Bio-Physics of Gene Expression : An Overview
Together with Rahul Kulkarni (University of Massachusetts Boston) and Hodjat Pendar (Virginia Tech) I am working on understanding cellular pathways regulating gene expression. Our research is focused on combining analytical approaches from statistical physics and mathematics with numerical simulations to model and understand stochasticity in gene expression and its regulation.
Our Current Research : Partitioning Poisson Processes to Develop a Mapping
If obtaining exact analytical results for protein distributions is a challenging task for all but the simplest models, we recently showed how the partitioning property of Poisson processes can be used to simplify the analysis of stochastic models of gene expression. We developed an mapping that connects protein distributions to mRNA distributions for models with promoter-based regulation. Using this mapping, we derive exact analytical results for steady-state and time-dependent protein distributions for the basic 2-stage model of gene expression. We also obtain exact protein steady-state distributions for models that include the effects of post-transcriptional and post-translational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.
Another Research Project : Regulation by small RNAs via coupled degradation
Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The nonlinearity inherent in this regulatory scheme indicates that exact analytical solutions for the corresponding stochastic models are intractable. Here, we present a variational approach to analyze a well-studied stochastic model for regulation by sRNAs via coupled degradation. The proposed approach is efficient and provides accurate estimates of mean mRNA levels as well as higher-order terms. Results from the variational ansatz are in excellent agreement with data from stochastic simulations for a wide range of parameters, including regions of parameter space where mean-field approaches break down. The proposed approach can be applied for quantitative modeling of stochastic gene expression in complex regulatory networks.