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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Chem Biol Drug Des. Author manuscript; available in PMC 2010 April 28.
Published in final edited form as:
PMCID: PMC2860775
NIHMSID: NIHMS188453

Toward the design of mutation-resistant enzyme inhibitors: Further evaluation of the substrate envelope hypothesis

Abstract

Previous studies have shown the usefulness of the substrate envelope concept in the analysis and prediction of drug resistance profiles for HIV protease mutants. This study tests its applicability to several other therapeutic targets: Abl kinase, chitinase, thymidylate synthase, dihydrofolate reductase, and neuraminidase. For the targets where many (≥6) mutation data are available to compute the average mutation sensitivity of inhibitors, the total volume of an inhibitor molecule that projects outside the substrate envelope Vout, is found to correlate with average mutation sensitivity. Analysis of a locally computed volume suggests that the same correlation would hold for the other targets if more extensive mutation data sets were available. It is concluded that the substrate envelope concept offers a promising and easily implemented computational tool for the design of drugs that will tend to resist mutations. Software implementing these calculations is provided with the supplemental material.

Keywords: mutation resistance, substrate envelope

1 INTRODUCTION

Drug-resistance is a serious challenge in the treatment of many diseases, leading to morbidity, mortality, and medical costs (13). Resistance typically emerges when a population of pathogens or cancer cells is subjected to selection pressure in the course of treatment with a drug. Under these conditions, resistant variants can come to dominate the cellular population, making the drug ineffective. A number of mechanisms can lead to drug-resistance, including decreased transport of drug to its site of action, increased elimination from the site of action, metabolic inactivation of the drug, ineffective activation of a pro-drug, up-regulation of alternative pathways, overexpression of the targeted protein, and mutation of the target to reduce its affinity for the drug (4). Ideally, such mechanisms would be accounted for in the course of drug-discovery in order to prevent the emergence of resistance at the outset, rather than having to address it after it appears. The present study explores a method of designing drugs that will be robust in the face of mutations in a targeted enzyme.

Adaptive inhibitors(5), which contain rotatable bonds that can position several alternative functionalities at variable regions of the binding site, offer one important strategy for the design of mutation-resistant inhibitors. Such compounds may retain affinity when the target protein mutates because they can adapt conformationally, apposing their most complementary moieties to the mutated residue. The present study elaborates a different approach, the design of enzyme inhibitors that fit within the known “substrate envelope” of the targeted enzyme (6).

According to the substrate envelope hypothesis, inhibitors fitting within the three-dimensional region occupied by the enzyme’s natural substrate should tend to resist mutations because mutations that could knock out inhibitor binding would also knock out substrate binding, rendering the enzyme ineffective. This idea was first advanced in the context of human immunodeficiency virus (HIV), which cleaves the Gag-Pol polyprotein at sites with a number of different amino acid sequences (7). Chellappan and coworkers retrospectively evaluated the substrate envelope hypothesis for HIV protease by computing the volumes of clinically approved HIV-1 protease inhibitors lying outside the substrate envelope (Vout) (8), and comparing these volumes with the mutation-resistance profiles of the respective inhibitors. They found that the values of Vout correlated with the sensitivity of the inhibitors to clinically relevant mutations, although the correlation was somewhat dependent on the mutation set chosen. In a second study, Chellappan et al. furthermore used Vout prospectively, as part of a scoring function for the computational design of a compound library targeting HIV protease, and observed that the compounds with the smallest values of Vout were most robust to clinically relevant protease mutations(9). Thus, although the substrate envelope hypothesis is based upon a somewhat simplistic steric model, early studies suggest that it may be a useful guide to the design of mutation-resistant drugs. More recently, Altman et al. applied inverse design using substrate envelope to develop mutation robust subnanomolar inhibitors of HIV protease (10).

It is now interesting to consider whether the substrate envelope hypothesis is applicable to other drug targets, as recently suggested (11). Encouragingly, Colman and co-workers (1214) have observed that those inhibitors of flu virus neuraminidase which are most similar to the transition state of the enzyme’s natural substrate are the most mutation-resistant, although they did not suggest a quantifying measure of this relationship. This paper describes a retrospective study of the applicability of a quantitative form of the substrate envelope concept, suitable for use in structure-based drug design, to a series of additional enzymes regarded as drug-targets.

