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FIG_SIM_pert_Lin.m
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FIG_SIM_pert_Lin.m
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%% FIGURE : I-, PI-, and ID- control %%
%%%%%%%%% Linearized system %%%%%%%%%
%%%%%%%%% Adaptation dynamics %%%%%%%%%
% Mariana Gómez-Schiavon
% December, 2017
clear;
% Kinetic parameters:
k.gD = 0; % Dilution
k.mu = 1;
k.Y = 300;
k.et = 0.01;
k.th = 0.3;
k.g1 = 0.1;
k.bC = 0.1;
k.gC = 0.1;
k.bA = 1.5;
k.gA = 1.5;
k.KA = 1;
k.gA0= 0.1;
k.bM = 5/12;
k.gM = 1.5;
k.KM = 1;
% DEFAULT - I-Control
k.bI = 0.06;
k.bP = 0.15;
k.bD = 0.3;
% Perturbation
% k.Pn = 'Y'; % Variable to be perturbed
% k.P = [0,1000,3000; % Time points
% 1,1.2,0.8]; % Multiplicative perturbation (or [1,2,0.2])
k.Pn = 'bC'; % Variable to be perturbed
k.P = [0,1000,3000; % Time points
1,1.1,1.2]; % Multiplicative perturbation (or [1,1.5,2])
%% Find steady states:
% Aproximated steady states
XC = k.mu*k.Y/k.th;
X1 = XC*k.gC/k.bC;
A = k.bM*k.Y/k.gM;
M = ((k.gA*XC)+(k.gA0*A))/k.bA;
Z1 = ((k.g1*X1)-(k.bP*k.Y*k.mu*k.Y/((k.th*XC)...
+(k.mu*k.Y)))-(k.bD*A))/k.bI;
Z2 = k.th*XC/(k.et*Z1);
% Numerical steady states
O = k;
k.P = [0;1];
save('Par_ODE.mat','k');
[t,ySS] = ode45(@FN_ODE_PID,[0:5000],[Z1 Z2 X1 XC A M]);
k = O;
k.SS = ySS(length(t),:);
figure(); plot(t,ySS)
clear t O ySS
%% ODE - Linearized
save('Par_ODE.mat','k');
[tL,yL] = ode15s(@FN_ODE_PID_Lin,[0 max(k.P(1,:))+2000],[Z1 Z2 X1 XC A M]);
%% FIGURE
fig = figure();
fig.Units = 'inches';
fig.Position = [8 2 4 4];
fig.PaperPosition = fig.Position;
axes(fig,'Position',[0.2 0.15 0.725 0.825])
hold on;
for i = 1:6
plot(tL,k.SS(i)+yL(:,i),'LineWidth',2)
end
if(strcmp(k.Pn,'Y'))
plot([k.P(1,1) k.P(1,2) k.P(1,2) k.P(1,3) k.P(1,3) k.P(1,3)+2000],...
(k.mu*k.Y/k.th)*[k.P(2,1) k.P(2,1) k.P(2,2) k.P(2,2) k.P(2,3) k.P(2,3)],...
'LineWidth',2,'LineStyle',':','Color',[0 0 0]+0.7)
else
plot([tL(1),tL(length(tL))],[0 0]+(k.mu*k.Y/k.th),...
'LineStyle',':','LineWidth',2,'Color',[0 0 0]+0.7)
end
legend({'Z_1','Z_2','X_1','X_C','A','M','\muY/\theta'})
ylabel('Concentration (nM)','FontSize',14)
xlabel('Minutes','FontSize',14)
legend('show')
xlim([750 5000])
set(gca,'XTick',[1000:2000:5000],'XTickLabel',[0:2000:5000])
ylim([0 1700])
box('on')
set(gca,'FontSize',14,'XGrid','on')
annotation('textbox',[0.18 0.7 0.45 0.2],...
'String',{cat(2,'\mu=',num2str(k.mu),...
'; Y=',num2str(k.Y),...
'; \eta=',num2str(k.et),...
'; \gamma_D=',num2str(k.gD),...
'; \theta=',num2str(k.th),...
'; \gamma_1=',num2str(k.g1),...
'; \beta_C=',num2str(k.bC),...
'; \gamma_C=',num2str(k.gC),...
'; \beta_A=',num2str(k.bA),...
'; \gamma_A=',num2str(k.gA),...
'; K_A=',num2str(k.KA),...
'; \gamma_{A_0}=',num2str(k.gA0),...
'; \beta_MY=',num2str(k.bM*k.Y),...
'; \gamma_M=',num2str(k.gM),...
'; K_M=',num2str(k.KM),...
'; \beta_I=',num2str(k.bI),...
'; \beta_P=',num2str(k.bP),...
'; \beta_D=',num2str(k.bD))},...
'FitBoxToText','off');
%% ODE - Full system
save('Par_ODE.mat','k');
[tF,yF] = ode15s(@FN_ODE_PID,[0 max(k.P(1,:))+2000],[Z1 Z2 X1 XC A M]);
%% FIGURE
fig = figure();
fig.Units = 'inches';
fig.Position = [8 2 4 4];
fig.PaperPosition = fig.Position;
axes(fig,'Position',[0.2 0.15 0.725 0.825])
hold on;
plot(tF,yF,'LineWidth',2)
if(strcmp(k.Pn,'Y'))
plot([k.P(1,1) k.P(1,2) k.P(1,2) k.P(1,3) k.P(1,3) k.P(1,3)+2000],...
(k.mu*k.Y/k.th)*[k.P(2,1) k.P(2,1) k.P(2,2) k.P(2,2) k.P(2,3) k.P(2,3)],...
'LineWidth',2,'LineStyle',':','Color',[0 0 0]+0.7)
else
plot([tF(1),tF(length(tF))],[0 0]+(k.mu*k.Y/k.th),...
'LineStyle',':','LineWidth',2,'Color',[0 0 0]+0.7)
end
legend({'Z_1','Z_2','X_1','X_C','A','M','\muY/\theta'})
ylabel('Concentration (nM)','FontSize',14)
xlabel('Minutes','FontSize',14)
legend('show')
xlim([750 5000])
set(gca,'XTick',[1000:2000:5000],'XTickLabel',[0:2000:5000])
ylim([0 1700])
box('on')
set(gca,'FontSize',14,'XGrid','on')
annotation('textbox',[0.18 0.7 0.45 0.2],...
'String',{cat(2,'\mu=',num2str(k.mu),...
'; Y=',num2str(k.Y),...
'; \eta=',num2str(k.et),...
'; \gamma_D=',num2str(k.gD),...
'; \theta=',num2str(k.th),...
'; \gamma_1=',num2str(k.g1),...
'; \beta_C=',num2str(k.bC),...
'; \gamma_C=',num2str(k.gC),...
'; \beta_A=',num2str(k.bA),...
'; \gamma_A=',num2str(k.gA),...
'; K_A=',num2str(k.KA),...
'; \gamma_{A_0}=',num2str(k.gA0),...
'; \beta_MY=',num2str(k.bM*k.Y),...
'; \gamma_M=',num2str(k.gM),...
'; K_M=',num2str(k.KM),...
'; \beta_I=',num2str(k.bI),...
'; \beta_P=',num2str(k.bP),...
'; \beta_D=',num2str(k.bD))},...
'FitBoxToText','off');
%% END