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RunForce_pCa.m
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% RunForcepCa
clear; close all;
var = [ 1.7386*1.7 1.5022 1.4040 1.8637 1.4793 1.4693*1.05 0.6281*0.2 1.9245 0.5000*0.2 2.3293*1.35]
% set the axis font size for the figure plots
flag_plot_state_var = 1; % if "para.flag_plot = 1" plots every state variable else does not plot.
flag_plot_force = 1;
flag_plot_fig3 = 1;
flag_plot_fig3_USR_UNR = 1;
AxisFontSize = 18; LabelFontSize = 18;
%% Defining the parameters into the parameter (para)
% Set temperature and initial SL (Sarcomere length)
% From Tewari etal JMCC paper one
TmpC =37.5; % centigrade
lstyle = {'-g','-b','-r','-k'}; k = 0;
% filename = {'Ca_05.mat','Ca_1.mat','Ca_15.mat','Ca_2.mat','Ca_25.mat','Ca_3.mat'};
% Set metabolite concentrations,
%mean SHAM rat
MgATP = 7.93; % mM
MgADP = 43.17e-3; % mM
Pi = 1; % mM
kstiff1 = var(1)*5.1535e+03; %kPa/um (Tewari et al)
kstiff2 = var(1)*1.0974e+05; % kPa/um (Tewari et al)
% kstiff1 = var(1)* 2827.1 * Q10s(4)^((TmpC-17)/10) % kPa/um (9/5 BM)
% kstiff2 = var(1)* 51871 * Q10s(6)^((TmpC-17)/10) % kPa/um (9/5 BM)
dr = 0.01; % Power-stroke Size; Units: um
k_passive = var(2)* 40/7.5; % mN / mm^2 / micron
Kse = 1400;
SLset = [1.90,2.1,2.3];
% Defining the time vector
tspan = 0:0.0001:0.3; nn = length(tspan);
%%Defining the Ca range for the study
% Ca_frction = 1; %Unit uM
Ca_fraction = [0.005:0.01:1.5,1.6:0.1:20,30:5:500]; %Unit uM
% Ca_fraction = [0.2:0.1:50]; %Unit uM
t_T = tspan;
tic;
SL0 = [1.90,2.3]; % Set sarcomere length, Units: um
for j = 1: length (SL0)
init = [zeros(1,10),SL0(j),0.2]; % Initial conditions for the model
init(10) = 1;% setting the initial value for nonpermissible state equal to 1
for k = 1: length (Ca_fraction)
para = [TmpC, MgATP, MgADP, Pi, 1, kstiff1, kstiff2, k_passive SLset(j) 1 1 1 1 Kse];
% Solving the system of diffrential equations
options = odeset('RelTol',1e-3,'AbsTol',1e-6,'MaxStep',5e-3);
[Time, Y] = ode15s(@Model_XB_Ca_Sensitivity,tspan,init,options,para,var,Ca_fraction(k));
p2_1 = Y(:,5);
p3_0 = Y(:,7);
p3_1 = Y(:,8);
N = Y(:,10);
SL = Y(:,11);
UNR = Y(:,12);
%% Overlap function (Tewari et al.)
Lthin = 1200; % nm
Lthick = 1670; % nm
Lbare = 100; % nm Thick filament bare zone
OV_Zaxis = min(Lthick/2,1000*SL/2);
OV_Mline = max(1000*SL/2-(1000*SL-Lthin),Lbare/2);
LOV = OV_Zaxis - OV_Mline;
% N_overlap = LOV/Lthin;
N_overlap_thick = LOV*2/(Lthick - Lbare);
% Active Force
dr = 0.01; % Power-stroke Size; Units: um
B_process = kstiff2 * dr * p3_0; % Force due to XB ratcheting
C_process = kstiff1 * ( p2_1 + p3_1 );% Force due to stretching of XBs
F_XB = N_overlap_thick.*( B_process + C_process ); % Active Force
% (linear) passive force model
%% Titin force
Lsref = 1.9;
% Collagen force
SLcollagen = 2.25; % threshold for collagen activation, microns
PConcollagen = 0.01*7.5; % contriubtion of collagen (??)
