Project Poster

A computational model for light adaptation in
the Zebrafish circadian clock
Francesco Atzeni – [email protected]. Supervisors: Peter Krusche and David Rand.
Student department: Mathematics. Project department: Systems Biology.
Summary
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Zebrafish is an exceptional organism for
clock modelling because all peripheral cells
are photoreceptive. No comprehensive
model for the clock is available.
I analysed an available model and found
discrepancies for skeleton photoperiods.
Experimental Cry traces for LD cycles are
not matched by simulated patterns and
suggest that a light adaptation mechanism
should be included.
Integrated such mechanism as a negative
feedback loop for Cry production.
Analysed revised model showing much
better entrainment capabilities.
Quick guide to terminology:
DD = constant darkness, LL = costant light, LD = alternating light
and dark phases of equal length, skeleton photoperiod = 1
hour long light pulse every cycle. Light is the system forcing.
References
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M.A. Esparza-Franco et al. Modelling circadian rhythms in zebrafish. MSc Project,
2011.
T. K. Tamai, L. C. Young, and D. Whitmore. Light signaling to the zebrafish
circadian clock by cryptochrome 1a. Proceedings of the NAS, 2007.
K. Tsumoto, G. Kurosawa, T. Yoshinaga, and K. Aihara. Modeling light adaptation
in circadian clock: Prediction of the response that stabilizes entrainment. PLoS
ONE, 2011
Original model (by Alex Esparza-Franco et al.)
How it works:
• Light induces Cry production
• Cry represses Per and Bmal oscillations
What can it do:
• Reproduces DD, LL and LD experimental traces
• Can not reproduce experimental traces for
skeleton photoperiods
• Simulated Cry traces do not match experiments
Light adaptation mechanism
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DD, LL and LD simulated patterns
Purely mathematical model to fit range of biological behaviours
Negative feedback loop for Cry mRna production
Cry repression with a fixed delay
Close reproduction of experimental Cry trace
Experimental and simulated Cry traces
Bifurcation analysis explained
• Bifurcation = point of change in qualitative behaviour
• Trace bifurcations varying coupling strength (= light intensity) and
forcing to free running period ratio
• Identify parameter regions, enclosed by bifurcations,
for different behaviours:
- big peak-little peak: enclosed by period doubling bifurcations
Double peak behaviour for light
adaptation model with 12-hour LD cycle
- chaotic oscillations: enclosed by torus bifurcations
Chaotic oscillations for light adaptation
model with a light pulse every 18 hours
- 1 to 1 coupling: outside other regions
Analysis on light adaptation model
• LD Cycle
- coupling for all values
=> much better entrainment
capabilities
=> can fit experimental data
with double peak behaviour
• Skeleton light pulses
- much wider period doubling region
for forcing period close to 12h
- can still reproduce DD, LL
and LD experiments
=> can fit experimental data with
double peak behaviour
1 to 1 coupling for light adaptation
model with 40-hour LD cycle
Analysis on original model
• LD Cycle
- always couples unless light is
too weak
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Skeleton light pulses
- very tiny period doubling region
for period close to 12h (in red box)
- intense light required for entrainment

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