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− | <h2 style="width: | + | <h2 style="width:70%;margin-left:15%" >Michaelis-Menten Kinetics</h2> |
− | <h3 style="width: | + | <h3 style="width:70%;margin-left:15%">Introduction</h3> |
− | <p style="width: | + | <p style="width:70%;margin-left:15%">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 | 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 | values for concentrations and reactions rates are used as inputs, and the file produces the various | ||
rates of change with respect to the concentrations.</p> | rates of change with respect to the concentrations.</p> | ||
− | <h3 style="width: | + | <h3 style="width:70%;margin-left:15%">Governing Equations</h3> |
− | <p style="width: | + | <p style="width:70%;margin-left:15%">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 | represented as [S], [P] and [E] respectively. Additionally, known reaction rates for the | ||
forward, reverse, and catalytic directions are represented as <em>k<sub>f</sub>, k<sub>r</sub>,</em> and | forward, reverse, and catalytic directions are represented as <em>k<sub>f</sub>, k<sub>r</sub>,</em> and | ||
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change of concentration with respect to time through the following first order ordinary differential equations:</p> | change of concentration with respect to time through the following first order ordinary differential equations:</p> | ||
− | <div style="width: | + | <div style="width:70%;margin-left:15%"> |
<em>d[E]/dt = -k<sub>f</sub>[E][S] + k<sub>r<</sub>[ES] + k<sub>cat</sub>[ES]</em><br> | <em>d[E]/dt = -k<sub>f</sub>[E][S] + k<sub>r<</sub>[ES] + k<sub>cat</sub>[ES]</em><br> | ||
<em>d[S]/dt = -k<sub>f</sub>[E][S] + k<sub>r<</sub>[ES]</em><br> | <em>d[S]/dt = -k<sub>f</sub>[E][S] + k<sub>r<</sub>[ES]</em><br> | ||
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</div> | </div> | ||
− | <h3 style="width: | + | <h3 style="width:70%;margin-left:15%">Use</h3> |
− | <p style="width: | + | <p style="width:70%;margin-left:15%">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 | in the noted areas. After running the file, the reaction rates will appear in the MATLAB command | ||
window.</p> | window.</p> | ||
− | <h3 style="width: | + | <h3 style="width:70%;margin-left:15%">References</h3> |
− | <p style="width: | + | <p style="width:70%;margin-left:15%">Beard, D [Daniel Beard]. (2014, 8 27). Enzyme Kinetics with MATLAB 2 [Video file]. Retrieved |
from <a href="https://www.youtube.com/watch?v=g-MApXluAaE&pbjreload=10" target="_blank">https://www.youtube.com/watch?v=g-MApXluAaE&pbjreload=10</a></p> | from <a href="https://www.youtube.com/watch?v=g-MApXluAaE&pbjreload=10" target="_blank">https://www.youtube.com/watch?v=g-MApXluAaE&pbjreload=10</a></p> | ||
− | <h3 style="width: | + | <h3 style="width:70%;margin-left:15%">Matlab Code</h3> |
− | <pre class="prettyprint" style="width: | + | <pre class="prettyprint" style="width:70%;margin-left:15%"> |
%********READ ME******** | %********READ ME******** | ||
Revision as of 22:50, 18 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[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
%********READ ME******** %The following is a simple Michaelis–Menten rate of change calculator %The commented out portion of the code is just the governing equations %Fill in the parameters of dXdT in terms of s,p, and e %Fill in the reaction rates (all set to 1 by default) %The output will be the various rates %Governing Equations %E + S <> ES > E + P %s=[S]; %p=[P]; %e=[E]; %c=[ES]; %ds/dt = -kForward*e*s + kReverse*c %dp/dt = kCat*c %de/dt = -kForward*e*s + kReverse*c + kCat*c %dc/dt = kForward*e*s - kReverse*c - kCat*c %de/dt + dc/dt = 0 %d(e+c)/dt = 0 %E0 = e + c %ds/dt = -kForward*e*s + kReverse*(E0-e) %dp/dt = kCat*(E0-e) %de/dt = -kForward*e*s + kReverse*(E0-e) + kCat*(E0-e) s = 1; %Enter substrate concentration p = 1; %Enter product concentration e = 1; %Enter enzyme concentration dXdT([s p e]) function [f] = dXdT(x) kForward = 1; %Enter forward reaction rate kReverse = 1; %Enter reverse reaction rate kCat = 1; %Enter catalytic reaction rate E0 = 1; %Enter initial concentration s=x(1); p=x(2); e=x(3); dsdt = -kForward*e*s + kReverse*(E0-e); dpdt = kCat*(E0-e); dedt = -kForward*e*s + kReverse*(E0-e) + kCat*(E0-e); f = [dsdt; dpdt; dedt]; end %***Acknowledgments*** %Daniel Beard - Enzyme Kinetics with MATLAB 2