Mechanism-independent method for predicting response to multidrug combinations in bacteria

Abstract

Drugs are commonly used in combinations larger than two for treating bacterial infection. However, it is generally impossible to infer directly from the effects of individual drugs the net effect of a multidrug combination. Here we develop a mechanism-independent method for predicting the microbial growth response to combinations of more than two drugs. Performing experiments in both Gram-negative ( Escherichia coli) and Gram-positive ( Staphylococcus aureus ) bacteria, we demonstrate that for a wide range of drugs, the bacterial responses to drug pairs are sufficient to infer the effects of larger drug combinations. To experimentally establish the broad applicability of the method, we use drug combinations comprising protein synthesis inhibitors (macrolides, aminoglycosides, tetracyclines, lincosamides, and chloramphenicol), DNA synthesis inhibitors (fluoroquinolones and quinolones), folic acid synthesis inhibitors (sulfonamides and diaminopyrimidines), cell wall synthesis inhibitors, polypeptide antibiotics, preservatives, and analgesics. Moreover, we show that the microbial responses to these drug combinations can be predicted using a simple formula that should be widely applicable in pharmacology. These findings offer a powerful, readily accessible method for the rational design of candidate therapies using combinations of more than two drugs. In addition, the accurate predictions of this framework raise the question of whether the multidrug response in bacteria obeys statistical, rather than chemical, laws for combinations larger than two.

Optimization of drug combinations using Feedback System Control

“…In our experience, this method has been sufficient to accurately describe cell behavior in response to drug combinations 43 . Moreover, others have also described the contribution of higher-order terms (third order and above) as being minimal (representing < 3% of the data variation) 25 . Various other groups have also described the response surface of cells to drug combinations as "highly nonlinear" 28,30 where "sometimes nonlinear curve fitting is desirable or actually required" 44 -for example, the in use of a polynomial fit for the response to a combination of anesthetic drug interactions 45 .…”

“…By using all data points obtained during the preceding optimization, a stepwise regression model 24 can be generated, which mathematically describes the cellular activity (in terms of the selected bioassay output) in response to the drug combinations administered to the cells (i.e., the system input). The second-order regression model includes terms that describe the contributions of each single drug (first and second order, β i and β ii , respectively), as well as those of the two-drug interactions (β ij ) 7,8,14,25 to the overall cell output response. …”

Uncovering emergent interactions in three-way combinations of stressors

“…Although our study is currently more limited with regard to understanding ranges of drug concentrations as studied by Wood et al [36] and Zimmer et al [37], there are a few central contributions represented by our approach. First, our study provides a clear conceptual derivation for the simple algebraic measures presented below, and in so doing, further reveals a way to differentiate between the emergent interaction (an interaction that only exists when all three drugs are present) and the net interaction (the overall interaction in comparison to single-drug effects).…”

“…Second, in contrast to other higher-order interaction studies, we also rescale the raw magnitude of our metrics in order to compare information and categories that correspond to baselines for synergistic and antagonistic interactions, as previously done by Segre and colleagues for pairwise interactions [38]. Third, we consider a much larger set of three-antibiotic combinations (20 as opposed to six [36]), though we only take measurements at fixed concentrations for these combinations. We also identify higher levels of net and emergent three-way (E3) interactions, including both synergy and antagonism, than previous studies on higher-order interactions, as explained in the Discussion section.…”

“…In particular, Wood et al [36] applied maximum entropy methods to six combinations of three antibiotics that varied across a range of concentrations. In this way, they searched for three-way interactions that could not be predicted from pairwise interactions.…”