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Energetic basis for the molecular-scale organization of bone
SI Appendix
a,b
c
Jinhui Tao , Keith C. Battle , Haihua Pand, E. Alan Salterc, Yung-Ching Chiena,e,
Andrzej Wierzbickic,1 and James J. De Yoreoa,b,1
a
Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720;
b
Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA
99352; cDepartment of Chemistry, University of South Alabama, Mobile, AL 36688;
d
Qiushi Academy for Advanced Studies, Zhejiang University, Hangzhou, 310027
China; and eDepartment of Preventive and Restorative Dental Sciences, University of
California, San Francisco, CA 94143
1
Corresponding authors email: [email protected] and [email protected]
SI APPENDIX
3
1. SI Materials and Methods
3
1. 1. Chemicals
3
1. 2. Calcium phosphate crystals preparation
3
1. 3. Collagen Adsorption on Crystal Surfaces
5
1. 4. Collagen mineralization
6
1. 5. Collagen orientation analysis
6
1. 6. Dynamic force spectroscopy analysis
6
1. 7. Tip Decoration and DFS Measurement
11
1. 8. Dentine and bone TEM sample preparations
12
1. 9. Characterization
12
1. 10. Molecular Dynamics Simulation Methods
13
SI APPENDIX REFERENCES
16
SI APPENDIX TABLES
18
SI APPENDIX FIGURES
20
2
1. SI Materials and Methods
1. 1. Chemicals
Sodium hydroxide (NaOH, 99.99% purity), hydrochloric acid (37 wt%), CaCl2
(99.99% purity), Na2HPO4 (99.95% purity), phosphate buffer saline (PBS),
polyaspartic acid (Mw=2000-11000 Da), Tris (99.9% purity), K2SO4 (99.99% purity),
Nitric acid (HNO3, 70 wt%), hexamethylenetetramine (HMT, 99.5% purity), Urea,
ethanol and acetone were purchased from Sigma-Aldrich. Ca(NO3)2·4H2O (99.995%
purity), NH4H2PO4(99.995% purity), and ammonia solution (5M) were bought from
Alfa Aesar.
All the chemicals were used without further purification. Milli-Q water
(resistivity=18.2 MΩ·cm at 25 °C) was used in all experiments. All solutions were
filtered through filters with 0.2 µm pore size (Corning) prior to use.
1. 2. Calcium phosphate crystals preparation
The single-phase HAP nanocrystals used as the starting material for the molten salt
synthesis of the micron-size HAP hexagonal prisms were synthesized as follows. The
preparation was done at the boiling point of the precipitating solution. Heating was
achieved by means of a heating plate. 18 mL water was introduced into the Teflon
vial. All reactants were simultaneously added to the vial dropwise (1 mL/min): 20 mL
solution 0.5 M Ca(NO3)2 and 20 mL solution 0.3 M NH4H2PO4, over a time period of
20 min. A 5 M NH3 solution was added to maintain the pH at 10 during precipitation.
After precipitation was completed, the crystals were filtered and washed thoroughly
with distilled water. The HAP nanocrystals were resuspended in distilled water, and
the slurry was hydrothermally processed at the 110 ºC for 24 h. The suspension was
then aged for 1 month, while the pH was maintained at 7.5-8.0 by the addition of NH3
solution. Following the aging period, the solid material was filtered, dried at 90°C,
and kept in storage for further study. Finally, the HAP nanocrystals were calcinated in
an air atmosphere at 1000°C for 12 h at the heating rate of 10 ºC/min and then
naturally cooled to room temperature.
3
The calcinated HAP powders were dry-mixed in an agate mortar with potassium
sulfate at K2SO4-to-HAP weight ratios in the range 1.5, for a total sample weight of
0.5 g. The mixtures were then placed into clean alumina boats with a volume of 7.5
cm3 and set inside a tube furnace (Lindberg/Blue M, TF55035A). The samples were
heated from the ambient to the peak temperature 1100°C at a rate of 5°C/min.
Following soaking times ranging from 4 to 7.5 h at the peak temperatures, the samples
were cooled naturally to room temperature within the shut-off furnace. The single
crystal were separated from the solidified mass by washing the mass several times
with hot (~90°C) deionized water. Finally, the cleaned HAP crystals were stored in
water.
