underlying
processes can be described in differential equations that are explained below.
4.a.2
Bacterial growth and death
The general population dynamics are based on a classic logistic growth model.
dNg
= r · ωg · Ng − (dg + κg ) · Ng
dt
(4.1)
Here Ng is the number of bacteria of a specific genotype. r is the replication rate
of the bacteria, which is modified by the fitness ωg of the strain. The population is
reduced by the natural death rate dg and the drug-induced killing κg .
The fitness of a specific genotype is influenced by the fitness costs that are imposed
by resistance mutations.
n
Y
(1 − cl )
ωg =
(4.2)
l=1
cl is the cost of a resistance allele at the locus l and n is the number of resistance
loci. Susceptible wild-type alleles do not confer any costs.
The death rate dg depends on the overall population density that is influenced by
bacteria of every genotype.
dg = r ·
N
K
(4.3)
Here K is the carrying capacity.
4.a.3
Pharmacodynamics
The killing rate κg is calculated by using the sigmoid Emax model by Czock et al. [108].
We extend it to include the effects of multiple drugs.
κg =
n
X
d=1


Emax,d · 1 −
1
Cd
KC50,d
+1
 · νg,d
(4.4)
73
74
considering antibiotic stress-induced mutagenesis
The killing rate depends on the additive effects of all drugs to which the specific
bacterial strain is susceptible. The potency of a drug is governed by Emax,d , which is
the maximal death rate. It is modified by the drug concentration Cd and the KC50,d
concentration, which represents the concentration at which the drug exerts its halfmaximal bactericidal potential. The Boolean parameter νg,d determines whether the
drug is effective or whether the bacteria strain is resistant against the drug. Drug
resistance is assumed to be absolute.
The Emax value is obtained by adopting the equation from the enhanced-death constant replication model [108].
C
dN
= r · N − Emax · N ·
dt
KC50 + C
(4.5)
When the drug concentration C is equal to the minimum inhibitory concentration
(MIC) growth and killing cancel each other out and we get the following equation
that determines the Emax value.
Emax =
4.a.4
r · (MIC + KC50 )
MIC
(4.6)
Resistance mutations
The increase of the mutation rate m by a stress-inducing drug follows a curve that is
defined by a sigmoid function [155].
m(t) =
n
Y
m · Md −
d=1
Md − 1
Cd
mut50
+1
!!
(4.7)
If we assume that resistance to a drug is granted by the mutation of a single allele,
then the number of drugs n is the number of resistance loci. m is the base mutation
rate and M is the maximum increase of this rate that is achievable by a drug. The
turning point of the sigmoid curve is defined by the mut50 concentration.
4.a.5
Pharmacokinetics
If the drug concentration in the simulation is not kept constant, classic absorption
and excretion kinetics are applied to the drug concentration.
Two drug compartments are simulated in the model: At the time point of drug administration, the whole dosage is instantly added to the compartment of unabsorbed
drug D. From the first compartment D the drug is absorbed into the compartment C
of the pharmacodynamically effective drug. From compartment C the drug concentration constantly decays due to excretion. The decrease of the drug concentration in
compartment D is calculated according to the following equation:
dD
= −ka · D
dt
(4.8)
4.A supplementary material
ka here is the absorption rate constant. The dynamics in compartment C are governed accordingly:
dC
= ka · D − ke · C
dt
(4.9)
ke is the excretion constant of the drug. To calculate the absorption rate constant
ka we use the following equation that describes the relationship between the absorption rate constant, the excretion rate constant ke and the time until the maximum
concentration peak is reached tmax :
tmax =
ln(ka ) − ln(ke )
ka − ke
(4.10)
From this we can derive an equation that enables us to calculate the absorption
rate constant for a known tmax and ke .
ka = −
W−1 (−e−ka ·tmax · ke · tmax )
tmax
(4.11)
W−1 denotes the lower branch of the Lambert function. The excretion rate constant
ke is derived by from the concentration half-life t1/2 .
ke =
ln(2)
t1/2
(4.12)
To calculate the initial amount of drug D0 that has to be administered in order to
reach a predefined peak concentration Cmax , we use the Bateman equation [127; 128],
which is also the solution to equation 4.9 to calculate the drug concentration at any
given time point considering drug absorption and excretion:
C(t) =
D · ka
· (e−ke ·t − e−ka ·t )
ka − ke
(4.13)
From this we derive a formula that calculates the required D0 .
