sb3-hw12-2016 - JHU 580.429 SB3 HW12 Stochastic dynamics 1...

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JHU 580.429 SB3 HW12: Stochastic dynamics 1. Consider our standard model for the dynamics of a single mRNA species with copy number n , with transitions n n + 1 n n - 1 and corresponding rates β and α n . Use parameter values β = 1 / min and α = 0 . 1 / min. (a) What is average lifetime of a transcript in minutes? For stochastic dynamics at equilib- rium, what are the theoretical values for the mean and variance of n ? (b) Using the variable X to denote a continuous approximation to the particle number n , what is the ODE corresponding to the stochastic dynamics? What is the steady-state value of X , defined as h X i ? (c) Write a Gillespie simulation for this system and provide your source code. A code framework will be available as a starting point. Perform a stochastic simulation for the dynamics of n using your simulation software. Have the program output the value of n at regular intervals of 1 minute. This takes some care because the random transitions will not necessarily occur at these fixed intervals.
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