2 METHODS

2.1 Concepts and Approach

The central question to be addressed is whether the volume of an inhibitor falling outside the region of the active site occupied by bound substrate correlates with the tendency of the inhibitor to lose affinity in the face of mutations that do not destroy enzyme activity. Answering this question retrospectively requires affinity data for multiple inhibitors with wild-type and mutant enzyme, along with three-dimensional structural data. An ideal data set would include mutations in many parts of the active site, so that any extension of the inhibitor outside the substrate envelope would be probed by at least one mutation. In this case, the total volume of inhibitor outside the substrate envelope, Vout (Section 2.3), might be expected to correlate with the average, over all mutants, of the loss of affinity, expressed for each mutant i as the sensitivity si=log(Kmut,iKwt). Here Kmut,i and Kwt are, respectively, the dissociation constants or IC50 values of the inhibitor with mutant i and the wild type, and the logarithm generates a quantity proportional to the difference in binding free energy. When a large set of mutation data are available, the average of si over the mutants i quantifies the overall sensitivity of the inhibitor to mutations.

When less comprehensive mutation data are available, an extension of the ligand outside the substrate envelope may not be probed by any of the available mutations, so loss of affinity may fail to correlate with Vout. However, such an instance does not necessarily invalidate the substrate envelope hypothesis, because, in the clinical setting, it is likely that the targeted cell population will in fact generate mutations that probe other parts of the active site. In this case, the full degree to which the ligand extends outside the substrate envelope may indeed become important. For less comprehensive mutation sets, it is still of interest to determine whether the volume of an inhibitor outside the substrate envelope in the vicinity of the mutated residues in the available data set, here termed Vout,loc (Section 2.3), correlates with sensitivity to those mutations. Such a result would tend to support the general idea that the most mutation-resistant inhibitors are those which fall entirely within the substrate envelope.

2.2 Experimental data

For each enzyme to be analyzed, the present study employs crystal structures with substrate and the inhibitors of interest, along with the measured affinities of the inhibitors for the wild type enzyme and a collection of mutants. Table 1 lists the enzymes, substrates and inhibitors studied here, along with the Protein Data Bank IDs (15) of the crystal structures employed. Table 2 shows the mutations considered, the inhibitors, and the nature of the affinity data (Kd, Ki or IC50). The mutation sensitivities for each inhibitor used in this paper are listed in Table S1 of the Supporting Materials available from this journal’s web site. Most of the affinity data were drawn from BindingDB (16). The investigated mutations arose in vivo as a response to a drug, or were produced in the course of directed mutagenesis studies aimed at discovering resistance mutations of the inhibitors.

Table 1
Structures of substrates and ligands used for calculations.a
Table 2
Mutation set data sources used in this paper.

As shown in Table 2, all 4 Abl kinase inhibitors have been tested experimentally against the same set of 8 mutant enzymes, all 3 chitinase inhibitors have been tested against the same set of 6 mutants, and both thymidylate synthase inhibitors have been tested against the same 11 mutants. However, 2 of the 4 inhibitors of DHFR have been tested against 2 mutants, and the other 2 inhibitors have been tested against a different mutant. For the sake of consistency, the two pairs of inhibitors are analyzed separately, each with respect to its own set of mutant data. Similarly, two separate analyses are done for the neuraminidase inhibitors, one for the inhibitors tested only against R292K, the other for the inhibitors tested against the larger set of 6 mutants, as listed in Table 2.

2.3 Calculation of inhibitor volumes outside substrate envelope

The volume of an inhibitor outside the substrate envelope, Vout, was computed much as done previously (8). One difference is that the prior studies of HIV protease constructed a model of the substrate envelope from multiple crystal structures, each with a different substrate bound, but here, there is only a single substrate structure for each enzyme. Another important difference, detailed below, concerns the treatment of inhibitor atoms that extend out of the active site and far into solution. The algorithm works as follows.

A cubic lattice with 0.2 Å spacing is superimposed on the binding site of the enzyme with bound substrate, and each grid point ijk within the van der Waals volume, using commonly accepted van der Waals radii (17), of any substrate atom other than hydrogen is assigned a value of Sijk =1. All other grid points are assigned a value of Sijk =0. (The present software also allows fractional values between 0 and 1 as an indication of the percentage of substrate molecules lying on each grid point in order to handle cases, such as HIV protease, in which multiple substrate-bound structures are available.) The structure of the inhibitor-bound complex of interest is aligned with the substrate-bound complex using structural alignment program SHEBA (18), and an analogous, overlapping cubic lattice with values Iijk is computed for the inhibitor. The value of Vout can then be computed as the number of grid points ijk with Iijk=1 and Sijk=0, multiplied by the volume of one grid cell, 0.008 Å3. Similarly, the volume of the inhibitor inside the substrate envelope, Vin, can be computed from the number of inhibitor grid points with Iijk=Sijk=1.

