modeling a kinetic reaction network with changing concentration

Hello All,

I'm trying to model a kinetic reaction network with a changing initial antibody concentration step. I also want to track the changing concentration of the antibody during the reaction itself.

I'm getting an error (see below) but I'm not sure how to solve it.

Error:

Unable to perform assignment because the left and right sides have a different number of elements.

Error in mazorbsabs_competition (line 60)

x(1) = Ab_0;

function bsabs_competition
close all;
clear all

tic

k_on_1CD70 = 1e5; %M-1s-1 on rate 
k_d_1CD70 = 25e-9;
k_off_1CD70 = k_d_1CD70*k_on_1CD70

k_on_1CD4 = 1e5; %M-1s-1 on 
k_d_1CD4 = 70e-9;
k_off_1CD4 = k_d_1CD4*k_on_1CD4

k_off_2CD70 = k_off_1CD70;
k_on_2CD70=2e6*k_on_1CD70;
kd_2p= k_off_2CD70/k_on_2CD70;

k_off_2CD4 = k_off_1CD4;
k_on_2CD4=2e6*k_on_1CD4;
kd_2c= k_off_2CD4/k_on_2CD4;

receptor_count_CD70 = 5.2e4;
number_unbound_CD70 = receptor_count_CD70;
CD70_0= number_unbound_CD70;
   
receptor_count_CD4 =4.6e4;
number_unbound_CD4 = receptor_count_CD4;
Cd4_0= number_unbound_CD4;

Ab_initial_conc = logspace(-11,-5,60); 
free_Ab=Ab_initial_conc;
Ab_0=free_Ab;

time_at_measurement = 1; % hrs, length of simulation 

%Common parameters changed are above this line
%______________________________________________________________________________________________________________

eqtime = [0, time_at_measurement*3600];
   
options = odeset('Maxstep',15,'RelTol',[1e-15],'AbsTol',[1e-15]);


x=zeros(6,1); % 6 species
%initialvalues:
x(1) = Ab_0; % tracking antibody
x(2) = CD70_0; % CD70 receptors
x(3) = Cd4_0; % CD4 receptors  
x(4) = 0; % monovalent bound CD70
x(5) = 0; % monovalent bound CD4
x(6) = 0; % Crosslinked antibodies


for k = 1:numel(Ab_0) % vector space which makes the size the size of the changing variable
    
    currentAb = Ab_0(k); % current is a name of a new varialbe name to calculate psy and P  

    [T,X] = ode15s(@(t,x)odesystem(t,x,currentAb), eqtime,x, options); % insert current name  
free_ab= X(end,1);    
free_cd70 = X(end,2);
free_cd4 = X(end,3);
monovalent_cd70 = X(end,4);
monovalent_cd4 = X(end,5);
crosslinked = X(end,6);
blocked = (receptor_count_CD70+receptor_count_CD4-X(end,1)-X(end,2))./(receptor_count_CD70+receptor_count_CD4);

ab(k)=free_ab;
pd1(k) = free_cd70;
cd(k) = free_cd4;
mpd (k) = monovalent_cd70;
mcd(k) = monovalent_cd4;
xl (k) = crosslinked;

end;

function xdot = odesystem(t,x,Ab_0)
 
xdot =[-k_on_1CD4*x(1)*x(3)+k_off_1CD70*x(4)-k_on_1CD70*x(1)*x(2)+k_off_1CD4*x(5);...
    -k_on_1CD70*x(1)*x(2) + k_off_1CD70*x(4) - k_on_2CD70*x(2)*x(5) + k_off_1CD70*x(6);...
       -k_on_1CD4*x(1)*x(3)+k_off_1CD4*x(5)-k_on_2CD4*x(3)*x(4)+k_off_1CD4*x(6);...
       k_on_1CD70*x(1)*x(2)-k_off_1CD70*x(4)-k_on_2CD4*x(3)*x(4)+k_off_1CD4*x(6);...
       k_on_1CD4*x(1)*x(3)-k_off_1CD4*x(5)-k_on_2CD70*x(2)*x(5)+k_off_1CD70*x(6);...
       k_on_2CD4*x(3)*x(4)+k_on_2CD70*x(2)*x(5)-k_off_1CD4*x(6)-k_off_1CD70*x(6)];

end

free_ab= X(:,1);
free_cd70 = X(:,2);
free_cd4 = X(:,3);
monovalent_cd70 = X(:,4);
monovalent_cd4 = X(:,5);
crosslinked = X(:,6);
blocked = (receptor_count_CD70+receptor_count_CD4-X(:,1)-X(:,2))./(receptor_count_CD70+receptor_count_CD4);

Aba_conc = num2str(Ab_initial_conc);
graph_title = ['Ab1 conc=' Aba_conc];

%plotting
scrsz = get(0,'ScreenSize');
figure('Position',[0 scrsz(4) scrsz(3)/1.5 scrsz(4)/3]);   %positioning plot on screen
subplot(1,2,1);

plot(T/3600,free_cd70,T/3600,free_cd4,T/3600,monovalent_cd70,T/3600,monovalent_cd4,T/3600,crosslinked)
xlabel('Time')
ylabel('Receptors with antibody')
legend('Free PD 1','Free CD 137 ','PD1-Ab (mono)','CD137-Ab (mono)','Crosslinked')
title('species concentration')

figure
semilogx(Ab_initial_conc,pd1);
xlabel('Concentration')
ylabel(' Receptors with antibody')
%legend('Test')
title('Free CD70')
hold on

legend('numerical result')
hold off

figure
semilogx(Ab_initial_conc,cd);
xlabel('Concentration')
ylabel('Receptors with antibody')
%legend('Test')
title('Free CD4')
hold on

legend('numerical result')
hold off

figure
semilogx(Ab_initial_conc,mpd);
xlabel('Concentration')
ylabel('Receptors with antibody')
%legend('Test')
title('Mono Bound CD70')
hold on


hold on
legend('numerical result')
hold off

figure
semilogx(Ab_initial_conc,mcd);
xlabel('Concentration')
ylabel('Receptors with antibody')
%legend('Test')
title('Mono Bound CD4')
hold on
legend('numerical result')
hold off

figure
semilogx(Ab_initial_conc,xl);
xlabel('Concentration')
ylabel('Receptors with antibody')
%legend('Test')
title('Crosslinked')
hold on

legend('numerical result')
hold off


X(end,:)

toc

end

[Torsten]

You try to set x(1) to a vector with 60 elements (logspace(-11,-5,60)).

[Reginald]

I understand that, but I'm not sure how to seperate the two. I want to track the antibody species over the range as well as within each individual reaction. When I tried to set it to equal the currentab, i recieved an error about the cleared variable.

Answer 1

[Torsten]

Define x(1) in the k-loop:

...
x=zeros(6,1); % 6 species
%initialvalues:
%x(1) = Ab_0; % tracking antibody
x(2) = CD70_0; % CD70 receptors
x(3) = Cd4_0; % CD4 receptors  
x(4) = 0; % monovalent bound CD70
x(5) = 0; % monovalent bound CD4
x(6) = 0; % Crosslinked antibodies
for k = 1:numel(Ab_0) % vector space which makes the size the size of the changing variable
    x(1) = Ab_0(k);
    currentAb = Ab_0(k); % current is a name of a new varialbe name to calculate psy and P  
...