Difference between revisions of "Team:Dundee/Modeling/Appendix3"
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Cu vis partem graeci facilisis. Falli inciderint mei no. Assentior suscipiantur mea id. Vis quas electram prodesset cu, choro omnium conclusionemque an his. Vis latine equidem perfecto ad.</p> | Cu vis partem graeci facilisis. Falli inciderint mei no. Assentior suscipiantur mea id. Vis quas electram prodesset cu, choro omnium conclusionemque an his. Vis latine equidem perfecto ad.</p> | ||
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Revision as of 13:46, 9 September 2015
Dry Lab
Appendix 3: Chromate Biosensor Code
Chromate Model Code
The figures shown in the chromate detector model were created using MATLAB. Two files were written to perform sensitivity analysis; one to set the function (chromate.m) and one to solve the function and plot the results in Figure 3, Figure 4 , Figure 5 and Figure 6 (run_chromate.m). Both files are shown below, where the green is comments to aid in understanding of the scripts.
MATLAB code from chromate.m file % Function to define the system of ODEs describing the modified chromate pathway. %% Section 1: Function to define the system of ODEs describing the modified chromate pathway. % The vector u has seven dimensions where; % u(1) = ChrB protein concentration, % u(2) = ChrB dimer concentration, % u(3) = Cv, the hexavalent chromate added to the system concentration, % u(4) = Dimer and Cv complex concentration, % u(5) = Pc, the closed (bound and non-functioning) promoter concentration, % u(6) = Po. the open (unbound and functioning) promoter concentration, % u(7) = GFP output concentration. % Parameter t is time that the simulation runs over. % Parameters k1..k8 represent the kinetic rates of the system. % L represents leakiness of the system. function f=chromate(t,u,L); k1 = 1; k2 = 1; k3 = 1; km3 = 1; k4 = 1; km4 = 1; k5 = 1; k6 = 1; km6=1; k7 = 1; % k8 divided by 60 as in minutes not hours. k8=(0.25/60); % Set S1 and S2 at specific times which represent whether chromate is present or not % S is the signal input. S1=0; S2=1; if (t<500)% Where time is less than 500 seconds. S=S1; else if (t>500) && (t<3100)% Where time is more than 500 seconds and less than 3100 seconds. S=S2; else if (t>3100)% Where time is more than 3100 seconds. S=S1; end end end % If and else if loop sets the times when chromate is present or absent from the system. % Define f as a vector where the input is the right hand side of the systems of ODEs representing the pathway with signal input incorporated. f=[k1 - k2*u(1)+km3*u(2)-k3*u(1)*u(1); k3*u(1)*u(1)-km3*u(2)+(km4*u(4))-(k4*u(2)*u(3)*S)-k5*u(2)+(km6*u(5)*S)-k6*u(2)*u(6); -k4*u(2)*u(3)*S+km4*u(4); k4*u(2)*u(3)*S-km4*u(4); k6*u(6)*u(2)-km6*u(5)*S; -k6*u(6)*u(2)+km6*u(5)*S; L+k7*u(6)*S-k8*u(7)]; % End function. end % This function can then be called using the @chromate command in run_chromate.m file. % END OF FILE MATLAB code from chrom_wt.m file %% Function to define the system of ODEs describing the original chromate pathway. % The vector u has seven dimensions where; % u(1) = ChrB protein concentration, % u(2) = ChrB dimer concentration, % u(3) = Cv, the hexavalent chromate added to the system concentration, % u(4) = Dimer and Cv complex concentration, % u(5) = Pc, the closed (bound and non-functioning) promoter concentration, % u(6) = Po. the open (unbound and functioning) promoter concentration, % u(7) = GFP output concentration. % Parameter t is time that the simulation runs over. % Parameters k1..k8 represent the kinetic rates of the system. % L represents leakiness of the system. function f=chrom_wt(t,u,L); k2 = 1; k3 = 1; km3 = 1; k4 = 1; km4 = 1; k5 = 1; k6 = 1; km6=1; k7 = 1; % k8 divided by 60 as in minutes not hours. k8=(0.25/60); % Set S1 and S2 at specific times which represent whether chromate is present or not. % S is the signal input. S1=0; S2=1; if (t1<500)% Where time is less than 500 seconds. S=S1; else if (t1>500) && (t1<3100)% Where time is more than 500 seconds and less than 3100 seconds. S=S2; else if (t1>3100)% Where time is more than 3100 seconds. S=S1; end end end % If and else if loop sets the times when chromate is present or absent from the system. % Define f as a vector where the input is the right hand side of the systems of ODEs representing the pathway with signal input