The HAP (110) face for DFS measurement was cut using a Zeiss CrossBeam 1540
EsB FESEM-FIB system (Carl Zeiss Microscopy GmbH, Germany). Milling was
performed with a 30 keV gallium beam. The coarse milling of the sections was
performed with a current of 200 pA, the final polishing step with 50 pA. Then
incubated in PBS for more than 2 h to equilibrate the solid crystal surface with the
solution environment before DFS measurement.
The HAP platelets with (100) were synthesized by hydrothermal method by
controlled ammonia release (1). Typically, calcium solution with 40 mM Ca(NO3)2
and 100 mM hexamethylenetetramine (HMT) and phosphate solution with 24 mM
NH4H2PO4 and 100 mM HMT were prepared. The pH of both calcium and phosphate
solutions were adjusted to 5.60±0.05 with 0.5 M HNO3. Then, the equal volume
phosphate solution was dropped into calcium solution at a rate of 1.5 mL/min to
obtain a clear mixed solution. Afterwards, the solution was moved to a
poly(tetrafluoroethene) (PTFE) vessel capped by a PTFE cover and placed into a
stainless steel autoclave. The autoclave was sealed and subjected to the heat treatment
with temperature of 170 °C for 19 h.
The HAP platelets with (110) were also synthesized by hydrothermal method by
controlled ammonia release (1). Typically, calcium solution with 3.2 mM CaCl2 and
80.9 mM HMT and phosphate solution with 26.4 mM Na2HPO4 and 80.9 mM HMT
were prepared. HAP (110) surface is stabilized by the excess amount of HPO42- ions
4
in solution. The pH of both calcium and phosphate solutions were adjusted to
5.00±0.05 with concentrated HCl solution (37% by weight). Then, the equal volume
phosphate solution was dropped into calcium solution at a rate of 1.5 mL/min to
obtain a clear mixed solution. Afterwards, the solution was treated with temperature
of 130 °C for 15 h.
CAP (~5 wt% carbonate) plates were synthesized hydrothermally with urea as pHand carbonate-control reagent. Typically, calcium solution with 334 mM Ca(NO3)2
and 500 mM urea and phosphate solution with 200 mM NH4H2PO4 and 500 mM urea
were prepared before adjusting their pH to 3.00±0.05 with 0.5 M HNO3.
The
phosphate solution was then mixed with calcium solution with same volume.
Afterwards, the solution was processed with temperature of 91 °C for 88 h.
OCP crystals were synthesized by heating with controlled ammonia release.
Specifically, calcium solution with 20 mM Ca(NO3)2 and 50 mM HMT and phosphate
solution with 20 mM Na2HPO4 and 50 mM HMT were prepared. The pH of both
calcium and phosphate solutions were adjusted to 4.70±0.05 with with 0.5 M HNO3.
The equal volume calcium solution was dropped into phosphate solution at a rate of
1.5 mL/min to obtain a solution. The solution was stirred and heated to 80 °C for 18
min.
CDAP crystals were synthesized by using the same supersaturated solution for OCP
and the solution was hydrothermally heated at 100 °C for 2 h. The CDAP crystals
were formed from the hydrolysis of initially formed metastable OCP phase. The
reaction vessels were then cooled to room temperature naturally.
The products were carefully separated, collected by filtration, washed with distilled
water for 4 times, and finally dispersed in water.
1. 3. Collagen Adsorption on Crystal Surfaces
The collagen was purchased from Advance Biomatrix Corporation. Branded as
Purecol (Mw~300kDa), it is a 3.1 mg/ml, pH 2 solution of purified bovine Type I
collagen (97%) and Type III collagen (3%). For collagen adsorption on HAP
hexagonal prism (100), HAP platelet (110), HAP platelet (100), carbonated HAP
5
(100), OCP (100) and CDAP (100) surfaces, a small amount of different crystals was
transferred from water into 500 µL collagen (40 nM) in PBS solution (Sigma-Aldrich)
and kept statically for 30 min, then the collagen-adsorbed crystals were transferred
onto newly cleaved mica and set in PBS solution for another 10 min. The
non-adsorbed collagen in solution was discarded by removing the solution and further
washing with 100 µL PBS for 6 times. The prepared samples were imaged
immediately under AFM after wash. All the procedures were performed at 25 °C.
1. 4. Collagen mineralization
In order to minimize the size, shape and orientation effect on the Raman spectra of
minerals, hydroxyapatite platelets were formed within a collagen matrix similar to
that in the analyzed bone tissues as a control. Remineralized collagen in presence of
polyaspartic acid (pAsp) was achieved by incubating the rat tail tendon in Tris buffer
(50 mM, pH 7.4) containing CaCl2 (4.5 mM), Na2HPO4 (2.1 mM), NaCl (150 mM)
and polyaspartic acid (10 µg/ml) at 37 ˚C, as first proposed by Gower et al. elsewhere
(2). The mineralization lasted for 15 days. Then washed with Tris buffer and run
Raman measurement in Tris buffer.
