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cody2 authored Jul 2, 2022
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%% N803_shared.m - solves model for 2 cohorts with shared parameters
%
% /--------------------------------------------------------------\
% | Date: 07/02/2022 |
% | Author: Jonathan Cody |
% | Affiliation: Purdue University |
% | Weldon School of Biomedical Engineering |
% | Pienaar Computational Systems Pharmacology Lab |
% \--------------------------------------------------------------/
%
% Nomenclature: V = SIV virions [#/無]
% T8 = total CD8+ T cells [#/無]
% E0 = resting SIV-specific CD8+ T cells [#/無]
% Ea = active SIV-specific CD8+ T cells [#/無]
% B0 = resting bystander CD8+ T cells [#/無]
% Ba = active bystander CD8+ T cells [#/無]
% X = N803 at absorption site [pmol/kg]
% C = N803 plasma concentration [pM]
% R = regulation [] (dimensionless quantity)
%
%% ========================================================================
% INPUTS
% ========================================================================
%
% SoluTimes = ascending vector of days at which to evaluate solution
%
% DoseTimes{c} = ascending vector of days at which to administer doses
% (elements of 'DoseTimes' must also be in 'SoluTimes')
%
% AllPars = vector of parameters (see list in function)
%
%% ========================================================================
% OPTIONS
% ========================================================================
%
% SkipTimes{c} = [min max] time point beyond which to skip model solving
% (outputs before 'min' will be made equal to output at 'min')
% (leave as [] to ignore and solve for all 'SoluTimes')
%
% oneCohort = scalar to run model for just one cohort ('1' or '2')
% (leave as [] to ignore and solve for both cohorts)
%
% All additional inputs will be passed as a cell vector to 'N803_model_2'
% and used to define options (see function for list)
% EX: N803_single(SoluTimes,DoseTimes,AllPars,'AbsTol',1e-2}
% will set ode solver absolute tolerance to 1e-2
%
%% ========================================================================
% OUTPUTS
% ========================================================================
%
% Y_OUT(:,1) = V at points in 'SoluTimes' [log fold change] cohort 1
% Y_OUT(:,2) = T8 at points in 'SoluTimes' [fold change] cohort 1
% Y_OUT(:,3) = V at points in 'SoluTimes' [log fold change] cohort 2
% Y_OUT(:,4) = T8 at points in 'SoluTimes' [fold change] cohort 2
%
% PARS(1,:) = parameters for cohort 1 (see code)
% PARS(2,:) = parameters for cohort 2 (see code)
%
%% ========================================================================
% FUNCTION
% ========================================================================
function [Y_OUT,PARS] = ...
N803_shared(SoluTimes,DoseTimes,AllPars,SkipTimes,oneCohort,...
varargin)

if isempty(oneCohort) ; RunCohort = [ 1 1 ] ;
elseif oneCohort == 1 ; RunCohort = [ 1 0 ] ;
else ; RunCohort = [ 0 1 ] ;
end

Y_Cohort = cell(1,2) ;% cell for storing outputs
P_Cohort = cell(1,2) ;% cell for storing parmeters

% Rename inputed parameters -----------------------------------------------
Vi(1) = AllPars(01) ;% V initial value [log(#/mL)] (cohort 1)
Vi(2) = AllPars(02) ;% V initial value [log(#/mL)] (cohort 2)
EBi(1) = AllPars(03) ;% E+B initial value [#/無] (cohort 1)
EBi(2) = AllPars(04) ;% E+B initial value [#/無] (cohort 2)
fE(1) = AllPars(05) ;% initial frequency: E/(E+B) (cohort 1)
fEn = AllPars(06) ;% normalized E/(E+B) (co 2)
fE(2) = fE(1)+(0.5-fE(1))*fEn ;% initial frequency: E/(E+B) (cohort 2)

q = AllPars(07) ;% V growth rate (if E+B were absent) [/d]
psi = AllPars(08) ;% ratio of base killing rates gB0/gE0
V50E = AllPars(09) ;% 50% viral stimulation saturation for E [#/mL]
V50B = AllPars(10) ;% 50% viral stimulation saturation for B [#/mL]
mEn = AllPars(11) ;% normalized Ea reversion rate constant []
mBn = AllPars(12) ;% normalized Ba reversion rate constant []

EB50 = AllPars(13) ;% 50% E+B proliferation saturation [#/無]
p0n = AllPars(14) ;% nomalized E0/B0 proliferation rate constant [/d]
pE = AllPars(15) ;% Ea proliferation rate constant [/d]
pB = AllPars(16) ;% Ba proliferation rate constant [/d]
d = AllPars(17) ;% E0/B0 death rate constant [/d]
dA = AllPars(18) ;% Ea/Ba death rate constant [/d]