Inhibitor atoms that protrude far outside of the protein and into solution are not likely to be affected by mutations and thus, arguably, should not contribute to Vout. This issue is addressed by neglecting lattice points from the inhibitor grid that lie more than 4 Å from the nearest protein atom (see also Section 3.1). This threshold can cause part of the van der Waals volume of a ligand within a large binding cavity also to be excluded. This should not pose a problem, because these atoms presumably contribute little to the interaction with the protein.

Crystallographic water molecules are ignored in the present calculations. However, when a crystallographic water that bridges the substrate and enzyme is thought to be critical to substrate binding, one may expect that mutations near the water molecule will affect substrate binding. In such cases, it may be useful to include the bound water as part of the substrate when defining the substrate envelope. If, on the other hand, a displaced water molecule is not thought to be essential for substrate binding, it likely can be ignored in the present approach.

Subsection 3.3 analyzes the neuraminidase and DHFR systems, for which only a few mutation data are available. In these cases, values of Vout,loc were computed by furthermore neglecting lattice points from the inhibitor grid that lie more than 4 Å (unless specified otherwise) from any atom of a residue in the mutation set.

The Supplementary Materials provide the FORTRAN source code for generating the substrate envelope grid, calculating Vout and Vout,loc, and converting the substrate envelope grid into a DX grid format viewable with molecular graphics programs.

3 RESULTS

3.1 Vout correlates with overall mutation-sensitivity of an inhibitor

The proposed correlation between Vout and the average sensitivity to mutation is best evaluated for a system with well-investigated mutant resistance profiles for multiple inhibitors, such as HIV protease. Figure 1 examines this correlation for the 5 inhibitors and 11 mutants with data taken from a previous study by Chellapan et al (8). Good correlation is observed for the largest mutation set, ANAM-11, while a relatively low correlation is observed for L10I/L90M. Encouragingly, the overall sensitivity of an inhibitor to mutation, captured by the average of si over all mutants i (Section 2.1), shows a smooth, monotonic increase with Vout, as shown by the thick line in Figure 1.

Figure 1
Correlation between the mutation sensitivity and Vout. for 5 clinically approved HIV protease inhibitors and 11 mutation sets. From left to right, the points correspond to the following inhibitors: amprenavir, nelfinavir, indinavir, saquinavir, ritonavir. ...

Figure 2 similarly plots average sensitivity to mutation against Vout for the other enzymes studied here; the plot for HIV protease, drawn from Figure 1, is included for comparison. The number of mutated residues is highest for the top graphs and falls for the lower graphs. It is therefore expected that any correlation that is observed will be clearest for the top graphs. This expectation is borne out by the data, as the top four graphs show a fairly high correlation between the mutation-sensitivity and Vout, while the two bottom graphs do not. The latter will be analyzed in Section 3.3 with the quantity Vout,loc. The slopes of the graphs, however, vary from system to system even among the top graphs with their more extensive mutation sets. Despite the different slopes, these results show that Vout correlates with the inhibitors’ sensitivity to target mutation for several different systems.

Figure 2
Average sensitivity to mutation of enzyme inhibitors versus volume outside the substrate envelope, Vout, for six systems: a. HIV protease (amprenavir, nelfinavir, indinavir, saquinavir, ritonavir; data from Chellappan et al. (8)). b. Abl kinase (VX-680, ...

The three systems with the broadest data sets, HIV protease, Abl kinase, and chitinase, were further analyzed. Table 3 presents the correlation coefficients R of the average mutation sensitivity with Vin, Vout, ratio Vout/Vin, several measures of inhibitor size (Vtot, M.W., Nheavy), and Tanimoto coefficients (FP2, FP3) representing chemical similarity between substrate and ligands. Only Vout consistently correlates with the average mutation sensitivity for all the systems; R≥0.90. Interestingly, although one might expect that measures of chemical similarity between substrate and ligand, such as Tanimoto coefficients, would be useful in this context, in fact they do not perform as reliably as Vout (Table 3). This might reflect the fact that most of the ligands considered in Table 3 are very chemically different from the substrate: the average Tanimoto coefficient is only 0.38. It is also worth inquiring why the molecular size descriptors correlate with inhibitor sensitivity in only two of three cases, while Vout correlates well in all three. When the inhibitors lie in essentially the same region as the substrate, as in HIV protease and chitinase, it is reasonable to expect that Vout will be roughly proportional to the size of the ligand. Indeed, Vout and molecular weight are strongly correlated for HIV protease and chitinase (R = 0.97 and 0.99). However, if the inhibitor and substrate binding modes differ markedly, as in the large binding site of Abl kinase (Figure 3), the correlation between Vout and M.W. can be much lower (0.45 for Abl kinase), and the sensitivity of the inhibitors to mutations correlates with Vout but not with simple measures of molecular size. These results are in accordance with the substrate envelope hypothesis.

