Correlated electrostatic mutations provide a reservoir of stability in HIV protease

Abstract

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 model's 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.

Figure 1. Structure of HIV protease subtype B.

The backbone structure of HIV protease subtype B (PDB ID: 1NH0) is depicted in ribbon format. The 18 electrostatically active residues are highlighted. Residue positions which have a predominantly negatively charged non-neutral residue in the sequence database are depicted in red. Residues which have a predominantly positively charged non-neutral residue in the database are depicted in blue.

Figure 2. Average electrostatic free energy of folding as a function of the number of electrostatic mutations.

Each point on a curve corresponds to , where is the number of sequences with electrostatic mutations, is the probability of the th sequence under a given model conditional upon the number of mutations, and is its electrostatic folding energy (Equation (1); see Methods). All points are plotted relative to , the average of observed sequences with one electrostatic mutation. The black curve shows the average energies of observed sequences , the red curve represents the average energies of sequences under a model in which each charge state occurs with equal frequency, the blue curve shows the average energies of sequences under a model in which each charge state occurs with frequencies observed in the data, and the green curve represents the average energy of sequences under a pair correlation model which preserves observed pair frequencies. The error bars on the black curve are the standard errors of the mean of observed sequences. Note that for .

Figure 3. Comparison of the sequence probabilities in the tail of the Lee database and the pair correlation model with the sequence probabilities in the Stanford database.

The probabilities of sequences under the pair correlation model, , predicted using the Bethe approximation, are plotted as a function of the sequence probabilities from the Lee database, . Sequences with a probability of 0 in the Lee database, i.e. unobserved sequences, are plotted to the left of the abscissa break. Every sequence is shaded using a color gradient corresponding to , which represents the number of times the sequence occurs in the Stanford database, relative to its probability in the Lee database. Sequences that occur frequently in the Stanford database as compared to the Lee database have a higher ratio and are shaded red, while the sequences that do not occur as frequently in the Stanford database as compared to the Lee database have a lower ratio and are shaded blue. Sequences that are shaded green have equal probabilities in both databases. Sequences unobserved in the Lee database (leftmost row in the graph), but observed in the Stanford database have a ratio that is artificially set to equal 4, which corresponds to the color red. Unobserved Lee sequences that are also unobserved in the Stanford database are shaded green because . Sequences with probabilities are shaded according to the average value of for a window of 10 sequences around the sequence of interest. Sequences with probabilities or are not shown. The indices (0), (1), (2), etc mark the locations of sequences observed zero, once, twice (etc) in the Lee database. Each dot corresponds to a unique sequence.

Figure 4. Distance between like and unlike-charge pairs as a function of the statistical coupling parameter, .

The statistical coupling parameter is a fitting parameter that describes the statistical interaction energy between pairs of states. Since the Bethe mean field pair correlation model is a good approximation for this data, a negative indicates that a pair of states is enhanced (positively correlated), while a positive indicates that a pair of states is suppressed (negatively correlated). Using simple electrostatics, we observe that like-charge patterns (blue) are mostly suppressed while unlike-charge patterns (red) are enhanced. The sign of is able to correctly predict the charge patterns for of the top 35 most significantly correlated charge pairs out of a total of 135 pairs. The p-value for the statistical significance of this result is . The reason there are 135 pairs is as follows: For each pair of residues, there are 4 possible sets of like and unlike charge combinations, resulting in a total of 612 like/unlike charge pair combinations. However, not all pairs exist in the database or are significantly correlated. Filtering results in 135 pairs with probability greater than 0.001%.