The objective of this project is to develop a theory of perturbation analysis for stochastic biochemical reaction systems and to use this theory to uncover the stochastic properties of a variety of biological network motifs. Cellular processes are controlled by networks of interacting proteins, genes and small molecules. Traditionally such systems have been described using a continuum/deterministic model, often based on differential equations. In these models it is assumed that the concentrations of the various molecular species can be described using continuous variables. In a number of cases this is quite reasonable because the number of molecules of any particular species can be large. However there are some cellular subsystems, such as gene networks, where the number of molecules might be as low as a few. In such systems a continuous model is inappropriate. Moreover, because the molecular numbers are so small, the stochastic nature of chemical processes becomes a dominant feature. In this project the deterministic theory will be reformulated in order to develop a general analytical theory of noise propagation in biochemical networks. The project will use the theory to understand the stochastic properties of different network motifs and to make predictions which can be tested experimentally.
Biological cells contain millions of molecules randomly colliding and reacting. The net effect of all this activity is noise, called stochastic noise. Electrical engineers have to deal with unwanted noise in electronic circuits all the time and they go to great efforts to eliminate it. Experimentally, noise in cells can be measured but what is lacking is an understanding of how this noise behaves in such complicated systems. If noise could be better understood, engineers would be in a better position to control it. This project will develop a mathematical theory that will allow scientists and engineers to understand and predict how noise spreads inside a cell. This project impinges on many areas of science, including molecular biology, computer science, control theory, signal processing and electrical circuit theory. Undergraduate and graduate students will participate in this project and they will be trained in multidisciplinary science.