Xi = AllPars(19) ;% X initial condition [pmol/kg]
ka = AllPars(20) ;% N803 absorption rate constant [/d]
ke = AllPars(21) ;% N803 elimination rate constant [/d]
vd = AllPars(22) ;% N803 'volume of distribution'/'bioavailability' [L/kg]
C50 = AllPars(23) ;% 50% N803 stimulation concentration [pM] (Cohort 1)
pm = AllPars(24) ;% E0/B0 maximum proliferation rate []
aE1 = AllPars(25) ;% E activation stimulation factor []
aB1 = AllPars(26) ;% B activation stimulation factor []

dR = AllPars(27) ;% R decay rate constant [/d]
sig = AllPars(28) ;% ratio of initial regulation due to B/E
p2 = AllPars(29) ;% E0/B0 proliferation regulation factor []
gB2 = AllPars(30) ;% B killing regulation factor [] (cohort 1)

%% ------------------------------------------------------------------------
% Calculate some initial conditions & parameters --------------------------

Vi = 10.^(Vi - 3) ;% converting V initial value [#/無]
V50E = V50E/1000 ;% 50% viral stimulation saturation for E [#/無]
V50B = V50B/1000 ;% 50% viral stimulation saturation for B [#/無]
YE = Vi ./ (Vi+ V50E) ;% initial V/(V50E+V) [cohort 1,2]
YB = Vi ./ (Vi+ V50B) ;% initial V/(V50B+V) [cohort 1,2]

% calculate initial R, and sE,sB
z = YE + sig*YB ;
Ri = [ 1 , (z(2)/z(1)) ] ;% initial regulation [cohort 1,2]
R = Ri(2) ;% initial regulation (cohort 2)
sE = dR / ( YE(1) + sig*YB(1) ) ;% R generation due to E0 activation [/d]
sB = sig*sE ;% R generation due to B0 activation [/d]

% restrict mE and mB such that initial activation aE and aB are positive
UE = (2*pE/(pE+dA))^7 ;
UB = 2*pB/(pB+dA) ;
mE = mEn*dA/(UE-1) ;% Ea reversion rate constant [/d]
mB = mBn*dA/(UB-1) ;% Ba reversion rate constant [/d]

% solve for initial ratios below (based on active steady-state)
ZE = UE/(mE+dA) ;
for i = 1:7
ZE = ZE + (2*pE)^(i-1)/(pE+dA)^i ;% EAi/aEi/E0i
end
ZB = 1/(pB+dA) + UB/(mB+dA) ;% BAi/aBi/B0i

WE = 1 ;
for i = 1:7
WE = WE + (mE+dA)*(pE+dA)^(i-1)/(2*pE)^i ;% EAi/E8i
end
WB = 1 + (mB+dA)/(2*pB) ;% BAi/B2i

QE = mE/WE - 1/ZE ;% collection
QB = mB/WB - 1/ZB ;% collection

% restrict p0 to ensure same sign for E0/EA and for B0/BA
p0_max = min( d*(1+p2*Ri).*(EB50+EBi)/EB50 ) ;% maximum value for p0
p0 = p0n * p0_max ;% E0/B0 prolif rate constant [/d]
p1 = pm/p0 ;% E0/B0 proliferation stimulation factor
pi = p0*EB50./(EB50+EBi)./(1+p2*Ri) ;% initial E0/B0 prolif rate [/d]

% calculate aE0,aB0 and aE2,aB2
aEi = (d-pi)/QE/ZE ;% initial E0 activation rate [/d]
aBi = (d-pi)/QB/ZB ;% initial B0 activation rate [/d]
z = aEi./YE ;
aE2 = ( z(1)-z(2) ) / ( R*z(2)-z(1) ) ;% E0 activation rate constant [/d]
aE0 = aEi(1) / YE(1) * (1+aE2) ;% E activation regulation factor []
z = aBi./YB ;
aB2 = ( z(1)-z(2) ) / ( R*z(2)-z(1) ) ;% B0 activation rate constant [/d]
aB0 = aBi(1) / YB(1) * (1+aB2) ;% B activation regulation factor []

% solve for initial values of E0,Ea,B0,Ba each cohort
Ei = EBi.*fE ;% initial E
Bi = EBi.*(1-fE) ;% initial B
E0 = Ei./(1+ZE*aEi) ;% initial E0
B0 = Bi./(1+ZB*aBi) ;% initial B0
EA = E0.*(ZE*aEi) ;% initial EA
BA = B0.*(ZB*aBi) ;% initial BA

