Transcription of Mathematical Modelling in Systems Biology: An Introduction
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Mathematical Modelling in Systems Biology: An IntroductionBrian IngallsApplied MathematicsUniversity of 18, 20122 PrefaceSystems techniques are integral to current research in molecular cell biology. These Systems ap-proaches stand in contrast to the historically reductionist paradigm of molecular biology. The shifttoward a Systems perspective was gradual; it passed a turning point at the end of the 20thcen-tury, when newly developed experimental techniques provided system-level observations of cellularnetworks. These observations revealed the full complexityof these networks, and made it clearthat traditional (largely qualitative) molecular biologytechniques are ill-equipped for the investi-gation of these Systems , which often exhibit non-intuitivebehaviour. This point was illustrated in athought experiment proposed by Yuri Lazebnik (Lazebnik, 2002). He described a (failed) attemptto reverse-engineer a transistor radio using qualitative methods analogous to those used in tradi-tional molecular biology.
Chapter 8 covers modelling of electrophysiology and neuronal action potentials. An optional section contains a brief introduction to spatial modelling using partial differential equations. The book closes with three Appendices. The first reviews basic concepts from molecular cell biology. The second reviews mathematical concepts.
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