1. 5. Collagen orientation analysis
The orientation of collagen on each crystal surface was measured by manually trace
each collagen with many segments (small element) using software ImageJ. The local
orientation of each segment has been measured. We obtained the distribution of local
angles for all individual segments of collagen fiber. Next, we summed up the segment
length in each angle group to get the histogram. The probability density function
(PDF) of the local angles was then calculated by normalizing the histogram by the
sum of all segments. By this way, the length of segment was used as weighting
function in angle distribution. More than 500 elementary segments were used to cover
the collagen fibrils in each image analysis.
1. 6. Dynamic force spectroscopy analysis
We begin by considering the Kramers’ escape rates, which has a generalized form in
6
the presence of an applied force field:
F
n
-DG (1- )
F
FC
k ( F ) = n 0 (1 - )n -1 e
FC
/ k BT
(S1)
In our case, due to the applied force the reforming of bond is suppressed. At this
condition, the survival probability of bond at time t can be described by:
dp (t )
= - k (t ) p (t )
dt
(S2)
It is convenient to transform this process from time to force dependence and then put
it in integral by starting the bond loading process at Feq , instead of starting at 0,
ò
p
1
dp
1
=dF
p
dt
ò
F
Feq
(S3)
k ( F )dF
Combining equation (S1) and (S3) yields the relation ship between force and survival
probability as
F
ì
kT
ln p n1 ü
F ( p) = FC í1 - [(1 - eq )n - B ln(1 )] ý
FC
DG
X
î
þ
Feq
n 0e -DG / kBT k BT DG[1-(1- FC )
Where X =
e
dF
xt
dt
The mean rupture force is given by
a º ln(1 -
n
(S4)
]/ k BT
1
F = ò F ( p )dp , we define the function
0
ln p
)
X
1
+¥
0
X
a = ò a ( p)dp = e X ò
e- S
e -g
ds @ e X ln(1 +
)
s
X
(S5)
And treat F as the function of a , If we expand F around a
F = F( a ) +
1 ''
F ( a )s a2 + ×××
2
and then we find
(S6)
When for most potential energy well n Î [1, 2] , the higher order term in
be neglected.
F can
Combining equation S5 with equation S6, the approximate analytical
expression for the mean rupture force for single bond, based on previous analysis, is
then given by:
:
7
1
ì
ü
n
é
ù
F
eq n
ï
ï
- g -DG [1- (1) ]/ k BT
Fc
Feq n k BT
ï ê
dFS ú ï
e
FS = FC í1 - ê(1 ) ln(1 +
) ú ý (S7)
FC
DG
dt
0 k BT
ú ï
ï ê
ku
úû ï
xt
ï êë
î
þ
where FS is the single bond rupture force at any loading rate, DG is activation free
energy, the parameter n selects the particular model of the potential energy well:
n =3/2 models a linear-cubic potential and n =2 models a harmonic potential, and
n =1 recovers the phenomenological two-states model by Friddle et al (3, 4). xt is the
distance between the free-energy minimum and the transition state, FC = nDG / xt is
the critical force at which the activation barrier vanishes, Feq is the equilibrium
rupture force (i.e., at loading rate = 0), k B is Boltzmann constant, T is absolute
temperature, ku0 is the intrinsic unbinding rate coefficient for the system in absence of
applied force, g =0.577 is the Euler-Mascheroni constant, and
dFS
is the loading
dt
rate. The activation free energy DG of the collagen-substrate single bond interaction
can then be calculated by fitting the
FS
vs
dFS
.
dt
The rupture force for single collagen molecule on HAP is determined by:
Fs =
F
n
(S8)
Where F is rupture force and n is the number of collagen molecule.
Collagen molecules can introduce an additional complication due to their internal
bonds that act as highly nonlinear springs connected in series with the Hookean spring
defined by the cantilever. The gradient at the point immediately prior to rupture is
then equal to the spring constant of the n collagen molecules which act in parallel,
thus the loading rate for one collagen molecule was determined by
1 dF
k
dFs n dx x = r c
=
v
dF
dt
+ kc
dx x = r
(S9)
8
where kc is the cantilever spring constant and
dF
dx
is the gradient of the force
x =r
curve at the point immediately prior to rupture, while v is the retraction speed. The
value of cantilever spring constant is determined by deflection sensitivity and thermal
fluctuation measurements (5).
