"New Mathematical Methods for Systems Biology"
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Expectations and ambitions for the future of computational systems biology are ever growing, but several significant problems of applied mathematics and modeling stand in the way. These problems include the relations between stochastic and deterministic models and simulation algorithms, adequate models of molecular complexes, the role of spatial inhomogeneity at subcellular and multicellular scales, modeling biological graph structure and dynamics, inference from heterogeneous data sets, and the reuse and integration of modeling techniques across spatial scales from molecular to developmental and ecological.
Fortunately, there are relevant branches of applied mathematics that have been underexploited in attacking these problems, and itís not too hard to understand their foundations. I suggest that the basic mathematical toolkit for systems biology will come to include not only such staples as differential equation and graphical probabilistic models, but also operator algebras, contextsensitive grammars, stochastic field theory of both particle-like and extended objects , partition functions, aspects of algebraic geometry, and dynamical systems defined on static and dynamic graphs. I will explain why, what, and how, and give examples from many spatial and temporal scales: bacterial metabolism, eukaryotic transcriptional regulation and signal transduction, developmental biology of plants including phyllotaxis, and population biology.
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