incorporated. f=[L+k7*u(6)-k2*u(1)+km3*u(2)-k3*u(1)*u(1); k3*u(1)*u(1)-km3*u(2)+(km4*u(4))-(k4*u(2)*u(3)*S)-k5*u(2)+(km6*u(5)*S)-k6*u(2)*u(6); -k4*u(2)*u(3)*S+km4*u(4); k4*u(2)*u(3)*S-km4*u(4); k6*u(6)*u(2)-km6*u(5)*S; -k6*u(6)*u(2)+km6*u(5)*S; L+k7*u(6)*S-k8*u(7)]; % End function. end % This function can then be called using the @chrom_wt command in run_chromate.m file % % % END OF FILE MATLAB code from run_chromate.m file %% File to solve chromate functions. %% Section 1: Solving the modified system to investigate GFP production with chromate added and removed at specific times. % a = Initial ChrB protein concentration. a = 1; % b = Initial ChrB dimer concentration. b = 1; % c = Initial Cv, chromate, concentration. c =1; % d = Initial Cv and dimer complex concentration. d = 0; % e = Initial Pc, closed promoter, concentration. e = 0; % f = Initial Po, open promoter, concentration. f = 1; % g = Initial GFP concentration. g = 0.01; % T = Final time of simulation, in seconds. T=3600; % Solve the function using ode23 solver with set time range and defined initial conditions. % Save time values in vector t and u(1)..u(7) values in matrix u with no leakiness, L=0. [t,u]=ode23(@chromate,[0,T],[a,b,c,d,e,f,g],[],0); % Call up empty figure 1 to prevent overwriting figures. figure1=figure(1) % Plot t vector against the 7th column of the u matrix, that is the GFP concentration, and set linewidth to 3 so that it is easily read. plot(t,u(:,7), 'LineWidth',3); % Ensure that axis fits the data by using axis tight command. axis tight % Remove the values on the x and y axis as they are not relevant. set(gca,'YTick',[],'XTick',[]); % Annotate the figure by adding arrows along the x and y axis to represent increasing time and Fluorescence. annotation(figure1,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure1,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Annotate the figure by adding text arrow to highlight where the chromate is added and removed. annotation(figure1,'textarrow',[0.3875 0.25],... [0.346619047619048 0.119047619047619],'Color',[1 0 0],... 'String',{'Chromate Added'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); annotation(figure1,'textarrow',[0.682142857142857 0.789285714285714],... [0.779952380952381 0.919047619047619],'Color',[1 0 0],... 'String',{'Chromate Removed'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); % Set the labels of the x and y axis to Time and Fluorescence, respectively. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % Add a legend for GFP Response. legend1=legend('GFP Response'); % Make the box around legend bold and make font bigger, also position legend so that it is easily read. set(legend1,... 'Position',[0.468154768530456 0.149603206588803 0.360714277944395 0.0626984112082966],... 'LineWidth',2,... 'FontWeight','bold',... 'FontSize',12); % END OF SECTION % % %% Section 2: Sensitivity analysis on effect of chromate added to GFP production in modified pathway. % n = Number of different values of chromate evaluated. n=10; % T = Final time of simulation, in seconds. T=3600; % c1 = The range of values used for initial chromate concentration, with minimum at 0 and maximum at 400. c1=linspace(0,400,n); % Call up figure 2 to ensure no figures are overwritten. figure2=figure(2) % Set hold on so that multiple lines will be plotted on same figure. hold on % Set a for loop so that the n values for chromate are evaluated individually and the system solved for each of them. for i=1:n % Solve the chromate function using ode23 solver over set time range and same initial conditions for all variables except chromate. % The initial concentration of chromate will depend on the value of i within the for loop. % The values will be stored in the t vector and u matrix with no leakiness, L=0. [t,u]=ode23(@chromate,[0,T],[a,b,c1(i),d,e,f,g],[],0); % Plot the GFP concentration over time. plot(t,u(:,7), 'LineWidth',2); % End the for loop. end % Then switch hold off so that no more lines are plotted on figure. hold off % Set axis to tight so that plot fits the data. axis tight % Add a rectangle onto the graph to highlight the section that will be zoomed in on in figure 3. annotation('rectangle',[0.236714285714286 0.561904761904762 0.213285714285714 0.354761904761906], 'LineStyle','--'); % Remove the values of the x and y axis as they are not necessary. set(gca,'YTick',[],'XTick',[]); % Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration. annotation(figure2,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure2,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Annotate the figure by adding text arrow to highlight where the chromate is added and removed. annotation(figure2,'textarrow',[0.3875 0.25],... [0.346619047619048 0.119047619047619],'Color',[1 0 0],... 