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Revision as of 22:21, 8 September 2018

Michaelis-Menten Kinetics

Introduction

Michaelis - Menten kinetics is a model used to examine enzyme kinetic. The governing equations for this model were compiled in the MATLAB, with the goal of creating a calculator. Known values for concentrations and reactions rates are used as inputs, and the file produces the various rates of change with respect to the concentrations.

Governing Equations

The MATLAB code takes in the substrate concentration, product concentration, and enzyme concentration, represented as [S], [P] and [E] respectively. Additionally, known reaction rates for the forward, reverse, and catalytic directions are represented as kf, kr, and kcat respectively. The preceding values are put into a function which generates the rates of change of concentration with respect to time through the following first order ordinary differential equations:

d[E]/dt = -kf[E][S] + kr<[ES] + kcat[ES]
d[S]/dt = -kf[E][S] + kr<[ES]
d[P]/dt = kcat[ES]

The following substitution is used, where [E0] is the final substrate concentration

[E0]-[E]=[ES]

This yields the formulas used in the function, which are as follows

d[E]/dt = -kf[E][S] + kr<[E0-E] + kcat[E0-E]
d[S]/dt = -kf[E][S] + kr<[E0-E]
d[P]/dt = kcat[E0-E]

Use

To use the calculator, simply open the MATLAB file and enter the reaction rates and concentration in the noted areas. After running the file, the reaction rates will appear in the MATLAB command window.

References

Beard, D [Daniel Beard]. (2014, 8 27). Enzyme Kinetics with MATLAB 2 [Video file]. Retrieved from https://www.youtube.com/watch?v=g-MApXluAaE&pbjreload=10

Matlab Code