Minimal Biophysical Model Of Combined Antibiotic Action

Phenomenological relations such as Ohm's or Fourier's law have a venerable history in physics but are still scarce in biology. This situation restrains predictive theory. Here, we build on bacterial "growth laws," which capture physiological feedback between translation and cell growth, to construct a minimal biophysical model for the combined action of ribosome-targeting antibiotics. Our model predicts drug interactions like antagonism or synergy solely from responses to individual drugs. We provide analytical results for limiting cases, which agree well with numerical results. We systematically refine the model by including direct physical interactions of different antibiotics on the ribosome. In a limiting case, our model provides a mechanistic underpinning for recent predictions of higher-order interactions that were derived using entropy maximization. We further refine the model to include the effects of antibiotics that mimic starvation and the presence of resistance genes. We describe the impact of a starvation-mimicking antibiotic on drug interactions analytically and verify it experimentally. Our extended model suggests a change in the type of drug interaction that depends on the strength of resistance, which challenges established rescaling paradigms. We experimentally show that the presence of unregulated resistance genes can lead to altered drug interaction, which agrees with the prediction of the model. While minimal, the model is readily adaptable and opens the door to predicting interactions of second and higher-order in a broad range of biological systems.Author summaryApplying multiple antibiotics simultaneously can boost treatment effectiveness and aid against rampant antibiotic resistance. Because of the impractically large number of possible combinations of drugs, those that are effective are found by trial and error. Hence, a predictive theory to characterize drug cocktails would be of enormous value. Recently identified phenomenological laws ease the construction of predictive models of bacterial growth. Here, we build a model of the effects of antibiotic combinations on bacteria and show that it makes reliable predictions for experimental outcomes. Our model takes responses to individual drugs as inputs and predicts their combined effect. This output determines the type of drug interaction, which can range from antagonistic (the combined effect is weaker) to synergistic (the combined effect is stronger). We broaden the model by including the direct physical interaction on the target, drug resistance genes that alter the drug interaction, and drugs that mimic poor growth environments by choking the supply of growth-essential components, which we test experimentally. Our results prove how biophysical models that use empirical laws can predict responses to drug combinations. Importantly, such models can successfully predict mechanisms underlying interactions of drug combinations. This approach is extensible to combinations of more than two drugs and diverse biological systems.