D0 =
Cmax · (ka − ke )
ka · (e−ke·tmax − e−ka ·tmax )
(4.14)
75
5
GENERAL DISCUSSION
5.1
5.1.1
conclusions
Treatment of pulmonary tuberculosis
The initiation of the directly observed treatment, short course (DOTS) strategy implemented by the WHO had five main components: increasing government commitment, case detection by sputum smear microscopy, the standardization of treatment
by the application of a short course treatment regimen under professional supervision, providing sufficient drug supply and a standardized recording and reporting
system [16]. While DOTS was reported to be very successful [27] there were also
studies that showed the inadequacy of DOTS in areas with a high prevalence of drug
resistance [175; 55]. It was argued that the incautious application of treatment regimens within the DOTS program could lead to an amplification of drug resistance
among patients due to the undetected preexistence of mono- or multi-drug resistance
[176; 177].
In Chapter 3 we see that there is a substantial likelihood that treatment failure
coincides frequently with at least mono-resistance against isoniazid. Even if drug
susceptibility testing with a GeneXPert MTB/RIF test [129] would be performed
such patients would probably not be diagnosed as harboring MDR-TB (M. tuberculosis that is resistance against at least isoniazid and rifampicin). In Chapter 2 we find
that the retreatment of patients with a treatment history indeed bears the risk of accumulating additional resistance mutations if patients also fail the retreatment. This
confirms the concerns mentioned above that the application of standard treatment
for patients who are suspected to harbor Mtb with low resistance could lead to an
amplification of the resistance.
The DOTS-Plus strategy aims specifically at the diagnosis and optimal treatment
of MDR-TB patients [178]. Based on our results we argue that this might aim too
low. A thorough drug susceptibility testing that also screens for isoniazid-resistance
could help to prevent a potentially detrimental administration of ineffective drugs.
Not only is the patient more likely to fail the treatment if not all drugs are effective,
he or she could also be forced to suffer later through retreatment regimens that have
a lower success rate and are associated with more severe side-effects. Besides the personal disadvantages for the patient, MDR-TB or XDR-TB (extensively drug-resistant
TB: resistance against at least isonazid and rifampicin, a fluoroquinolone, and either
amikacin, kanamycin or capreomycin [179]) treatments are also considerably more
time-consuming and expensive [180; 181].
77
78
general discussion
5.1.2
Antibiotic stress-induced mutagenesis
Mutation rates are commonly assessed under ideal growth conditions for bacteria
[62]. When any other influences can be excluded the mutation rate for a specific
locus can be assumed to be dependent solely on the fidelity of the DNA replication
machinery. However, in different environments there exist factors that may change
mutation rates. The concept that mutation rates are not constant but can vary under
certain circumstances has not been discussed in the literature for a long time. It is
therefore not surprising that it is not customarily incorporated into within-host models that deal with mutation rates. Mutation rates are a key parameter for models
about the probability for the emergence of resistance [151; 182]. Several environmental stresses have been shown to increase mutation rates in bacteria. Among those
stresses is also the exposure to certain antibiotics [144]. In Chapter 4 we conceptually
show what the implications of antibiotic stress-induced mutagenesis (ASIM) may be
for the evolution of drug resistance in bacteria. When we compare the probabilities
for the emergence of resistance between a model that assumes a static mutation rate
and a model in which the antibiotic increases the mutation rate in a concentrationdependent manner, we observe a substantial increase of the probability for the emergence of drug resistance. This leads us to the conclusion that the concept of ASIM
should at least be considered in future models that attempt to quantify the probabilities for the emergence of mutations.
When we take ASIM into account we are also able to discover novel implications
for combination therapy. In a scenario in which a patient is treated with two drugs
against a bacterial infection we observe that it could be beneficial to administer the
drugs alternately rather than simultaneously if one of the drugs increases mutagenesis and the other does not. To my knowledge this study is the first to assess the
potential benefits of a cycling drug administration regimen for an individual regarding the emergence of resistance.
5.2
future directions
When one is engaged in the business of modeling one has to accept the intrinsic
shortcomings of models. Models try to represent actual systems in an abstract and
simplified form. The human mind constantly constructs models to get a grasp on the
reality around it and they help it to see and understand relationships and causalities.