Figure 3
Abl kinase substrate envelope (orange) with superimposed inhibitors VX-680 (purple), PD-180970 (yellow), dasatinib (blue), and imatinib (green). Superposed ADP-peptide substrate conjugate (PDB entry 2g1t) is shown in gray. The inhibitors are represented ...
Table 3
Correlation R between the average mutation resistance and volume outside of substrate envelope Vout, volume inside of substrate envelope Vin, ratio Vout/Vin, total molecular volume (heavy atoms) Vtot, molecular weight (M.W.), the number of non-hydrogen ...

The spatial overlap between inhibitor and substrate is quantified by Vin′ and the ratio r=Vin/Vout may be expected to bear on the ability of the molecular size descriptors to correlate with overall mutation sensitivity, based upon the logic in the preceding paragraph. This suggestion is born out by the fact that r <0.5 for the Abl kinase inhibitors, and r>0.8 for chitinase and r>1.2 for HIV protease. In summary, although simple measures of size of the inhibitor may correlate with its sensitivity to mutation for some receptors, only Vout is expected to be a more broadly applicable guide to the design of robust inhibitors.

The present results are reasonably robust with respect to the cutoff distance used in calculating Vout (Section 2.3). For example, using 3, 4 and 5 Å cutoffs for Abl kinase yields correlations R=0.89, 0.90 and 0.81, respectively, while chitinase yields the same correlation (R=0.97) for all three cutoffs.

3.2 Analysis of individual enzyme systems

3.2.1 Abl kinase

The values of Vout for four inhibitors of Abl tyrosine kinase, an important anti-cancer target (19), correlate well with their mutation-sensitivity averaged over eight imatinib-resistant mutants, as evident from Figure 2b and Table 3. The molecular graphics in Figure 3 provide insight into the spatial relationships in this system. None of the inhibitors conform well to the shape of the substrate, and imatinib in particular extends into a completely different region of the protein. As a consequence, only 62 Å3 of its total volume of 405 Å3 lie within the substrate envelope. The other three inhibitors are smaller and fit the substrate envelope better (Figure 3), though still not especially well: their total volumes range from 312 to 366 Å3, and their volumes within the substrate envelope range from 67 to 84 Å3. A recent report on the emergence of dasatinib-resistant mutations V299L, T315A and F317I, which were not observed for imatinib previously (20), supports the observed lack of fit of dasatinib to the substrate envelope, and its consequent sensitivity to Abl kinase mutations. The large values of Vout for other inhibitors, even though they are smaller than imatinib, suggest that new mutations could lead to resistance to the non-imatinib inhibitors.

Whether these four inhibitors would fit the substrate envelope better if one considered the substrate to be a protein tyrosine instead of the ADP substrate needs also to be considered. Superposition of a crystal structure of Abl kinase with a bound ADP-peptide conjugate (gray sticks in Figure 3) shows that the peptide moiety extends away from the bound inhibitors. Indeed, Vout computed for the investigated ligands using substrate envelope based upon ADP-peptide conjugate yield the same results as using ADP only.

It should be noted that Abl kinase can adopt both active and inactive conformations(21). While the calculations presented in the paper were performed using an active form of the kinase, we also computed values of Vout volumes using substrates bound to inactive (PDB id: 2g2f) and Src-like inactive (2g1t) conformations of Abl kinase (21). The correlation of the Vout vs. s results are essentially the same (R differs by 0.01) for the three investigated conformations.

