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Focus Group Meeting: Mathematical and computational models in biological networks Organizers: Marty Feinberg, Eduardo Sontag, and Gheorghe Craciun
Modern biological research attempts to systematically catalogue various types of molecules, cells, tissues, organisms, populations, and ecosystems, and interactions between them [1,2]. A very large amount of experimental data describes the structure of biological interaction networks, but this does not always lead to understanding the role played by these interactions. In particular, there is a great need to understand how these interactions determine the function enormously complex biological networks. In order to understand how biological networks work, various types of mathematical and computational models have been proposed [1-3]. From the mathematical point of view, at the level of elementary interactions taken with classical mass-action kinetics, each new network gives rise to its own system of differential equations, which is almost always nonlinear. In this way, biology presents a huge and bewildering array of nonlinear dynamical systems, each determined in a precise way by the underlying network up to parameter values (e.g., rate constants). One of the most interesting properties of nonlinear dynamics is multistability, i.e., the existence of two or more stable steady states for the same dynamical system. Multistability is of particular relevance to biological systems that switch between discrete states, generate oscillatory responses, or "remember" transitory stimuli. Standard mathematical methods allow the detection of multistability in some very simple feedback systems (for example systems with one or two proteins or genes that either activate each other or inhibit each other), but realistic depictions of complex signaling networks are invariably much more complex [4]. Our particular focus will be on the relationship between reaction network structure and the capacity for multistability, i.e., the capacity for a biological network to switch between two distinct (and perhaps very different) steady states in response to external signals [2,3]. More precisely, we would like to find criteria to determine, for reasonably large biological networks, which networks might admit multistability for at least some parameter values, and which cannot admit multistability no matter what values the parameters take. This is a difficult question, because even moderately complex reaction networks give rise to large, intricate systems of nonlinear differential equations in which a large number of parameters appear; moreover, slightly different biological networks can have very different capacities for multistability. A general answer to this question will be very relevant to understanding very diverse problems in biology, such as the mechanisms of cell cycle checkpoints, intercellular interactions, cellular differentiation and tissue formation, and dynamics of infectious diseases. References [1] Baltazar Aguda, Gheorghe Craciun, and Rengul Cetin-Atalay, Data Sources and Computational Approaches for Generating Models of Gene Regulatory Networks, book chapter, Reviews in Computational Chemistry, Vol. 21, edited by Kenny Lipkowitz, Raima Larter, and Thomas R. Cundari, 2005. [2] David Angeli, James Ferrell, Jr., and Eduardo Sontag, Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems, Proceedings of the National Academy of Sciences, 101:7, 1822-1827, 2004. [3] Gheorghe Craciun, Yangzhong Tang, Martin Feinberg, Understanding Bistability in Complex Enzyme-Driven Reaction Networks, Proceedings of the National Academy of Sciences, 103:23, 8697-8702, 2006. [4] Joseph Pomerening, Eduardo Sontag, and James Ferrell, Jr., Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2, Nature Cell Biology, 5(4):346-351, 2003. If you are interested in participating in this meeting please send your CV and an explanation of your interests to rebecca@mbi.osu.edu. Accepted Participants: David Anderson Initiate Focused Math-Bio Research Groups The MBI is calling for proposals for Focused-Discovery Groups (FDG). The FDG idea is for a group of researchers from different institutions to get together at the MBI for a period of (typically) one week in order to discuss, intensively investigate, and aim to resolve a significant problem in the biosciences. The MBI will pay the local expenses of the participants, and will provide facilities (office space, computer support). Proposals should be sent to the Director or one of the Associate Directors. A proposal should describe the problem to be addressed (one or two pages) and list the people who have agreed to participate. The proposed dates of MBI residence for the FDG should be between six months and one year from the time of submission. |
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