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David Goodsell's artistic rendering of the interior of an eukaryotic cell gives a vivid sense of the extraordinary diversity and density of molecular components. Behind this static picture there also lies ceaseless thermal agitation and diffusion, the more regulated movement of motors, cargos and cellular traffic and the global reorganisations that take place during mitosis or differentiation. |
The molecular networks inside an eukaryotic cell are extraordinarily complex and give rise to the wide range of behaviours exhibited during cellular physiology and organismal development. A central problem in modern biology is to characterize these behaviors and to explain how they are implemented by the mechanisms within the networks.
Recently, mathematical methods have emerged which provide a new approach to this. These methods differ from traditional mathematical modelling in biology by using ideas from pure mathematics, which lead to theorems and algorithms for studying networks without having to resort to numerical integration and simulation. These methods have the potential to rise above molecular complexity.
The material in these slides was drafted in 2009, to provide background for an NSF award, DMS-0856285.