Because models are a simplification of reality they are also never absolutely true
because they cannot fully capture the nature of reality. However, models are not
meant to replicate the real world. Their task is to show whether certain assumptions
are sufficient or necessary to give a reasonably accurate representation of the natural
world. Still, one has to constantly answer the question whether a model reflects
reality accurately enough to provide a sufficiently trustworthy answer to the specific
question one is trying to tackle.
In this section I would like to talk about aspects that we could not implement in
our projects. There are various reasons for why we did not include certain things but
it generally left me behind with some unrest. For the aforementioned reasons I have
to constantly question my confidence in my models and their predictions because
5.2 future directions
not considering some aspects of the disease dynamics may open up the door for
unjust conclusions. At the same time this attitude also helps me to maintain a critical
eye on my own work and that of my colleagues and to think about possibilities for
improvements of current models and future directions to explore.
5.2.1
Pharmacodynamics
Antibacterial drugs are commonly divided in two main classes: bacteriocidal drugs
and bacteriostatic drugs. Bacteriocidal drugs are characterized by their ability to kill
bacteria while bacteriostatic drugs merely inhibit the proliferation of bacteria. If you
try to put an antimicrobial drug in one of these two categories you may discover that
this is not always a straightforward task. Many antibiotics have a predominantly bacteriostatic effect at low concentrations but may actually exhibit bacteriocidal activity
at higher concentrations. It could even be taken into question whether a drug is bacteriostatic at low concentrations if one could just observe that a colony does not grow
anymore. The classification of bacteriostatic and bacteriocidal drugs is usually done
at a population level. Hence, if one would examine the drug efficacy at a cellular
level it is conceivable that the bacteriocidal activity of a drug and the bacterial proliferation just about cancel each other out and therefore no net growth of the colony
is observed. Therefore, a bacteriocidal drug could at low concentrations be mistaken
for being bacteriostatic.
In fact one of the simplifications that we did in all chapters of this thesis is to
assume that the activity of antimicrobial drugs is exclusively bacteriocidal. This
simplification may lead to an overestimation of the probability of resistance emergence. If a drug is also at least partially bacteriostatic it would reduce the number
of cell divisions and thereby the number of opportunities for mutations to arise. In
early stages of the development we experimented with a pharmacodynamic model
that also incorporated bacteriostatic activity. When we tried to fit this model to in
vitro time-kill curves of anti-tuberculosis drugs [90] we observed negative growth
inhibition at some concentrations (data not shown) and other unrealistic behavior.
Eventually we settled for a pharmacodynamic model that only considered the bacteriocidal effect of drugs. This simplified model allowed us to achieve reasonably good
fits to the in vitro time-kill curves for most drugs (see Supplementary Material 2.A).
However the effects of rifampicin, at least for higher concentrations, could not be fit
very well. This is an indication that a single pharmacodynamic model is probably
not sufficient to capture the activity of all drugs accurately. To further improve the
pharmacodynamic model it would be desirable if drug actions could be experimentally observed at the cellular level. Eventually, we would be able develop a tailored
function for every drug that describe their action more accurately.
Another simplification of our pharmacodynamic model is the omission of the postantibiotic effect [183]. The post-antibiotic effect inhibits growth for a certain time
period even when the drug is not present anymore [184; 80]. The presence of the
post-antibiotic effect has been reported in in vitro studies for most first-line drugs
against M. tuberculosis [111]. It is reasonable to assume that it may last for several
hours [185]. Neglecting the post-antibiotic effect may overestimate the risks in con-
79
80
general discussion
nection to intermittent therapy (see Chapter 3) and the risk for the emergence of
drug resistance.
5.2.2
Pharmacokinetics
One factor that may be highly influential in the transferability of in vitro experiments
to in vivo models is bioavailability. I am using here the pharmacological definition
of bioavailability, which states that the bioavailability is a measurement of the rate
and extent to which a drug reaches the site of action [186]. In this thesis the concept
of bioavailability is embodied in the TB model as the ratio between the serum drug
concentration and the concentration in the epithelial lining fluid within the lung [83]
and it also influenced the relative drug efficacy parameters. For example, the relative
drug efficacy parameters were assumed to be lower in macrophages if the drugs were
reported to have a low cell-penetration [69; 68; 70; 77]. The ratio between the serum
concentration and the epithelial lining fluid on the other hand is a global parameter
because it changes the drug exposure in all simulated compartments.