3.2.2 Chitinase

Chitinases belong to the glycohydrolase family of enzymes and are responsible for the degradation of chitin into β(1,4)-N-acetyl-D-glucosamine monomers (22). Inhibitors of chitinases have chemotherapeutic potential against pathogenic fungi, insects, malaria transmission and human asthma (23). The values of Vout for 3 inhibitors solved with a Family 18 chitinase are found here to correlate well with their sensitivity to mutation, averaged over 6 mutants which emerged in organisms exposed to two of the inhibitors considered here, argifin and argadin (23) (Figure 2c and Table 3). The substrate in the present analysis is an N-acetylglucosamine pentamer, which occupies a narrow and deep groove in the enzyme spanning subsites −2 to +3 (24). Argifin and argadin are large, cyclic pentapeptides that overlap with part of the substrate, occupying subsites between −1 and +2 (23), and somewhat extending out of the binding cavity into solution, especially argifin (not illustrated here). This extension outside the binding site was one of the main motivations for employing a ligand-protein distance cutoff in the calculation of Vout (see Methods).

Pentoxifylline, the third inhibitor considered here, is considerably smaller than argifin and argadin, and crystallography shows two molecules of pentoxifylline in distinct locations of the active site (Figure 4). It is not known which location is more stable and hence more relevant enzymatically, although binding energy estimates (not detailed here) with the CHARMM (25) and DREIDING (26) force fields suggest that the first molecule (residue 1434 in the PDB file) binds more strongly than the second molecule (residue 1435), perhaps because the former occupies a deeper binding site inside the protein. Pentoxifylline in the conformation of residue 1434 (white in Figure 4), fits the substrate envelope much better (Vout = 75 Å3) than the other residue 1435 (purple in Figure 4; Vout=141 Å3). According to the substrate envelope hypothesis, conformation 1434 should be the one less affected by mutation and hence should be the preferred mode of binding to the mutants. Therefore, this conformation was the chief focus in the present study.

Figure 4
Chitinase substrate envelope (orange) with superimposed inhibitors pentoxifylline (white and purple), argadin (blue), and argifin (green). Argifin has the largest Vout, followed by argadin. Out of two pentoxifylline molecules in the binding site, the ...

The enzymatic assay used to study this system provided quantitative data only for chitinase mutants that still bind the inhibitors fairly strongly. As a consequence, no data are available for highly resistant mutants, and the average resistance values in Fig 2c and Table 3 accordingly are relatively small. Interestingly, the Y245F chitinase mutant, which for the same reason is absent from Figure 2c and Table 3, abrogates binding to argifin within the sensitivity limit of the method (23) but binds argadin detectably. This observation is consistent with the smaller Vout for argadin relative to argifin.

The structure with bound substrate corresponds to Aspergillus fumigatus chitinase, but the crystal structures with the 3 inhibitors correspond to the chitinase of the bacterium Serratia marcescens. The sequence identity of the two chitinases is only 27%, but the structural match is good: the root-mean-square deviation (RMSD) between the Cα coordinates of the two chitinases is 1.4 Å for all three inhibitor-bound structures. The match is even better inside the binding site. For example, residues that neighbor argifin in Aspergillus fumigatus chitinase have 71% identity with those in Serratia marcescens, and the RMSDs of argifin and argadin bound to Serratia marcescens chitinase (27), relative to Aspergillus fumigatus chitinase, are only 1.02 and 1.03 Å, respectively. These similarities supports the significance of the present substrate envelope analysis.

3.2.3 Thymidylate synthase

Human thymidylate synthase (TS) is the target of a number of existing and developmental cancer drugs (28), and has been the subject of extensive studies. For the present study, we identified two TS inhibitors, raltitrexed (tomudex) and BW1843U89, for which there are crystal structures bound to TS as well as resistance data for 11 TS mutants involving 6 sequence locations. Raltitrexed (Vout = 85 Å3) fits the substrate envelope better than BW1843U89 (Vout = 188 Å3) (Figure 5). This is consistent with the substrate envelope hypothesis, because it retains affinity for the mutants of TS better than BW1843U89 does (Figure 1d). Mutations of residues Ile 108 and Phe 225 have the strongest effect upon the binding of these inhibitors, and they, along with Leu 221, are also the residues that lie closest to the bound inhibitors, especially BW1843U89 (Figure 5).

Figure 5
Thymidylate synthase substrate envelope (orange) with superimposed inhibitors BW1843U89 (blue) and raltitrexed (green). Only residues I108 and F225 whose mutations most strongly affect binding of these inhibitors are labeled. The larger sensitivity of ...

The mutational affinity data considered here are based upon human TS, while the structural data are for E. coli TS, because the requisite inhibitor structures were not available for the human enzyme. The structural data are considered relevant, however, because the two enzymes have overall 0.77 Å Cα RMSD with 97% of structurally matched residues. Furthermore, the gap between the values of Vout for the two inhibitors is substantial and cannot be accounted for by a structural mismatch between the two enzymes.

