diff --git a/N803_model_2.m b/N803_model_2.m index 50252c8..0d9edd9 100644 --- a/N803_model_2.m +++ b/N803_model_2.m @@ -2,14 +2,14 @@ % and NK cells during a subcutaneously administered regimen of N803 % /--------------------------------------------------------------\ -% | Date: 07/12/2021 | +% | Date: 07/13/2021 | % | Author: Jonathan Cody | % | Affiliation: Pienaar Computational Systems Pharmacology Lab | % | Weldon School of Biomedical Engineering | % | Purdue University | % \--------------------------------------------------------------/ -% -% Version 2A + +% Version 2B % % Nomenclature: V = SIV virions [#/無] % K = NK cells [#/無] @@ -71,10 +71,11 @@ %% ------------------------------------------------------------------------ % Rename inputed parameters ----------------------------------------------- -Vi = Pars(01) ;% V initial condition [log(#/mL)] -Ki = Pars(02) ;% K initial condition [#/無] -Ei = Pars(03) ;% E initial condition [#/無] -fEA = Pars(04) ;% active E initial frequency +Vi = 10^(Pars(01)-3) ;% V initial condition [#/無] +Ki = Pars(02) ;% K initial condition [#/無] +Ei = Pars(03) ;% E initial condition [#/無] +E0i = Ei*(1-Pars(04)) ;% E0 initial condition [#/無] +EAi = Ei*( Pars(04)) ;% EA initial condition [#/無] (sum of E1 to E8) gK_Ki = Pars(05)*Pars(06) ;% K initial killing rate [/d] gE_EAi = Pars(06) ;% E initial killing rate [/d] @@ -97,25 +98,22 @@ rE1_d0 = Pars(21) ;% E0 maximum growth rate [/d] a1 = Pars(22) ;% E activation stimulation factor [] -dR = Pars(23) ;% regulation decay rate constant [/d] -rK2 = Pars(24) ;% K proliferation regulation factor [] -rE2 = Pars(25) ;% E0 proliferation regulation factor [] -a2 = Pars(26) ;% E activation regulation factor [] +A50 = Pars(23)*EAi ;% EA half-saturation for R activation [#/uL] +dR = Pars(24) ;% regulation decay rate constant [/d] +rK2 = Pars(25) ;% K proliferation regulation factor [] +rE2 = Pars(26) ;% E0 proliferation regulation factor [] +a2 = Pars(27) ;% E activation regulation factor [] -N = Pars(27) ;% # of tolerance variables (delays + acting) -del = Pars(28) ;% tolerance rate constant [/d] -tau = Pars(29) ;% tolerance recovery [] -eta = Pars(30) ;% tolerance effect factor [] +N = Pars(28) ;% # of tolerance variables (delays + acting) +del = Pars(29) ;% tolerance rate constant [/d] +tau = Pars(30) ;% tolerance recovery [] +eta = Pars(31) ;% tolerance effect factor [] %% ------------------------------------------------------------------------ % Declare initial conditions & calculated parameters ---------------------- % some parameters are solved for by assuming an initially steady state -Vi = 10^(Vi-3) ;% V initial condition [#/無] -E0i = Ei*(1-fEA) ;% E0 initial condition [#/無] -EAi = Ei*( fEA) ;% EA initial condition [#/無] (sum of E1 to E8) - F5i = Vi/(Vi+V50) / (1+a2) ;% initial E activation rate modifiers [] % solve for activation rate a [/d] and E1 to E8 initial conditions [#/無] @@ -134,7 +132,7 @@ rE = (1+rE2) * (Em+Ei)/Em * ( d0 + a*F5i - fm*dA*sol(9)/E0i ) ;% E0 prolif rK1 = rK1_dK/dK ;% K proliferation stimulation factor [] rE1 = rE1_d0/d0 ;% E0 proliferation stimulation factor [] -psi = dR/F5i ;% R generation rate constant [/d] +psi = dR*(A50+EAi)/EAi ;% R generation rate constant [/d] % declare initial conditions for Y (see 'system' function) % V K E0 E1-8 X C R tolerance @@ -192,7 +190,7 @@ dY(11) = 2*p*EA(7) - dA*EA(8) ;% dE8/dt dY(12) = - ka*X ;% dX/dt dY(13) = ka*X/vd - ke*C ;% dC/dt - dY(14) = psi*F(15) - dR*R ;% dR/dt + dY(14) = psi*F(16) - dR*R ;% dR/dt % calculate rates of change for tolerance if N ~= 0 @@ -211,6 +209,7 @@ V = Y(:,01) ;% SIV virions [#/無] K = Y(:,02) ;% NK cells [#/無] E = sum(Y(:,03:11),2) ;% CD8+ T cells [#/無] + EA = sum(Y(:,04:11),2) ;% active CD8+ T cells [#/無] C = Y(:,13) ;% N803 plasma concentration [pM] R = Y(:,14) ;% immune regulation [] T = Y(:,13+N)+Y(:,14+N) ;% drug tolerance [] @@ -221,18 +220,19 @@ F(:,01) = C ./ (C50+C) ;% N803 effect [] F(:,02) = 1 ./ (1+eta*T) ;% tolerance effect [] F(:,03) = F(:,1) .