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solver_release_all.m
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solver_release_all.m
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%clear all;
clc;
global Xdim; % number of species: 1~14
global tdim;
global k; % all rate constants: k(i,1)=k_i^+, k(i,2)=k_i^-
vol=1; % 0: neglect volume factor
expFdiff=50;
Xdim=14; % 14 species
k=ones(11,2);
tdim=20;
tinterval=[0 tdim];
% X0: initial conditions
X0=[ 50 50 0 0 5 0 50 50 25 0 0 5 0 50];
% X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14
%index=0.04:.005:.25;
theta=0:1:120; % free [T]/[D]
RanDfraction=zeros(1,length(theta));
RanTfraction=zeros(1,length(theta));
Cargonufraction=zeros(1,length(theta));
Cargocytofraction=zeros(1,length(theta));
Transporternu2cyto=zeros(1,length(theta));
%TransportEffic=zeros(1,length(theta));
NTF2nufraction=zeros(1,length(theta));
NTF2cytofraction=zeros(1,length(theta));
TCnu2cyto=zeros(1,length(theta));
EP=zeros(1,length(theta));
for in2=1:length(theta)
%theta2=1/20; % free parameter Eq.(41): ratio of free [D]/ free [T] at cyto
%theta5=1/20; % free parameter Eq.(33): ratio of free [T]/ free [D] at nucl
theta2=1/theta(in2);
theta5=theta(in2);
% below specify the kinetics rate constants (SM section II). Note that
% cytosolic and nuclear volume effects will be taken care of in reaction2.m
% We simulated cases both with and without volume factor. In fact, apart from the
% change in the exact value of the steady-state nuclear localizatio measures (i.e. NL, EP etc.),
% the qualitative behavior remains robust (i.e. same functional behavior of NL, EP
% as one varies the importin, cargo, NTF2 concentrations)
k=[0.1 ,2.5;...
expFdiff*theta2,1;...
1,1;...
0.1, 1;...
expFdiff*theta5, 1;...
1, 1;...
20,1;...
1,1;...
1,1;...
1, 20;...
1,0.2];
if vol==0
[T,X] = ode45(@reaction,tinterval,X0);
elseif vol==1
[T,X] = ode45(@reaction2,tinterval,X0);
end
RanDfraction(in2)=X(length(T),2)/(X(length(T),2)+X(length(T),9)); % @SS
RanTfraction(in2)=X(length(T),9)/(X(length(T),2)+X(length(T),9)); % @SS
Cargonufraction(in2)=X(length(T),12)./(X(length(T),12)+X(length(T),5)); % @SS [C]_nu/[C]_cyto
Cargocytofraction(in2)=X(length(T),5)./(X(length(T),12)+X(length(T),5));
NTF2nufraction(in2)=X(length(T),8)/(X(length(T),8)+X(length(T),1));
NTF2cytofraction(in2)=X(length(T),1)/(X(length(T),8)+X(length(T),1));
TCnu2cyto(in2)=X(length(T),11)/X(length(T),4);
Transporternu2cyto(in2)=X(length(T),14)/X(length(T),7); % time it takes to reach half max of [C]_nu
normalization=sum(X(length(T),:));
Xtemp=X(length(T),:);
Pss=X(length(T),:)/normalization;
Kdd=zeros(1,5);
Kdd(2)=(k(2,1)/(k(2,1)+k(3,2)))/(k(2,2)*Xtemp(7)*Xtemp(2)/(k(2,2)*Xtemp(7)*Xtemp(2)+k(1,1)*Xtemp(1)*Xtemp(2)));
Kdd(1)=(k(1,2)/(k(1,2)+k(6,1)))/(k(1,1)*Xtemp(1)*Xtemp(2)/(k(1,1)*Xtemp(1)*Xtemp(2)+k(2,2)*Xtemp(7)*Xtemp(2)));
Kdd(4)=(k(4,2)/(k(4,2)+k(3,1)))/(k(4,1)*Xtemp(14)*Xtemp(9)/(k(4,1)*Xtemp(14)*Xtemp(9)+k(5,2)*Xtemp(8)*Xtemp(9)));
Kdd(5)=(k(5,1)/(k(5,1)+k(6,2)))/(k(5,2)*Xtemp(8)*Xtemp(9)/(k(5,2)*Xtemp(8)*Xtemp(9)+k(4,1)*Xtemp(14)*Xtemp(9)));
EP(in2)= Pss(6)*(k(2,1)/(k(2,1)+k(3,2)))*log(Kdd(2))...