3.2.4 Dihydrofolate reductase and neuraminidase

Dihydrofolate reductase (DHFR) is a target for anticancer (29), antibacterial (30) and antiprotozoal (31) treatments, while neuraminidase is one of the main therapeutic targets in the treatment of influenza (32). Here, the substrate envelope hypothesis is analyzed for two inhibitors and two mutants, involving 4 residues, of Plasmodium falciparum DHFR (Figure 2e, solid line); two inhibitors and one mutant, involving two residues, of P. vivax DHFR (Figure 2e, dashed line); and three inhibitors and 6 mutants, involving four residues, of neuraminidase (Figure 2f). The data summarized in Figures 2e and 2f do not show an overall correlation between an inhibitor’s Vout and its sensitivity to mutation. This lack of correlation may result in part from the fact that the values of Vout for the inhibitors of DHFR and neuraminidase studied here cover relatively small ranges: compare the horizontal axes of Figures 2a–d with those of Figures 2e–f. Furthermore, the loss of correlation on moving to these two systems from the ones represented in Figures 2a–d is consistent with our expectation that the correlation would weaken as the number of residues probed by mutations falls (Section 3.1): few mutated residues means more parts of the binding site where an inhibitor can project outside the substrate envelope without penalty.

3.3 Vout,loc probes the local environment of the substrate envelope

This subsection examines in more detail those systems for which Vout was not found to correlate well with an inhibitor’s sensitivity to mutation; these are the same systems for which we have only a few mutation data, as noted above. In particular, we explore the idea that the sensitivity of an inhibitor to mutation correlates with the volume of the inhibitor outside the substrate envelope and close to the specific residues that are mutated, Vout,loc. The value of Vout is closely related to the sum of Vout,loc across multiple mutations. Therefore, if we find a correlation between the sensitivity to an individual mutation and Vout,loc, we can expect that a good correlation would be obtained between Vout and overall mutation sensitivity if we had a larger set of mutations that more completely probed the region around each inhibitor. Thus, the study of Vout,loc bears on the utility of Vout as a predictor of mutation sensitivity.

3.3.1 Dihydrofolate reductase

We focus first on Plasmodium falciparum DHFR (Figure 2e, solid line), for which the inhibitor with the larger value of Vout, WR99210, is less sensitive to the studied mutations than the inhibitor with the smaller value of Vout, pyrimethamine. The part of WR99210 which extends outside the substrate envelope (Figure 6) remains far from the four residues affected by the mutations considered here. Pyrimethamine, on the other hand, does not extend as far outside the substrate envelope, but its extension is close to one of the mutated residues, Ser 108. These observations rationalize the observation that pyrimethamine is more sensitive than WR99210 to the mutations studied here even though its value of Vout is smaller. This idea is quantified by calculation of Vout,loc, which limits attention to places where an inhibitor extends outside the substrate envelope and also is close to a mutated residue. Figure 7 shows that this quantity does, in fact, correlate with the sensitivity of pyrimethamine and WR99210 to the mutations considered here.

Figure 6
Plasmodium falciparum DHFR substrate envelope (orange) with superimposed inhibitors pyrimethamine (blue), WR99210 (green). Residue Cys59 is hidden behind the substrate envelope.
Figure 7
Mutation sensitivity as a function of local Vout for P. falciparum DHFR: (a) mutation set K1 CB1, and (b) mutation set V1/S.

In the case of Plasmodium vivax DHFR, (Figure 2e dashed line) the inhibitor’s sensitivity to mutation does increase with Vout, for these mutations. The location where pyrimethamine (Figure 8) extends outside the substrate envelope is near one of the mutated residues, Ser 117. Deschloropyrimethamine fits the substrate envelope better there, and thus has a lower value of Vout and less sensitivity to mutation.

Figure 8
Plasmodium vivax DHFR substrate envelope (orange) with superimposed inhibitors pyrimethamine (blue) and deschloropyrimethamine (purple).

