Concept of reaction volume in the in vivo ligand-receptor model

In vivo quantification of receptor concentration and ligand affinity using data obtained with PET is based on the compartmental analysis of ligand-receptor interactions. There is, however, an inconsistency between the assumed homogeneity of the ligand concentration in each compartment, a basic hypothesis of the compartmental analysis, and the obvious heterogeneity of the tissue. Our goal was to study the effects of the free ligand concentration heterogeneity on the parameters describing in vivo binding reaction and to introduce the concept of reaction volume, VR, to account for that heterogeneity.

The reaction volume is defined as the volume in which the free ligand mass present in 1 ml of tissue would have uniformly distributed with the same concentration as that in the vicinity of the receptor sites. The consequence of the heterogeneity of the free ligand concentration is that the equilibrium dissociation rate constant estimated from PET data corresponds to KdVR and not to Kd alone (defined by the ratio of the dissociation over the association rate constants). As a consequence, it is proposed to estimate the reaction volume as the ratio between the equilibrium dissociation constants obtained from in vivo and in vitro data (KdVR and Kd, respectively).

We used data obtained from studies performed with eight different molecules and found a correlation between the reaction volume and the molecule lipophilicity. This correlation can be used as a method to estimate the order of magnitude of VR from the lipophilicity which is easily accessible experimentally.

Reaction volume is an important parameter in in vivo ligand-receptor interaction modeling.