Quantitatively predicting optimal antibiotic dose levels from drug-target binding 1 2

Abstract Improved predictions of antibiotic efficacy can inform the development of new antibiotics and extend the effectiveness of existing drugs and thereby help combatting the global antibiotic resistance crisis. We describe a computational model (COMBAT-COmputational Model of Bacterial Antibiotic Target-binding) that leverages accessible biochemical parameters to quantitatively predict the antimicrobial effects of antibiotics based on their drug-target affinity. We validate our model with MICs of a range of quinolone antibiotics in clinical isolates demonstrating that antibiotic efficacy can be predicted from drug-target binding (R2>0.9). Conversely, we experimentally demonstrate that changes in drug-target binding can be predicted from antibiotic efficacy with 92-94% accuracy by exposing bacteria overexpressing target molecules to ciprofloxacin. To test the generality of COMBAT, we predict target molecule occupancy at MIC from antimicrobial action with 90% accuracy for a different antibiotic class, the beta-lactam ampicillin. Finally, we predict antibiotic concentrations that can select for resistance due to novel resistance mutations. COMBAT provides a framework to inform optimal antibiotic dose levels that maximize efficacy and minimize the rise of resistant mutants.


Introduction 31
The rise of antibiotic resistance represents an urgent public health threat. In order to effectively 32 combat the spread of antibiotic resistance, we must optimize the use of existing drugs and 33 develop new drugs that are effective against drug-resistant strains. Accordingly, methods to 34 improve antibiotic dose levels to i) maximize efficacy against susceptible strains and ii) 35 minimize resistance evolution play a key role in our defense against antibiotic resistant 36 pathogens. 37 38 It is noteworthy that dosing strategies for treatment of susceptible strains (e.g., dosing level 1 , 39 dosing frequency 2 , and treatment duration 3-5 ) have recently been substantially improved, even for 40 antibiotic treatments that have been standard of care for decades. This suggests that there likely 41 remains significant room for optimization in our antibiotic treatment regimens. It also highlights 42 the difficulty in identifying optimal dosing levels for new antibiotics. Indeed, optimizing dosing 43 is one of the biggest challenges in drug development. Typically, time-consuming trial-and-error 44 approaches are used and each failed drug candidate makes this process more expensive 6 . 45 46 It is even more challenging to optimize dose levels to minimize the emergence of antibiotic 47 resistance, both for existing and novel antibiotics. There remains substantial debate about which 48 dosing strategies best prevent the emergence of resistant mutants during treatment 7-9 . In this 49 context, a useful concept that links antibiotic concentrations with resistance evolution is the 50 resistance selection window (mutant selection window) that ranges from the lowest 51 concentration at which the resistant strain grows faster than the wild-type, usually well below the 52 wild-type minimum inhibitory concentration (MIC), to the MIC of the resistant strain 10-12 . 53 Antibiotic concentrations above the resistance selection window safeguard against de novo 54 resistance emergence. Antibiotic concentrations below the resistance selection window do not 55 kill the susceptible strain, but also do not favor the resistant strain and therefore do not promote 56 emergence of resistance. The latter may be preferable if one cannot dose above the MIC of the 57 resistant strain due to toxicity or solubility limits. To limit resistance emergence, it is therefore 58 important to identify the resistance selection window and optimize dosing accordingly. In this report, we describe a mechanistic computational modeling framework (COMBAT-79 COmputational Model of Bacterial Antibiotic Target-binding) that allows us to predict drug 80 effects based solely on accessible biochemical parameters describing drug-target interaction. 81 These parameters can be determined early in drug development. We use this framework to 82 investigate how changes in drug target binding, either due to improvements in existing 83 antibiotics or due to resistance mutations in bacteria, affect antibiotic efficacy. We first show that 84 COMBAT accurately predicts bacterial susceptibility as a function of drug-target binding and, 85 conversely, allows inference of these biochemical parameters on the basis of observed patterns of 86 bacterial growth suppression or killing. We then use COMBAT to predict the susceptibility of 87 newly arising resistant variants based on the molecular mechanism of resistance and determine 88 describes the binding and unbinding of antibiotics to their targets and predicts how such binding 130 dynamics affects bacterial replication and death (Fig. 2a). In previous work linking drug-target 131 binding kinetics with bacterial replication 18 , we described a population of bacteria with target 132 molecules per cell with a system of + 1 (bacteria with 0, 1, …, bound target molecules) 133 ordinary differential equations (ODEs). This system increases in complexity with the number of 134 target molecules and makes fitting the model to data computationally too demanding for most 135 settings. To simplify this prior approach, we developed new mathematical models based on (2) 152 153 The term for binding kinetics is given in brown, the term for replication in blue and the term for 154 death in red. 155 Overall, we found that COMBAT could fit the time-kill curves well (R 2 = 0.93, Fig. 3a). Like previously reported, we find that increasing gyrase content makes E. coli more susceptible 205 to ciprofloxacin 32 . We fitted net growth rates allowing the target molecule content, i.e. gyrase 206 A2B2, to vary. We assumed that the only change between the different conditions was the amount 207 of target. We further assumed that the relationship between bound target and bacterial replication 208 or death did not differ between the control strain containing a mock plasmid (no IPTG) and the 209 experiments with overexpression ( Fig. 4b, between 0 % and 100 %). Finally, we assumed that 210 the maximal kill rate at very high antibiotic concentrations was accurately measured in our 211 experiments and forced the function describing bacterial death through the measured value when 212 all target molecules are bound. We found the best fit for a 1.31x increase in GyrA2B2 target 213 molecule content for bacteria grown in the presence of 10 µM IPTG and a 2.02x increase in 214 GyrA2B2 target molecule content for those grown in the presence of 100 µM IPTG. 215 We subsequently tested these predictions experimentally by analyzing Gyrase A and B content 217 by western blot Fig. 4c; Supplementary Fig. S2). Using realistic association and dissociation 218 rates for biological complexes 33 , we predicted a range of functional tetramers based on the 219 relative amount of Gyrase A and B proteins (Fig. 4d). Supplementary Tab. S3 details the 220 individual measurements, and the procedure to estimate tetramers is provided in the methods 221 section. We found that the observed overexpression was very close to our theoretical prediction

