PD model for discrete (noncontinuous) target conversion

Phoenix Certara Forums Modelling and Simulation
1

Dear forum, Please advise how to address the following in phoenix using indirect response models:

an endogenous target “E”.

On a weekly basis and only on a fixed day of each week (e.g., monday) for 8 weeks, 20% of the target “E” is chemically modified to “E_mod”. The chemical modification is assumed to be instantaneous. “E_mod” has a different(slower) turnover rate (kout) than “E”.

“E” is an endogenous enzyme. “E_mod” is not endogenous.

Observation is total amount of “E” + “E_mod”

how do I write an indirect response model to describe this type discrete (noncontinuous) target conversion?

many thanks

2

I think you would probably do this within the sequence statement, perhaps with some sort of switch and a sleep statement and/or precursor pools of the endogenouos and synthetic E. Do you have a publication or other reference that gives a bit more background about what you are trying to do? It’s an interesting problem and I am trying to follow the assumptions e.g why 20% and why instantaneous?

Simon.

3

thanks, Simon. Please see attache project file and codes i attempted (didn’t work)

I tried sequence statement:

sequence{
if(Treatment==1){
E_mod=E0.2
E=E0.8
}
else{
deriv(E=kin-kout1E)
deriv(E_mod=-kout2E_mod)
}
}

20% is the percent of target “E” chemically modified.

“Instantaneous” is to simplify the modification kinetics.

I hope to model this discrete PD target modification.

4

project file attached. thanks

discrete target engagement.phxproj (129 KB)

5

A colleague suggested the following model

test(){

fcovariate(Treatment)#Treatment is chemical modification on target “E”. “1” = yes treatment

sequence{

E=6.5 #initial value of target “E”

E_mod=0#initial value of target “E_mod”

while(1){

if(Treatment==1){

E_mod=E*0.2 #on given day with treatment, 20% of “E” converted to 'E_mod"

E=E*0.8 # 80% of “E” left

}

sleep(1)

}

}

deriv(E=kin-kout1*E)#without treatment

deriv(E_mod=-kout2*E_mod)

error(E_totalEps = 1)

E_total = E + E_mod

observe(E_totalObs = E_total + E_totalEps)

fixef(kin = c(0, 3.55, ))

fixef(kout1 = c(0, 0.5, ))

fixef(kout2 = c(0, 0.1, ))

}

please note that in case of Treatment and observation in the same line, sequence (modification) always comes first!

Also note that it will work for the integer time points only (sleep(1))