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model_hb_bcd.m~
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model_hb_bcd.m~
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%% model_hb_bcd.m
%
%
% Alistair Boettiger Date Begun: 12/11/10
% Levine Lab Version Functional: 12/11/10
% Last Modified: 12/12/10
%
%% Code Description:
% Model hb expression to match binding site data without cooperativity.
% adapted from model_hb.m to account for bicoid binding sites explicitly
% Essent
%
function model_hb_bcd
clear all;
N = 20; T = 50;
x = linspace(0,1,N);
tau = 1/5; % from Gregor 2007
bcd = exp(-x/tau);
% figure(1); clf; plot(x,bcd,'g');
hbM = .1;
hb = hbM*ones(N,1);
P = ones(N,1);
PB1 = zeros(N,1);
PB2 = zeros(N,1);
PB3 = zeros(N,1);
PB4 = zeros(N,1);
PB5 = zeros(N,1);
PB1H = zeros(N,1);
PB2H = zeros(N,1);
PB3H = zeros(N,1);
PB4H = zeros(N,1);
PB5H = zeros(N,1);
PB1H2 = zeros(N,1);
PB2H2 = zeros(N,1);
PB3H2 = zeros(N,1);
PB4H2 = zeros(N,1);
PB5H2 = zeros(N,1);
R0 = [hb;P;PB1;PB2;PB3;PB4;PB5;PB1H;PB2H;PB3H;PB4H;PB5H;PB1H2;PB2H2;PB3H2;PB4H2;PB5H2];
[t,R] = ode15s(@sys,[0,T],R0,[],[N,bcd]);
hb = R(:,1:N);
P = R(:,N+1:2*N); %
PB1 = R(:,2*N+1:3*N); %
PB2 = R(:,3*N+1:4*N); %
PB3 = R(:,4*N+1:5*N);
PB4 = R(:,5*N+1:6*N);
PB5 = R(:,6*N+1:7*N);
PB1H = R(:,7*N+1:8*N);
PB2H = R(:,8*N+1:9*N);
PB3H = R(:,9*N+1:10*N);
PB4H = R(:,10*N+1:11*N);
PB5H = R(:,11*N+1:12*N);
PB1H2 = R(:,12*N+1:13*N);
PB2H2 = R(:,13*N+1:14*N);
PB3H2 = R(:,14*N+1:15*N);
PB4H2 = R(:,15*N+1:16*N);
PB5H2 = R(:,16*N+1:17*N);
PB = zeros(size(P));
for j = 1:15
PB = PB + R(:,(j+1)*N+1:(j+2)*N);
end
save test; % load test
f=2;
figure(f); set(gcf,'color','w');
for i= length(t)
figure(f); clf; subplot(2,1,1);
plot(x,hb(i,:),'b','LineWidth',3); hold on;
plot(x,bcd,'g','LineWidth',3);
legend('hb','bcd');
figure(f); subplot(2,1,2);
plot(x,P(i,:),'k','LineWidth',3); hold on;
plot(x,PB(i,:),'c','LineWidth',5);
% plot(x,PB2(i,:),'c','LineWidth',2);
% plot(x,PB3(i,:),'c','LineWidth',3);
% plot(x,PB4(i,:),'c','LineWidth',4);
plot(x,PB2H(i,:),'m','LineWidth',3);
plot(x,PB2H2(i,:),'r','LineWidth',3);
% legend('free Pr','Pr-bcd','Pr-bcd-hb','Pr-bcd-hb_2');
end
function dRdt = sys(t,R,Pars)
N = Pars(1);
bcd = Pars(2:end)';
hb = R(1:N); %
P = R(N+1:2*N); %
PB1 = R(2*N+1:3*N); %