3.3.2 Neuraminidase

Strains of the influenza virus show resistance to some of the neuraminidase inhibitors (33). Varghese et al. (12) noted a qualitative correlation between the degree of resistance of the R292K mutant and the degree of structural dissimilarity of the inhibitor to the transition-state analogue. Here, similarly, Vout and Vout,loc are used to quantify the dissimilarity between substrate and inhibitors. Plots of Vout and Vout,loc against mutation sensitivity are compared (Figure 9) for 6 single-point mutations. Note that mutation sensitivity data for R292K are available for seven inhibitors while the other 5 mutations (E199G, E119A, E119D, R152K, H274Y) have data for three inhibitors; for this reason Figure 2f also contains three data points. Figure 10 shows that all the neuraminidase inhibitors analyzed here have shapes closely resembling the substrate; accordingly their Vout and Vout,loc values are relatively small, as evident from Figure 9b. Table 4 shows, not surprisingly, that Vout correlates poorly with the individual mutation sensitivities s of the inhibitors, with a mean correlation coefficient <R>=0.06. However, Vout,loc exhibits a much better correlation with sensitivity (Fig. 9b and column 2 of Table 4): <R>=0.69. When the distance cutoff used in calculating Vout,loc is changed from 4 Å to 3 or 5 Å, the mean correlation for Vout,loc becomes 0.56 and 0.62 respectively. We therefore used the same 4 Å cutoff for the Vout,loc calculations as in the Vout calculations. However, the 4 Å cutoff failed to include H274Y mutation into the Vout,loc analysis (Figure 9) since van der Waals spheres of all ligand atoms are beyond the 4 Å from His274 residue.

Figure 9
Mutation sensitivity against total (a) and local (b) volumes outside substrate envelope plotted for several neuraminidase mutations. The black points and line (corresponding to the average for three inhibitors) in (a) corresponds to the graph in Fig. ...
Figure 10
Neuraminidase substrate envelope (orange) with superimposed inhibitors 4AM (yellow), G20 (green), G28 (cyan), Neu5Ac2en (red), oseltamavir (purple), peramivir (blue), zanamivir (pink).
Table 4
Correlation R between the mutation sensitivity against Vout and Vout,loc of neuraminidase inhibitors used in this study.

The correlations observed here are consistent with the intuitive notion that a larger value of Vout,loc means a stronger interaction between the ligand and the mutated residue, and hence greater sensitivity to the mutation. On the other hand, the degree to which affinity is lost upon mutation of a given residue necessarily depends upon the details of the mutation (e.g. E199G, E119A or E119D); since Vout,loc is insensitive to these chemical details, it cannot be expected to provide precise predictions.

The comparatively extensive data for R292K were examined in more detail. The correlation coefficient, R, between Vout,loc and mutation sensitivity is 0.89, significantly higher than R=0.61 for Vout. In addition, the inhibitor that is most sensitive to the mutation, oseltamivir, is also the inhibitor with the largest value of Vout,loc: the van der Waals volume of oseltamivir extends beyond the substrate envelope near R292 (purple wireframe in Figure 11). On the other hand, the plot of sensitivity versus Vout,loc for R292K (Figure 9b) shows significant scatter. This may result in part from the small range of Vout,loc for the inhibitors for which R292K sensitivity data are available. In addition, the range of mutation sensitivity is quite high, extending from 16- to 540-fold losses in affinity for the four inhibitors. The large range of sensitivities, despite a small range of Vout,local, means that additional factors contribute significantly to the sensitivity of these inhibitors.

Figure 11
Visualization of volumes Vout,loc of neuraminidase inhibitors and off the substrate envelope (silver) in the neighborhood of Arg292 (represented by red balls-and-sticks): 4AM (yellow), G20 (green), G28 (cyan), Neu5Ac2en (red), oseltamavir (purple), peramivir ...

While we showed that Vout,loc can be a useful quantity which could help our understanding of a sensitivity of a ligand toward a particular mutation, other factors may need to included into a more comprehensive analysis, such as the chemical nature of the part of the ligand extending outside of the substrate envelope, shape and chemical moiety change invoked by the mutation, ligand flexibility and protein conformational changes upon binding and/or mutation. Because this paper introduces a simple shape-based descriptors of Vout,loc (and Vout), extended analysis of these factors is beyond the scope of this paper.

4 DISCUSSION

This retrospective analysis further supports the hypothesis that enzyme inhibitors which fit the substrate envelope tend to retain affinity in the face of clinically relevant mutations. By analyzing five additional enzyme systems, it generalizes prior studies which were limited to HIV protease (8, 9). The present analysis also provides a deeper understanding of the underlying rationale for the substrate envelope hypothesis. In particular, we observe better correlation between Vout and the overall sensitivity of an inhibitor to a set of mutations when the set of mutations is extensive and thus probes ligand interactions with much of the binding pocket.

