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Proteins.m
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clear all
clc
close all
%%
tspan = [0:0.5:100];
y1_0 = 1.5903; y2_0 = 1.304; y3_0 = 1.601; y4_0 = 2.6014; y5_0 = 2.334;
y6_0 = 2.414; y7_0 = 2.8311132;y8_0 =2.5232; y9_0 = 3.45; y10_0 = 3.73;
y11_0 = 2.603; y12_0 = 2.504; y13_0 = 2.301; y14_0 = 2.1014;
y15_0=2.153; y16_0=2.153; y17_0=2.353; y18_0=2.0153; y19_0=2.2153;
y20_0=2.0153; y21_0=2.0353; y22_0=2.043; y23_0=2.0353;
vPs = 2.2; vCs= 2.3; vBs= 2.32; vRs= 2.04; vRes= 2.14;
% k =0.408; k1 =0.39; k2 =0.47; k3=0.42; k4=0.419;
% d_mP = 0.34; d_mC=0.324; d_mB = 0.46; d_mR = 0.372; d_mRe = 0.382; Kpco =0.3; kcbpc =0.39; dclbn= 0.30;
% dpcn=0.15; kdcbpc = 0.46;
%vPs= 1.7;
init=[y1_0 y2_0 y3_0 y4_0 y5_0 y6_0 y7_0 y8_0 y9_0 y10_0 ...
y11_0 y12_0 y13_0 y14_0 y15_0 y16_0 y17_0 y18_0 y19_0 ...
y20_0 y21_0 y22_0 y23_0];
params=[vPs,vCs,vBs,vRs,vRes];
[Tt,Y] = ode45(@new2,tspan,init,[],params);
%%
state.time=tspan;
state.ydata=Y;
state.y0 = init;
for i = 1:5
k00 = params+2.8.*abs(randn(1,5));
[fit,rss] = fminsearch(@new_ss1,k00,[],state);
mse = rss/(length(state.ydata)-4);
%fit is the new parameter values from the optimization.
[T,Yfit] = ode45(@new2,tspan,init,[],fit);
Yall(:,:,i) = Yfit;
fitall(:,i)= fit;
rssall(:,i) = rss;
end
%%
for j=1:5
figure
plot(Tt,Y(:,j),'LineWidth',2)
hold on
for i=1:5
plot(T,Yall(:,j,i),'LineWidth',1.5)
% plot(T,Yall(:,j,i),'--b')
end
xlabel('Time(h)');
ylabel('Concentration (nM)');
legend('Parameters','Optimized 1' ,'Optimized 2','Optimized 3','Optimized 4','Optimized 5')
end
%%
% figure
% plot(fitall(:,1), 'r'); hold on
% plot(fitall(:,2), 'b'); hold on
% plot(fitall(:,3), 'k');
function dydt = new2(t,y,values)
dydt = zeros(23,1);
%%
vPs =values(1);
vCs=values(2);
vBs=values(3);
vRs=values(4);
vRes=values(5);
%%
%%
n=4; m=6; p=8; q=7; O=8;l= 8; r=8; s=7; t=8; u=6;
%vPs = 2.2;
kiP=0.242; d_mP = 0.34;
d_mC=0.324; kiC = 0.262;
% vCs= 2.3;
d_mB = 0.46;
% vBs= 2.32;
kiB = 0.13;
d_mR = 0.372;
% vRs= 2.04;
kiR = 0.27;
d_mRe = 0.382;
% vRes= 2.14;
kiRe = 0.25;
k =0.408;
Kpco =0.3; Kpc1=0.362;Kpc=0.304; Kppc= 0.39; dpc=0.23;
k1 =0.39;
Kcc = 0.365; Kcpc = 0.306; dcc=0.18;
k2 =0.47;
Kbcc = 0.342; Kbc=0.298; Kbpc=0.385; dbc=0.07;
k3=0.42;
Krcc=0.394; Krc=0.361; Krpc=0.166; drc=0.05;
k4=0.419;
Krecc=0.374; Krec=0.3611; Krepc=0.3363; drec=0.06;
Kpcc=0.375; Kpcp = 0.24412; Kpcpc=0.3623; dpcc=0.017;
