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Drug resistance is a significant obstacle in the effective treatment of diseases with rapidly mutating targets, such as AIDS, malaria, and certain forms of cancer. Such targets are remarkably efficient at exploring the space of functional mutants and at evolving to evade drug binding while still maintaining their biological role. To overcome this challenge, drug regimens must be active against potential target variants. Such a goal may be accomplished by one drug molecule that recognizes multiple variants or by a drug "cocktail"--a small collection of drug molecules that collectively binds all desired variants. Ideally, one wants the smallest cocktail possible due to the potential for increased toxicity with each additional drug. Therefore, the task of designing a regimen for multiple target variants can be framed as an optimization problem--find the smallest collection of molecules that together "covers" the relevant target variants. In this work, we formulate and apply this optimization framework to theoretical model target ensembles. These results are analyzed to develop an understanding of how the physical properties of a target ensemble relate to the properties of the optimal cocktail. We focus on electrostatic variation within target ensembles, as it is one important mechanism by which drug resistance is achieved. Using integer programming, we systematically designed optimal cocktails to cover model target ensembles. We found that certain drug molecules covered much larger regions of target space than others, a phenomenon explained by theory grounded in continuum electrostatics. Molecules within optimal cocktails were often dissimilar, such that each drug was responsible for binding variants with a certain electrostatic property in common. On average, the number of molecules in the optimal cocktails correlated with the number of variants, the differences in the variants' electrostatic properties at the binding interface, and the level of binding affinity required. We also treated cases in which a subset of target variants was to be avoided, modeling the common challenge of closely related host molecules that may be implicated in drug toxicity. Such decoys generally increased the size of the required cocktail and more often resulted in infeasible optimizations. Taken together, this work provides practical optimization methods for the design of drug cocktails and a theoretical, physics-based framework through which useful insights can be achieved.

Optimal Drug Cocktail Design: Methods for Targeting Molecular Ensembles and Insights from Theoretical Model Systems