In the free energy analysis, to minimize effects from possible multi-molecular
interactions and internal energy release through collagen stretching before complete
desorption, the rupture event occurring at the largest tip-surface separation was used
to characterize the collagen-HAP binding energy. The most straightforward way to
estimate the magnitude of the single bond free energy between collagen and HAP
(100) and HAP (110) is by assuming one bond (n=1) in the final rupture of force
curves. We calculated the instantaneous loading rate from the slope of the collagen
extension curve close to the rupture event at the largest tip-surface separation. No
extension model for the molecule is needed in this analysis. The dynamic force
spectra for the rupture of bonds between collagen and HAP (100) and HAP (110) with
dwell times of 0 s (blue) and 5 s (red) are showed in Figs. 2C and 2D and the fitting
parameters are shown in Table S1. From the analysis, we obtain single-bond free
energies of -7.5±0.2 kBT and -7.6±2.4 kBT on HAP (100) and values of -8.1±0.3 kBT
and -8.0±0.6 kBT on HAP (110) for dwell times of 0 s and 5 s, respectively. Similarly, if
we assume the number of bonds in the final rupture to be two (n=2), the fitted
single-bond free energies are -6.7±0.2 kBT and -7.0±1.6 kBT on HAP (100) and
-6.9±0.1 kBT and -7.3±0.6 kBT on HAP (110) for dwell times of 0 s and 5 s as indicated
in Table S2.
In this analysis, the number of collagen molecules involved in rupture event is
revealed by the steepness of point just before rupture.
However, collagen molecules
can introduce an additional complication due to their internal bonds that act as highly
nonlinear springs.
In order to get the more accurate number, we first analyze the
steepness of the force curve (force versus tip-surface separation) using the worm-like
chain (WLC) model using a nonlinear least squares fitting method, as described
elsewhere (6, 7):
9
FA x
1
1
= +
k BT L 4(1 - x ) 2 4
L
(S10)
Where A and L are the apparent persistence and contour lengths of the collagen
molecules obtained by fitting the peak before desorption and x is tip-surface
separation. The steepness of each force curve is measured by the apparent persistence
length. The distribution of apparent persistence lengths was plotted based on the value
from each force curve (Fig. S8). The peak at the largest apparent persistence length
~0.5 nm is most likely to correspond to the single collagen triple helix (6, 8). This
value of the persistence length is close to the value of 0.61 nm determined from a
previous AFM-based study of single collagen triple helix adsorption on mica (7) if we
also use the WLC model to fit that data.
As indicated by the in-situ AFM images of collagen on HAP surfaces in Fig. 1B,
the collagen triple helices are in a dispersed form without obvious aggregation on the
crystal surface. Thus it is reasonable to infer that collagen triple helices have
negligible interaction with each other on the HAP surface and we can treat the
collagen triple helices as interacting independently with HAP. Herein, the number of
collagen triple helices for the interaction was calculated based on (8):
n=
Am
A
(S11)
Where Am is the apparent persistence length for single collagen triple helices. A
similar protocol has been used to calculate the number of bonds in specific binding
events between PEG tethered antibodies and Mucin1 molecules (9).
In our case, the
collagen itself is used as tether for the last rupture between its end and crystal surface.
Using the distribution of persistence lengths in Fig. S8, eqn. S11 gives a range for n of
approximately 1 to 3.
While the WLC model works well for entropic elasticity characterized by rather
low tensile force below 100 pN (10), for tensile force larger than 100 pN, enthalpy
contributions take over and play an increasing role during stretching of the molecule.
Under these high-force conditions, one should fit the force curve with modified WLC
(MWLC) model, which includes an extra term due to molecular extensibility given by
10
(7):
FA x
1
1 F
= +
- k BT L 4(1 - x + F )2 4 F
L F
(S12)
Where the extra term F is the elastic modulus, which is reflects a molecule's tendency
to be stretched. The magnitude of the elastic modulus of a collagen triple helix is
unknown, but for double-stranded DNA it can be up to 1000 pN (11). The fit of the
WLC and modified WLC to the same experimental force-extension curve yield very
similar fits to the data but they give different absolute persistence length values
depending on whether we assume F to be 400, 500, 1000, 2000 and 3000 pN. The
modified WLC model shifts the apparent persistence length to larger values when
smaller values of F are used. The apparent persistence length is as large as 9.27 nm
for a F of 400 pN (Table S3). Fortunately, the ratio between the persistence lengths
of any two typical force curves stays almost constant within error, regardless of
whether the WLC or modified WLC with a range of F values is used (Table S3).
