Matlab Assignment

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AIM: to model the positive feedback loop that creates Circadian rhythms – the daily pattern of waking and sleeping.

BACKGROUND: Our daily pattern of sleeping and waking is driven by a positive feedback loop consisting of molecular interactions. The details of this are complex and so for the purposes of this assignment we will look at a simplified model that captures the key elements of the feedback process:

The process is driven by the daily cycle of daylight and darkness.
During darkness hours a TIMER protein is produced by CYCLE proteins.

These TIMER proteins then bind to CYCLE proteins to produce TIMER-CYCLE conjugates.

During daylight hours there is a photo-degradation of TIMER proteins (and hence the number of TIMER-CYCLE conjugates is also reduced).

Create a set of 3 coupled rate equations that describe the time dependent change in the number of TIMER, CYCLE and TIMER-CYCLE molecules. These equations will involve the following rate constants:

kTim – TIMER production coefficient
kTimCyc – TIMER-CYCLE production coefficient

Create a sequence of time steps in your code and an associated sequence of light intensity that mimics the daily on/off pattern of daylight. Extend this time series over a 96 hour period. Plot out the time dependence of your daylight variable.
Loop through each time step and at each time point calculate the number of TIMER, CYCLE and TIMER-CYCLE molecules, using the 3 rate equations you have constructed. [NOTE: the rate equations give the CHANGE in number]. Start your simulation during the dark part of the cycle with the following initial parameters: TIMER number = 50; CYCLE number = 1000; TIMER-CYCLE number = 0.
Plot out the time dependent variation in TIMER, CYCLE and TIMER-CYCLE, on the same plot.
Tune the values of your rate constants to produce a repeatable, daily oscillation in the values of each of the molecular populations and hence mimic the Circadian rhythm. Plot out your results. [NOTE: you will need to think carefully about a logical approach to this, an approach of just guessing the parameter values is unlikely to work].

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