Progress in genomic research has led to the realization that effective models for predicting cellular behavior must take into account the network interactions that dynamically mediate gene regulation. Since behavior arising from these complex interactions is difficult to predict without quantitative models, there is a need for experimentally validated computational modeling approaches that can be used to understand the complexities of gene regulation. Working in close collaboration with Jeff Hasty's Systems Biodynamics lab at the Bioengineering Department, UCSD, we develop nonlinear stochastic models for the dynamics of genetic regulatory modules and their interactions in living cells.

Some of the specific projects we are currently working on include

• Study of intrinsic and extrinsic noise in the dynamics of genetic modules.
There is strong experimental evidence that the level of expression from the same gene varies significantly from one cell to another within a genetically-identical colony [Elowitz, 2002, Hasty and Collins, 2002] . Such variations are observed in the cells of organisms ranging in complexity from bacteria to mammals. Theoretically, with mRNA numbers that are often less than ten, the stochastic nature of the underlying biochemical reactions must lead to large fluctuations. Stochasticity in gene expression is generally believed to be detrimental to cell function because fluctuations in protein levels can corrupt the quality of intracellular signals. One the other hand, randomness, can provide a mechanism for phenotypic and cell-type diversification. In order to address the issues of randomness in genetic regulation networks, sophisticated analytical and numerical tools are being developed.

Recent studies have demonstrated that a significant component of expression variability arises from extrinsic factors thought to influence multiple genes in concert [M.Elowitz, 2002, 2005, Raser & O'Shea, 2005], yet the biological origins of this extrinsic variability have received little attention. We combine computational modeling with fluorescence data generated from multiple promoter-gene inserts in Saccharomyces cerevisiae to identify two major sources of extrinsic variability [Volfson et al, 2006]. One unavoidable source arising from the coupling of gene expression with population dynamics leads to a ubiquitous noise floor in expression variability. A second source originating from a common upstream transcription factor exemplifies how regulatory networks can convert intrinsic or extrinsic noise in regulator expression into extrinsic noise at the output of a target gene. Our results highlight the importance of the interplay of gene regulatory networks with population heterogeneity for understanding the origins of cellular diversity.

We developed modifications to the classical Gillespie algorithm which allow it to be emplyed for growing and dividing cells [Lu et al, 2004], as well as for non-Markovian delayed reactions [Bratsun et al, 2005].

• Role of transcriptional delays in the dynamics of genetic regulatory networks
We study the stochastic properties of gene regulation taking into account the non-Markovian character of gene transcription and translation [Bratsun et al, 2005]. We show that time delay in protein production or degradation may change the behavior of the system from stationary to oscillatory even when a deterministic counterpart of the stochastic system exhibits no oscillations. Assuming signicant decorrelation on the time scale of gene transcription, we deduce a truncated master equation of the reactive system and derive an analytical expression for the autocorrelation function of the protein concentration. For weak feedback the theory agrees well with numerical simulations based on the modified direct Gillespie method.
• The coupling of genetic modules.
Our research in this area builds upon previous investigations of elementarty synthetic genetic circuits. This work includes the development of positive feedback [Hasty et al., 2000,Isaacs et al., 2003] and co-repressive switching networks [Gardner et al., 2000], as well as an oscillating circuit [Elowitz and Leibler, 2000]. These previous studies have explored several of the building-block modules that constitute large-scale genomic wiring, and thus represent a first step towards an understanding of whole-genome regulatory complexity. We intend to build upon these previous studies by designing and constructing higher order networks consisting of coupled genetic regulatory modules.
• Study of circadian oscillations and related spatiotemporal pattern formation in Neurospora Crassa Neurospora Crassa, alnog with Drosofila, is one of the salient organisms which biologists use to study the nature of circadian oscillations [Dunlap, 1999, Lakin-Thomas, 2000]. Circadian rhythm in Neurospora can be seen in a petri dish by the periodic spore formation in the form of bands on the agar surface (see photo below).

  

  (photo courtesy S. Brody)

  In this work we introduce and investigate a stochastic model of spatio-temporal pattern formation in Neurospora driven by a circadian oscillator. The local dynamics of the model is based on the delayed coupling between two frequency gene fcc and white-collar wcc heterodimeric complex. This model reproduces he obser4ved nearl-24h period of local oscillations and formation of bands in the growing cell. This model can be applied to understand the mechanisms of pattern formation in the wild-type Neurospora crassa as well as in various Neurospora mutants.

  (joint work with Stuart Brody's group at the Biology department, UCSD)