Mathematics of Synthetic Gene Networks

Arizona State University, Scottsdale AZ

Investigators

Abstract

This project uses the combination of mathematical, engineering, and biological techniques to construct, monitor, and analyze novel engineered gene networks. The objective of the research is to expand the mathematical framework used in the modeling and analysis of synthetic gene networks. First, the investigators systematically study stochasticity at separatrices of bistable synthetic gene networks. Recently developed yeast bistable gene networks are used for the first time to initialize gene networks on their separatrices. In particular, the difference between Gillespie algorithm and Chemical Langevin equation (CLE) based algorithms in simulating stochastic processes near bifurcation points is investigated, both analytically and experimentally. With the experience in studying bistable systems, the next step is to mathematically and experimentally analyze nonlinear stochastic dynamics in three potential well systems. Nonlinear stochastic dynamics in multi potential well systems have not been well studied. This network is constructed using available, well-characterized components and techniques and by combining microfluidics devices, single cell live imaging and stochastic modeling to observe and study noise induced random state switching. Finally, methods of high dimensional analysis of gene networks are developed. Tools for dynamical analysis of high dimensional gene networks have been lacking. This project develops mathematical methods to expand the analysis of gene networks from two dimensions into higher dimensionalities. High throughput network identification methods that utilize parallel computing are developed. Bifurcation analysis of high dimensional dynamical systems with applications in gene networks is tested. Novel systematic understanding of cell differentiation and reprogramming derives from the study of synthetic multistable gene networks. Synthetic multistable systems provide unique opportunities to study the core mechanisms of cell pluripotency and differentiation because highly connected small transcription networks regulating cell differentiation have topological similarities with the synthetic gene networks under consideration in this project. Constructing and analyzing small multistable gene network deepens our understanding of multistability, which can arise from similar topologies in stem cell gene regulations. Additionally, mathematical theories and tools to study high dimensional nonlinear dynamics and stochasticity in the context of gene networks are developed. Currently, theoretical efforts to study cellular multistable systems are lacking. This research fills the gap between technological progress and available analytical tools to facilitate future biotechnological development. In addition, both undergraduate and graduate students carry out synthetic biology experiments and analysis. By participating in the international Genetically Engineered Machine (iGEM) competition, these students promote developments of modern biological technologies at Arizona State University. K-12 students and teachers in the Phoenix metropolitan area will also have opportunities to participate in cutting-edge research activities with scientific and infrastructure support from the principal investigators and the university.