Testing homology modeling on mutant proteins: predictingstructural and thermodynamic effects in the Ala98→Val mutantsof T4 lysozymeChristopher Lee
Background: Current approaches to homology modeling predict how aminoacid substitutions will alter a protein’s structure, primarily by modeling sidechainconformations upon essentially immobile backbone frameworks. However, recentcrystal structures of T4 lysozyme mutants reveal significant shifts of themainchain and other potentially serious problems for sidechain rotamer-basedmodeling. This paper evaluates the accuracy of structural and thermodynamicpredictions from two common sidechain modeling approaches to measure errorscaused by the fixed-backbone approximation.
Results: Tested on a series of T4 lysozyme mutants, this sidechain rotamerlibrary approach did not handle mainchain shifts well, correctly predicting thesidechain conformations of only two of six mutants. By contrast, allowingsidechains to move more flexibly appeared to compensate for the rigidity of themainchain and gave reasonably accurate coordinate predictions (rms errors of0.5–1.0 Å for each mutated sidechain), better on average than 90% of possibleconformations. The calculated packing energies correlated well withexperimental stabilities (r2=0.81) and correctly captured the cooperativeinteractions of several neighboring mutations.
Conclusions: Mutant modeling can be relatively accurate despite the fixed-backbone approximation. Mainchain shifts (0.2–0.5 Å) cause increasedsidechain coordinate errors of 0.1–0.8 Å, torsional errors of 10–30°, andexaggerated strain energy for overpacked mutants, compared with the samecalculations performed with the correct mutant backbones.
IntroductionHomology modeling is a widely used technique forprotein modeling that yields good results in regions wheresequence is strongly conserved. However, accurate predic-tion of the structure of segments where sequence changeshas proven to be more difficult [1,2] and remains an activearea of research. This problem has two separate compo-nents: structural predictions for inserted or deleted regions(particularly loops), and modeling of amino acid substitu-tions. Recently, there has been much interest in usingmethods for sidechain placement [3–12] to predict thestructural effects of amino acid substitutions.
These methods are based on two simplifying assumptionsabout protein structure. As crystal structures have shownthat proteins with strong sequence homology adopt similarfolds, these approaches assume that the backbone fold of aprotein will remain unchanged by limited amino acid sub-stitutions. Specifically, they hold the protein mainchainfixed while seeking optimal conformations for the side-chains. Secondly, as most protein sidechains in high-reso-lution crystal structures fit rotamer conformations closely,nearly all of these methods check only the standard
rotamer conformations. This reflects an algorithmic strat-egy of ‘conformational restriction’ as a key to reducing thecomplexity of the problem, exploiting statistical patternsto ignore unusual conformations.
Starting from a backbone-only model of a protein, thesemethods can predict all the sidechain coordinates with aroot-mean-square (rms) error of 1.5–2.0 Å. Particularlywithin the interior of the protein, these methods can pre-dict 80–90% of sidechain conformations correctly. Accord-ingly, there has been hope that this approach could give agood approximation for amino acid substitutions by accu-rately modeling the resulting sidechain rearrangements.
Analyses of crystal structures of mutated proteins can testthis in an especially clear way. By reducing the ‘homologymodeling’ problem to only a single amino acid differencebetween two structures, one can delineate detailed struc-tural changes arising from a specific cause. This is generallynot possible when comparing homologous structures thatdiffer by many substitutions. Furthermore, mutant proteinsprovide a key test of homology modeling methods. If thesemethods are to give accurate results for homologues with
Department of Chemistry, MC 5080, Stanford,University Stanford, California, USA.E-mail address: [email protected]
20–50% of the residues replaced, they should giveextremely accurate predictions for ‘easy’ problems, such asa mutant protein with only one or two amino acid changes.The solution of crystal structures of a wide variety ofmutants of bacteriophage T4 lysozyme [13–16] has raisedimportant questions about the applicability of sidechainmodeling calculations to homology modeling [17].
The structures of these mutants do not appear to fit amodel of sidechain rotamer rearrangement. Instead of sig-nificant changes in sidechain torsional angles on a fixedbackbone, these structures reveal a mixture of sidechainand mainchain shifts, with only slight rotations ofsidechain torsions. Although sidechain atoms shift some-what more than the mainchain atoms, these movementsarise as much from changes in the orientation and positionof the backbone as from changes in sidechain torsions.Thus, knowing how the backbone moves would appear tobe as important for predicting sidechain coordinates aspredicting the sidechain torsions. Furthermore, mutantproteins adopted the same rotamers as the wildtype,undergoing small torsional shifts (<20°) too fine to be pre-dicted directly by rotamer methods. Rotamer librariesallow only 3–7 conformations for a typical sidechain, dif-fering by 90–120° in their torsional angles [18]. In thislight, the problem of predicting the structures of proteinmutants would appear to be simultaneously trivial andinsoluble for many current methods: the answer they tryto predict (sidechain rotamers) is already known, and thefactor underlying most of the structural changes (back-bone shifts) they have no mechanism to predict.