While in vitro data suggests that isoniazid and rifampicin have comparable bacteriocidal activity at clinically relevant serum concentrations [90] the picture changes
when we also consider the amount of drug that actually reaches the bacteria. Because the rifampicin concentration in the epithelial lining fluid is only about a third
as high as in the serum [83] it loses a substantial amount of its potency relative to
isoniazid that actually is more concentrated in the epithelial lining fluid than in the
blood serum [83]. This phenomenon also partially explains the strong survival benefit of isoniazid-resistance for M. tuberculosis relative to rifampicin-resistance that we
observed in the results of Chapter 3.
Somewhat related to that issue is the limited certitude about the conditions inside
granulomas. Because the pathogenesis of a tuberculosis infection is different from
the progression in animal models [187; 188] the knowledge about processes inside
granulomas remains vague. The population growth dynamics inside granulomas as
well as the pharmacokinetics and pharmacodynamics are largely based on assumptions, less on actual measurements. It is not known whether the bioavailability of
drugs is similar to the one in the epithelial lining fluid, and the premises about the
efficacy of drugs is largely based on the assumptions of low bacterial growth and a
low pH [19]. Furthermore, it is debatable whether all granulomas develop similarly
and progress into open cavities during an acute infection. It is possible that the bacterial populations in single granulomas remain dormant and are mostly unaffected
by a treatment. Such granulomas could then at a later time point cause a relapse —
probably with fully susceptible bacteria. Although, one has to keep in mind that the
possibility of relapse, caused either by the regrowth of previously dormant bacteria
or by reinfection, is anyway excluded in our model. If we included these possibilities
they would decrease our net treatment success rate.
5.2.3
Immune system and life history traits
In our TB model apart from the role of macrophages as a compartment we do not explicitly simulate the effect of the immune system on the progression of the infection.
5.2 future directions
We assume that the immune system of the patients is weak enough for the infection
to become acute and are therefore neglecting any contributions of it to contain the
infection. This is a reasonable assumption for an untreated infection, however, it is
possible that after the initiation of treatment the infection is suppressed well enough
that the immune system becomes less overwhelmed and is able to suppress the last
remains of an infection even if patient adherence is suboptimal. This would imply
that the treatment success rate could be underestimated.
A classic simplification in our model is the absence of a natural death rate of
bacteria. Bacteria may only die because of the limited population density inside the
compartments or because of bacteriocidal drug actions. Such an assumption is a
classical logistic growth model [2]. If we assumed a natural unconditional death rate
and a correspondingly increased birth rate we could achieve the same net growth
rate that we originally assumed. The difference would be that we would have a
higher turnover of bacteria. With a higher turnover we would get more birth events
and therefore more opportunities for resistance mutations to emerge. This means
that our model may underestimate the probability for the emergence of resistance.
Unfortunately, the growth rate of M. tuberculosis in vivo can only be estimated with
limited certainty [189] and measurements of the natural birth and death rate in vitro
do not exist in the literature.
The definition of drug resistance that we apply in the models of this thesis is rather
absolute. We assume that a particular mutation in a locus confers complete resistance
to the corresponding drug. This definition is more strict than the common conception that states that drug resistance is characterized by a reduction in effectiveness of
a drug [190]. Measurements of the mutation frequency usually determine the ratio
of bacteria that are able to grow or at least persist at drug concentrations above the
MIC [62; 93; 191]. Such measurements are at risk to also include bacteria that are
phenotypically drug tolerant. Drug tolerance has been described in M. tuberculosis
and attributed to a slow down of metabolism [192] or an increased expression of
efflux pumps [96]. Drug tolerance may serve as a stepping stone for the evolution
of higher genetic drug resistance [192]. Genotypes with low levels of drug resistance
may then accumulate further mutations that grant higher levels of drug mutation. In
our model we do not simulate the stepwise acquisition of resistance mutations that
render their carrier increasingly more drug resistant because currently available data
does not allow for more accurate modeling. A more detailed model may also not
provide much additional benefit because resistance mutations that grant low levels
of resistance or that infer high fitness costs are not particularly relevant for the evolution of resistance. In a previous study it has been found that of several rifampicin
resistance mutations the one that conferred the least fitness costs is predominantly
found in clinical isolates [193]. It could therefore be justified to not consider the
emergence of all resistance mutations but only the ones that provide a sufficient
protection from drug actions without affecting the fitness too much.
