An emerging theme in modern biology is the development of computational and experimental techniques for modeling and monitoring cellular behavior. There have been considerable efforts to build mathematical and computational models for cellular processes, including transcription regulation.

Transcription regulation is a fundamental mechanism of living cells, which allows them to determine their actions and properties by selectively choosing which proteins to express and by dynamically controlling the amounts of those proteins. In this project, we study the problem of modeling transcription regulation in single cells. We have developed a deterministic approach for modeling the macroscopic behavior of transcription regulation in a large population of cells. This was done by adopting a biologically motivated continuous model for gene transcription and mRNA translation, based on .rst-order rate equations, coupled with a set of nonlinear equations that model cis-regulation. We have viewed the processes of transcription and translation as being discrete, which, together with the need to use computational techniques for large-scale analysis and simulation, has motivated us to model transcriptional regulation by means of a nonlinear discrete dynamical system. Classical arguments from chemical kinetics have allowed us to specify the nonlinearities underlying cis-regulation and include both activators and repressors in our formulation.

We are focusing on a stochastic approach to modeling transcription regulation in single cells. Our approach can be used to model transcription regulation in both prokaryotic and eukaryotic cells, and provides a rather simple and computationally ef.cient tool for rapid stochastic characterization of the time evolution of molecular copy numbers in nonlinear transcriptional networks.