Baldwin et al. [17] point out another difficulty inherent incurrent modeling approaches. These methods seek toreduce the complexity of the problem by excluding con-formational possibilities—for example by holding themainchain fixed, considering only a few rotamer con-formations, enforcing strict ‘unacceptable’ contact rules,etc. Assuming such artificial constraints on the structure’sflexibility risks excluding the correct answer, which may not exactly fit ideal values. Indeed, in tests of astandard rotamer library on the T4 lysozyme mutants, notone of the mutant proteins was judged to be stericallyacceptable by contact rules commonly used in modeling,although all were viable experimentally [17]. Even whenthe calculations were repeated using the crystallo-graphically determined mainchains of the mutant pro-teins, most of the mutants were still not predicted to be‘allowed’ [17].
Thus, it is important to test homology modeling onmutant proteins to assess how seriously these problemsrestrict current approaches. In this paper, I compare theo-retical predictions against both experimentally deter-mined mutant structures and thermostabilities, focusingon mutations that induce a high level of strain. Such muta-
tions, characterized by decreased protein stability due topacking strain, cause significant mainchain distortions andpose a challenge to the fixed-mainchain modeling calcula-tions. Dao-pin et al. [15] have reported crystal structuresand thermodynamic measurements for an intriguing seriesof six T4 lysozyme mutations that exactly fit this descrip-tion. Mutation of a buried alanine (residue 98) to thelarger amino acid valine destabilizes the protein by nearly5 kcal mol–1. This substitution causes a variety of main-chain shifts that push apart and slightly bend two helicessurrounding the mutation. Furthermore, Dao-pin et al.[15] used mutagenesis to generate a wealth of structuraland thermodynamic data about the interactions of the sub-stituted residue with its neighbors. My results indicatethat fixed-mainchain approaches can give reasonably accu-rate predictions of the structural details of these mutantproteins and their stability effects, if sidechain conforma-tions are not limited to standard rotamers but are insteadallowed full torsional flexibility.
ResultsTwo common sidechain modeling approaches were testedto assess the impact of mainchain shifts on their accuracy:1. rotamer-based modeling; 2. highly flexible sidechains,allowing free χ torsion rotations in approximately 10°
2 Folding & Design 1996, Vol 1 No 1
Figure 1
A schematic of self-consistent ensemble optimization (SCEO).
.
Calculate New Ensemble pi(χi) = 1/q i eEi(χi)/kT
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steps. Coordinates for a zone of sidechains surroundingand including the mutations (see Materials and methods)were deleted from the wildtype T4 lysozyme crystal struc-ture. These sidechains were then modeled by self-consis-tent ensemble optimization (SCEO; Fig. 1) using eitherrotamer conformations only (SCEO-rotamer) or fullyflexible sidechains (SCEO-continuous). Throughout thispaper, the various mutants will be referred to by the one-letter codes of the amino acids at positions 98, 149 and152, respectively, in lower-case for wildtype residues, andcapitalized for a mutation. Thus the wildtype protein,which has alanine, valine and threonine respectively inthese positions, would be designated as ‘avt’ and theA98→V/T152→S mutant would be ‘VvS’.
First, the reproducibility of the resulting predictions wastested by assessing the convergence to a global minimumstructure and energy. Seven prediction runs on wildtypelysozyme were started from different random conforma-tions. The predicted rotamer conformations were identicalover the set of seven runs and closely matched the crystalstructure (Fig. 2). Similarly, the predicted energies con-verged with little variation from run to run, indicating aconsistent global minimum (Fig. 3a). The standard devia-tion of the final energies of the seven runs was less than 1 kcal mol–1.
The energies predicted by the rotamer method were com-pared with the experimentally measured thermostabilities(Fig. 3b). There appears to be a correlation, with lowerpredicted energies corresponding to increased meltingtemperatures. The correlation coefficient for the set ofseven data points (wildtype plus six mutants) is r2=0.785.However, the mutants are strongly clustered into two dis-tinct groups: those containing alanine at position 98 (avt,avS, and aCt) and those with valine at 98 (Vvt, VvS, VCS,and VIS). The overall correlation does not hold withinthese distinct groups. The sign of the slope is lost (for theAla98 cluster the best-fit line is flat; for the Val98 mutantsthe line actually has a positive slope), and the points showno correlation (correlation coefficients of r2=0.007 andr2=0.101 for the Ala98 and Val98 clusters, respectively).Thus, the only demonstrable predictive value of therotamer calculations is the destabilizing effect ofAla98→Val.
To assess the possible errors due to the use of only ideal-ized, rotamer conformations, these calculations wererepeated using the SCEO-continuous protocol, introdu-cing full sidechain flexibility into the model. The stabilitycorrelation is significantly better (Fig. 3c, comparison with∆Tm; Fig. 3d, comparison with ∆∆G). Overall, the correla-tion coefficient is r2=0.807; moreover the correlation holds
Research Paper Testing homology modeling on mutant proteins Lee 3
Figure 2
The A98→V prediction zone. (a) Theprediction zone surrounding the A98→Vmutations; each residue included in themolten zone is labeled. The backbone isshown as a Cα trace (dotted lines) for clarity,with sidechains shown as solid lines. (b) The‘empty-core’ starting model used for thepredictions; all sidechain coordinates for themolten zone have been deleted.
