S1: Code for CMV Example in Vitro Neutralization Experiment

Supplemental Materials S1: code for CMV example in vitro neutralization experiment

;Dosing specifications STARTTIME = 0 ;simulation start time [d] STOPTIME = (1+3+24)/24 ;simulation stop time [d] DTMAX = 0.001 ;[d] TD1 = DTMAX ;[d] ?time first dose started?

Conc = 0 ;mAb concentration [ug/mL] Vpl = 50 /1e6 ;plate volume [L] Dose1 = Conc*Vpl ;[mg] Tau1 = 140 ;dosing interval [d] NDoses1 = STOPTIME/Tau1 ;number of doses at Dose1

;mAb properties ; molecular weight, IgG MWD = 150000/1e6 ;[mg/nmole] ; number of mAb binding affinities N = 5 ; dissociation constants (Kd = koff/kon), D-L complex Kd[1] = 0.001 ;[nM] Kd[2] = 0.03 ;[nM] Kd[3] = 0.1 ;[nM] Kd[4] = 0.5 ;[nM], A233 Kd[5] = 1 ;[nM] ; association rate constants, D-L complex kon = 100 ;[1/(nM d)] ; dissociation rate constants, D-L complex koff[1..N] = Kd[i]*kon ;[1/d]

;Virus (ligand, L) biology ; molecular weight, CMV g/mol = mg/mmol * mmol/1e6 nmol MWV = 1e8/1e6 ;[mg/nmol]

; endogenous virus concentration n_bs = 100 ;number of binding sites on virus surface Vn = 5000 /Vpl/1000 ;total initial number of CMV, [copies/mL] L0 = Vn*n_bs*Vpl/6e11 ; initial mol of CMV [nmol]

; viral load model parameters HL = 1 ;CMV half-life [d] kL = logn(2)/HL ;CMV elimination rate constant [1/d] HIC = 4 ;infected cell half-life [d] kIC = logn(2)/HIC ;infected cell elimination rate constant [1/d] HTC = 30 ;target cell half-life [d] (assume) kTC = logn(2)/HTC ;target cell elimination rate constant [1/d] TC0 = 0 *Vpl/6e11 ;target cell initial concentration [nM] sTC = 0 ;target cell synthesis rate constant [nmol/d] ki = 1.2e-6 *6e11 ;virus infection rate [1/(nM d)] pV = 100 ;virus production rate [/d]

; clearance of D-L complexes, assume D-L complexes are eliminated as fast as virus kDL = kL ;[1/d]

;Solver specifications METHOD STIFF DTMIN = 0.001 DTOUT = 0 TOLERANCE = 1e-3

;Input doses of antibody drug as pulse dose 1 IN1[1..N] = PULSE(Dose1/MWD,TD1,Tau1) TC1 = PULSE(1e4/6e14,1/24,Tau1) EmptyD[1..N] = PULSE(D[i]*4,4/24,Tau1) ; for washout EmptyL[1..N] = PULSE(L[i]*4,4/24,Tau1) EmptyDL[1..N] = PULSE(DL[i]*4,4/24,Tau1)

;Inital conditions ; [nmol] INIT(D[1..N]) = 0 INIT(L[1..N]) = L0 INIT(DL[1..N]) = 0 INIT(TC[1..N]) = TC0 INIT(IC[1..N]) = 0

;Mass balances d/dt(D[1..N]) = IN1[i] -kon/Vpl*D[i]*L[i]/n_bs +koff[i]*DL[i] -EmptyD[i] d/dt(L[1..N]) = -kL*L[i] -kon/Vpl*D[i]*L[i]/n_bs +koff[i]*DL[i] +pV*IC[i]*n_bs -EmptyL[i] d/dt(DL[1..N]) = -kDL*DL[i] +kon/Vpl*D[i]*L[i]/n_bs -koff[i]*DL[i] -EmptyDL[i] d/dt(TC[1..N]) = TC1 +sTC -kTC*TC[i] -(1-inhibition[i])*ki*L[i]*TC[i]/Vpl/n_bs d/dt(IC[1..N]) = (1-inhibition[i])*ki*L[i]*TC[i]/Vpl/n_bs -kIC*IC[i]

; Ligand occupancy rate affect the inhibition rate of infection X1 = 0.3 X2 = 0.9 a = 1/(X2-X1) b = -X1/(X2-X1) ;D-L/(D-L + L) occupancy rate occupancy[1..N] = DL[i]/(DL[i]+L[i]) inhibition[1..N] = IF occupancy[i]<=X1 THEN 0 ELSE IF occupancy[i]>X2 THEN 1 ELSE a*occupancy[i]+b