The mutation rate for drug resistance mutations itself is also less certain than
what would be desirable to improve the predictions of models. There has been a
debate about whether there are M. tuberculosis strains (e.g. Beijing strain) that have
a genotypically higher mutation rate than other strains [131; 194; 66]. Furthermore,
there are even discussions whether mutation rates could change transiently due to
81
82
general discussion
environmental influences. While some excluded the possibility for the induction
of mutations by oxidative stress [195; 196] others still consider this as a possible
explanation for the the observation of high mutation frequencies during latency [197;
189]. It has also been observed that genes for DNA repair and DNA stability were
down regulated in clinical multi-drug resistant isolates of M. tuberculosis [192]. This
could be an indication that M. tuberculosis is able under the influence of stress to
increase its mutation rate and faster adapt to averse conditions.
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101
ACKNOWLEDGEMENTS
I would like to thank here all the people who contributed to my thesis and those who
made my years here in the group of Theoretical Biology a great experience. First of
all I am immensely grateful for having Sebastian Bonhoeffer as my supervisor. I
could not wish for a more accommodating doctoral father. He provided a stimulating environment and granted me the freedom to pursue the studies that interested
me. By granting me the personal freedom to explore various directions and also
occasionally divert from an originally chosen path I sometimes may have gotten lost
but it also allowed me through introspection to learn to keep the bigger picture in
perspective. At the same time he provided me always the support when I requested
it. With this attitude and by his example he cultivated an environment that fostered
a way of independent and critical thinking.
It would be difficult to exaggerate the influence that Pia Abel zur Wiesch had
on my doctoral studies. She is probably the single most responsible person for me
choosing to pursue my doctoral studies. From my master’s thesis throughout my
Ph.D. she fulfilled the role of my supervisor at least as much as Sebastian did. I
think the mere fact that she was involved in every study in this thesis as well as a
previous publication speaks volumes. I am forever grateful for all the knowledge
and experience that she shared with me. It is a privilege to have collaborated with
someone for whom I foresee an outstanding scientific career.
Many thanks also go to Roger Kouyos who introduced me to the field of infectious
disease modeling. He was my first mentor in the group of Theoretical Biology and
much of what he taught me is still at the roots of all my mathematical models. I am
always amazed by his capability to almost instantly capture concepts of rather complex issues that he is being confronted with. This was frequently highly appreciated
when I called for his support or opinion.
Special thanks go to Ted Cohen and Roland Regoes who kindly agreed to be in
my examination committee. It humbles me to know that my work is being judged
by people whose expertise I value greatly.
Unfortunately, it would exceed the appropriate length of an acknowledgement
section if I would express my heartfelt gratitude towards every former or current
member in the group of Theoretical Biology, Experimental Ecology, Microbial Molecular Biology, Evolutionary Biology and Pathogen Ecology. I just want to state that I
consider myself incredibly lucky to have been allowed to not only share office space
but also share many stories and beers during countless hours of stimulating discussions with people, none of which I would not consider a friend. Thanks for all
the exhaustive runs up to the Waldhüsli, the beer brewing, hikes, skiing weekends
and parties! I sincerely hope that we will stay in touch and that the procrastinating
discussions continue.
I definitely have to thank my sister, Eliane, with whom I shared a home for many
years. Thank you for your patience and your leniency when I did not fully adhere to
the house cleaning schedule!
103
104
Bibliography
Last but certainly not least I thank my parents, Ruth and Edgar. They spurred
my ambition to always progress and develop further. Even when I diverted from
my original path and they may have struggled initially to embrace my new goals
I was absolutely sure that they would support me. Thank you very much for your
confidence and your encouragement!