CA(161 TYR) CA(153 PHE)CA(152 THR)
CA(149 VAL)
CA(102 MET)
CA(98 ALA)
CA(94 VAL)
CA(6 MET)
CA(161 TYR) CA(153 PHE)CA(152 THR)
CA(149 VAL)
CA(102 MET)
CA(98 ALA)
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CA(6 MET)
(b) "Empty core" model
(a) Prediction zone
4 Folding & Design 1996, Vol 1 No 1
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true within the Ala98 and Val98 subsets (the correlationcoefficients within these subgroups are r2=0.648 andr2=0.867, respectively). For r2=0.807 and a sample sizen=7, the 95% confidence interval for the actual correlationcoefficient ρ is 0.4 < ρ < 0.98 (see Table X in [19]). Thusthe null hypothesis that there is no actual correlation(ρ=0), and that the observed correlation occurred simplyby chance, lies outside this interval and can be rejectedwith >95% confidence.
In contrast to the rotamer calculations, all of the mutantswere predicted by the SCEO-continuous protocol to beless stable than the wildtype, as indeed they are. Also, Vvtwas correctly identified as the most destabilized mutant,with very high levels of van der Waals strain (18.3 kcalmol–1) against the wildtype backbone structure (held fixedin my calculations). SCEO-rotamer incorrectly predictedVIS to be the least stable mutant. However, both calcula-tions greatly exaggerated the total magnitude of destabi-lization caused by the mutation—the measured freeenergy of unfolding (∆∆Gu) of Vvt is reduced by only 4.9kcal mol–1 [15]. This is a consequence of holding themainchain fixed, preventing the mainchain shifts that inreality diffuse this strain. The rotamer runs possessedeven less structural flexibility (because of their rigidsidechains); consistent with this hypothesis, they exagger-ated the steric strain of Vvt much more (>45 kcal mol–1
higher than wildtype).
In addition, SCEO-continuous correctly predicted thecooperative interactions of Val149 and Thr152 with residue98. Positions 149 and 152 lie on one face of an α-helix adja-cent to residue 98, sandwiching it between them (see Fig.2a). In the wildtype background, the calculations predictedthat both Thr152→Ser (avS) and Val149→Cys (aCt) desta-bilize the protein, by loss of the hydrophobic γ-methylsVal149 Cγ1 and Thr152 Cγ2. The predicted destabilizationsfor these mutants versus wildtype were 1.45 kcal mol–1 foraCt and 1.21 kcal mol–1 for avS. Experimentally, these
mutants are 2.2 and 2.6 kcal mol–1 less stable than wild-type, respectively. In the context of the Ala98→Val muta-tion, however, these mutations were predicted to producean opposite, stabilizing effect. They create extra space forthe sidechain of Val98, reducing its steric strain to anextent that more than compensates for the lost hydropho-bic burial. Experimentally, VvS is 0.9°C more stable, andVCS 2.7°C more stable, than Vvt [15]. However, the calcu-lations greatly overestimated the magnitude of these ener-getic effects. CVS, for example, was predicted to be nearly10 kcal mol–1 less strained than Vvt, whereas experi-mentally it is only 0.5 kcal mol–1 more stable. The fixed-backbone calculations overestimate the magnitude ofstrain available to be ‘released’ by the compensating muta-tions, resulting in a noticeable parabolic curvature in thecorrelation plot.
A critical question for rotamer-based modeling is whethersubsequent refinement steps can correct for the errorsresulting from its idealized conformations. According tothis approach, selection of the best rotamers gives anapproximate solution that could be refined to the trueglobal minimum, if the initial rotamer were near therefinement method’s convergence radius. Alternatively,the rotamer prediction might be too far off to converge, ormight even fail to pick the right rotamer due to the highsensitivity of the energy functions to even slight coordi-nate errors. To test this, the final structures predicted bythe rotamer runs were refined by energy minimization.First, conjugate-gradient minimization was performed oneach structure until its energy converged, and the finalenergies graphed against experimental stability (Fig. 3e).The resulting correlation does show less clustering thanthe original rotamer calculations. Overall, however, thecorrelation coefficient gets worse (r2=0.56), and the corre-lations within the Ala98 and Val98 groups are still poor(r2=0.125 and r2=0.425, respectively). The mutant VvS ispredicted to be much less stable (nearly 50 kcal mol–1)than Vvt, the least stable mutant experimentally. The
Research Paper Testing homology modeling on mutant proteins Lee 5
Figure 3
(a) Convergence of SCEO ensemble energy. Superposition of energyplots from seven different SCEO-rotamer runs, showing convergenceof the ensemble energy during rotamer modeling of the wildtypeprotein, as a function of the optimization cycle number. Each run wasstarted from a different, random sidechain conformation. Ecalc is theaverage ensemble energy during a cycle. The first 15 cycles cool from6000K to 298K; the last 10 cycles are equilibrated at 298K (seeMaterials and methods). (b) Comparison of SCEO-rotamer predictedenergies with the measured mutant thermostability. Predicted packingenergy change relative to the wildtype (∆Ecalc) versus the experimentalchange in melting temperature (∆Tm), predicting sidechains in rotamerconformations (see text). Each mutant is labeled by the one-lettercodes of the amino acids at positions 98, 149, and 152, consecutively,in lower-case for wild-type residues and capitalized for mutations. (c)Comparison of SCEO-continuous predicted energies with themeasured mutant thermostability. Predicted packing energy change
relative to the wildtype (∆Ecalc) versus the experimental change inmelting temperature (∆Tm). (d) Comparison of SCEO-continuouspredicted energies with the measured free energy. Predicted packingenergy change relative to the wildtype (∆Ecalc) versus the experimentalchange in the free energy of unfolding (∆∆Gu). (e) Energy minimizationof SCEO-rotamer models versus measured mutant thermostability.Total system energy relative to that of the wildtype (∆Emin), following1000 cycles of conjugate gradient energy minimization of the rotamer-modeled mutant structures, versus the experimental change in meltingtemperature (∆Tm) for the mutants. (f) Zone energy minimization ofSCEO-rotamer models versus measured mutant thermostability: zoneenergy relative to that of the wildtype (∆Emin), following 1000 cycles ofconjugate gradient energy minimization of the rotamer-modeled mutantstructures, versus the experimental change in melting temperature(∆Tm) for the mutants. Zone minimization allowed only the residues inthe molten zone to shift during the minimization (see text).