;Drug concentrations ;free mAb in plasma [µg/mL, mg/L] CFD[1..N] = MWD*D[i]/Vpl ;total mAb in plasma [µg/mL, mg/L] CTD[1..N] = MWD*(D[i]+DL[i])/Vpl ;free virus concentration in plasma CFV[1..N] = L[i]/Vpl*6e11/n_bs ;[copies/mL] ;uninfected cell concentration in plasma CTC[1..N] = TC[i]/Vpl*6e11 ;[copies/mL] ;infected cell concentration in plasma CIC[1..N] = IC[i]/Vpl*6e11 ;[copies/mL]

RI[1..N] = IF IC[i]+TC[i]=0 THEN 0 ELSE IC[i]/(IC[i]+TC[i])/0.453

2 S2: code for CMV example in human

;Dosing specifications STARTTIME = 0 ;simulation start time [d] STOPTIME = 100 ;simulation stop time [d] DTMAX = 0.001 ;[d] TD1 = DTMAX ;[d] Dose1 = 1 ;[mg/kg] Tau1 = 28 ;dosing interval [d] NDoses1 = STOPTIME/Tau1 ;number of doses at Dose1

;Pharmacokinetic parameters, human (70 kg) WT = 70 ;body weight [kg] CLD = 0.2 ;clearance of free mAb, IgG [L/d] Vpl = 2.5 ;plasma volume [L] Vti = 2.6 ;tissue interstitial volume [L] PS = 0.5 ; plasma-tissue exchange, IgG [L/d]

;mAb properties ; molecular weight, IgG MWD = 150000/1e6 ;[mg/nmole] ; number of mAb binding affinities N = 5 ; dissociation constants (Kd = koff/kon), D-L complex Kd[1] = 0.001 ;[nM] Kd[2] = 0.03 ;[nM] Kd[3] = 0.1 ;[nM] Kd[4] = 0.5 ;[nM] Kd[5] = 1 ;[nM] ; association rate constants, D-L complex kon = 100 ;[1/(nM d)] ; dissociation rate constants, D-L complex koff[1..N] = Kd[i]*kon ;[1/d]

;Virus (ligand, L) biology ; molecular weight, CMV g/mol = mg/mmol * mmol/1e6 nmol MWV = 1e8/1e6 ;[mg/nmol]

; virus parameters n_bs = 100 ;number of binding sites on virus surface Vn = 1 ;total initial number of CMV, [copies/mL] L0 = Vn*n_bs*Vpl/6e11 ; initial mol of CMV [nmol]

; viral load model parameters HL = 1 ;CMV half-life [d] kL = logn(2)/HL ;CMV elimination rate constant [1/d] HIC = 4 ;infected cell half-life [d] kIC = logn(2)/HIC ;infected cell elimination rate constant [1/d] HTC = 30 ;target cell half-life [d] kTC = logn(2)/HTC ;target cell elimination rate constant [1/d] TC0 = 1e5 *Vpl/6e11 ;target cell initial concentration [nM] sTC = TC0*kTC ;target cell synthesis rate constant [nmol/d] ki = 1.2e-6 *6e11 ;virus infection rate [1/(nM d)] pV = 100 ;virus production rate [/d]

; clearance of D-L complexes, assume D-L complexes are eliminated as fast as virus kDL = kL ;[1/d]

;Solver specifications METHOD STIFF DTMIN = 0.001 DTOUT = 0 TOLERANCE = 1e-3

3 ;Input doses of antibody drug as pulse dose. IN1[1..N] = PULSE(Dose1*WT/MWD,TD1,Tau1)

;Inital conditions ; [nmol] INIT(D[1..N]) = 0 INIT(Dti[1..N]) = 0 INIT(L[1..N]) = L0 INIT(DL[1..N]) = 0 INIT(TC[1..N]) = TC0 INIT(IC[1..N]) = 0

;Mass balances d/dt(D[1..N]) = IN1[i]-CLD/Vpl*D[i]+PS*(Dti[i]/Vti-D[i]/Vpl) -kon/Vpl*D[i]*L[i]/n_bs +koff[i]*DL[i] d/dt(Dti[1..N]) = PS*(D[i]/Vpl-Dti[i]/Vti)-CLD/Vti*Dti[i] d/dt(L[1..N]) = -kL*L[i] -kon/Vpl*D[i]*L[i]/n_bs +koff[i]*DL[i] +pV*IC[i]*n_bs d/dt(DL[1..N]) = -kDL*DL[i] +kon/Vpl*D[i]*L[i]/n_bs -koff[i]*DL[i] d/dt(TC[1..N]) = sTC -kTC*TC[i] -(1-inhibition[i])*ki*L[i]*TC[i]/Vpl/n_bs d/dt(IC[1..N]) = (1-inhibition[i])*ki*L[i]*TC[i]/Vpl/n_bs -kIC*IC[i]

