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<h3 style="width:70%;margin-left:15%">Introduction</h3> | <h3 style="width:70%;margin-left:15%">Introduction</h3> | ||
− | <p style="width:70%;margin-left:15%">Michaelis - Menten kinetics is a model used to examine enzyme kinetic. The governing equations | + | <p style="width:70%;margin-left:15%">Michaelis - Menten kinetics is a model used to examine enzyme kinetic. Luciferase's activity can be modeled by Michaelis-Menten kinetics as they perform the simple conversion of a substrate into a product and a photon. Our project relied on the light producing NanoLuc Luciferase as a signal in our devices. We were able to model this relationship with MATLAB. 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 generic calculator which teams may use in the future. 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> |
Revision as of 01:58, 11 October 2018
Michaelis-Menten Kinetics
Introduction
Michaelis - Menten kinetics is a model used to examine enzyme kinetic. Luciferase's activity can be modeled by Michaelis-Menten kinetics as they perform the simple conversion of a substrate into a product and a photon. Our project relied on the light producing NanoLuc Luciferase as a signal in our devices. We were able to model this relationship with MATLAB. The governing equations for this model were compiled in the MATLAB, with the goal of creating a generic calculator which teams may use in the future. 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