HIV protease, an aspartyl protease crucial to the life cycle of HIV, is the target of many drug development programs. Though many protease inhibitors are on the market, protease eventually evades these drugs by mutating at a rapid pace and building drug resistance. The drug resistance mutations, called primary mutations, are often destabilizing to the enzyme and this loss of stability has to be compensated for. Using a coarse-grained biophysical energy model together with statistical inference methods, we observe that accessory mutations of charged residues increase protein stability, playing a key role in compensating for destabilizing primary drug resistance mutations. Increased stability is intimately related to correlations between electrostatic mutations - uncorrelated mutations would strongly destabilize the enzyme. Additionally, statistical modeling indicates that the network of correlated electrostatic mutations has a simple topology and has evolved to minimize frustrated interactions. The models statistical coupling parameters reflect this lack of frustration and strongly distinguish like-charge electrostatic interactions from unlike-charge interactions for [Formula: see text] of the most significantly correlated double mutants. Finally, we demonstrate that our model has considerable predictive power and can be used to predict complex mutation patterns, that have not yet been observed due to finite sample size effects, and which are likely to exist within the larger patient population whose virus has not yet been sequenced.