+Pss(6)*(k(3,2)/(k(2,1)+k(3,2)))*log((k(3,2)/(k(2,1)+k(3,2)))/(k(3,1)/(k(3,1)+k(4,2))))...
+ (Pss(2)+Pss(1))*(k(1,1)*Xtemp(1)*Xtemp(2)/(k(1,1)*Xtemp(1)*Xtemp(2)+k(2,2)*Xtemp(7)*Xtemp(2)))*log(1/Kdd(1))...
+(Pss(2)+Pss(7))*(k(2,2)*Xtemp(7)*Xtemp(2)/(k(2,2)*Xtemp(7)*Xtemp(2)+k(1,1)*Xtemp(1)*Xtemp(2)))*log(1/Kdd(2))...
+Pss(3)*(k(6,1)/(k(6,1)+k(1,2)))*log((k(6,1)/(k(6,1)+k(1,2)))/(k(6,2)/(k(6,2)+k(5,1))))...
+Pss(3)*(k(1,2)/(k(1,2)+k(6,1)))*log(Kdd(1))...
+Pss(10)*(k(5,1)/(k(5,1)+k(6,2)))*log(Kdd(5))...
+Pss(10)*(k(6,2)/(k(5,1)+k(6,2)))*log((k(6,2)/(k(5,1)+k(6,2)))/(k(6,1)/(k(6,1)+k(1,2))))...
+(Pss(14)+Pss(9))*(k(4,1)*Xtemp(14)*Xtemp(9)/(k(4,1)*Xtemp(14)*Xtemp(9)+k(5,2)*Xtemp(8)*Xtemp(9)))*log(1/Kdd(4))...
+(Pss(8)+Pss(9))*(k(5,2)*Xtemp(8)*Xtemp(9)/(k(5,2)*Xtemp(8)*Xtemp(9)+k(4,1)*Xtemp(14)*Xtemp(9)))*log(1/Kdd(5))...
+Pss(13)*(k(3,1)/(k(3,1)+k(4,2)))*log((k(3,1)/(k(3,1)+k(4,2)))/(k(3,2)/(k(3,2)+k(2,1))))...
+Pss(13)*k(4,2)/(k(4,2)+k(3,1))*log(Kdd(4));
end
%[row,col] = find(RanD2RanT==max(max(RanD2RanT)));
figure(1);
subplot(221);
plot(theta,RanDfraction,theta,RanTfraction,'LineWidth',2.5);
axis([0 max(theta) 0 1]);
grid on;
xlabel('\theta', 'fontsize', 20);
legend('n_{RanGDP}','n_{RanGTP}')
title('fraction of RanGD(T)P');
set(gca,'Fontsize',18);
subplot(2,2,[3,4]);
plot(theta,Cargonufraction./Cargocytofraction,...
theta,Transporternu2cyto,...
theta,TCnu2cyto,'LineWidth',2.5);
grid on;
xlabel('\theta', 'fontsize', 20);
title('Nu to Cyto ratio');
legend('[C]_{nu}/[C]_{cyto}','[T]_{nu}/[T]_{cyto}','[TC]_{nu}/[TC]_{cyto}')
set(gca,'Fontsize',18);
subplot(222);
plot(theta,EP,'LineWidth',2.5);
axis([0 max(theta) min(EP) 1.03*max(EP)]);
grid on;
xlabel('\theta', 'fontsize', 20);
title('EP/k_B T');
set(gca,'Fontsize',18);
str=['expF' num2str(expF) 'theta' num2str(min(theta)) 'to' num2str(max(theta))];