Several experimental reports have shown that in 'isogenic' populations in the 'same' environment, individuals differ in phenotype, probably due to stochastic variation resulting from the low number of molecules of key components of the cellular regulatory network. Theoretically, such variation can be modeled using the chemical master equation. This equation can be 'solved' to give the mean, variance, and higher moments of the distribution of the number of molecules of each of the reacting components. Computationally, several 'exact' methods and approximate methods have been developed in order to compute the moments for reaction networks involving nonlinear reactions (for instance bimolecular reactions such as DNA-protein binding).
At NCL, we use both theoretical and computational approaches to investigate the stochastic behavior of biological signaling networks. A review paper can be accessed in the Attachments section of this page.
Recent results and ongoing projects:
1. Theoretical analysis:
Usually, for the same reaction network, the mean behavior predicted using the chemical master equation to study system dynamics is identical to the prediction of system dynamics using a ordinary differential equation approach that assumes that the dynamics are continuous and deterministic. However this is not the case for certain systems, i.e. the mean predicted by the discrete stochastic kinetics approach differs from the prediction of the continuous deterministic kinetics approach. A paper describing these results is available here. In ongoing work, we seek to identify and understand such reaction networks, in particular whether it is possible to a priori predict such an anomalous behavior, and to study the dependence of the extent of the difference on parameters such as the initial state and the reaction rate parameters. We have also explored how the choice of the metric used to quantify noisiness can influence the conclusions.
2. Computational analysis
Apart from computing the distribution for some systems such as autocatalytic production and virus infection that exhibit the kind of anomalous behavior discussed in the previous paragraph, we work on simulations to address how the distribution is affected by the nature of the regulatory network. In particular, we are studying gene regulatory networks where a single mutation has been experimentally shown to result in the distribution shifting from a unimodal to a bimodal distribution. We are also investigating the effect of stochastically varying environments on survival of individuals in an isogenic population that shows such distributions.
There is an opening for one PhD student and one intern for work in this area.