'String',{'Chromate Added'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); annotation(figure2,'textarrow',[0.682142857142857 0.789285714285714],... [0.779952380952381 0.919047619047619],'Color',[1 0 0],... 'String',{'Chromate Removed'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); % Set the labels of the x and y axis to Time and Concentration, respectively. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % % We will now replot figure 2 but zoom in on a specific section for clarity. % % % Call up empty figure 3 to prevent overwriting figures. figure3=figure(3) % Set hold on so that multiple lines will be plotted on same figure. hold on % Set a for loop so that the n values for chromate are evaluated individually and the system solved for each of them. for i=1:n % Solve the chromate function using ode23 solver over set time range and same initial conditions for all variables except chromate. % The initial concentration of chromate will depend on the value of i within the for loop. % The values will be stored in the t vector and u matrix with no leakiness, L=0. [t,u]=ode23(@chromate,[0,T],[a,b,c1(i),d,e,f,g],[],0); % Plot the GFP concentration over time. plot(t,u(:,7), 'LineWidth',2); % End the for loop. end % set hold off, so that no more lines are plotted. hold off % Ensure that axis fits the data by using axis tight command. axis tight % Remove the values on the x and y axis as they are not relevant and set the x and y limits so that we get a zoomed in section of the plot. set(gca,'YTick',[],'XTick',[], 'XLim',[909.850230414748 1359.85023041475],'YLim',[163.478891218168 187.138947135872]); % Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration. annotation(figure3,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure3,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Add a 3rd arrow to the plot to show increasing initial concentration of Cv in the legend. annotation(figure3,'arrow',[0.817857142857141 0.817857142857143],... [0.597619047619051 0.238095238095238],'LineWidth',4); % Set legend as just lines with no text, as text will be added later using paint (see wiki figures). legend2=legend('','','','','','','','','',''); % Set the position of the legend and the width of the box line. set(legend2,... 'Position',[0.631547602609266 0.207142857142858 0.255952397390734 0.413492042689934],... 'LineWidth',2); % Set the labels of the x and y axis to Time and Concentration, respectively. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % END OF SECTION % % %% Section 3: Solving the original system to investigate GFP production with chromate added and removed at specific times. % The same initial conditions are used as modified systems so they do not need to be redefined. % Solve the chrom_wt function using ode23 solver with set time range and defined initial conditions. % Save time values in vector t and u(1)..u1(7) values in matrix u with no leakiness, L=0. [t,u]=ode23(@chrom_wt,[0,T],[a,b,c,d,e,f,g],[],0); % Call up a new figure to ensure figures are not overwritten. figure4=figure(4) % Plot t vector against the 7th column of the u matrix, that is the GFP concentration, and set linewidth to 3 so that it is easily read. plot(t,u(:,7), 'LineWidth',3); % Ensure that axis fits the data by using axis tight command. axis tight % Remove the values on the x and y axis as they are not relevant. set(gca,'YTick',[],'XTick',[]); % Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration. annotation(figure4,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure4,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Add line to show modified level in comparrison. annotation(figure4,'line',[0 1],... [0.9310344828 0.9310344828],'Color',[1 0 1],'LineWidth',2,... 'LineStyle','--'); % Add text box. annotation(figure4,'textbox',... [0.147428571428571 0.714285714285715 0.116857142857143 0.145238095238096],... 'Color',[1 0 1],... 'String',{'Modified','Pathway','Max','GFP'},... 'LineStyle','none',... 'FontWeight','bold',... 'FontSize',12,... 