Department of Mathematics

Spatial and Temporal Information Processing in Biochemical Networks

In this project, I will examine the ability of biochemical networks to process spatial and temporal information e.g. the biochemical networks responsible for cell fate determination. During the developmental stages, the fate of the embryonic cells is often decided as a response to the local concentration of a network of proteins.Although the interaction network of genes and proteins are quite well understood, much less is known about the desired spatial and temporal pattern produced. Since the interactions are directed from early stages toward later ones, a set of multiple, intra-stage, nonlinear interactions could drastically influence the precision and robustness of patterning. Additionally, the low concentration of species contribute to the stochastic nature of such processes. The aim of the project is to understand the network’s features essential for the reliable patterning in the presence of external and internal fluctuations. In principle, numerical simulations are very well suited for integrating in vivo and in vitro experimental results. In this project, I will improve an existing particle based algorithm for reaction-diffusion models. The approach is based on Green’s functions that correctly integrates over the small time and length scale collision events. After implementing the algorithm, I apply it to developmental genetic processes in Drosohphila embryo as the model system in developmental studies.