MCB111: Mathematics in Biology (Fall 2019)
week 10:
Molecular Population Dynamics as a Markov Process
Stochastic simulation of transcriptional bursting
We are going to simulate the gene regulation Markov process that we described in class. The process includes 6 reactions.
r  reaction  propensity  

1  
2  
3  
4  
5  
6 

Implement the Gillespie algorithm to generate 5 time trajectories for (a) gene activity, (b) RNA population, and (c) protein populations.

Plot the trajectories of those stochastic processes, and compare to their steadystate solutions.

Design one set of rate values that would produce transcriptional bursting, and another set of values that would not. Reason your findings.
I have also added hints about how to sample from a exponential distributions easily, and about implementing the Gillespie algorithm.