6 Folding & Design 1996, Vol 1 No 1
Table 1. Root-mean-square (RMS) errors of predicted mutant structures.
Mutants are designated by the one-letter codes of the amino acids atpositions 98, 149 and 152, respectively, in lower-case for wildtype
residues and capitalized for mutations.
Mutants are designated by the one-letter codes of the amino acids atpositions 98, 149 and 152, respectively, in lower-case for wildtype
residues and capitalized for mutations.
range of energy differences among the set of mutants isenormously exaggerated (139 kcal mol–1 differencebetween wildtype and VvS). The energy range of theinput rotamer structures was <60 kcal mol–1. Surprisingly,energy minimization appears to have magnified this range,rather than reduced it.
The large energy range may indicate that the energy mini-mization approach used was not powerful enough tohandle such a large number of degrees of freedom andlocate an energetically meaningful minimum. To examinethis possibility, zone minimization was also performed onthe subset of residues constituting the molten-zone in theSCEO calculations (Fig. 3f). The range of minimizedenergies was reduced to <10 kcal mol–1 (compared with 5kcal mol–1 experimentally). Thus the method did appearto be more consistently successful in minimizing theenergy of the smaller zone. However, little improvementin the correlation with experimental stability wasobserved; the compensatory mutants (VvS, VCS, and VIS)were incorrectly predicted to be highly destabilizing.
To understand the problems in the SCEO-rotamer ener-gies, I have compared the predicted models with themutant crystal structures (Tables 1–3). Although most ofthe mutant sidechain conformations were very close torotamers, the mutation Ala98→Val was poorly fit by therotamer calculations, which predicted a completely dif-ferent conformation from both the SCEO-continuous cal-culations and the crystal structures (see mutants Vvt, VvS,and VIS). Because of this, the rotamer modeling matched
the mutant sidechain conformations in only two of the sixmutants: aCt and VCS. Mutant aCt consists of a singlemethyl group deletion from the wildtype, with minimalalteration of the sidechain packing. The incorrect rotamerassignments in the other models are likely to impederefinement by subsequent energy minimization, as thesteric barriers to moving from one rotamer to another are very high. These errors may explain the failure ofsimple refinement steps to improve the rotamer energypredictions.
Intriguingly, the only Val98 mutant accurately predictedby rotamers was VCS, which had the smallest mainchainshift at this position (see Table 1). This suggests thatmainchain shifts may be a significant factor hindering theSCEO-rotamer calculations. To test this hypothesis, therotamer modeling was repeated using the mutant crystalstructure backbones. All errors for Val98 were corrected(data not shown), showing that the mainchain shiftsbetween wildtype and mutant structures (0.2–0.5 Å) wereresponsible for the problems encountered in the rotamermodeling.
I have analyzed the SCEO-continuous models in detail toassess their accuracy, and to see whether they are similarlysensitive to such mainchain shifts. To measure the statisti-cal significance of these results, the rank of each predic-tion was calculated as a percentile score versus all possiblepredictions. That is, if a given sidechain prediction has arank of 90th percentile, it is more accurate (as measuredby coordinate rms deviations from the crystal structure)
Research Paper Testing homology modeling on mutant proteins Lee 7
Table 3. Percentile rank scores of predicted mutant structures.
Position Mutant Percentile rank Percentile rank Percentile rank Percentile rankrotamer versus rotamer versus continuous versus continuous versus
Percentile rank scores for each sidechain prediction (i.e. the fraction ofthe sidechain’s possible conformations that are less accurate than theprediction is; see Materials and methods), are given for both the rotamerand continuous torsion models. Percentile ranks were calculated for
each model against both all the conformations possible based on thewildtype backbone, and based on the mutant crystal structurebackbone. This latter measure ranks the accuracy of the model againstthe ideal case where mutant backbone shifts are known perfectly.
8 Folding & Design 1996, Vol 1 No 1
Figure 4
Comparison of predicted mutant structureswith the crystal structures. For each mutant,the predicted sidechain positions are shownas solid lines; the crystal structurecoordinates are shown as dashed lines. (a)avt (the wildtype protein), modeled from thewildtype backbone. (b) Vvt. (c) VvS. (d) avS.(e) VCS. (f) aCt. (g) VIS.