'FitBoxToText','off'); % Annotate the figure by adding text arrow to highlight where the chromate is added and removed. annotation(figure4,'textarrow',[0.3875 0.25],... [0.346619047619048 0.119047619047619],'Color',[1 0 0],... 'String',{'Chromate Added'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); annotation(figure4,'textarrow',[0.682142857142857 0.789285714285714],... [0.779952380952381 0.919047619047619],'Color',[1 0 0],... 'String',{'Chromate Removed'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); % Set the x and y labels to Increasing Time and Increasing concentration. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % Add a legend for GFP Concentration. legend3=legend('GFP Response'); % Set the legend position, box line width and font size/style. set(legend3,... 'Position',[0.468154768530456 0.149603206588803 0.360714277944395 0.0626984112082966],... 'LineWidth',2,... 'FontWeight','bold',... 'FontSize',12); % END OF SECTION % % %% Section 4: Sensitivity analysis on effect of chromate added to GFP production in original pathway. % Again set n as the number of values used for initial chromate. n=10; % T = Final time of simulation, in seconds. T=3600; % c1 = The range of values used for initial chromate concentration, with minimum at 0 and maximum at 400. c1=linspace(0,400,n); % Call up figure 5 to ensure no figures are overwritten. figure5=figure(5) % Set hold on so that multiple lines will be plotted on same figure. hold on % Set a for loop so that the n values for chromate are evaluated individually and the system solved for each of them. for i=1:n % Solve the chromate function using ode23 solver over set time range and same initial conditions for all variables except chromate. % The initial concentration of chromate will depend on the value of i within the for loop. % The values will be stored in the t vector and u matrix with no leakiness, L=0. [t,u]=ode23(@chrom_wt,[0,T],[a,b,c1(i),d,e,f,g],[],0); % Plot the GFP concentration over time. plot(t,u(:,7), 'LineWidth',2); % End the for loop. end % Then switch hold off so that no more lines are plotted on figure. hold off % Set the axis to tight so that the data fits the plot. axis tight % Add a rectangle onto the graph to highlight the section that will be zoomed in on in figure 6. annotation('rectangle',[0.236714285714286 0.561904761904762 0.213285714285714 0.354761904761906], 'LineStyle', '--'); % Remove the values on the x and y axis as they are not relevant. set(gca,'YTick',[],'XTick',[]); % Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration. annotation(figure5,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure5,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Annotate the figure by adding text arrow to highlight where the chromate is added and removed. annotation(figure5,'textarrow',[0.3875 0.25],... [0.346619047619048 0.119047619047619],'Color',[1 0 0],... 'String',{'Chromate Added'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); annotation(figure5,'textarrow',[0.682142857142857 0.789285714285714],... [0.779952380952381 0.919047619047619],'Color',[1 0 0],... 'String',{'Chromate Removed'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); % Set the x and y labels as increasing Time and Increasing Concentration respectively. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % % We now want to replot figure 5 with a section zoomed in. % % Call up figure 6 so that no other plots are overwritten. figure6=figure(6) % Set hold on so that multiple line can be plotted on one graph. hold on % Set a for loop so that the n values for chromate are evaluated individually and the system solved for each of them. for i=1:n % Solve the chromate function using ode23 solver over set time range and same initial conditions for all variables except chromate. % The initial concentration of chromate will depend on the value of i within the for loop. % The values will be stored in the t vector and u matrix with no leakiness, L=0. [t,u]=ode23(@chrom_wt,[0,T],[a,b,c1(i),d,e,f,g],[],0); % Plot the GFP concentration over time. plot(t,u(:,7), 'LineWidth',2); % End the for loop. end % Set hold off so that no more lines are plotted on the figure. hold off % Ensure that axis fits the data by using axis tight command. axis tight % Remove the values on the x and y axis as they are not relevant and set the x and y limits so that we get a zoomed in section of the plot. set(gca,'YTick',[],'XTick',[], 'XLim',[909.850230414748 1359.85023041475],'YLim',[163.478891218168 