Team:Dundee/Modeling/Appendix2

Dry Lab

Appendix 2: Fingerprint Aging Code

Principal Component Analysis Code

Principal component analysis MATLAB code.

Squalene Epoxide Model Code

MATLAB code for the binding between squalene epoxide and lanosterol synthase mathematical model.

Principal Component Analysis Code

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Back to Top View Description of PCA

Squalene Epoxide Model MATLAB Code

The figure shown in the squalene epoxide and lanosterol synthase were created using MATLAB. Before using MATLAB the original system of equations was non-dimensionalised to the system:

$$ \begin{eqnarray*} \frac{dLS}{d\tau}&=&PC-\lambda LS \cdot SE,\\ \frac{dSE}{d\tau}&=&PC-\lambda LS \cdot SE,\\ \frac{PC}{d\tau}&=&\lambda LS \cdot SE-PC-\gamma PC,\\ \frac{dLa}{d\tau}&=&\gamma PC. \end{eqnarray*} $$

The initial conditions were also non-dimensionalised to become:

$$ \begin{eqnarray*} LS(0)&=&v_{0},\\ SE(0)&=&1,\\ PC(0)&=&0,\\ La(0)&=&0. \end{eqnarray*} $$

Two files were written to perform sensitivity analysis; one to set the function (squalene.m) and one to solve the function and plot the results in Figure 1 (run_squalene.m). Both files are shown below, where the green is comments to aid in understanding of the scripts.

  
MATLAB code from squalene.m file
% File to solve the system of ODEs describing lanosterol synthase and squalene epoxide binding.
% The vector u has 4 dimensions;
% u(1) = Lanosterol synthase concentration, {non-dimensionalized A eqn}
% u(2) = Squalene epoxide concentration, {" "   "   "}
% u(3) = Protosterol cation (1st Intermediate), {" "   "   "}
% u(4) = Lanosterol. {" "   "   "}
% t is the time that the simulation is run over.
% lambda is the 1st binding parameter ((k1/k2)B0).
% gamma is the 2nd binding parameter (k3/k2).
function f = squalene(t,u,lambda,gamma);
% Then set f as the RHS of the system of ODEs.
f = [u(3)-lambda.*u(1)*u(2);
    u(3)-lambda.*u(1)*u(2);
    lambda.*u(1)*u(2)-u(3)-gamma.*u(3);
    gamma.*u(3)];
% Then end the function.
% This function can then be solved using ode23 in the file run_squalene.m
% by using the @squalene command.
% END OF FILE.
Back to Top View Description of Model

To see the MATLAB code for the BioSpray section of the project or the Chromate Biosensor section of the project use the following buttons.

Appendix 3: Chromate Biosensor Appendix 1: BioSpray