6 MET 98 VAL
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152 THR 161 TYR
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(a) avt
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than 90% of the possible conformations for that residue.For the overall set of 11 sidechain substitutions present inthese mutants, the probability of obtaining the observedlevel of accuracy by chance was P=1.58 × 10–11. Thus, theresults are clearly significant. The geometric mean rank ofthe predicted coordinates for this set was 90th percentile,
substantially better than simply picking the correct rota-mer region (66th percentile). This corresponds to a qualityfactor (the ratio of conformation space farther from theX-ray structure than the model is, divided by the fractionthat is closer than the model is; see Materials andmethods) 10-fold better than random. Even when these
Research Paper Testing homology modeling on mutant proteins Lee 9
Figure 4 continued
6 MET 98 ALA
102 MET
149 CYS
152 THR 161 TYR
6 MET
98 ALA
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6 MET 98 VAL
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(e) VCS
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6 MET 98 VAL
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152 SER 161 TYR
6 MET 98 VAL
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152 SER 161 TYR
(g) VIS
predictions, based on the fixed wildtype backbone, areranked against all possible predictions generated from thecorrect mutant backbones, the statistical significance ofmy results remains high (Table 3, ‘continuous versusmutant backbone’). These rankings are typically only3–10 percentile points lower than the rankings based onthe wildtype backbone and are 81st percentile or better.Thus the accuracy of the current, fixed-backbone predic-tions ranks well even against the ideal case where oneassumes that the mutant backbone could be predictedperfectly prior to performing the sidechain modeling. Therms errors, torsions, and percentile ranks of the SCEO-continuous predictions for individual residues are given inTables 1–3.
The SCEO-continuous structure prediction for the Vvtmutant (Fig. 4b) closely matched the crystal structurecoordinates, despite the neglect of mainchain shifts. Theoverall rms error for the predicted sidechain coordinateswas 0.75 Å, approximately the same as that for wildtypepredicted from its own backbone (0.67 Å, a control involv-ing no mainchain shifts). For the substituted residue(Ala98→Val), the rms error was 0.49 Å, due almost entirelyto the mainchain shift of this residue in the Vvt crystalstructure (0.40 Å). Of the other residues in the zone,Val149 was predicted to shift significantly from its wild-type position, moving away from Val98.
The predicted sidechain torsion angles deviated some-what from the Vvt crystal structure. Experimentally, theχ1 of Val149 is rotated 5° relative to its position in thewildtype crystal structure, away from the preferred transconformation. It also undergoes a significant mainchainshift (0.27 Å). Together, these effects move its Cγ1 carbon,which lies closest to residue 98, 0.70 Å away from its wild-type position. In the model, by contrast, Val149 was pre-dicted to rotate 34° from its wildtype position. However,this excessive rotation placed the Val149 Cγ1 atom inalmost perfect superposition with its actual coordinate inthe Vvt crystal structure (0.16 Å deviation). The sidechainmodeling accomplished by torsional rotations what thereal structure accomplishes primarily by backbone shifts:the essential movement of Val149 Cγ1 away from theenlarged sidechain of residue 98. Although this correctlypredicts the sidechain coordinate shifts that accommodateVal98, it does not necessarily give the best overall rmsdeviation from the crystal structure. Val149 Cγ1 was pre-dicted very close to its position in the crystal structure, butthe Cγ2 atom was 0.8 Å off, twisted out of position inmoving the Cγ1 away from Val98. Indeed, the SCEO-rotamer prediction for this residue had a slightly lower rmsdeviation (see Table 1).
The first of the ‘compensatory’ mutations, Thr152→Ser(VvS), deletes a single methyl group (Fig. 4c). The overallsidechain rms error of the SCEO-continuous prediction
was 0.69 Å, and the compensating substitution, Ser152, ispredicted accurately. By contrast, in the single mutant avS(containing the mutation Thr152→Ser in the wildtypebackground), all the residues except Ser152 were correctlyplaced (Fig. 4d). The wildtype sidechain at 152 (threo-nine) is β-branched, and consequently there are two freepositions which the γ-hydroxyl group of Ser152 couldoccupy.
By adding a third mutation, Val149→Cys, Dao-pin et al.[15] constructed the triple mutant VCS, effectively delet-ing a second methyl group. SCEO-continuous predicts itsconformation with an overall sidechain rms of 0.72 Å (Fig.4e). Dao-pin et al. [15] also crystallized the single-sitemutant aCt (Fig. 4f). The calculations predict that themutant sidechain Cys149 will adopt very differentrotamers in the Ala98→Val versus wildtype contexts: transin aCt, versus gauche in VCS. This change between confor-mations is indeed observed in the crystal structures (seeFig. 4e,f). A second triple mutant, VIS, replaces Val149with an even bulkier residue, isoleucine. In the crystalstructure, this mutation produces a larger backbone shiftat residue 149 (0.48 Å, as opposed to 0.36 Å in VvS).Despite these shifts, the predicted conformation of Ile149appears reasonably accurate (Fig. 4g).
To directly test the sensitivity of the SCEO-continuousmethod to the fixed backbone approximation, modelswere calculated based on backbones from the mutantcrystal structures and measured the reductions in rms error(Table 1). A slight but significant improvement wasobserved for most conformations of the three mutatedpositions (98, 149, and 152), giving typical rms errors perresidue of 0.1–0.5 Å, similar to that obtained for the wild-type sidechains on the wildtype backbone (cf. SCEO-con-tinuous for avt). The wildtype-based predictions had rmserrors of 0.3–1.0 Å for these positions. This difference inaccuracy is fully accounted for by the slight mainchainshifts observed between the wildtype and mutant crystalstructures (0.2–0.5 Å rms). This corresponds to a drop inprediction rank from 90–99th percentile (using the correctmutant backbones; data not shown) to 80–95th percentile(using the fixed, wildtype backbone). Thus, although thepredictions based on the wildtype mainchain are reason-ably accurate, most of their errors are attributable to thefixed-backbone approximation.