187.138947135872]); % Annotate the figure by adding arrows along the x and y axis to represent increasing time and concentration annotation(figure6,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure6,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Add a 3rd arrow to the plot to show increasing initial concentration of Cv in the legend. annotation(figure6,'arrow',[0.817857142857141 0.817857142857143],... [0.597619047619051 0.238095238095238],'LineWidth',4); % Set legend as just lines with no text, as text will be added later using paint (see wiki figures). legend4=legend('','','','','','','','','',''); % Set the position of the legend and the width of the box line. set(legend4,... 'Position',[0.631547602609266 0.207142857142858 0.255952397390734 0.413492042689934],... 'LineWidth',2); % Set the x and y labels to Increasing Time and Increasing Concentration respectively. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % % % END OF SECTION %% Section 5: Leakiness of both the modified and original pathways. % All parameters are set as previous sections. % Solve the chrom_wt function using ode23 solver with set time range and defined initial conditions. % Save time values in vector t and u(1)..u(7) values in matrix u with leakiness L set at 0.05. [t,u]=ode23(@chrom_wt,[0,T],[a,b,c,d,e,f,g],[],0.05); % Solve the chromate function using ode23 solver with set time range and defined initial conditions. % Save time values in vector t1 and u1(1)..u1(7) values in matrix u1 with leakiness L set at 0.05. [t1,u1]=ode23(@chromate,[0,T],[a,b,c,d,e,f,g],[],0.05); % Call up a new figure to ensure figures are not overwritten. figure7=figure(7); % Plot t vector against the 7th column of the u matrix and plot t1 against the 7th column of u1 on the same plot for comparrison. % Set linewidth to 2 so that it is easily read. hold on plot(t,u(:,7),'LineWidth',2); plot(t1,u1(:,7),'LineWidth',2); hold off % Ensure that axis fits the data by using axis tight command. axis tight % Remove the values on the x and y axis as they are not relevant. set(gca,'YTick',[],'XTick',[]); % Annotate the figure by adding arrows along the x and y axis to represent increasing Time and Fluorescence. annotation(figure7,'arrow',[0.133928571428571 0.914285714285714],... [0.0466190476190482 0.0476190476190482],'LineWidth',4); annotation(figure7,'arrow',[0.0982142857142857 0.0982142857142857],... [0.103761904761905 0.919047619047619],'LineWidth',4); % Annotate the figure by adding text arrow to highlight where the chromate is added and removed. annotation(figure7,'textarrow',[0.3875 0.25],... [0.346619047619048 0.119047619047619],'Color',[1 0 0],... 'String',{'Chromate Added'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); annotation(figure7,'textarrow',[0.682142857142857 0.789285714285714],... [0.779952380952381 0.919047619047619],'Color',[1 0 0],... 'String',{'Chromate Removed'},... 'LineWidth',4,... 'FontWeight','bold',... 'FontSize',12); % Set the x and y labels to Time and Fluoresence. xlabel ('Time', 'FontSize', 15); ylabel ('Fluorescence','FontSize', 15); % Add a legend to distinguish between the to pathways. legend5=legend('Original pathway','Modified pathway'); % Set the legend position, box line width and font size/style. set(legend5,... 'Position',[0.468154768530456 0.149603206588803 0.360714277944395 0.0626984112082966],... 'LineWidth',2,... 'FontWeight','bold',... 'FontSize',12); % END OF SECTION % % %END OF FILE
Bone Incision Data
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↑ View description of experimentBone Incision Experiment Code
MATLAB code from bone.m file k=6.23*10^(-9);%wear coefficient W=zeros(1,101);%zero vector for calculated volume of bone incision m^3 s=(0:0.001:0.1);%range of values for blade length m, from 0 to 10cm p=(0:2:200);%range of values for applied force N, from 0 to 200N for i=1:101 for j=1:101 W(i,j)=k*p(i)*s(j); %Archards Equation in two for loops %to create a matrix of possible values for volume end end surf(p,s,W)%creates a surface plot, where the height and therefore colour are dependand on the matric W grid on title('Relationship Between Volume of Bone Incison, Force and Blade length') zlabel('Volume of Incision/m^3') ylabel('Blade Length/m') xlabel('Applied Load/N')↑ View description of experiment
To see the MATLAB code for the FluID section of the project or the Fingerprint Ageing section of the project use the following buttons.