Accurate prediction of target occupancy at MIC from time-kill data 227
Next, we tested whether COMBAT can be applied to the action of the beta-lactam ampicillin, a 228 very different antibiotic with a distinct mode of action from quinolones. Using published 229 pharmacodynamic data of E. coli exposed to ampicillin 31 also allowed us to compare COMBAT 230 predictions to established pharmacodynamic approaches. Most of the biochemical parameters for 231 ampicillin binding to its target, penicillin-binding proteins (PBPs), have been determined 232 experimentally (Supplementary Tab. S1). Ampicillin is believed to act as a bactericidal drug 34 , 233 and this mode of action is supported by findings from single-cell microscopy 26 . We therefore 234 assume that ampicillin binding does not affect bacterial replication. In order to model the 235 consumption of beta-lactams at target inhibition and eventual target recovery, we made small 236 adjustments to equation 13 (see Methods, description of beta-lactam action). 237

238
We fitted COMBAT to published time-kill curves of E. coli exposed to ampicillin (Fig. 5a). 239 Again, COMBAT provides a good fit to the experimental data between 0 min and 40-60 min. 240 After that time, observed bacterial killing showed a characteristic slowdown at high ampicillin 241 concentrations which is often attributed to persistence 18 (Fig. 5a). For the sake of simplicity, we 242 chose to omit bacterial population heterogeneity in this work and therefore cannot describe 243 persistence, even though COMBAT can be adapted to capture this phenomenon 18  It is possible to vary all parameters in COMBAT and explore their effect. We used this to test 261 how hypothetical chemical changes to ampicillin or ciprofloxacin would affect antibiotic 262 efficacy ( Supplementary Fig. S3-S11). These changes could reflect either bacterial resistance 263 mutations or modifications of the antibiotics themselves. We predict that changes in drug-target 264 affinity, KD, have more profound effects than changes in target molecule content, bacterial 265 reaction to increasingly bound target (i.e. d(x) and r(x)), or changes in target molecule content. 266 We also predict that the individual binding rates kr and kf, and not just the ratio of these terms, 267 the KD, are important factors in efficiency. The faster a drug binds, the more efficient we 268 predicted it will be. One intuitive explanation for the observation that kf drives efficacy is that a 269 slow binding fails to rapidly interfere with bacterial replication, which may allow for the 270 production of additional target molecules and thereby reduce the ratio of free antibiotic to target 271 molecules. 272 273