The sidechain torsion angles predicted in these runs(Table 2) matched the crystal structure better (inparticular for residues 98 and 149). This illustratesdirectly that the SCEO-continuous method resorts to dis-torted torsions for modeling mutant sidechain shifts onthe fixed wildtype backbone; given the correct mutantbackbones, its predictions return towards the relativelyunchanged rotamer conformations observed in the crystalstructures.
10 Folding & Design 1996, Vol 1 No 1
DiscussionThese calculations are the among the first tests of homol-ogy modeling on a set of mutant crystal structures [20],which could be a powerful tool for improving structureprediction methods. Crystal structures of site-directedmutants permit one to analyze the structural causes ofmodeling errors in a uniquely clear way. Because only oneor two amino acid substitutions are present, the causes ofstructural shifts can be clearly attributed and analyzed.Mutants can show in detail where methods fail andsucceed, and this should be very informative given thewealth of mutant structural and thermodynamic data nowavailable.
These results show that modeling of mutations as aproblem of sidechain rearrangement can yield useful struc-tural and energetic predictions. The Val98 mutants exam-ined here contain mainchain shifts of up to 0.5 Å in andaround the mutated residues, yet the prediction methodwas still able to give relatively accurate predictions of theirstructures and energetics. The sidechain coordinate pre-dictions for mutated residues ranged from 0.5–1.0 Å rmserror, only slightly larger than for the wildtype sidechainspredicted on the wildtype backbone (e.g. 0.67 Å rms forthe 10-residue prediction zone for the wildtype sequence).At least at this level of backbone shift (0.2–0.5 Å), theSCEO predictions retain most of their accuracy. The pre-dicted sidechain torsional shifts tended to be significantlylarger than those observed experimentally.
How general are these results? Tests of modeling on otherproteins with SCEO-continuous gave similar levels ofaccuracy. The blind prediction of the structure of theVal36→Leu, Met40→Leu, Val47→Ile mutant of λ repres-sor [21] has an rms error of 1.11 Å for the three substitutedsidechains versus the recently reported crystal structure[22], despite mainchain shifts of 0.60 Å. Homology model-ing by SCEO of the murine class I major histocompatibil-ity complex protein H-2Kb from the human HLA-A2 (72%identity) predicts the peptide binding cleft polymorphicresidues with an rms error of 1.0 Å (C Lee, unpublisheddata). The backbones of H-2Kb and HLA-A2 differ by0.66 Å rms. Similarly, Chung and Subbiah [23] reportedthat sidechain modeling by SCEO remained reasonablyaccurate up to backbone deviations of 1 Å rms. Thus,there is substantial evidence that SCEO’s use of sidechainflexibility to give reasonably accurate models despitemainchain shifts is generalizable to other systems andworks for a range of real-world homology modeling prob-lems. Obviously, this approach is not appropriate for pro-teins involving large mainchain shifts, such as those thatoccur between distantly related globins [24].
These results show that the mutants’ differing degrees ofbackbone movement do not prevent prediction of thepattern of the mutations’ stabilities, including cooperative
interactions between residues. The most evident conse-quence of the fixed mainchain was overestimation ofsidechain packing strain. Loss or gain of attractive van derWaals interactions generally produced energetic effectsrelatively close to those actually observed experimentally.On the other hand, losses and gains of van der Waalsrepulsions nearly always overestimated the real net ener-gies by 2–10-fold. This suggests caution in comparing themethod’s predicted energies for cavity-creating versusstrain-inducing mutations. A set of mutants with varyingmixtures of attractive and repulsive stability contributionscould confuse the current calculation method. Furtherwork must address this issue.
These tests on mutant crystal structures may have generalimplications for homology modeling. In particular, theysuggest reconsideration of my basic algorithmic strategiesfor overcoming the challenge posed by proteins’ combina-torial complexity. A major difficulty in protein modelingcalculations is the effectively infinite number of conforma-tions possible for any given prediction problem, and thedifficulty of eliminating them a priori without actuallyexamining them. Two distinct approaches to solving this‘combinatorial’ problem have emerged. First, researchershave sought to reduce the number of conformations thatneed to be considered, an approach one might call ‘confor-mational restriction’. For example, >80% of protein side-chains in recent high-resolution crystal structures fitrotamer conformations closely [18], suggesting that homol-ogy modeling calculations could be limited entirely torotamers without introducing many errors. Second, algo-rithms have been developed for searching the combinator-ial space more efficiently and comprehensively, anddemonstrating the ability to locate the global minimumreliably. Such an ‘efficient search’ approach can be com-bined with ‘conformational restriction’ (as in SCEO-rotamer), or used to expand the range of conformationsthat can be searched (as in SCEO-continuous).
