Stochastic Models of Biochemical Reaction Systems
Technical Report,01 Aug 2014,31 Jul 2017
University of Wisconsin - Madison Madison United States
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The interactions between the molecular constituents of a cell are often depicted graphically as a reaction network. Reaction 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 a variety of ways. Further, cellular systems often have different sub-systems that operate on multiple temporal and other scales, 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 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. The objective of this project is to discover what the important structures hidden in the complexity of biochemical networks are, and how to infer system behavior, on short, medium, and long time frames, from them. While we formally consider models from biochemistry, the mathematical models studied are quite universal. For example, many models at the level of populations such as models of disease spread satisfy equations with the same mathematical structure. One of the goals of systems and evolutionary biology is to combine models from the cellular level with those at the population level. Such twenty-first century models are already being developed, for example to understand the spread of malaria. These systems will be directly impacted by the project. Specific objectives of the project. The project had 9 stated objectives. These objectives focus on either stochastically or deterministically modeled biological interaction networks.
- Statistics and Probability