% calculate gE0,gB0 and gE2
beta = psi * BA ./ (1+gB2*Ri) ; z = beta(1) - beta(2) ;
a = z*R ; b = EA(1)*R - EA(2) + z*(1+R) ; c = EA(1) - EA(2) + z ;
gE2 = ( -b + sqrt(b^2 - 4*a*c) ) / (2*a) ;% E killing regulation factor []
gE0 = q / ( EA(1)/(1+gE2) + beta(1) ) ;% Ea killing rate constant [無/#-d]
gB0 = psi * gE0 ;% Ba killing rate constant [無/#-d]

%% Do for each cohort (NOT indenting loop) ================================
for c = 1:2

% solve for initial E1-8 and B1-2
E = zeros(1,8) ;% initial E1-E8
E(8) = EA(c)/WE ;% E8
E(7) = E(8) * (mE+dA)/(2*pE) ;% E7
for i = 6:-1:1
E(i) = E(i+1) * (pE+dA) / (2*pE) ;% E6 to E1
end
B = BA(c)/WB * [ (mB+dA) / (2*pB) , 1 ] ;% initial B1-B2

%% ------------------------------------------------------------------------
% Prepare parameter and initial value vectors and call 'N803_model_2' -----

Pars(01) = q ;% V growth rate (if E+B were absent) [/d]
Pars(02) = gE0 ;% Ea killing rate constant [無/#-d]
Pars(03) = gB0 ;% Ba killing rate constant [無/#-d]

Pars(04) = V50E ;% 50% viral stimulation saturation for E [#/無]
Pars(05) = V50B ;% 50% viral stimulation saturation for B [#/無]
Pars(06) = aE0 ;% E0 activation rate constant [/d]
Pars(07) = aB0 ;% B0 activation rate constant [/d]
Pars(08) = mE ;% Ea reversion rate constant [/d]
Pars(09) = mB ;% Ba reversion rate constant [/d]

Pars(10) = EB50 ;% 50% E+B proliferation saturation [#/無]
Pars(11) = p0 ;% E0/B0 proliferation rate constant [/d]
Pars(12) = pE ;% Ea proliferation rate constant [/d]
Pars(13) = pB ;% Ba proliferation rate constant [/d]
Pars(14) = d ;% E0/B0 death rate constant [/d]
Pars(15) = dA ;% Ea/Ba death rate constant [/d]

Pars(16) = Xi ;% X initial condition [pmol/kg]
Pars(17) = ka ;% N803 absorption rate constant [/d]
Pars(18) = ke ;% N803 elimination rate constant [/d]
Pars(19) = vd ;% N803 'volume of distribution'/'bioavailability' [L/kg]
Pars(20) = C50 ;% 50% N803 stimulation concentration [pM]
Pars(21) = p1 ;% E0/B0 proliferation stimulation factor []
Pars(22) = aE1 ;% E activation stimulation factor []
Pars(23) = aB1 ;% B activation stimulation factor []

Pars(24) = sE ;% R generation due to E0 activation [/d]
Pars(25) = sB ;% R generation due to B0 activation [/d]
Pars(26) = dR ;% R decay rate constant [/d]
Pars(27) = gE2 ;% E killing regulation factor []
Pars(28) = gB2 ;% B killing regulation factor []
Pars(29) = p2 ;% E0/B0 proliferation regulation factor []
Pars(30) = aE2 ;% E activation regulation factor []
Pars(31) = aB2 ;% B activation regulation factor []

% V E0-8 B0-2 X C R initial values
Yic = [ Vi(c) E0(c) E B0(c) B 0 0 Ri(c) Ri(c) ] ;

if any( [ Pars Yic ] < 0 )
error('Negative parameters or initial values.')
end

% If 'SkipTimes' is empty, do not skip any times
if isempty(SkipTimes{c}) ; SkipTimes{c} = [-inf inf] ; end

idLo = SoluTimes < SkipTimes{c}(1) ;% index of early times to skip soln
idHi = SoluTimes > SkipTimes{c}(2) ;% index of later times to skip soln
idSol = ~ ( idLo | idHi ) ;% index of times in 'SoluTimes' to solve

if RunCohort(c) == 1
Y_COH = N803_model_2(SoluTimes(idSol),DoseTimes{c},Pars,Yic,varargin) ;
Y_LO = ones(sum(idLo),1)*Y_COH(1 ,:) ;% constant Y for early times
Y_HI = ones(sum(idHi),1)*Y_COH(end,:) ;% constant Y for later times
Y_COH = [ Y_LO ; Y_COH ; Y_HI ] ;%#ok<AGROW> % total 'solution' matrix
Y_Cohort{c} = Y_COH ;
P_Cohort{c} = [ Pars Yic ] ;
end

end

%% Prepare main outputs 'Y_OUT' and 'PARS' ================================

Y_OUT = [ Y_Cohort{1} , Y_Cohort{2} ] ;
PARS = [ P_Cohort{1} ; P_Cohort{2} ] ;

end

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