dppc=0.023; dcpc = 0.019; dbpc=0.013; drpc = 0.02; drepc= 0.23; dpcpc = 0.025;
Kclbn=0.37; dbn=0.09;
Krn=0.3482; drn=0.0704;
Kren= 0.349; dren=0.0608;
kcbpc =0.39; dclbn= 0.30;
dpcn=0.15;
kdcbpc = 0.46;
%%
Per_mRNA = y(1);
Cry_mRNA = y(2);
Bmal1_mRNA = y(3);
Ror_mRNA = y(4);
Rev_erb_mRNA = y(5);
CYTOSOLIC_PER_PROTEIN = y(6);
CYTOSOLIC_CRY_PROTEIN = y(7);
CYTOSOLIC_BMAL1_PROTEIN = y(8);
CYTOSOLIC_ROR_PROTEIN = y(9);
CYTOSOLIC_REV_ERB_PROTEIN = y(10);
CYTOSOLIC_PER_CRY_PROTEIN = y(11);
PHOS_CYTOSOLIC_PER_PROTEIN = y(12);
PHOS_CYTOSOLIC_CRY_PROTEIN = y(13);
PHOS_CYTOSOLIC_BMAL1_PROTEIN = y(14);
PHOS_CYTOSOLIC_ROR_PROTEIN = y(15);
PHOS_CYTOSOLIC_REV_ERB_PROTEIN = y(16);
PHOS_CYTOSOLIC_PER_CRY_PROTEIN = y(17);
NUCLEAR_BMAL1_PROTEIN = y(18);
NUCLEAR_ROR_PROTEIN = y(19);
NUCLEAR_REV_ERB_PROTEIN = y(20);
NUCLEAR_CLOCK_BMAL1_PROTEIN = y(21);
NUCLEAR_PER_CRY_PROTEIN = y(22);
NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN = y(23);
%%
% this creates an empty column
%vector that you can fill with your two derivatives:
% EQUATIONS FOR THE TRANSCRIPTIONS FOR THE VARIOUS mRNA'S.(mRNAs of Per,
% Cry, Bmal1, Rev-erb and Ror)
%y(1)= Per mRNA, y(2)= Cry mRNA, y(3)= Bmal1 mRNA, y(4)= Rev-erb mRNA,
%y(5)= Ror mRNA y(21) = CLOCK-BMAL1 protein, y(22) = PER-CRY protein in the nucleus.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The equation for the transcription of the Per gene.
dydt(1) = ((vPs.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).^m)./(kiP.^m + ((NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN)).^n + (NUCLEAR_CLOCK_BMAL1_PROTEIN).^m)) - d_mP.*Per_mRNA;
% The equation for the transcription of the Cry gene.
dydt(2) = ((vCs.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).^p)./(kiC.^p + ((NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN)).^q + (NUCLEAR_CLOCK_BMAL1_PROTEIN).^p)) - d_mC.*Cry_mRNA;
% The equation for the transcription of the Bmal1 gene.
dydt(3) = ((vBs.*((NUCLEAR_ROR_PROTEIN).^O))./(kiB.^O + ((NUCLEAR_ROR_PROTEIN).*(NUCLEAR_REV_ERB_PROTEIN)).^l+ (NUCLEAR_ROR_PROTEIN).^O)) - d_mB.*Bmal1_mRNA;
% The equation for the transcription of the Ror gene.
dydt(4) = ((vRs.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).^r)./(kiR.^r + ((NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN)).^s + (NUCLEAR_CLOCK_BMAL1_PROTEIN).^r)) - d_mR.*Ror_mRNA;
% The equation for the transcription of the Rev-erb gene.
