Using mathematical modeling to infer the valence state of arsenicals in tissues: A PBPK model for dimethylarsinic acid (DMAV) and dimethylarsinous acid (DMAIII) in mice.

Chronic exposure to inorganic arsenic (iAs), a contaminant of water and food supplies, is associated with many adverse health effects. A notable feature of iAs metabolism is sequential methylation reactions which produce mono- and di-methylated arsenicals that can contain arsenic in either the trivalent (III) or pentavalent (V) valence states. Because methylated arsenicals containing trivalent arsenic are more potent toxicants than their pentavalent counterparts, the ability to distinguish between the +3 and +5 valence states is a crucial property for physiologically based pharmacokinetic (PBPK) models of arsenicals to possess if they are to be of use in risk assessment. Unfortunately, current analytic techniques for quantifying arsenicals in tissues disrupt the valence state; hence, pharmacokinetic studies in animals, used for model calibration, only reliably provide data on the sum of the +3 and +5 valence forms of a given metabolite. In this paper we show how mathematical modeling can be used to overcome this obstacle and present a PBPK model for the dimethylated metabolite of iAs, which exists as either dimethylarsinous acid, (CH3)2AsIIIOH (abbreviated DMAIII) or dimethylarsinic acid, (CH3)2AsV(O)OH (abbreviated DMAV). The model distinguishes these two forms and sets a lower bound on how much of an organ's DMA burden is present in the more reactive and toxic trivalent valence state. We conjoin the PBPK model to a simple model for DMAIII-induced oxidative stress in liver and use this extended model to predict cytotoxicity in liver in response to the high oral dose of DMAV. The model incorporates mechanistic details derived from in vitro studies and is iteratively calibrated with lumped-valence-state PK data for intravenous or oral dosing with DMAV. Model formulation leads us to predict that orally administered DMAV undergoes extensive reduction in the gastrointestinal (GI) tract to the more toxic trivalent DMAIII.