Bacterial defiance as a form of prodrug failure

Brandon Alexander Holt; Gabriel A. Kwong

Having demonstrated that bacteria exposed to a prodrug exhibit a binary outcomesusceptibility (i.e., death) or defiance (i.e., survival)we next sought to determine whether the behavior could be quantified by a metric of resistance that could be generalized across broad treatment conditions. Based on our model and experimental validation, we observed that under defiance, 15 populations of live bacteria expanded (i.e., positive growth rate) throughout the course of treatment, which implied that key bacterial growth parameters (e.g., r, Bmax) were greater in value than enzyme-driven death rate parameters (e.g., kcat, Km) (Fig. 2B, 3A) . Therefore, to derive a metric to discriminate between defiant and susceptible bacteria, we used Buckingham Pi theorem to identify a dimensionless quantity that represents the competing balance between growth rate 20 and enzymatic turnover, which we defined as the Bacterial Advantage Heuristic The copyright holder for this preprint (which was not peer-reviewed) is the author/funder. It . https://doi.org/10.1101/556951 doi: bioRxiv preprint This quantity reflects that bacteria have a higher probability of switching to the defiance phenotype under conditions that promote a faster growth rate, r, and slower enzymatic activity, kcat. To predict the onset of the defiance phenotype, we sought to determine the critical B.A.H. value that distinguishes defiant bacteria from susceptible populations. Using our mathematical model, we simulated >2000 prodrug treatment conditions covering a range of values for r, Bmax, kcat, and Km 5 and identified a critical value of BAH at which bacteria switch from susceptibility to defiance (BAHcrit ~ -11.37) (Fig. 3B) . In other words, for any environmental or genetic condition that produces a BAH > BAHcrit, the bacteria will survive the prodrug treatment, and for BAH < BAHcrit, the bacteria will die. To test the robustness of this switch-like behavior, we modeled treatment outcomes by varying bacterial growth rates (r) and enzymatic efficiencies (kcat) (> 100 points) and 10 found that BAHcrit was time-independent across a range of prodrug treatment durations. (Fig 3C-E) . Additionally, to demonstrate that BAHcrit is independent from any system parameter, we modeled treatment outcomes (> 500 points) by individually fixing each of the four parameters (i.e., r, Bmax, kcat, and Km) in turn and found that BAHcrit was invariant across all conditions tested (Fig 3F-I) . To confirm the value of BAHcrit experimentally, we first used the nine experimental 15 conditions previously tested (A1-3, B1-3, C1-3) to fit the values for kcat and r (Fig S2) , and then used the computationally-derived critical BAH threshold to classify the phenotype of nine bacteriaprodrug treatment conditions. By receiver-operating-characteristic (ROC) analysis, BAHcrit perfectly predicted the onset of defiance (Fig. 3J ,K AUROC = 1.00, n = 9) with 100% specificity and sensitivity. Our model results predicted that changing key system parameters to decrease 20 the B.A.H. below the critical threshold will result in successful treatment of defiant bacteria. To demonstrate this, we took three different AMP prodrugs with distinct linker sequences (Table S1) with increasing kcat values for OmpT to decrease the B.A.H. below BAHcrit, which allowed us to successfully treat previously defiant populations of bacteria (Fig. S3) . These findings are important for the successful design and administration of prodrug therapies, which