Mathematical Modeling Matlab Codefor Fig. S5

Supporting Dataset

Mathematical Modeling Matlab Codefor Fig. S5.

p.kex = 2.5e-5;

p.kt = 2.5e-5;

p.kmt = 1e-3;

p.VtVb= 0.05;

p.ka = 2336.4*0.6;

p.kma = p.ka*(381.4e-9);

p.kb = 2336.4*2;

p.kmb = p.kb*(31.3e-9);

p.VR = 100;

% p.kint= 0; %2.5e-6;

p.knon= 3e-5;

p.kmnon= 3e-6;

p.RTaC0 = 1e-8;

p.RTbC0 = 18*p.RTaC0;

p.RNaC0 = 0;

p.RNbC0 = 19*p.RTaC0;

p.RTaM0 = 1e-8;

p.RTbM0 = 18*p.RTaC0;

p.RNaM0 = 24*p.RTaC0;

p.RNbM0 = 0;

p.dose = 2.5e-9;

p.Vb = 0.5;

p.tf=48*3600;

p.CBC = p.dose/p.Vb;

p.CTuC = 0;

p.CTaC = 0;

p.CTbC = 0;

p.CTabC= 0;

p.CTintC=0;

p.CTnonC=0;

p.CNuC = 0;

p.CNaC = 0;

p.CNbC = 0;

p.CNabC= 0;

p.CNintC=0;

p.CNnonC=0;

p.CBM = p.dose/p.Vb;

p.CTuM = 0;

p.CTaM = 0;

p.CTbM = 0;

p.CTabM= 0;

p.CTintM=0;

p.CTnonM=0;

p.CNuM = 0;

p.CNaM = 0;

p.CNbM = 0;

p.CNabM= 0;

p.CNintM=0;

p.CNnonM=0;

y0=[p.CBC p.CTuC p.CTaC p.CTbC p.CTabC p.CTnonC p.CNuC p.CNaC p.CNbC p.CNabC p.CNnonC p.CBM p.CTuM p.CTaM p.CTbM p.CTabM p.CTnonM p.CNuM p.CNaM p.CNbM p.CNabM p.CNnonM];

%y0=[p.CB p.CTu p.CTa p.CTb p.CTab p.CTint p.CTnon p.CNu p.CNa p.CNb p.CNab p.CNint p.CNnon];

options = odeset('AbsTol', 1e-10, 'RelTol', 1e-7);

[t y] = ode15s(@modelhighrhs, [0 p.tf], y0, options, p);

CCKdata = [0 0 0; 14400 7.13 6.17; 86400 3.59 3.47; 172800 4.07 3.96];

MC1Rdata = [0 0 0; 14400 8.09 1.1; 86400 5.1 1.4; 172800 3.91 0.83];

TtotalC = y(:,2)+y(:,3)+y(:,4)+y(:,5)+y(:,6); %+y(:,7);

NtotalC = y(:,7)+y(:,8)+y(:,9)+y(:,10)+y(:,11); %+y(:,13);

RTaC = p.RTaC0 - y(:,3) - y(:,5);

RTbC = p.RTbC0 - y(:,4) - y(:,5);

TtotalM = y(:,13)+y(:,14)+y(:,15)+y(:,16)+y(:,17); %+y(:,7);

NtotalM = y(:,18)+y(:,19)+y(:,20)+y(:,21)+y(:,22); %+y(:,13);

RTaM = p.RTaM0 - y(:,14) - y(:,16);

RTbM = p.RTbM0 - y(:,15) - y(:,16);

SpecC = TtotalC ./ NtotalC;

SpecM = TtotalM ./ NtotalM;

figure(1);

subplot(2,2,1), plot (CCKdata(:,1), CCKdata(:,2))

title('Data: CCK tumor')

subplot(2,2,2), plot (t, TtotalC)

title('Model: CCK tumor')

subplot(2,2,3), plot (CCKdata(:,1), CCKdata(:,3))

title('Data: CCK control')

subplot(2,2,4), plot (t, NtotalC)

title('Model: CCK control');

figure(2)

subplot(2,2,1), plot (MC1Rdata(:,1), MC1Rdata(:,2))

title('Data: MC1R tumor')

subplot(2,2,2), plot (t, TtotalM)

title('Model: MC1R tumor')

subplot(2,2,3), plot (MC1Rdata(:,1), MC1Rdata(:,3))

title('Data: MC1R control')

subplot(2,2,4), plot (t, NtotalM)

title('Model: MC1R control');

figure(3);

subplot(2,2,1), plot (t, y(:,2))