PExpcollagen = 70; % expresion of collagen (??), unitless
sigma_collagen = PConcollagen*(exp(PExpcollagen*(SL - SLcollagen)) - 1).*(SL > SLcollagen);
F_passive = k_passive*(SL/2-Lsref/2) + sigma_collagen;
Ftotal = F_XB + F_passive;
SS_N_on (k,j)= 1 - N(end);
SS_USR (k,j) = 1 - UNR(end);
SS_UNR (k,j) = UNR(end);
SS_F_XB (k,j)= F_XB(end);
SS_Ftotal (k,j)= Ftotal(end);
% Max_F_XB (k,j)= max(F_XB);
end
toc;
% plots the state variables if the flag_plot == 1
if flag_plot_state_var ==1
figure(2)
plot(t_T ,p3_0/max(p3_0))
title('Normailized P30')
hold on
% figure(3)
% plot(t_T ,P)
% title('Pu')
% hold on
figure(4)
plot(t_T ,p3_0)
title('P30')
hold on
% figure(5)
% plot(t_T ,p1_0)
% title('P1o')
% hold on
% figure(6)
% plot(t_T ,p2_0)
% title('P2o')
% hold on
figure(7)
plot(t_T ,N)
title('Np')
hold on
figure(8)
plot(t_T ,UNR)
title('UNR')
hold on
figure(9)
plot(t_T ,SL)
title('SL')
hold on
end
end
if flag_plot_force == 1
figure(10)
plot(-log10(Ca_fraction*(10^(-6))),SS_F_XB(:,1),'-ro','linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_F_XB(:,2),'linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_F_XB(:,3),'linewidth',1.5)
set(gca, 'LineWidth',1.5, 'FontSize',AxisFontSize);
title(sprintf('F active'),'fontsize',14);
set ( gca, 'xdir', 'reverse' )
xlabel('pCa = - Log[Ca]','fontsize',LabelFontSize);
ylabel('Force Active(mN mm^{-2})','fontsize',LabelFontSize);
legend('SL = 1.9 um','SL = 2.1 um','SL = 2.3 um');
figure(120)
plot(-log10(Ca_fraction*(10^(-6))),SS_Ftotal(:,1),'-ro','linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_Ftotal(:,2),'linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_Ftotal(:,3),'linewidth',1.5)
set(gca, 'LineWidth',1.5, 'FontSize',AxisFontSize);
title(sprintf('F total'),'fontsize',14);
set ( gca, 'xdir', 'reverse' )
xlabel('pCa = - Log[Ca]','fontsize',LabelFontSize);
ylabel('Force Total (kPa)','fontsize',LabelFontSize);
legend('SL = 1.9 um','SL = 2.1 um','SL = 2.3 um');
end
if flag_plot_fig3 == 1
figure(12)
plot(-log10(Ca_fraction*(10^(-6))),SS_N_on(:,1),'-ro','linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_N_on(:,2),'linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_N_on(:,3),'linewidth',1.5)
set(gca, 'LineWidth',1.5, 'FontSize',AxisFontSize);
title(sprintf('N on'),'fontsize',14);
set ( gca, 'xdir', 'reverse' )
xlabel('pCa = - Log[Ca]','fontsize',LabelFontSize);
ylabel('N_on','fontsize',LabelFontSize);
legend('SL = 1.9 um','SL = 2.1 um','SL = 2.3 um');
end
if flag_plot_fig3_USR_UNR == 1
figure(16)
plot(-log10(Ca_fraction*(10^(-6))),SS_USR(:,1),'-ro','linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_USR(:,2),'linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_USR(:,3),'linewidth',1.5)
set(gca, 'LineWidth',1.5, 'FontSize',AxisFontSize);
title(sprintf('USR'),'fontsize',14);
set ( gca, 'xdir', 'reverse' )
xlabel('pCa = - Log[Ca]','fontsize',LabelFontSize);
ylabel('USR','fontsize',LabelFontSize);
legend('SL = 1.9 um','SL = 2.1 um','SL = 2.3 um');
figure(18)
plot(-log10(Ca_fraction*(10^(-6))),SS_UNR(:,1),'-ro','linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_UNR(:,2),'linewidth',1.5)
hold on
plot(-log10(Ca_fraction*(10^(-6))),SS_UNR(:,3),'linewidth',1.5)
set(gca, 'LineWidth',1.5, 'FontSize',AxisFontSize);
title(sprintf('UNR'),'fontsize',14);
set ( gca, 'xdir', 'reverse' )
xlabel('pCa = - Log[Ca]','fontsize',LabelFontSize);
ylabel('UNR','fontsize',LabelFontSize);
legend('SL = 1.9 um','SL = 2.1 um','SL = 2.3 um');
end
[hill_19 ec50_19]=doseResponse( (Ca_fraction')*10^(-6) ,SS_Ftotal(:,1))
Ca50_19=-log10(ec50_19)
[hill_23 ec50_23]=doseResponse( (Ca_fraction')*10^(-6),SS_Ftotal(:,2))
Ca50_23=-log10(ec50_23)