PB2 = R(3*N+1:4*N); %
PB3 = R(4*N+1:5*N);
PB4 = R(5*N+1:6*N);
PB5 = R(6*N+1:7*N);
PB1H = R(7*N+1:8*N);
PB2H = R(8*N+1:9*N);
PB3H = R(9*N+1:10*N);
PB4H = R(10*N+1:11*N);
PB5H = R(11*N+1:12*N);
PB1H2 = R(12*N+1:13*N);
PB2H2 = R(13*N+1:14*N);
PB3H2 = R(14*N+1:15*N);
PB4H2 = R(15*N+1:16*N);
PB5H2 = R(16*N+1:17*N);
% bcd binding matrix
kb = [0,1,0,0,0,0;
1,0,1,0,0,0;
0,1,0,1,0,0;
0,0,1,0,1,0;
0,0,0,1,0,1;
0,0,0,0,1,0];
% hb binding rates
kh1 = 1;
kh2 = 1;
kj1 = 1;
kj2= 1; % hb2 unbinding
% synthesis rates
kBs = [1,1,1,1,1];
kH1s = 2*[1,1,1,1,1];
kH2s = 3*[1,1,1,1,1];
kd = 1;
% promoter binding
dP = - kb(1,2).*bcd.*P + kb(2,1).*PB1;
dPB1 = - kb(2,1)*PB1 - kb(2,3).*bcd.*PB1 + kb(3,2).*PB2 + kb(1,2).*bcd.*P -kh1*PB1.*hb + kj1*PB1H; % 1->0 1->2, 2->1, 0->1
dPB2 = - kb(3,2)*PB2 - kb(3,4).*bcd.*PB2 + kb(4,3).*PB3 + kb(2,3).*bcd.*PB1 -kh1*PB2.*hb + kj1*PB2H;
dPB3 = - kb(4,3)*PB3 - kb(4,5).*bcd.*PB3 + kb(5,4).*PB4 + kb(3,4).*bcd.*PB2 -kh1*PB3.*hb + kj1*PB3H;
dPB4 = - kb(5,4)*PB4 - kb(5,6).*bcd.*PB4 + kb(6,5).*PB5 + kb(4,5).*bcd.*PB3 -kh1*PB4.*hb + kj1*PB4H;
dPB5 = - kb(6,5)*PB5 + kb(5,6).*bcd.*PB4 -kh1*PB5.*hb + kj1*PB5H;
dPB1H = kh1*PB1.*hb - kj1*PB1H - kh2*PB1H.*hb + kj2*PB1H2; %
dPB2H = kh1*PB2.*hb - kj1*PB2H - kh2*PB2H.*hb + kj2*PB2H2;
dPB3H = kh1*PB3.*hb - kj1*PB3H - kh2*PB3H.*hb + kj2*PB3H2;
dPB4H = kh1*PB4.*hb - kj1*PB4H - kh2*PB4H.*hb + kj2*PB4H2;
dPB5H = kh1*PB5.*hb - kj1*PB5H - kh2*PB5H.*hb + kj2*PB5H2;
dPB1H2 = kh2*PB1H.*hb - kj2*PB1H2; %
dPB2H2 = kh2*PB2H.*hb - kj2*PB2H2;
dPB3H2 = kh2*PB3H.*hb - kj2*PB3H2;
dPB4H2 = kh2*PB4H.*hb - kj2*PB4H2;
dPB5H2 = kh2*PB5H.*hb - kj2*PB5H2;
s = [kBs(1)*PB1 , kBs(2)*PB2 , kBs(3)*PB3 , kBs(4)*PB4 , kBs(5)*PB5 , ...
kH1s(1)*PB1H , kH1s(2)*PB2H ,kH1s(3)*PB3H ,kH1s(4)*PB4H ,kH1s(5)*PB5H , ...
kH2s(1)*PB1H2, kH2s(2)*PB2H2,kH2s(3)*PB3H2,kH2s(4)*PB4H2,kH2s(5)*PB5H2 ];
err = find(s<0);
%
% save test2;
% if length(err) > 10
% return
% end
dhb = kBs(1)*PB1 + kBs(2)*PB2 + kBs(3)*PB3 + kBs(4)*PB4 + kBs(5)*PB5 + ...
kH1s(1)*PB1H + kH1s(2)*PB2H +kH1s(3)*PB3H +kH1s(4)*PB4H +kH1s(5)*PB5H + ...
kH2s(1)*PB1H2 + kH2s(2)*PB2H2 +kH2s(3)*PB3H2 +kH2s(4)*PB4H2 +kH2s(5)*PB5H2 - kd*hb ;
dRdt = [dhb; dP;
dPB1; dPB2; dPB3; dPB4; dPB5;
dPB1H; dPB2H; dPB3H; dPB4H; dPB5H;
dPB1H2; dPB2H2; dPB3H2; dPB4H2; dPB5H2 ];
%%