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

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.