Numerical Integration in Computational Biology: Euler's Method & Enzyme-Substrate Kinetics, Slides of Computational Biology

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Computational Biology, Part 16

Biochemical Kinetics II

Robert F. Murphy

Numerical integration

 The simplest numerical integration method is Euler’s method. It simply converts each differential to a difference and calculates the value of the dependent variables by multiplying the right hand side of each differential equation by the step size.

Interactive demonstration

 (Model enzyme-substrate kinetics using

Euler’s method - consider timescale Use Named cells)

 (Explore effect of step size)

 (Model enzyme-substrate steady-state using circular references and “holders” for previous values)

Second simplification:

Assumption of quasi-steady state

 The assumption of substrate excess enables an exact solution for the differentials. A less demanding assumption is that S can change but only “slowly” such that C “keeps up” or dC dt

Interactive demonstration

 (Compare full kinetic model with analytical solution for C ( t ) under assumption of substrate excess)

 (Compare with quasi-steady state formulation)

 (Modify model to allow product feedback)