Application of Brunauer–Emmett–Teller (BET) theory and the Guggenheim–Anderson–de Boer (GAB) equation for concentration-dependent, non-saturable cell–cell interaction dose-responses

Abstract

To systematically assess the characteristics and potential utility of the Guggenheim-Anderson-de Boer (GAB) formulation of the Brunauer-Emmett-Teller (BET) equation from physical chemistry for modeling dose-responses in pharmaceutical applications. The GAB-BET equation was derived using pharmacodynamic first principles to underscore the assumptions involved and the functional characteristics of the equation were investigated. The properties of the GAB-BET equation were compared to the familiar Michaelis-Menten and Hill equations and its utility for pharmacokinetic-pharmacodynamic modeling was assessed by fitting the model equations to four diverse data sets from the literature. The results enabled the salient characteristics of the unconstrained GAB-BET equation and the corresponding GAB-BET equation with finite layers for modeling pharmacodynamic effects to be critically assessed. The GAB-BET approach allows for the accumulation of heterogeneous stacks containing multiple cells or molecules at the target site. The unconstrained GAB-BET equation is capable of describing concentration-dependent dose-response curves that do not exhibit saturation. The GAB-BET equation for finite layers exhibits saturation but increases more slowly than the comparable Michaelis-Menten and Hill equations. The fitting results of the model equations to literature data sets provided support for key aspects of the GAB-BET model. The GAB-BET equation may be a useful method for mechanistic modeling of diverse immune processes and drugs that recruit immune cell activity at the site of action.