A mathematical model for intracellular effects of toxins on DNA adduction and repair

The process by which certain classes of toxins compounds or their metabolites may react with DNA to alter the genetic information contained in subsequent generations of cells or organisms are a major component of hazard associated with exposure to chemicals in the environment. Many classes of chemicals may form DNA adducts and there may or may not be a defined mechanism to remove a particular adduct from DNA independent of replication. Many compounds and metabolites that bind DNA also readily bind existing proteins; some classes of toxins and DNA adducts have the capacity to inactivate a repair enzyme and divert the repair process competitively. This paper formulates an intracellular dynamic model for one aspect of the action of toxins that form DNA adducts, recognizing a capacity for removal of those adducts by a repair enzyme combined with reaction of the toxin and/or the DNA adduct to inactivate the repair enzyme. This paper model illustrates the possible saturation of repair enzyme capacity by the toxin dosage and shows that bistable behavior can occur, with the potential to induce abrupt shifts away from steady state equilibria. The model suggests that bistable behavior, dose and variation between individuals or tissues may combine under certain conditions to amplify the biological effect of dose observed as DNA adduction and its consequences as mutation. A model recognizing stochastic phenomena also indicates that variation in within-cell toxin concentration may promote jumps between stable equilibria.