The results presented in this paper suggest potentialproblems for methods that rely on rotamers[3,6,7,9–11,18]. For mutant and homology modeling,mainchain shifts make the rigidity of the rotamer set a dis-tinct disadvantage. Although the mutant crystal structureis likely to be close to a rotamer, the sidechain torsions onthe wildtype backbone that best approximate the mutan-t’s actual coordinate shifts may not be so near a rotamer. Inthe Ala98→Val (Vvt) mutant, for example, Val98 andVal149 were not modeled accurately using rotamers.Indeed, the full torsional flexibility provided by SCEOwas able to superimpose the key γ-methyl groups close totheir true coordinates only by using non-ideal torsions tocompensate for the unmoving backbone. The simulatedevolution method of Hellinga and Richards [25] employs asimilar ‘efficient search’ approach, allowing fine sidechaintorsional adjustment, and has obtained similar results. The
Research Paper Testing homology modeling on mutant proteins Lee 11
main failing of the SCEO-continuous calculations is thatthey still exclude important conformational possibilities—backbone movement. Rotamers may be somewhat worse,in that they also lack sidechain flexibility during the criti-cal evaluation step.
The emphasis on efficient search for mutant predictionproblems [21] has been questioned as a priori unnecessaryand inadequate to provide useful predictions [26].However, these tests of SCEO on mutant crystal struc-tures show that it does give useful predictions of mutantstructures, and that the focus on efficient search may be acentral new direction for homology modeling. Takingadvantage of the greater conformational flexibility thatefficient search permits, SCEO-continuous succeeded inpredicting mutants’ structural shifts where rotamers failed,and correctly captured important cooperative stabilityeffects due to interactions between adjacent mutations.The rule of thumb approach described by van Gunsterenand Mark [26] is extremely useful. However, it inherentlyignores such effects. The lysozyme tests suggest why thesimplistic SCEO calculation is able to predict stability: itpredicts mutant structures well and estimates the basicsteric effect of how well each mutation fits into the core.Recent applications to modeling of major histocompatibil-ity complex proteins ([27,28]; C Lee, unpublished data),bacteriophage repressors [21,23], loop prediction [29], β-strand threading [30] and other problems [12,31] suggestthat SCEO and related efficient search algorithms mayhave widespread utility.
Materials and methodsSelf-consistent ensemble optimization (SCEO)Reproducible convergence of multiple prediction runs to a consistentanswer is an important test of a method’s ability to find the globalminimum. Because simulation-based and gradient energy minimizationmethods give different answers when started from different sidechainconformations, they do not meet this criterion. Thus there is a need toredirect structure prediction strategies towards efficient search algo-rithms, explicitly designed to overcome the conformational searchproblem. To search efficiently, the calculation must visit and compareall the low-energy areas of ‘conformational space’. However, the pres-ence of high-energy barriers separating these multiple minima makesthis difficult, especially for gradient or simulation-based methods. Athigh simulation temperatures where the calculations can cross high-energy barriers, they will spend little time in the relatively sparse energyminima. At lower temperatures where the trajectory will be forced todescend into low-energy regions, it cannot cross barriers. This dilemmagives rise to the ‘insufficient sampling’ problem that complicates molec-ular dynamics approaches to structure and energy prediction [32]. Theproblem becomes especially acute as one introduces more flexibilityinto the prediction model, expanding the conformational space. Forexample, to switch from rotamers to 10° torsional rotations, assuming 5rotamers for a typical residue, and two χ torsion angles, multiplies thenumber of combinations by a factor >200n, where n is the number ofresidues in the prediction. For a 10-residue zone, the possibilities multi-ply by >1023. Thus, a more flexible approach puts a heavy stress onefficient conformational search.
I have developed a method to do this that operates not in conformationspace (where the variables being optimized correspond directly to the
conformational values of a particular structure), but instead in ensemblespace (where each variable measures the frequency of a particularstructure, in a thermal ensemble of multiple conformations). In ensem-ble space, high-energy conformations do not act as localized barriersthat impede movement in the space, because they are spread through-out the ensemble space. Thus, it is possible to develop efficientmethods to find the correct thermal ensemble, yielding detailed struc-tural and thermodynamic predictions. In particular, one can exploit aself-consistency condition from statistical mechanics for a ‘correct’ensemble, whose conformational energies and probabilities mustmatch each other through the following relations:
§1 Ei(χi→
) =j≠iΣN
∫ pj(χj→
)Uij(χi→
,χj→
)dχj→
(where Ei(χi→
) is the mean field energy of a residue i in a given conformation χi
→, averaged over its interactions with all other residues
j, in all their possible conformations χj→
; pj(χj→
) is the probability ofresidue j being in conformation χj
→; and Uij(χi
→,χj→
) is the potentialenergy of interaction of residue i in conformation χi
→, with residue j
in conformation χj→
).
From Gibbs’ derivation of the canonical ensemble, it is known:
§2 pi(χi→
)=qi–1
e–Ei(χi
→)/kT
where qi is the canonical ensemble partition function for residue i
qi = ∫e–Ei(χi
→)/kT
dχi→
A thermodynamically correct ensemble must obey both equations §1and §2, giving the self-consistency condition
Pcorrect →§1
Ecorrect →§2
Pcorrect→§1
Ecorrect→...
