Emergent Properties of Biological Interaction Systems

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Biologists have been successful in revealing many of the molecular components involved in cell biology. Attention is now moving from identification of components to understanding the emergent, or system, behavior of the connected components. It has been hoped that general principles would emerge via the study of mathematical models of specific systems, but to date this form of study has not generally proven effective at discovering the hidden principles of biology. How the complex networks found in biological systems produce their emergent properties and behaviors remains elusive. Theoretical mathematics offers a possible route forward, and one which could, in time, have a profound influence on biology. This research project aims to cut through the complexity of biological models to elucidate the general principles of cell biology. Additionally, the project aims to develop new computational methods that can address currently infeasible problems. There is high demand for well-trained mathematical scientists with the interest and expertise necessary to contribute to the solution of questions arising in biology; this project will provide fertile training ground for graduate students.Discrete-space, continuous-time Markov chain models are commonly used to model biological interaction networks, including gene regulatory networks, viral infections, signaling systems, neuronal networks, etc. These models can be depicted via a reaction graph, which is a graphical representation of the interactions between the constituent molecules of the model. Interaction networks can be extraordinarily complex; for example, there are over 20,000 genes in the human genome and the proteins they encode may be modified in myriad ways. Further, cellular systems often have different sub-systems that operate on multiple different scales (both temporally and in terms of copy numbers), with the species operating at one scale greatly influencing those at a different scale. The reaction networks currently studied in the literature are typically so complex that numerical simulation is often considered the only way to analyze them. However, hidden within the complexity there are often underlying structures that, if properly quantified, give great insight into the dynamical or stationary behavior of the system. This project aims to develop mathematical theory that relates the emergent properties of these systems to easily-checked properties of the associated reaction graphs. A second aspect of the project is development and analysis of computational methods for stochastic models of biochemical interaction networks. The primary tools and methods utilized will be from probability theory, stochastic analysis, dynamical systems theory, chemical reaction network theory, and computational mathematics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.