C U R R I C U L U M V I TA E
Dominique Richard Cadosch
Institute of Integrative Biology
CHN H76.1
Universitätstrasse 16
8092 Zürich
Switzerland
Phone: +41 44 632 89 22
Email: [email protected]
url: http://www.tb.ethz.ch/people/person-detail.html?persid=130634
Birth date: 30 May, 1984
Nationality: Swiss
Language skills: German (native), English (full professional proficiency), French
(limited working proficiency), Japanese (elementary proficiency)
education
Mar. 2012 – May. 2016
Doctoral student in Theoretical Biology
Thesis Title: Within-host population dynamics and the evolution of drug resistance
in bacterial infections
Supervisor: Prof. Sebastian Bonhoeffer
Institute of Integrative Biology, D-USYS, ETH Zürich
Zürich, Switzerland
Mar. 2010 – Nov. 2011
M.Sc. ETH in Ecology and Evolution
Thesis Title: Modelling the within-host infection and therapy of pulmonary tuberculosis
Supervisor: Prof. Sebastian Bonhoeffer
Institute of Integrative Biology, D-USYS, ETH Zürich
Zürich, Switzerland
Sep. 2005 – Feb. 2010
B.Sc. ETH in Biology
ETH Zürich
Zürich, Switzerland
105
106
curriculum vitae
Jul. 2004 – May. 2005
Military service
Mechanized infantry of the Swiss Army
Switzerland
Aug. 2000 – Jun. 2004
Gymnasial Matura
Alte Kantonsschule Aarau
Aarau, Switzerland
other research experience
Jan. 2014
Participation in the Swiss Epidemiological Winter School
Course: Applied Bayesian Statistics in Medical Research University of Bern
Wengen, Switzerland
Sep. 2010 – Jun. 2011
Research project in Theoretical Biology at the ETH Zürich
Title: Assessing the impact of adherence to anti-retroviral therapy on treatment
failure and resistance evolution in HIV
Supervisors: Roger Kouyos and Sebastian Bonhoeffer
ETH Zürich
Zürich, Switzerland
Sep. 2009 – Oct. 2011
Research project in the AI Lab of the University of Zürich
Title: Attempt on Plant-Machine Interface: Towards Self-monitoring Plant Systems
Supervisors: Dana Damian, Shuhei Miyashita, Rolf Pfeifer AI Lab, University of
Zürich
Zürich, Switzerland
teaching and supervisory experience
Sep. 2015 – Feb. 2016
Supervised seminar paper of a Master student
Theoretical Biology group, ETH Zürich
Sep. 2014 – Apr. 2015
Supervised term paper of a Master student
Theoretical Biology group, ETH Zürich
other professional activities
Referee or co-referee for: Nature Genetics, PLOS ONE, Infectious Diseases - Drug Targets.
curriculum vitae
publications
D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (2016) The role of adherence
and retreatment in de novo emergence of MDR-TB. PLOS Computational Biology 12(3):
e1004749. doi: 10.1371/journal.pcbi.1004749
DD Damian, S Miyashita, S Aoyama, D Cadosch, PT Huang, M Ammann, R Pfeifer
(2014) Automated physiological recovery of avocado plants for plant-based adaptive
machines. Adaptive Behaviour 22(2): 109-122. doi:10.1177/1059712313511919
D Cadosch, S Bonhoeffer, R Kouyos (2012) Assessing the impact of adherence to
anti-retroviral therapy on treatment failure and resistance evolution in HIV. Journal
of the Royal Society Interface 9(74), 2309-2320. doi:10.1098/rsif.2012.0127
D Cadosch, HP Huang, DD Damian, S Miyashita, S Aoyama, R Pfeifer (2011)
Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems.
IEEE International Conference on Systems, Man and Cybernetics pp. 791-796. IEEE.
doi:10.1109/ICSMC.2011.6083749
oral presentations
Sep. 2011
Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems.
IEEE International Conference on Systems, Man and Cybernetics
Anchorage AK, USA
poster presentations
D Cadosch, S Bonhoeffer (Aug. 2015) Antibiotic stress-induced mutagenesis and the
implications for the emergence of drug resistance.
Gordon Research Conference on Microbial Population Biology
Andover NH, USA
D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (Aug. 2014) The role of
adherence, retreatment and fitness costs for the emergence of MDR-TB.
Gordon Research Conference on Drug Resistance
Newry ME, USA
D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (Aug. 2013) Modelling the
within-host infection and therapy of pulmonary tuberculosis.
Gordon Research Conference on Drug Resistance
Easton MA, USA
D Cadosch, HP Huang, DD Damian, S Miyashita, S Aoyama, R Pfeifer (Sep. 2011)
Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems.
IEEE International Conference on Systems, Man, and Cybernetics
Anchorage AK, USA
107
108
curriculum vitae
D Cadosch, M Böller, M Ammann, DD Damian, S Miyashita, R Pfeifer (Jan. 2010)
Attempt towards the cyborg-plant – Robotic response to water stress in avocados.
4th International Conference on Cognitive Systems, CogSys 2010
Zürich, Switzerland
colophon
This document was typeset in LATEX, using the classicthesis style developed by
André Miede (http://code.google.com/p/classicthesis/).

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