title('Model: CTuC')

subplot(2,2,2), plot (t, y(:,3))

title('Model: CTaC')

subplot(2,2,3), plot (t, y(:,4))

title('Model: CTbC')

subplot(2,2,4), plot (t, y(:,5))

title('Model: CTabC');

figure(4);

subplot(2,2,1), plot (t, y(:,7))

title('Model: CNuC')

subplot(2,2,2), plot (t, y(:,8))

title('Model: CNaC')

subplot(2,2,3), plot (t, y(:,9))

title('Model: CNbC')

subplot(2,2,4), plot (t, y(:,10))

title('Model: CNabC');

figure(5);

subplot(2,2,1), plot (t, y(:,13))

title('Model: CTuC')

subplot(2,2,2), plot (t, y(:,14))

title('Model: CTaC')

subplot(2,2,3), plot (t, y(:,15))

title('Model: CTbC')

subplot(2,2,4), plot (t, y(:,16))

title('Model: CTabC');

figure(6);

subplot(2,2,1), plot (t, y(:,18))

title('Model: CNuC')

subplot(2,2,2), plot (t, y(:,19))

title('Model: CNaC')

subplot(2,2,3), plot (t, y(:,20))

title('Model: CNbC')

subplot(2,2,4), plot (t, y(:,21))

title('Model: CNabC');

figure(5);

subplot(2,2,1), plot (t, RTaC)

title('Model: RTaC')

subplot(2,2,2), plot (t, RTbC)

title('Model: RTbC')

subplot(2,2,3), plot (t, RTaM)

title('Model: RTaM')

subplot(2,2,4), plot (t, RTbM)

title('Model: RTbM');

% plot (t, y(:,1));

% xlabel ('Time'); ylabel ('Blood conc'); title ('Model CCK');

%

% figure(2);

% plot (t, Ttotal);

% xlabel ('Time'); ylabel ('Ttotal CCK model'); title ('Model CCK');

%

% figure(3);

% plot (CCKdata(:,1), CCKdata(:,3));

% xlabel ('Time'); ylabel ('CCK data control'); title ('Data CCK');

%

% figure(4);

% plot (t, Ntotal);

% xlabel ('Time'); ylabel ('Ntotal CCK model'); title ('Model CCK');

%

% figure(5);

% plot (t, y(:,7));

% xlabel ('Time'); ylabel ('Ntu'); title ('Concentration in Control');

%

% figure(6);

% plot (t, y(:,3));

% xlabel ('Time'); ylabel ('Ntotal'); title ('Concentration in Control');

% figure(7);

% plot (t, y(:,4));

% xlabel ('Time'); ylabel ('Ntotal'); title ('Concentration in Control');

% figure(8);

% plot (t, y(:,5));

% xlabel ('Time'); ylabel ('Ntotal'); title ('Concentration in Control');

% figure(8);

% plot (t, y(:,7));

% xlabel ('Time'); ylabel ('Ntotal'); title ('Concentration in Control');

% figure(4);

% plot (t, Spec);

% xlabel ('Time'); ylabel ('Specificity'); title ('Specificity');

function yp = modellowrhs (t, y, p);

CBC = y(1);

CTuC = y(2);

CTaC = y(3);

CTbC = y(4);

CTabC= y(5);

% CTint=y(6);

CTnonC=y(6);

CNuC = y(7);

CNaC = y(8);

CNbC = y(9);

CNabC= y(10);

% CNint=y(12);

CNnonC=y(11);

CBM = y(12);

CTuM = y(13);

CTaM = y(14);

CTbM = y(15);

CTabM= y(16);

% CTint=y(6);

CTnonM=y(17);

CNuM = y(18);

CNaM = y(19);

CNbM = y(20);

CNabM= y(21);

% CNint=y(12);

CNnonM=y(22);

yp=y;

RTaC = p.RTaC0 - CTaC - CTabC;

RTbC = p.RTbC0 - CTbC - CTabC;

RNaC = p.RNaC0 - CNaC - CNabC;

RNbC = p.RNbC0 - CNbC - CNabC;

RTaM = p.RTaM0 - CTaM - CTabM;

RTbM = p.RTbM0 - CTbM - CTabM;

RNaM = p.RNaM0 - CNaM - CNabM;

RNbM = p.RNbM0 - CNbM - CNabM;

%dCB/dt

yp(1) = -p.kex*CBC - 2*p.kt*CBC + p.kmt*CTuC*p.VtVb + p.kmt*CNuC*p.VtVb;

