PKPD xenograft model for covalent inhibition

Phoenix Certara Forums Modelling and Simulation
1

Hi all,

Can anybody help me in writing the basic code using phoenix for simulating xenograft model for covalent inhibition?

For this kind of model, we can use indirect model including Ksyn and Kdeg to simulate the biomarker itself. Bt the covalent compound that inhibit the target protein is also associated Kon/Koff those are related to occupany and Kinact and Ki those are associated with the activity of inhibition, the finaly the Kout of the effect such as tumor size.

Could someone help to provide the code for this complex and challenging case?

Thank you..

Jian

2

Hi Jian

I think that you should send the differential equations that represent your mode. Then I can help you with the implementation. It is too vague to just describe your system as you did.

Do you know to write your system equations?

Best Regards

Serge

3

Hi Serge,

Thank you for your reply. Here are the differential eqations that represent my case. The initial estimates may not fit this case well. Just want to know whether the DE that I created make sense for this kind of model.

Many thanks

Jian

#PK
deriv(Aa = - Ka * Aa)
deriv(A1 = Ka * Aa - Cl * C)

inhibition effect of drug on target enzyme E via a reversible occupancy (Kd =Koff/Kon)and covalent inhibition (Kinact

deriv(Inh=KinactE0(C/((koff/kon+C))

Inhibition response (R), such as the size of tumor size

deriv(R = Kin*(1- Inh)R - KoutR)

dosepoint(Aa)
C = A1 / V
sequence{R=R0}
error(EEps = 1)
observe(EObs = E + EEps)
stparm(Ka = tvKa * exp(nKa))
stparm(V = tvV * exp(nV))
stparm(Cl = tvCl * exp(nCl))
stparm(Kin = tvKin * exp(nKin))
stparm(Kout = tvKout * exp(nKout))
stparm(Kon = tvKon * exp(nKon))
stparm(Koff = tvKoff * exp(nKoff))
stparm(Kinact = tvKinact* exp(nKinact))
fixef(tvKa(freeze) = c(, 17.5, ))
fixef(tvV(freeze) = c(, 4600, ))
fixef(tvCl(freeze) = c(, 2500, ))
fixef(tvKin(freeze) = c(, 38, ))
fixef(tvKout(freeze) = c(, 0.38, ))
fixef(tvKinact = c(, 0.9, ))
fixef(tvon = c(, 3.9, ))
fixef(tvoff = c(, 2, ))

4

To me deriv(Inh=KinactE0(C/((koff/kon+C)) must be replaced by

deriv(Inh=E0*(C/((EC50+C))

The reason is that I of not see how Kinact and E0 are both identifiable as well as kon and koff.

Only the product Knact*E0 ansd the ratio koff/kon are identifiable.

If I understand correctly, you assume enzyme activation though a michaelis menten type of reaction.

Then if you tru what I said and your data allow estiation of all parameters, you should not have identifiability issue.

This means you have enough dose cohorts to capture the non linear kinetic you have in Inh.

Best Regards

Serge

5

Dear Serge,

Thank you very much for the feedback. Attached are the proposed mechanism based model for this case and a paper on covalent enzyme inhibition. Following your concern, I am trying to convert the product KinactE0 to KinactE. In that case, should I add the DE deriv(E= Ksyn-KdegE) and sequence{E= Ksyn/Kdeg}? Don’t how to link it with the reversible binding and covalent inhibition equation. It would be highly appreciated if you could kindly share your thoughts and experience about coding for a such complex case. Looking forward to your reply.

Best regards

Jian

Presentation2.pptx (37 KB)Kuzimic P Covalent Inhibition 2015 Analy Bio.pdf (679 KB)