When estimating intrinsic CL with MM kinetics optimized in PK-Sim, is the derived intrinsic CL for "unbound" or "total" drug?

[miao-chan]

Hi everyone,

I was trying to estimate intrinsic clearance with the Michaelis-Menten kinetics that I took from the final model developed in PK-Sim.

For example, the velocity (v) of the active uptake can be expressed as
v = (Vmax * [Substrate]) / (Km + [Substrate]) (Equation 1)

I used the following equation(s) to estimate the intrinsic clearance (CL_int)
CL_int = v / [Substrate] = Vmax / (Km + [Substrate]) (Equation 2)
assuming [Substrate] << Km, Equation 2 can be simplified as
CL_int = Vmax / Km (Equation 3)

In PK-Sim and MoBi, the active uptake process with Michaelis-Menten kinetics is expressed as
dN/dt = TM * kcat * K_water_src * C_src / (Km + K_water_src * C_src) (Equation 4)
where TM is the amount of uptake transporter at the source (interstitial space); K_water_src is the Partition coefficient (water/interstitial space); C_src is the substrate concentration in the interstitial space.

Based on Equations 3 and 4, I estimated the intrinsic clearance of active uptake with the corresponding optimized parameters in my developed model using the equation below.
CL_int,actup = (TM * kcat) / Km

However, looking at Equation 4, I am confused about whether the derived CL_int,actup is for "unbound" or "total" drug (Question 1), because I am not sure what K_water_src * C_src represents (Question 2). Does K_water_src * C_src denote the "unbound" concentration in interstitial space?
This is associated with Question 3 - whether CL_int,actup needs correction to become "unbound" intrinsic clearance and how to correct it.

I am aware of discussion #646 where the definition of the Partition Coefficient was explained:

K_water_cell and K_water_int represent the ratio bound to non-water components in the cellular or interstitial space. Their reciprocal value basically represents the unbound fractions in cell and interstitial space (which is why you then often see expressions like [C]/K_water_cell in equations/formulas that define inputs to cellular processes)

Partition coefficients (PC) reflect the ratio "dissolved" within two different "volume fractions" and are dimensionless (so do not convert dimensions). In this case, the PC describes the theoretical concentration ratio of compound dissolved within water and the "fluid" of a specific container (could be "intracellular" with the cellular space fluid consisting of e.g. water, lipids, and protein).
The theory is that only compound dissolved in water (i.e., unbound) is "available" for enzymatic degradation, hence the division of concentrations within that container with the "Partition coefficient (water/container)".

The second explanation makes sense to me, and if I get it correctly,
K_water_int = theoretical concentration dissolved within water of interstitial space/ theoretical concentration dissolved within the fluid of interstitial space
yet it seems to contradict the first explanation -- "the ratio bound to non-water components", which makes me more confused.

Thanks for reading the long description and questions. Any discussion and response is welcome and appreciated.

Kind regards,
Miao-Chan