%

% %dCTu/dt

yp(2) = p.kt*CBC*(1/p.VtVb) - p.kmt*CTuC - p.ka*CTuC*RTaC + p.kma*CTaC - p.kb*CTuC*RTbC + p.kmb*CTbC;

%

% %dCTa/dt

yp(3) = p.ka*CTuC*RTaC - p.kma*CTaC - p.kb*CTaC*RTbC*p.VR + p.kmb*CTabC; % - p.kint*CTa;

%

% %dCTb/dt

yp(4) = p.kb*CTuC*RTbC - p.kmb*CTbC - p.ka*CTbC*RTaC*p.VR + p.kma*CTabC; % - p.kint*CTb;

%

% %dCTab/dt

yp(5) = p.kb*CTaC*RTbC*p.VR - p.kmb*CTabC + p.ka*CTbC*RTaC*p.VR - p.kma*CTabC; % - p.kint*CTab;

%

% %dCTint/dt

%yp(6) = p.kint*(CTa + CTb + CTab);

%dCTnon/dt

yp(6) = p.knon*CTuC - p.kmnon*CTnonC;

%

% %dCNu/dt

yp(7) = p.kt*CBC*(1/p.VtVb) - p.kmt*CNuC - p.ka*CNuC*RNaC + p.kma*CNaC - p.kb*CNuC*RNbC + p.kmb*CNbC;

%

% %dCNa/dt

yp(8) = p.ka*CNuC*RTaC - p.kma*CNaC - p.kb*CNaC*RNbC*p.VR + p.kmb*CNabC; % - p.kint*CNa;

%

% %dCNb/dt

yp(9) = p.kb*CNuC*RNbC - p.kmb*CNbC - p.ka*CNbC*RNaC*p.VR + p.kma*CNabC; % - p.kint*CNb;

%

% %dCNab/dt

yp(10) = p.kb*CNaC*RNbC*p.VR - p.kmb*CNabC + p.ka*CNbC*RNaC*p.VR - p.kma*CNabC; % - p.kint*CNab;

%

% %dCNint/dt

%yp(12) = p.kint*(CNa + CNb + CNab);

%dCNnon/dt

yp(11) = p.knon*CNuC - p.kmnon*CNnonC;

%MC1R model...

%dCB/dt

yp(12) = -p.kex*CBM - 2*p.kt*CBM + p.kmt*CTuM*p.VtVb + p.kmt*CNuM*p.VtVb;

%

% %dCTu/dt

yp(13) = p.kt*CBM*(1/p.VtVb) - p.kmt*CTuM - p.ka*CTuM*RTaM + p.kma*CTaM - p.kb*CTuM*RTbM + p.kmb*CTbM;

%

% %dCTa/dt

yp(14) = p.ka*CTuM*RTaM - p.kma*CTaM - p.kb*CTaM*RTbM*p.VR + p.kmb*CTabM; % - p.kint*CTa;

%

% %dCTb/dt

yp(15) = p.kb*CTuM*RTbM - p.kmb*CTbM - p.ka*CTbM*RTaM*p.VR + p.kma*CTabM; % - p.kint*CTb;

%

% %dCTab/dt

yp(16) = p.kb*CTaM*RTbM*p.VR - p.kmb*CTabM + p.ka*CTbM*RTaM*p.VR - p.kma*CTabM; % - p.kint*CTab;

%

% %dCTint/dt

%yp(6) = p.kint*(CTa + CTb + CTab);

%dCTnon/dt

yp(17) = p.knon*CTuM - p.kmnon*CTnonM;

%

% %dCNu/dt

yp(18) = p.kt*CBM*(1/p.VtVb) - p.kmt*CNuM - p.ka*CNuM*RNaM + p.kma*CNaM - p.kb*CNuM*RNbM + p.kmb*CNbM;

%

% %dCNa/dt

yp(19) = p.ka*CNuM*RTaM - p.kma*CNaM - p.kb*CNaM*RNbM*p.VR + p.kmb*CNabM; % - p.kint*CNa;

%

% %dCNb/dt

yp(20) = p.kb*CNuM*RNbM - p.kmb*CNbM - p.ka*CNbM*RNaM*p.VR + p.kma*CNabM; % - p.kint*CNb;

%

% %dCNab/dt

yp(21) = p.kb*CNaM*RNbM*p.VR - p.kmb*CNabM + p.ka*CNbM*RNaM*p.VR - p.kma*CNabM; % - p.kint*CNab;

%

% %dCNint/dt

%yp(12) = p.kint*(CNa + CNb + CNab);

%dCNnon/dt

yp(22) = p.knon*CNuM - p.kmnon*CNnonM;

1