Therefore, as showed by equation S11, the number of molecules responsible for the
force curve in the different models should be unchanged and thus the estimated values
of the free energies will be unchanged. Consequently, we chose to work with the
WLC model to remove the unnecessary additional parameter of the modified WLC.
A comparison of the free energies obtained using the bond number determined
from the apparent persistence length in the WLC model (Table S4) with those
obtained using equation S7 assuming one or two bonds in the final rupture (Table S2)
shows that the latter are larger by ~2 kBT. However, the sequential order of the
values for each combination of faces and dwell times remains the same regardless of
which procedure is used to calculate the single bond free energies.
1. 7. Tip Decoration and DFS Measurement
Details of tip functionalization are found in the previous literature (3). In brief,
microlever Si3N4 AFM tips (Bruker, MSCT, CA) were gold coated and immersed in a
dimethylformamide (DMF) solution containing 0.9 mg/mL heterobifunctional
crosslinker LC-SPDP (Thermo Scientific) for 40 min, which bears a pyridyl disulfide
11
that binds to gold, leaving a low density of N-hydroxysuccinimide(NHS) ester groups
at the tip. The unbound crosslinker was removed by washing with DMF. The
ester-modified tips were immersed immediately in a collagen (40 nM) in PBS solution
for 12h to form a stable amide bond with a primary lysine residue or terminal amine of
the collagen. Force measurements between modified tips and HAP crystals were
performed in PBS solution. Measurements were made with the MFP3D Atomic Force
Microscope (Asylum Research, Santa Barbara, CA). A constant approach velocity of 1
µm/s and dwell times of 0 s and 5 s were used for six different pulling speeds of
399nm/s, 630nm/s, 1.00µm/s, 1.63µm/s, 2.60µm/s, 4.34µm/s, and more than 50
individual force curves were collected for each pulling rate. All the protocol and
measurements were performed at 25 °C.
1. 8. Dentine and bone TEM sample preparations
Permanent, fully-formed human third molars were obtained from the UCSF dental
hard tissue specimen core, courtesy of Dr. Grayson W. Marshall at Department of
Preventive and Restorative Dental Sciences UCSF. After extraction, the teeth were
sterilized with gamma radiation and stored intact in de-ionized water and thymol at 4
o
C (12). Pure dentine was cut from the mid-coronal region of the selected teeth
perpendicular to the tubule direction. For rat bone samples, 1-year old female rat
calvarial bones (Courtesy of Dr. Pamela K. DenBesten, Department of Oral and
Craniofacial Sciences, UCSF, SF, USA) were dissected and rinsed with 0.1 M sodium
cacodylate buffer (pH 7.4). Semi-thin slices of sample from human dentin or rat bone
were embedded after sequential ethyl alcohol and then acetone dehydration in Spurr’s
resin (Ted Pella, Redding, CA). Selected regions were trimmed, and ultrathin sections
(70 nm) were cut with a diamond knife on an ultramicrotome (Reichert-Jung Ultracut
E, Leica, Wetzlar, Germany). Ultrathin tissue sections were placed on Formvar™
copper grids before TEM observation.
1. 9. Characterization
Both ex-situ and in-situ crystal surface topography and collagen orientation data were
12
collected by tapping mode with a Digital Instruments (Santa Barbara, CA)
Multi-mode AFM with a Nanoscope V controller. High resonance NanoWorld
NCL-W (NanoWorld AG, Switzerland) non-contact probes with a 48 N/m spring
constant and a composite structure consisting of Si a tip on silicon nitride cantilever
(Bruker, SNL-10, CA) with 0.24 N/m spring constant were used for ex-situ and in-situ
measurements. One µm2 images were scanned at 1 Hz at a resolution of 512×512 data
points.Transmission electron microscopy (TEM) observations of bone and dentine
were performed by using JEOL 2100F field-emission analytical TEM (JEOL, Japan)
at an acceleration voltage of 200 kV. Scanning electron microscopy (SEM)
characterization was performed on Zeiss Gemini Ultra-55 analytical scanning electron
microscope (Carl Zeiss Microscopy GmbH, Germany) with a secondary electron
detector and an acceleration voltage of 5 kV. The phase of the solids was examined by
X-ray diffraction (XRD) by a Bruker AXS D8 Discover GADDS X-ray
Diffractometer
(Bruker,
WI)
with
monochromatized
Cu
Ka
radiation
(wavelength=1.541Å) operated at 40 kV and 20 mA, with a scanning step of 0.02°.