Forecasting the resistance selection window 274
Finally, we illustrate how COMBAT can be used to explore how the molecular mechanisms of 275 resistance mutations affect antibiotic concentrations at which resistance can emerge, i.e., the 276 resistance selection window. We compared predicted net growth rates as a function of 277 ciprofloxacin concentrations for a wild-type strain and an archetypal resistant strain. For this 278 analysis, we assumed that the resistant strain has a 100x slower drug-target binding rate (i.e. 279 ~100x increased MIC, realistic for novel point mutations 36 ) and that the maximum replication 280 rate of the resistant strain is 85 % of the wild type strain 37 . We then predicted the antibiotic 281 concentrations at which resistance would be selected. Interestingly, when comparing COMBAT 282 to previous pharmacodynamics models (Fig. 5), we observed that estimates of replication rates 283 depend on the selected time frame (Fig. 6a). When the timeframe for MIC determination is set to 284 18 h as defined by CLSI 38 , the "competitive resistance selection window", i.e., the concentration 285 range below the MIC of both strains where the resistant strain is fitter than the wild type, ranges 286 from 0.002 mg/L to 0.014 mg/L for ciprofloxacin (Fig. 6a) and 1 mg/L to 2.6 mg/L for 287 ampicillin ( Supplementary Fig. S12), respectively. This corresponds well with previous 288 observations that ciprofloxacin resistance is selected for well below MIC 11 . However Optimizing dosing levels of antibiotics is important for maximizing drug efficacy against wild-304 type strains as well as for minimizing the rise of resistant mutants. The determination of optimal 305 dosing strategies typically requires expensive empirical studies; the need for such studies arises 306 in part from our currently limited capacity to predict how antibiotics will affect bacteria at a 307 given concentration. In fact, drug attrition is mainly due to insufficient predictions of efficacy 308 (pharmacodynamics) rather than pharmacokinetics 6  In the most basic version of COMBAT, we ignored differences between extracellular and 402 intracellular antibiotic concentrations and only followed the total antibiotic concentration A, 403 assuming that the time needed for drug molecules to enter bacterial cells is negligible. We model 404 ciprofloxacin (to which there is a limited diffusion barrier 46 ) and ampicillin (where the target is 405 not in the cytosol, even though the external membrane in gram negatives has to be crossed to 406 reach PBPs). We therefore believe that this assumption is justified in wild-type E. coli. This 407 basic version of COMBAT is therefore more accurate for describing antibiotic action where the 408 diffusion barrier to the target is weak.

Distribution of target molecules upon division 456
We assume that the total number of target molecules doubles at replication, such that each 457 daughter cell has the same number as the mother cell. We also assume that the total number of 458 drug-target complexes is preserved in the replication and that the distribution of x bound target 459 molecules of the mother cell to its progeny is described by a hypergeometric sampling of n We consider several potential functional forms of the relationship between the percentage of 488 bound targets and replication and death rates, because the exact mechanisms how target 489 occupancy affects bacteria is unknown (Supplementary Fig. S1). We use a sigmoidal function 490 that can cover cases ranging from a linear relationship to a step function. When the inflection 491 point of a sigmoidal function is at 0 % or 100 % target occupancy, the relationship can also be 492 described by an exponential function. We assume that replication in bactericidal and death in 493 bacteriostatic drugs is independent of the amount of bound target. With sufficient experimental 494 data, the replication rate r(x) and/or the death rate ( ) can be obtained by fitting COMBAT to verified that the Courant-Friedrichs-Lewy condition is satisfied. For fitting the experimental data 544 of bacteria exposed to ciprofloxacin and ampicillin, we used the particle swarm method 545 ("particleswarm" function in Matlab, MathWorks software). 546 547

Concentrations of gyrase A2B2 tetramers 548
We assumed that gyrases A and B first homo-dimerize to A2 and B2, respectively, which in turn 549 bind to each other to form the tetramer TR 48 . approach from a biologically plausible range where the association rates are between 10 7 -10 9 559 M -1 s -1 and the dissociation rates between 10 -3 -10 -1 s -1 33 . This results in 10 4 estimates for each of 560 the six experimental replicates quantifying gyrase A and B (Fig. 4, Supplementary Fig. S2