This condition can be applied to optimize any ensemble, consisting of aset of probability values pi(χi
→) for all its residue conformations, by mini-
mizing the difference between its pi(χi→
) and that calculated by applying§1 and §2. A thermal ensemble is obtained when the difference falls tozero. Steepest descent minimization of this function is very straightfor-ward; furthermore, a fast stochastic sampling approximation to §1allows it to be performed in minutes on a desktop workstation [31]. Togeneralize this procedure, one begins from the trivial T=∞ ensemble (inwhich all pi(χi
→) are equal), and cool to the desired temperature (298K),
using the self-consistency condition to correct the calculated ensembleconstantly during cooling (Fig. 1). One advantage of the SCEOapproach is that the size of conformational sample required for conver-gence is constant for sidechain modeling, independent of the size ofthe molten zone being modeled [31].
Force-fieldThe physical model employed in the work described in this paper is asimplistic treatment of sidechain packing, emphasizing steric inter-actions. Its main simplifications are:
1. the protein backbone is held fixed. Structure prediction is treatedentirely as a problem of searching the possible side-chain rearrange-ments, with the backbone fold held rigid. Sidechain flexibility ismodeled as free rotations around their χ torsions (treated at a coarse-ness of about 10° steps), with rigid bond lengths and angles.
2. the energy function consists entirely of a van der Waals potential foratom pairs closer than 6 Å, and a threefold symmetric alkane torsionalpotential.
(1L50), and A98→V/V149→I/T152→S (1L51) were obtained from theBrookhaven Protein Data Bank [34].
All SCEO calculations described in this paper were performed exactlyas previously described [21,31], starting from the wildtype structure.First, side-chain coordinates for a 10-residue zone surrounding themutations (Met6, Asp10, Val94, Ala98, Met102, Trp138, Val149,Thr152, Phe153, Tyr161) were deleted and rebuilt in random confor-mations using the desired amino acid sequence for each mutant. Allcalculations were started from the wildtype structure (Brookhaven PDB3LZM). One water molecule, HOH 170, was observed to make a badvan der Waals contact with Thr152 in the wildtype crystal structureand was omitted from all the calculations.
SCEO calculations were generated using linear cooling from 6000K to298K over 15 cycles with ‘heavy’ data collection, followed by 10 cyclesof equilibration at 298K [31]. These calculations were repeated seventimes for each mutant, with different random number seeds, and therun with the lowest final energy used for the predictions. Structure pre-dictions for each residue were taken from its highest probability confor-mation in the calculated ensemble of the final equilibration cycle.Packing energy predictions (Ecalc) were taken from the average energyof the final ensemble for each mutant. All calculation steps and parame-ters were as previously described [31]. However, the jump frequencywas reduced to one jump per 100 steps, and the minimum conforma-tional sample per cycle was increased to 5000.
Rotamer modeling was performed by restricting the SCEO calculationsto a set of rotamer conformations [18]; each rotamer’s initial conforma-tional probability was set to its reported frequency in high-resolutionprotein structures [18]. A jump frequency value of 1 was used for therotamer runs, so that new conformations were generated entirely byjump (rather than step) moves [31].
Energy minimizationGradient energy minimization was performed with the programENCAD, using parameters and procedures previously described [35].Minimization was done in vacuo, using steepest descent until the totalenergy per atom fell below 2 kcal mol–1, followed by 1000 conjugategradient steps. The final converged energy for each structure was thevalue reported in the text. Minimization was either performed on theentire protein, or upon just the residues in the molten zone used forSCEO (see Results).
GraphicsVisual examination of the wildtype and mutant optimal-packing struc-tures, and comparison with the crystal structures, was done using theMidasPlus software system from the Computer Graphics Laboratory,University of California, San Francisco [36].
Model evaluationBecause the crystal structures of the T4 lysozyme mutants were solvedin the same unit cell and packing as the wildtype protein [15], the coor-dinates of the SCEO models were directly compared to the mutantcrystal structures, without any superposition by least-squares fit. Therms numbers given in the text and tables are true root-mean-squarevalues, not ‘mean’ or ‘averaged’ root-mean-square distances, which aresignificantly smaller.
To measure the statistical significance of each mutant sidechain pre-diction, its percentile rank was calculated against all possible confor-mations for that sidechain. This statistic will be referred to as fbetter, thefraction of conformational space whose rms deviation from the crystalstructure is higher than that of the predicted model (i.e. the predictionis better). The set of all possible conformations was approximated byrotating all sidechain χ torsions in discrete steps of about 12°, usingeither the wildtype or mutant backbone (see Table 3 legend). I havealso defined a quality factor, q, which measures the statistical degreeof improvement of the prediction over that of a random distribution:
q = fbetter
fworse�� = �
fbetter
1–fbetter��
where fbetter is the fraction of conformations the prediction is betterthan, and fworse is the fraction of conformations it is worse than. For arandom distribution of conformations, q=1.
AcknowledgementsThe author wishes to thank T Anderson, M Gerstein, E Huang, D Lau-rents, M Liang, and M Levitt for their extensive critical reading andadvice on this manuscript. During the period of this work, C Lee was aHoward Hughes Medical Institute Predoctoral Fellow, and was sup-ported by postdoctoral fellowship PF-4220 from the American CancerSociety. This work was supported by NIH grant GM 45514 to M Levitt,and a grant from the Office of Naval Research (ONR-N00014-90-J-1407) to H McConnell.
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