PLoS Computational Biology · 2007 · 18 citations · 16 references
EngineeringBiologyBiophysicsBiological Systems ModelingStochastic ModelingStochastic ProcessesCell Population DynamicsMathematical BiologyStochastic Differential EquationsStochastic NetworksStochastic Processes In BiophysicsCellular Heat Shock ResponseEmpirical LawsHeat Shock ResponseStochastic Biological ModelingStochastic KineticsStochastic Nonlinear DynamicsStochastic Processes In Biology
In many biological systems, the interactions that describe the coupling between different units in a genetic network are nonlinear and stochastic. We study the interplay between stochasticity and nonlinearity using the responses of Chinese hamster ovary (CHO) mammalian cells to different temperature shocks. The experimental data show that the mean value response of a cell population can be described by a mathematical expression (empirical law) which is valid for a large range of heat shock conditions. A nonlinear stochastic theoretical model was developed that explains the empirical law for the mean response. Moreover, the theoretical model predicts a specific biological probability distribution of responses for a cell population. The prediction was experimentally confirmed by measurements at the single-cell level. The computational approach can be used to study other nonlinear stochastic biological phenomena.
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Stochastic Processes in Physics and Chemistry
Van Kampen · 1992 · 3.1K citations
Natural Sciences, Chemistry, Physics +12