• Lab 5 (7.2.2020): 1) Implement a simulation model of the Kai cyanobacterial clock
Use the equations and parameters provided in the lecture script. For nu- merical integration use a quality built-in solver (such as ode45 in Matlab or scipy.integrate.solve_ivp in Python, both of which use a Runge-Kutta(4,5) method as default). Enjoy reading the paper: Ordered phosphorylation gov- erns oscillation of a three-protein circadian clock. Rust MJ, Markson JS, Lane WS, Fisher DS, O’Shea EK. Science. 2007 Nov 2;318(5851):809-12.
a) Plot timecourses of the variables T, S, D, U, and A. Confirm that the period of your clock is approximately 21 hours.
b) [Advanced, will not be assessed in Assignment 2] Having a mathe-
matical model of a biological system enables us to make predictions that can be
ideally tested in experiments, in order to validate the model. Perturbation ex-
periments are one approach to achieve that. Here we want to test how sensitive
the phase of the clock is to a pulse of A (active KaiA) at different timepoints
during the clock cycle. Define the phase of the clock by letting τ = 0 when U is
at its maximum and τ = 2π at the end of one cycle. At different timepoints τ
during the cycle probe the response of the system by instantaneously setting A
to [KaiA], the total KaiA concentration, so that all A is active. The response
we measure is R, the relative change in the period (T = tτ=2π − tτ=0, t being
the absolute time) of the clock, that is R = Tperturbed . Plot R against τ. Can Tunperturbed
you indentify phases in the cycle where the perturbation advances or delays the clock? Discuss possible ways of entraining the clock by a mechanism where external signals such as light could act in a similar way as our perturbation.
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