It is important to consider situations in which the substrate envelope concept might break down. One is the case where the receptor adopts significantly different conformations in the context of bound substrate relative to bound inhibitor. This issue is addressed in part in the context of Abl kinase (Section 3.2.1), where the correlation between Vout and the mutation sensitivity of various inhibitors was found to be insensitive to the choice of receptor conformation. However, when more extensive conformational changes occur, it may become difficult to convincingly overlay the substrate envelope, computed from the substrate-bound conformation, on the inhibitor, bound to its very different protein conformation. In such cases, it might be possible to generalize the present approach by designing inhibitors which contact only those residues which contact the substrate, in relevant conformations of the enzyme. Alternatively, one could define the substrate envelope separately for each variant conformation of the enzyme, and total mutation resistance for the purpose of drug design could be considered as a combination of the Vout values for each conformation. The correlation between Vout and the sensitivity of an inhibitor to mutations could also break down due to flexibility of the inhibitor itself, as previously noted (10). In particular, an inhibitor that extends outside the substrate envelope may retain affinity to a mutant enzyme if the inhibitor adapts to the mutant by a change of conformation. Such adaptive inhibitors (5) offer another important avenue to robust inhibitors which may be pursued in parallel with inhibitors that achieve robustness by remaining within the substrate envelope.

The functional dependence of Vout and mutation sensitivity is not necessarily linear, largely because Vout is insensitive to the specific chemistry of the inhibitor and mutations. Nonetheless, when a large mutation set is analyzed, a monotonic or close to monotonic increase is expected because sensitivity should not drop as Vout increases. This expectation is confirmed by the correlation between Vout and s for Abl kinase, chitinase, thymidylate synthase, and P. vivax DHFR, although the strength of the dependence of mutation-sensitivity to Vout varies from one system to the next. However, for P. falciparum DHFR and neuraminidase, the mutation sensitivity drops as Vout increases. This observation was rationalized by the fact that the available mutations are few and thus do not probe all the interactions of the inhibitors with their binding pockets. However, the mutation sensitivity of these inhibitors does correlate with the quantity Vout,loc, which measures the degree to which an inhibitor projects from the substrate envelope near known mutations. This observation strongly suggests that the sensitivity of inhibitors to mutation would indeed correlate with Vout if a larger mutation set were available.

The fit of an inhibitor or candidate inhibitor to the substrate envelope, as measured by the quantity Vout, represents a simple way to anticipate its robustness in the face of mutations both known and unknown, and the present study shows that this idea is applicable to many therapeutic targets. The software included in the Supplementary information quickly provides the value of Vout (and Vout,loc) for a bound ligand, and the Vout can then be used as a figure of merit along with the usual binding score. Although the quantity Vout,loc can be useful in analyzing known mutations, Vout should be more useful in the prospective design of new inhibitors. The use of such relatively simple parameters should help future novel inhibitors to retain affinity to the wide and unpredictable range of target mutations that can occur in a quickly evolving, highly mutable therapeutic enzyme target.

Supplementary Material

SubstrateEnvelopeCode

Supporting Information

Acknowledgments

We thank Fundação para a Ciência e a Tecnologia (Portugal) for Grant SFRH/BPD/41787/2007 attributed to V. Kairys and SFRH/BPD/30954/2006 attributed to V. Lather. This publication was made possible by the National Institute of General Medical Sciences (NIGMS) of the NIH Grants No. GM61300, GM62050 (to M. K. Gilson) and GM65347, GM66524 (to C. A. Schiffer). The contents of this publication are solely the responsibility of the authors and do not necessarily represent the official views of the NIGMS.

Abbreviations

DHFR
dihydrofolate reductase
FP2/FP3
Tanimoto coefficient based on Daylight/hexadecimal type fingerprints
HIV
human immunodeficiency virus
IC50
concentration to achieve 50% of inhibition
M.W
molecular weight
Nheavy
number of non-hydrogen atoms
RMSD
root mean square deviation
Vin
volume of the inhibitor inside of the substrate envelope
Vout
volume of the inhibitor outside of the substrate envelope
Vout, loc
volume of inhibitor outside of substrate envelope and local to mutated residues

Footnotes

Supporting Information Available

1. The list of inhibitor mutation sensitivities which were used in the paper (Table S1); 2. FORTRAN programs: (a) to generate the substrate envelope grid; (b) to convert it into a grid format viewable with several molecular graphics programs; and (c) to compute Vout and Vout,loc. This material is available free of charge via the Internet at http://pubs.acs.org.

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