Stochasticity in Biochemical Reaction Networks

(in alphabetic order by speaker surname) Speaker: Michael Chevalier (University of California, San Francisco) Title: An exact CME/SSA formulation for separating timescales in stochastic biological networks Abstract: Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-cell variability even in clonal populations. Stochastic biochemical networks are typically modeled as continuoustime, discrete-state Markov processes whose probability density functions evolve according to a chemical master equation (CME). The CME is not solvable but for the simplest cases, and one has to resort to kinetic Monte Carlo techniques to simulate the stochastic trajectories of the biochemical network under study. A commonly used such algorithm is the stochastic simulation algorithm (SSA). Because it tracks every biochemical reaction that occurs in a given system, the SSA presents computational difficulties especially when there is a vast disparity in the timescales of the reactions or in the number of molecules involved in these reactions. This is common in cellular networks, and many approximation algorithms have evolved to alleviate the computational burdens of the SSA. Here, we present a rigorously derived modified CME framework based on the partition of a biochemically reacting system into restricted and unrestricted reactions. Although this modified CME decomposition is as analytically difficult as the original CME, it can be naturally used to generate a hierarchy of approximations at different levels of accuracy. Most importantly, some previously derived algorithms are demonstrated to be limiting cases of our formulation. Time permitting, we will also discuss some spatial effects in stochastic biological networks. Speaker: Mary Dunlop (Lawrence Berkeley National Laboratory) Title: Regulation Revealed by Correlations in Gene Expression Noise Abstract: Gene regulatory interactions are context-dependent, active in some cellular conditions but not in others. I will discuss a method for determining when a regulatory link is active given temporal measurements of gene expression. Correlations in time series data are used to determine how genes influence each other and their causal relationships. Natural stochastic noise is shown to aid in the process of network identification by perturbing the expression of genes; the speed and direction at which the noisy signal propagates shows how the network is connected. I will present results from a three-color synthetic gene circuit imaged with time-lapse single-cell microscopy. By using a synthetic gene circuit with well-characterized connections we were able to validate our approach by reproducing known system characteristics. In addition, I will discuss results where a synthetic reporter construct was used to measure gene-expression in a natural regulatory network responsible for galactose metabolism.