Executive Summary : | Biochemical interaction between molecules is crucial for understanding intracellular signaling pathways and designing drugs with improved efficacy and decreased toxicity. The Hill-Langmuir equation-based-two-state model is widely used to study drug-receptor interactions, but recent experimental studies have shown a bell-shaped (bi-phasic) dose-response curve where interaction between two species is mediated via a third species, known as a mediator molecule. This chemical reaction network (CRN), also known as a three-body binding CRN, is found in various natural and engineered systems to process complex dynamics. Drug efficacy and toxicity are directly proportional to the amounts of ternary complex and mediator molecule, and it is desired to maximize the amount of ternary complex while minimizing the amount of mediator molecule to improve drug efficacy and reduce toxicity. However, mathematical analysis of this CRN is not straightforward due to its mutually dependent redundant pathways. A recent attempt resulted in a better understanding of this CRN in deterministic settings and applied to specific cases. In stochastic settings, the mediator may have an absorbing state where the output remains unaffected. A generalized theoretical study of the three-body binding CRN in deterministic and stochastic settings is proposed. Determining the correct amount of drug dose is key in treating various types of cancer, as there is a strong relationship between drug concentration, efficacy, and toxicity. Careful investigation is needed to determine critical factors that govern the dose repones curve, which could enable clinicians to develop better personalized cancer immunotherapies and improve patient treatment and management. |