dydt(5) = ((vRes.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).^t)./(kiRe.^t + ((NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN)).^u + (NUCLEAR_CLOCK_BMAL1_PROTEIN).^t)) - d_mRe.*Rev_erb_mRNA ;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EQUATIONS FOR PER, CRY, BMAL1, REV-ERB, ROR AND PER-CRY PROTEIN IN THE
% CYTOSOL
% y(4) = PER PROTEIN, y(5) = CRY PROTEIN, y(6) = BMAL1 PROTEIN, and y(7) = PER-CRY PROTEIN IN THE
% CYTOSOL.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The Equations for Unphosphorylated PER Protien in the Cytosol
dydt(6)= k.*Per_mRNA + Kpc1.*(CYTOSOLIC_PER_CRY_PROTEIN) - Kpco.*(CYTOSOLIC_PER_PROTEIN).*(CYTOSOLIC_CRY_PROTEIN) -Kpc.*((CYTOSOLIC_PER_PROTEIN)) + Kppc.*(PHOS_CYTOSOLIC_PER_PROTEIN) - dpc.*(CYTOSOLIC_PER_PROTEIN);
%The Equations for Unphosphorylated CRY Protien in the Cytosol
dydt(7)= k1.*Cry_mRNA + Kpc1.*(CYTOSOLIC_PER_CRY_PROTEIN) - Kpco.*(CYTOSOLIC_PER_PROTEIN).*(CYTOSOLIC_CRY_PROTEIN) - Kcc.*((CYTOSOLIC_CRY_PROTEIN)) + Kcpc.*(PHOS_CYTOSOLIC_CRY_PROTEIN)- dcc.*(CYTOSOLIC_CRY_PROTEIN);
%The Equations for Unphosphorylated BMAL1 Protien in the Cytosol
dydt(8)= k2.*Bmal1_mRNA - Kbcc.*(CYTOSOLIC_BMAL1_PROTEIN)- Kbc.*((CYTOSOLIC_BMAL1_PROTEIN)) + Kbpc.*(PHOS_CYTOSOLIC_BMAL1_PROTEIN) - dbc.*(CYTOSOLIC_BMAL1_PROTEIN);
%The Equations for Unphosphorylated ROR Protien in the Cytosol
dydt(9)= k3.*Ror_mRNA - Krcc.*(CYTOSOLIC_ROR_PROTEIN)- Krc.*((CYTOSOLIC_ROR_PROTEIN)) + Krpc.*(PHOS_CYTOSOLIC_ROR_PROTEIN) - drc.*(CYTOSOLIC_ROR_PROTEIN);
%The Equations for Unphosphorylated REV-ERB Protien in the Cytosol
dydt(10)= k4.*Rev_erb_mRNA - Krecc.*(CYTOSOLIC_REV_ERB_PROTEIN)- Krec.*((CYTOSOLIC_REV_ERB_PROTEIN)) + Krepc.*(PHOS_CYTOSOLIC_REV_ERB_PROTEIN) - drec.*(CYTOSOLIC_REV_ERB_PROTEIN);
%The Equations for Unphosphorylated PER-CRY Protien in the Cytosol
dydt(11)= Kpco.*((CYTOSOLIC_PER_PROTEIN).*(CYTOSOLIC_CRY_PROTEIN)) - Kpcc.*(CYTOSOLIC_PER_CRY_PROTEIN) - Kpc1.*(CYTOSOLIC_PER_CRY_PROTEIN)- Kpcp.*((CYTOSOLIC_PER_CRY_PROTEIN))+ Kpcpc.*(PHOS_CYTOSOLIC_PER_CRY_PROTEIN)-dpcc.*(CYTOSOLIC_PER_CRY_PROTEIN);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The Equations for phosphorylated PER Protien in the Cytosol
dydt(12)= Kpc.*((CYTOSOLIC_PER_PROTEIN)) - Kppc.*(PHOS_CYTOSOLIC_PER_PROTEIN) - dppc.*(PHOS_CYTOSOLIC_PER_PROTEIN);
%The Equations for phosphorylated CRY Protien in the Cytosol
dydt(13)= Kcc.*(CYTOSOLIC_CRY_PROTEIN) - Kcpc.*(PHOS_CYTOSOLIC_CRY_PROTEIN) - dcpc.*(PHOS_CYTOSOLIC_CRY_PROTEIN);
%The Equations for phosphorylated BMAL1 Protien in the Cytosol
dydt(14)= Kbc.*((CYTOSOLIC_BMAL1_PROTEIN)) - Kbpc.*(PHOS_CYTOSOLIC_BMAL1_PROTEIN) - dbpc.*(PHOS_CYTOSOLIC_BMAL1_PROTEIN);
%The Equations for phosphorylated ROR Protien in the Cytosol