The Raman spectra were collected from 100 to 4000 cm-1under backscattering
geometry by a LabRAM ARAMIS confocal Raman Microscope (HORIBA scientific,
Japan) operated at a resolution of 2 cm-1 with an excitation wavelength of 532 nm.
1. 10. Molecular Dynamics Simulation Methods
A Type I collagen triple helix (~80 Å) with sequence [NH3+-(Pro-Hyp-Gly)10-COO-]3
was adapted from pdb ID 1CGD by making a necessary single substitution (Ala to
Gly) at position 15 of each of the three peptide chains. The CHARMM22 force field
parameter set (13) was assigned to the collagen peptide, with nonstandard
hydroxyproline parameters taken from Park et al (14). Charge-neutral HAP slabs of
dimensions 113 Å×110 Å×~21 Å (α=β=γ=90°) and 110 Å×114 Å×~20 Å (α=β=γ=90°)
were constructed for the (100) and (110) surfaces, respectively, using Cerius2 crystal
builder software (Accelrys, San Diego, CA). Modeling requires specific choices of
surface terminations to be made, and for the (100) surface, there are several possible
choices of surfaces with protruding surface phosphates (taken to be fully deprotonated
13
at physiological pH), which would be consistent with a negative zeta potential
reported by Habelitz group (15). As the zeta potential is not surface specific and only
an averaged, bulk measurement found outside the crystal surface, the precise surface
terminations at atomic level remain unidentified. However, based on this data,
Ca2+-terminated surfaces (with fully-occupied calcium positions) can be eliminated as
possibilities. Fairly flat surfaces can be readily constructed by beginning with the
Ca2+-terminated surface, then stripping away calcium ions to create surface vacancies
as others have done for modeling (16). The orientations of the hydroxide columns of
the
HAP
crystal
lattices
were
randomly
chosen
using
custom
code.
CHARMM-compatible HAP parameters (3) based on the potential energy function
with rigid phosphates developed by Hauptmann et al. (17), and later adapted by
Bhowmik et al. (18), were assigned to set up simulations of the HAP/collagen systems
using NAMD 2.8 (19).
The peptide helix was aligned horizontally on the (100) surface of HAP along the
[0-11], [0-21], and [001] (c-axis) vectors, and on the (110) surface, along the [001],
[1-10], and [1-13] vectors. A dielectric representing water was imposed (ε = 80) under
3-D periodic boundary conditions matching the 2-D dimensions of the slab surface
with 500 Å in the z-direction.
The atoms of the crystal lattice were held fixed.
Multiple manual docking attempts were made by translating the helix down and
parallel to the chosen vector, as well as by rotation of the helix; the structure with the
lowest system energy after a minimization/dynamics/minimization sequence was
selected for follow-up dynamics with pseudo-bonds. Pseudo-bonds were introduced at
the N-termini to cross-link the three chains at that end of the triple helix and at points
along the length of the helix to prevent unraveling at the HAP surface. After
minimization (1000 steps), NVT equilibration (200,000 steps by 1fs/step, 298 K), and
a follow-up minimization (1000 steps), the peptide helix was detached from the
surface using Constant Velocity Steered Molecular Dynamics (cv-SMD) (20) along
the z-direction, with the joined N-termini as the center of the applied steering force (k
= 4 kcalmol-1Å-2) over 8,000,000 steps, at a rate of 0.00001 Å/step.
14
Twenty
independent cv-SMD trials were performed, and the resulting force profiles were
integrated and averaged to yield potentials of mean force (PMFs) and approximate
free energies of binding (ΔGB).
For comparison, relative binding energies were
computed as ΔΔEB = ΔEB(orientation 2) - ΔEB(orientation 1) = ESystem(orientation 2) –
ESystem(orientation 1), where ESystem is the minimized system energy.
15
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16
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17
SI Appendix Tables
(100)
Surface
(110)
dwell time
0s
5s
0s
5s
ku0 (s-1)
0.81±0.50
0.58±0.23
2.38±0.57
0.84±0.31
xt (nm)
0.13±0.02
0.09±0.01
0.02±0.01
0.02±0.01
DG (kBT)
7.52±0.18
7.55±2.39
8.09±0.34
7.96±0.63
Table S1. Fitted parameters for desorption of collagen from HAP (100) and (110)
faces with dwell time of 0s and 5s obtained by fitting harmonic potential (ν=2) by
assuming one bonds in the final rupture event in each force curve.