; Ligand occupancy rate affect the inhibition rate of infection X1 = 0.3 X2 = 0.9 a = 1/(X2-X1) b = -X1/(X2-X1) ;D-L/(D-L + L) occupancy rate occupancy[1..N] = DL[i]/(DL[i]+L[i]) inhibition[1..N] = IF occupancy[i]<=X1 THEN 0 ELSE IF occupancy[i]>X2 THEN 1 ELSE a*occupancy[i]+b

;Drug concentrations ;free mAb in plasma [µg/mL, mg/L] CFD[1..N] = MWD*D[i]/Vpl ;total mAb in plasma [µg/mL, mg/L] CTD[1..N] = MWD*(D[i]+DL[i])/Vpl ;free virus concentration in plasma CFV[1..N] = L[i]/Vpl*6e11/n_bs ;[copies/mL] log10V[1..N] = log10(CFV[i]) ;uninfected cell concentration in plasma CTC[1..N] = TC[i]/Vpl*6e11 ;[copies/mL] ;infected cell concentration in plasma CIC[1..N] = IC[i]/Vpl*6e11 ;[copies/mL]

4 S3: code for target cell receptor example in monkey

;Trial specifications for Dose-Range Finding study in monkey (single intravenous dose) STARTTIME = -10 ;days STOPTIME = 70 ;days N=4 ;number of dose levels Dose[1]= xx ;mg/kg Dose[2]= xx ;mg/kg Dose[3] = xx ;mg/kg Dose[4] = xx ;mg/kg Tau = 14 ;days. dosing interval, not used here NDoses = 1 ;number of administered doses, here one for single dose

;Receptor target and cell turnover NRB = xx ;receptor number per cell NBC = xx ;target cell number per liter of blood in absence of drug Avog= 6.023e23 ;Avogadro's number R0 = NRB*NBC/Avog*1e9 ;nM. baseline receptor concentration in blood THR = xx ;day. receptor half-life kout = logn(2)/THR ;per day. Elimination rate of target cells without drug. kin = R0*Vbl*kout ;nmole/day. Constant target cell synthesis/entrance rate in blood R0[1..N] = kin[i]/kR IC50 = 0.25 ;receptor occupancy when drug-induced target cell death rate is 50% of its maximal value gamma = 1 ;Hill coefficient Emax = xx

;Binding constants between drug and receptor target Kd= xx ;nM. dissociation equilibrium constant Drug-Receptor complex kon = 10 ;per nM per day. Assume moderately fast association rate kon koff = Kd*kon ;per day. koff for Drug-Receptor complex dissociation (single binding)

;TMDD parameters Vmax = xx ; nanomoles per day Km = xx ; nanomoles per liter

;System physiology & basic parameter values centered on 70 kg person -> use body weight to estimate values for monkey WT = 3 ;kg. body weight MWD = 150000/1e6 ;mg/nmole. Molecular weight IgG CLD = 0.6*(3/70)^0.8 ;L/d. Clearance of free monoclonal antibody drug Vpl = 2.5*(3/70)^1 ;liters. plasma volume (for mAb) Vbl = 2*Vpl ;liters. blood volume (for target cells) Vti = 2.6*(3/70)^1 ;liters. tissue interstitial volume PS = 0.8*(3/70)^0.8 ;L/d. permeability*surface area IgG plasma to/from tissue fluid

;Integration settings METHOD STIFF ;STIFF is Rosenbrock integrator DTMIN = 0.01 ;days. minimum time step DTOUT = 0 ;output all time points if 0 TOLERANCE = 1e-6 DTMAX = 45/(60*24) ;days. maximum time step(45 minutes). Use this for drug input time TD1 = DTMAX ;time when first dose started

;Input doses of antibody drug as pulses. Note use of DTMAX to ensure correct mass input ;Pulse actually occurs over the timeframe of DTMAX, it is not instantaneous. IN[1..N] = IF TIME<=ndoses*tau THEN PULSE(Dose[i]*WT/MWD,TD1,Tau) ELSE 0

5 ;Differential equations written as amounts in nmoles. ; D=drug (available data to be fitted), Dti=drug in tissue interstitial, R=receptor ;(available data to be fitted), DR=drug-receptor complex, Cell= target cell ; (available data to be fitted)

D'[1..N] = IN[i] -CLD/Vpl*D[i] +PS*(Dti[i]/Vti-D[i]/Vpl) -kon/Vpl*D[i]*R[i] +koff*DR[i] - Vmax*D[i]/(Km + D[i])

Dti'[1..N]= -PS*(Dti[i]/Vti-D[i]/Vpl)