dydt(15)= Krc.*((CYTOSOLIC_ROR_PROTEIN)) - Krpc.*(PHOS_CYTOSOLIC_ROR_PROTEIN) - drpc.*(PHOS_CYTOSOLIC_ROR_PROTEIN);
%The Equations for phosphorylated REV-ERB Protien in the Cytosol
dydt(16)= Krec.*((CYTOSOLIC_REV_ERB_PROTEIN)) - Krepc.*(PHOS_CYTOSOLIC_REV_ERB_PROTEIN) - drepc.*(PHOS_CYTOSOLIC_REV_ERB_PROTEIN);
%The Equations for phosphorylated PER-CRY Protien in the Cytosol
dydt(17)= Kpcp.*((CYTOSOLIC_PER_CRY_PROTEIN)) - Kpcpc.*(PHOS_CYTOSOLIC_PER_CRY_PROTEIN) - dpcpc.*(PHOS_CYTOSOLIC_PER_CRY_PROTEIN);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% EQUATIONS FOR PER, CRY, BMAL1, REV-ERB, ROR AND PER-CRY PROTEIN, CLOCK PROTEIN and
%CLOCK-BMAL1 PROTEIN IN THE NUCLEUS
% y(12)= BMAL1 PROTEIN, y(13) = CLOCK-BMAL1 PROTEIN and y(14) = PER-CRY PROTEIN IN THE
% NUCLEUS.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%The Equations for BMAL1 Protien in the Nucleus
dydt(18)= Kbcc.*(CYTOSOLIC_BMAL1_PROTEIN) - Kclbn.*(NUCLEAR_BMAL1_PROTEIN) - dbn.*(NUCLEAR_BMAL1_PROTEIN);
%The Equations for ROR Protien in the Nucleus
dydt(19)= Krcc.*(CYTOSOLIC_ROR_PROTEIN) - Krn.*(NUCLEAR_ROR_PROTEIN) - drn.*(NUCLEAR_ROR_PROTEIN);
%The Equations for REV-ERB Protien in the Nucleus
dydt(20)= Krecc.*(CYTOSOLIC_REV_ERB_PROTEIN) - Kren.*(NUCLEAR_REV_ERB_PROTEIN) - dren.*(NUCLEAR_REV_ERB_PROTEIN);
%The Equations for CLOCK-BMAL1 Protien in the Nucleus
dydt(21)= Kclbn.*(NUCLEAR_BMAL1_PROTEIN) - kcbpc.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN) + kdcbpc.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN) - dclbn.*(NUCLEAR_CLOCK_BMAL1_PROTEIN)+dpcn.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN);
%The Equations for PER-CRY Protien in the Nucleus
dydt(22)= Kpcc.*(CYTOSOLIC_PER_CRY_PROTEIN) - kcbpc.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN) + kdcbpc.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN) - dpcn.*(NUCLEAR_PER_CRY_PROTEIN)+dclbn.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN);
%The Equations for PER-CRY/CLOCK-BMAL1 Protien in the Nucleus
dydt(23)= kcbpc.*(NUCLEAR_CLOCK_BMAL1_PROTEIN).*(NUCLEAR_PER_CRY_PROTEIN) - kdcbpc.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN) - dclbn.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN)-dpcn.*(NUCLEAR_CLOCK_BMAL1_PER_CRY_PROTEIN);
end
function ss = new_ss1(p,data)
% sum-of-squares for the system.
% Function takes in the parameters
% as a vector p, data as the time and system values.
%
%
time = data.time; %time from the previous system
Aobs = data.ydata; % system values
y0=data.y0;
[~,y] = ode45(@new2,time,y0,[],p); %function to solve the ode
%with new parameters p
Amodel = y; %keep new system first values
ss = sum((Aobs - Amodel).^2); %sum of squares error of the new system and previous system
ss = ss(1);
end