Dimensionless parameter predicts bacterial prodrug success.

Understanding mechanisms of antibiotic failure is foundational to combating the growing threat of multidrug-resistant bacteria. Prodrugs-which are converted into a pharmacologically active compound after administration-represent a growing class of therapeutics for treating bacterial infections but are understudied in the context of antibiotic failure. We hypothesize that strategies that rely on pathogen-specific pathways for prodrug conversion are susceptible to competing rates of prodrug activation and bacterial replication, which could lead to treatment escape and failure. Here, we construct a mathematical model of prodrug kinetics to predict rate-dependent conditions under which bacteria escape prodrug treatment. From this model, we derive a dimensionless parameter we call the Bacterial Advantage Heuristic (BAH) that predicts the transition between prodrug escape and successful treatment across a range of time scales (1-10 4  h), bacterial carrying capacities (5 × 10 4 -10 5  CFU/µl), and Michaelis constants (K M  = 0.747-7.47 mM). To verify these predictions in vitro, we use two models of bacteria-prodrug competition: (i) an antimicrobial peptide hairpin that is enzymatically activated by bacterial surface proteases and (ii) a thiomaltose-conjugated trimethoprim that is internalized by bacterial maltodextrin transporters and hydrolyzed by free thiols. We observe that prodrug failure occurs at BAH values above the same critical threshold predicted by the model. Furthermore, we demonstrate two examples of how failing prodrugs can be rescued by decreasing the BAH below the critical threshold via (i) substrate design and (ii) nutrient control. We envision such dimensionless parameters serving as supportive pharmacokinetic quantities that guide the design and administration of prodrug therapeutics.