(100)
Surface
(110)
dwell time
0s
5s
0s
5s
ku0 (s-1)
1.06±0.39
0.80±0.47
3.31±1.23
2.67±1.35
xt (nm)
0.16±0.03
0.17±0.02
0.03±0.01
0.02±0.01
DG (kBT)
6.73±0.10
7.04±1.56
6.93±0.05
7.25±0.59
Table S2. Fitted parameters for desorption of collagen from HAP (100) and (110)
faces with dwell time of 0s and 5s obtained by fitting harmonic potential (ν=2) by
assuming two bonds in the final rupture event in each force curve.
18
Force curve 1
Force curve 2
3.89±0.72
9.27±1.81
0.419±0.199
1.52±0.43
3.45±0.52
0.440±0.226
0.47±0.04
1.15±0.23
0.409±0.145
0.31±0.01
0.80±0.12
0.388±0.083
0.27±0.01
0.72±0.10
0.375±0.077
0.22±0.01
0.59±0.07
0.373±0.069
MWLC
Ratio
F =400pN
MWLC
F =500pN
MWLC
F =1000pN
MWLC
F =2000pN
MWLC
F =3000pN
WLC
Table S3. Persistence length (in unit of nm) of collagen in two typical force curves
fitted by using WLC model and modified WLC (MWLC) model and the
corresponding ratio of persistence length between these two models.
(100)
Surface
(110)
dwell time
0s
5s
0s
5s
ku0 (s-1)
3.83±1.34
3.86±1.08
1.11±0.39
0.72±0.17
xt (nm)
0.17±0.04
0.19±0.03
0.28±0.04
0.22±0.01
DG (kBT)
5.40±0.53
5.57±0.38
6.25±0.48
6.32±0.71
Table S4. Fitted parameters for desorption of collagen from HAP (100) and (110)
faces with dwell time of 0s and 5s obtained by fitting harmonic potential (ν=2). The
molecule number is determined by using WLC model to fit the extension part of force
curve. The modified WLC model should result in the same values due to almost
constant value of ratio between apparent persistence length of different curves.
19
SI Appendix Figures
Fig. S1. Phase, surface index, and morphology of synthesized crystals. (A) XRD
pattern of crystals with different exposed faces; the red curve corresponds to
hexagonal prism and the blue curve corresponds to nanoplate, the thin lines
correspond to the standard spectrum of HAP (JCPDS No. 09-0432, a=b=9.418 Å,
c=6.884 Å). (B) A model structure of an elongated hexagonal rod-shaped HAP single
crystal. The specific crystallographic directions and surfaces are indicated. Scanning
electron microscopy (SEM) image of HAP crystal shows the crystal is mainly covered
by six equivalent (100) surfaces. (C) AFM image of hexagonal HAP surface. In the
inset, the histogram of the step heights gives an average value of 0.815 nm, which
agrees well with the d-spacing of HAP (100) with theoretical value of 0.817 nm. (D)
AFM image of HAP nanoplate surface with average step height of 0.475 nm, which
matches the d-spacing of HAP (110) with theoretical value of 0.472 nm.
20
Fig. S2. Phase and chemical properties of CAP by XRD and Raman spectra. (A).
XRD pattern of CAP. The thin lines correspond to the standard spectrum of HAP
(JCPDS No. 09-0432). (B) Magnified Raman spectra of CAP. The compound peaks at
1072 cm-1 and 1046 cm-1 were decomposed into five peaks centered at 1078 cm-1,
1070 cm-1, 1045 cm-1, 1041cm-1, and 1038 cm-1 with different peak widths by fitting
with Gaussian basis set. The peaks at 1078 cm-1 and 1070 cm-1 are due to symmetric
stretching mode (ν1) of CO32- and the triply degenerate asymmetric stretching mode of
PO43-. The area ratio between peak at 1070 cm-1 and 960 cm-1 was found to be 0.19,
with the regression equation CO3wt%=35.23A1070/A960-1.585 from Fig. 3A in (21),
the carbonate content of CAP is then 5.2 wt%.