R'[1..N] = kin -kout*R[i] *( 1 + Emax*(DR[i]/(DR[i]+R[i]))^gamma/(IC50^gamma+ (DR[i]/(DR[i]+R[i]))^gamma)) -kon/Vpl*D[i]*R[i] +koff*DR[i]

DR'[1..N] = -kout*DR[i]*( 1 + Emax*(DR[i]/(DR[i]+R[i]))^gamma/(IC50^gamma+ (DR[i]/(DR[i]+R[i]))^gamma)) +kon/Vpl*D[i]*R[i] -koff*DR[i]

;Initialization of differential equations INIT D[1..N] = 0 INIT Dti[1..N] = 0 INIT R[1..N] = R0*Vbl ;does not take account of interaction with natural ligand init DR[1..N] = 0

;Derived variables Cell[1..N]= (R[i]+DR[i])/NRB ;Target cell count RecOcc[1..N] = 100*DR[i]/(DR[i]+R[i]) ;%. receptor occupancy Perc_R[1..N] = 100*R[i]/(DR[i]+R[i]) ;%. free receptor target

;Derived concentrations CFD[1..N] = MWD*D[i]/Vpl ;µg/mL=mg/L. free antibody in plasma CFR[1..N] = R[i]/Vbl ;free (unoccupied) receptor in blood CDR[1..N] = DR[i]/Vbl ;drug-receptor complexes in blood CTR[1..N] = (R[i]+DR[i])/Vbl ;total receptor : free + occupied in blood

6 S4: code for target cell receptor example in human

Code for HUMAN simulations:

; Trial specifications for dose escalation study in human (single intravenous dose) STARTTIME = -10 ;days STOPTIME = 70 ;days N=3 ; number of dose levels Dose[1]= 0.02 ;mg/kg Dose[2]= 0.8 ;mg/kg Dose[3]= 16 ;mg/kg Tau = 14 ;days. dosing interval, not used here NDoses = 1 ;number of administered doses, here one for single dose

;Receptor target and cell turnover NRB = xx ;receptor number per cell NBC = xx ;target cell number per liter of blood in absence of drug Avog= 6.023e23 ;Avogadro's number R0 = NRB*NBC/Avog*1e9 ;nM. baseline receptor concentration in blood THR = xx ;day. receptor half-life kout = logn(2)/THR ;per day. Elimination rate of target cells without drug. kin = R0*Vbl*kout ;nmole/day. Constant target cell synthesis/entrance rate in blood R0[1..N] = kin[i]/kR IC50 = 0.25 ;receptor occupancy when drug-induced target cell death rate is 50% of its maximal value gamma = 1 ;Hill coefficient Emax = xx

;Binding constants between drug and receptor target Kd= xx ;nM. dissociation equilibrium constant Drug-Receptor complex kon = 10 ;per nM per day. Assume moderately fast association rate kon koff = Kd*kon ;per day. koff for Drug-Receptor complex dissociation (single binding)

;TMDD parameters Vmax = xx ; nanomoles per day Km = xx ; nanomoles per liter

;System physiology & basic parameter values centered on 70 kg person WT = 70 ;kg. body weight MWD = 150000/1e6 ;mg/nmole. Molecular weight IgG CLD = 0.6 ;L/d. Clearance of free monoclonal antibody drug Vpl = 2.5 ;liters plasma volume (for mAb) for 70 kg person Vbl = 2*Vpl ;liters. blood volume (for target cells) Vti = 2.6 ;liters. tissue interstitial volume (for mAb) PS = 0.8 ;L/d. permeability*surface area IgG plasma to/from tissue fluid

;Integration settings METHOD STIFF ;STIFF is Rosenbrock integrator DTMIN = 0.01 ;days. minimum time step DTOUT = 0 ;output all time points if 0 TOLERANCE = 1e-6 DTMAX = 45/(60*24) ;days. maximum time step(45 minutes). Use this for drug input time TD1 = DTMAX ;time when first dose would start

;Input doses of antibody drug as pulses. Note use of DTMAX to ensure correct mass input ;Pulse actually occurs over the timeframe of DTMAX so is not instantaneous anyway IN[1..N] = IF TIME<=ndoses*tau THEN PULSE(Dose[i]*WT/MWD,TD1,Tau) ELSE 0 ;Infusion input (infusion dosing) to assess steady-state suppression without pulsation

7 ;IN[1..N] = IF TIME>0 AND TIME<=(DTMAX+TD1+TAU*(NDoses)) THEN Dose*WT/MWD/Tau ELSE 0

;Differential equations written as amounts in nmoles. ; D=drug (available data to be fitted), Dti=drug in tissue interstitial, R=receptor ;(available data to be fitted), DR=drug-receptor complex, Cell= target cell ; (available data to be fitted)