* F(:,2) ;% N803 effect (with tolerance) [] - F(:,04) = 1 + rK1*F(:,3) ;% K proliferation stimulation [] - F(:,05) = 1 + rE1*F(:,3) ;% E0 proliferation stimulation [] - F(:,06) = 1 + a1*F(:,3) ;% activation stimulation [] - F(:,07) = 1 ./ (1+rK2*R) ;% K proliferation regulation [] - F(:,08) = 1 ./ (1+rE2*R) ;% E0 proliferation regulation [] - F(:,09) = 1 ./ (1+ a2*R) ;% activation regulation [] - F(:,10) = Km./ (Km +K) ;% K proliferation density dependence [] - F(:,11) = Em./ (Em +E) ;% E0 proliferation density dependence [] + F(:,04) = 1 + rK1*F(:,3) ;% K proliferation stimulation [] + F(:,05) = 1 + rE1*F(:,3) ;% E proliferation stimulation [] + F(:,06) = 1 + a1*F(:,3) ;% E activation stimulation [] + F(:,07) = 1 ./ (1+rK2*R) ;% K proliferation regulation [] + F(:,08) = 1 ./ (1+rE2*R) ;% E proliferation regulation [] + F(:,09) = 1 ./ (1+ a2*R) ;% E activation regulation [] + F(:,10) = Km./ (Km +K) ;% K proliferation density dependence [] + F(:,11) = Em./ (Em +E) ;% E proliferation density dependence [] F(:,12) = V ./ (V50+V) ;% activation antigen dependence [] - F(:,13) = F(:,4) .* F(:,7) .* F(:,10) ;% K proliferation modifier [] - F(:,14) = F(:,5) .* F(:,8) .* F(:,11) ;% E0 proliferation modifier [] - F(:,15) = F(:,6) .* F(:,9) .* F(:,12) ;% activation modifier [] + F(:,13) = F(:,4) .* F(:,7) .* F(:,10) ;% K proliferation modifier [] + F(:,14) = F(:,5) .* F(:,8) .* F(:,11) ;% E proliferation modifier [] + F(:,15) = F(:,6) .* F(:,9) .* F(:,12) ;% E activation modifier [] + F(:,16) = EA./ (A50+EA) ;% R activation modifier [] end @@ -260,25 +260,26 @@ Y_OUT(:,8) = Y(:,14) ;% R [] Y_OUT(:,9) = (Y(:,13+N)+Y(:,14+N)) * (N~=0) ;% T [] -F = terms(Y) ;% modifiers for 'rK','rE','a' +F = terms(Y) ;% modifiers for 'rK','rE','a' Y_OUT(:,10) = F(:,01) ;% N803 effect [] Y_OUT(:,11) = F(:,02) ;% tolerance effect [] Y_OUT(:,12) = F(:,03) ;% N803 effect (with tolerance) [] -Y_OUT(:,13) = F(:,04) ;% K proliferation stimulation [] -Y_OUT(:,14) = F(:,05) ;% E0 proliferation stimulation [] -Y_OUT(:,15) = F(:,06) ;% activation stimulation [] -Y_OUT(:,16) = F(:,07)/F(1,07) ;% K proliferation regulation [fold change] -Y_OUT(:,17) = F(:,08)/F(1,08) ;% E0 proliferation regulation [fold change] -Y_OUT(:,18) = F(:,09)/F(1,09) ;% activation regulation [fold change] -Y_OUT(:,19) = F(:,10)/F(1,10) ;% K prolif density dependence [fold change] -Y_OUT(:,20) = F(:,11)/F(1,11) ;% E0 prolif density dependence [fold change] -Y_OUT(:,21) = F(:,12)/F(1,12) ;% activ antigen dependence [fold change] -Y_OUT(:,22) = F(:,13)/F(1,13) ;% K proliferation modifier [fold change] -Y_OUT(:,23) = F(:,14)/F(1,14) ;% E0 proliferation modifier [fold change] -Y_OUT(:,24) = F(:,15)/F(1,15) ;% activation modifier [fold change] +Y_OUT(:,13) = F(:,04) ;% K proliferation stimulation [] +Y_OUT(:,14) = F(:,05) ;% E proliferation stimulation [] +Y_OUT(:,15) = F(:,06) ;% E activation stimulation [] +Y_OUT(:,16) = F(:,07)/F(1,07) ;% K proliferation regulation [fold change] +Y_OUT(:,17) = F(:,08)/F(1,08) ;% E proliferation regulation [fold change] +Y_OUT(:,18) = F(:,09)/F(1,09) ;% E activation regulation [fold change] +Y_OUT(:,19) = F(:,10)/F(1,10) ;% K prolif density dependence [fold change] +Y_OUT(:,20) = F(:,11)/F(1,11) ;% E prolif density dependence [fold change] +Y_OUT(:,21) = F(:,12)/F(1,12) ;% E activ antigen dependence [fold change] +Y_OUT(:,22) = F(:,13)/F(1,13) ;% K proliferation modifier [fold change] +Y_OUT(:,23) = F(:,14)/F(1,14) ;% E proliferation modifier [fold change] +Y_OUT(:,24) = F(:,15)/F(1,15) ;% E activation modifier [fold change] +Y_OUT(:,25) = F(:,16)/F(1,16) ;% R activation modifier [fold change] % NK killing proportion -Y_OUT(:,25) = gK*Y(:,2) ./ ( gK*Y(:,2) + gE*sum(Y(:,04:11),2) ) ; +Y_OUT(:,26) = gK*Y(:,2) ./ ( gK*Y(:,2) + gE*sum(Y(:,04:11),2) ) ; end \ No newline at end of file