Fig. S3. Crystal structure of OCP, the apatitic layer and hydrated layer are
21
alternatively arranged along [100] axis of OCP. The structure of HAP (100) is quite
similar to OCP (100) apatitic layer by only about 2.1% mismatch in b axis and 0.2%
in c axis. The phosphate ions at different sites can be resolved by Raman spectra. The
Raman spectrum of OCP is different from that of HAP by splitting the peak at 960
cm-1 into doublet at 960 and 967 cm-1, as well as the appearance of peaks due to
lattice HPO42- at 880 (HPO42- (P5) located in the hydrated layer, P-(OH) ν1 stretch),
920 (HPO42- (P6) located at the junction of the apatitic and hydrated layers, P-(OH) ν1
stretch), 1011 (HPO42- ν1 stretch) and 1113 cm-1 (HPO42- (P5) ν3 stretch) (22). The
hydrolysis of OCP to CDAP is evident by the decrease in HPO42- peaks relative to
PO43- peaks in the Raman spectra, including decreased HPO42- peak heights at 880,
920, 1011, and 1113 cm-1. The disappearance of ν1 band at 920 cm-1 and ν3 band at
1113 cm-1 suggests that the HPO42- (P6) and HPO42- (P5) change their symmetry and
chemical environment by movement or recombination (22). Moreover, the ν1
stretching band of the HPO42- group at 880 and 1011 cm-1 shifted to 875 and 1001
cm-1. These shifts to lower wavenumbers are expected for vibrational modes which
experience decreased repulsive forces by eliminated hydrogen bonds between HPO42and water.
Fig. S4. TEM image and SAED pattern of CDAP. (A) The nanoplate with angle
126.5º enclosed by adjacent edges. (B) The lattice fringe image of the location labeled
by white square in (A). The two lateral faces are assigned to (1-20) and (1-22) based
on SAED and d-spacing. The calculated angle between these two faces is 126.2º
according to HAP structure from Wilson et al. (23).
22
Fig. S5. The structural relationship between collagen fibrils and HAP nanoplate based
on structural data on collagen from Orgel et al. (24), TEM observations of HAP
orientation from Fig. 5, and the HAP crystal structure (23). Here, the structure of HAP
is used as general representation of the apatites, including CDAP. (A) Ribbon
structure of D-staggered collagen segments within a single unit cell (cell axis matches
c axis of HAP) with overlap and gap zone showing how individual triple helices twist
through the fibril to make a supertwisted right-handed structure and illustrating HAP
platelets penetrated in successive gap channels with different rotation and tilt from
each other. (B) Conformations with largest local angles between collagen axis and
HAP [001] orientation. The largest local angle between collagen axis and HAP [001]
is 14.7º, which is much smaller than ~70º observed in AFM measurements of the
alignment of adsorbed collagen.
Fig. S6. Raman spectra of (A) bone apatite and (B) remineralized rat tail tendon
collagen. The spectrum of rat tail tendon was used as background to subtract the
23
collagen peaks. (A) has HPO42-, and more CO32- (larger I 1073/I1047)and much less OH(invisible peak at 3571 cm-1) than (B).
Fig. S7. Dynamic force spectra for the effect of number of bonds on the single bond
free energy between collagen and (A) (100) (spring constant of 23.20 pN/nm) and (B)
(110) (spring constant 30.03 pN/nm) faces of HAP, respectively, for dwell times of 0
s (blue) and 5 s (red). No model is used to fit the last rupture and number of molecule
in the final rupture is assumed to be two (n=2). Solid curves are fits to a harmonic
potential model indicated by equation S7 with n=2.
Fig. S8. Distribution of apparent persistence length for 181 force curves measured in
24
collagen-HAP (100) interaction based on WLC fit of the final ruptures. The apparent
persistence length of the single collagen triple helix is identified as ~0.52 nm.
Fig. S9. Dynamic force spectra for the rupture of single bond between collagen and
(100) (spring constant of 23.20 pN/nm) and (110) (spring constant 30.03 pN/nm)
faces of HAP, respectively, for dwell times of 0 s (blue) and 5 s (red). Solid curves are
fits to a harmonic potential model indicated by equation S7 with n=2. The forces for
the multi-bond rupture events were normalized to the number of bonds. The peaks at
largest tip-surface separation were fitted by worm-like chain (WLC) model (See
equation S10), which gives a distribution of apparent persistence length. The single
molecule event is identified by the largest apparent persistence length. The number of
collagen triple helices in the final desorption event is calculated by equation S11. The
single bond rupture force and loading rate was calculated by equations S8 and S9.
25

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