Simulation of Unbound fraction

Hi all,

Can anybody help me in writing the code using phoenix for the picture depicted in the attachment.

The explanation for the picture is the drug is present in the plasma (tissue chamber in this case) and the free drug passes through the membrane in to the buffer chamber.

There can be elimination from both chambers due to instability of the compound (indicated as KelT and KelB from tissue and buffer chambers respectively).

KonDP and Koff DP indicate association and dissociation of drug protein complex.

Is it possible to do graphically in phoenix?

Thanks in advance

RC

protein binding.docx (46.3 KB)

Dear colleagues

The processes you describe are not first order but second order at least. Therefore you cannot define the model graphically. You need to write down the differential equations using the pml language.

Please write the equations and I can help you with the code. If you have trouble writing the equaitons, let me know but define the processes that occur and the assumptions if any you are making.

Best

Serge

Hi Serge,

Thank you for the reply,

the following are the equations ,

Tissue Compartment
dDtissue/ dt =  PSA/V × (Dbuffer − Dtissue) − Dtissue(kon,DP×Ptissue ) +  koff ,DP × DPtissue  − Dtissue × kel,T

dDPtissue / dt = kon,DP × Dtissue × Ptissue − koff ,DP × DPtissue

dPtissue / dt = koff ,DP × DPtissue − kon,DP × Dtissue × Ptissue

Buffer Compartment (Receiver)

dDbuffer / dt = PSA /V x (Dtissue − Dbuffer) − Dbuffer × kel,B

The following are the definitions of the terms used:
Dtissue: Drug present in the tissue compartment or chamber
PSA: polar surface area and is a constant 
Dbuffer:  drug present in buffer chamber
Kon,DP : Formation rate constant of Drug + protein complex
Koff,DP : dissociation rate constant of Drug + protein complex
DPtissue : Drug protein complex in the tissue chamber 
Ptissue: Protein present in the tissue compartment
kel,T: Elimination of drug from the tissue compartment due to instability
kel,B: elimination of drug from the buffer compartment due to instability
V is the volume of the chamber

Thanks in advance

Raghav

Hi serge,

Greetings.,…,

I am attaching the paper that described the equations for simulation of concentrations in both dosing and buffer chamber of equilibrium dialysis.

Impact of Recovery on Fraction Unbound Using.pdf (299 KB)

Is it possible to do the same with phoenix / numerical methods ?

Thanks in advance

Best REgards,

Raghav