Key words: mutant T4 lysozyme; S-2-amino-3- cyclopentylpropanoic acid; free energy simulation; protein stability; packing interaction

Transcription

1 PROTEINS: Structure, Function, nd Genetics 32: (1998) Cn One Predict Protein Stbility? An Attempt To Do So for Residue 133 of T4 Lysozyme Using Combintion of Free Energy Derivtives, PROFEC, nd Free Energy Perturbtion Methods Lu Wng, Dvid L. Veenstr, Rndll J. Rdmer, nd Peter A. Kollmn* Deprtment of Phrmceuticl Chemistry, University of Cliforni t Sn Frncisco, Sn Frncisco, Cliforni ABSTRACT Free energy derivtives, pictoril representtion of free energy chnges (PROFEC) nd free energy perturbtion methods were employed to suggest the modifictions tht my improve the stbility of mutnt T4 lysozyme with S-2-mino-3-cyclopentylpropnoic cid residue (Cpe) t position 133. The free energy derivtives nd PROFEC methods were used to locte promising sites where modifictions my be introduced. The effects of severl cndidte modifictions on the enzyme s stbility were nlyzed by the free energy perturbtion method. We found tht this scheme is ble to effectively suggest modifictions tht my increse the enzyme s stbility. The modifictions investigted re the introduction of methyl, tert-butyl or trifluoromethyl group t the C 2 position nd cyclopropyl group between the C 2 nd C 2 position on the cyclopentyl ring. The stereochemistry of the introduced groups (in the or configurtions) ws studied. Our clcultions predict tht the introduction of methyl group in the configurtion or cyclopropyl group in the configurtion will increse the stbility of the enzyme; the introduction of the two groups in the other configurtions nd the other modifictions will decrese the stbility of the enzyme. The results indicte tht pcking interctions cn strongly influence the stbility of the enzyme. Proteins 32: , Wiley-Liss, Inc. Key words: mutnt T4 lysozyme; S-2-mino-3- cyclopentylpropnoic cid; free energy simultion; protein stbility; pcking interction INTRODUCTION To chieve its exquisite specificity nd high ctlytic efficiency, n enzyme must dopt precise folded three-dimensionl structure in solution. In contrst, the unfolded stte of n enzyme, which is much less ordered thn the folded stte, usully loses its bility to ctlyze chemicl rections. An enzyme s stbility is defined s its bility to mintin its folded stte under certin conditions. From thermodynmic point of view, n enzyme s stbility is mesure of the free energy difference between its folded nd unfolded sttes. Over the yers, much effort, using both experimentl 1 4 nd theoreticl pproches, 5 8 hs been devoted to the studies of enzyme stbility. There re two min purposes of these studies. The first is to understnd the underlying forces tht stbilize n enzyme, to better understnd protein structure nd function. The second is to pply the knowledge gined in the studies to prcticl pplictions such s protein engineering. The ltter is especilly importnt becuse in protein engineering, it is often required tht n enzyme ctlyzes rections in environments which my be distinctively different from those in which it hs evolved to function in nture. 9 For these problems, the mjor limittion is the enzyme s stbility. For exmple, subtilisin my enhnce the clening power of detergents. However, wild-type subtilisin is not stble in bsic nd high temperture solutions, the conditions under which most clenings re performed. Therefore, to mke full use of the enzyme s ctlytic power, the enzyme needs to be engineered so tht it is stble t high temperture nd in bsic conditions. 10 To solve this problem, n understnding of the forces tht stbilize the enzyme is essentil. It is now possible to lter n enzyme s stbility by substituting ny of its mino cids with one of the other 19 nturl mino cids by site-directed mutgenesis of its cloned gene. From these experimentl mutgenesis studies, severl contributions such s hydrophobic interction, 4,11 electrosttic interctions, 12,13 hydrogen bonding, 14 pcking, 11,15 nd entropic effect 16 hve been identified s importnt contributions to n enzyme s stbility. Theoreticl moleculr modeling techniques, i.e., energy minimi- Grnt sponsor: Ntionl Institutes of Helth; Grnt number: GM *Correspondence to Dr. Peter A. Kollmn, Deprtment of Phrmceuticl Chemistry, University of Cliforni t Sn Frncisco, Sn Frncisco, CA E-mil: pk@cgl.ucsf.edu Received 4 December 1997; Accepted 7 April WILEY-LISS, INC.

2 CAN ONE PREDICT PROTEIN STABILITY? 439 ztion, 8 moleculr dynmics (MD), 17 nd free energy simultions, 5 7,18 hve been pplied to study enzyme stbility with some success. Idelly, one should be ble to experimentlly lter n enzyme s stbility in controlled wy nd be ble to predict the results from theoreticl methods prior to experiments. However, it hs been rgued 19,20 tht the uncertinties in representing the unfolded stte of protein, conformtionl smpling in the simultions, nd interprettion of free energy results prevent free energy simultions from being ble to predict protein stbility. There is no doubt tht predicting n enzyme s stbility is complicted problem tht involves the contributions nd subtle blnces of mny forces 2,21 nd is inherently relted to the unsolved protein folding problem. 22 Much work is still needed to study the detiled energetics of the contributing forces nd develop theoreticl methods for predicting stbility chnges. Recently, Noren et l 23 introduced method tht cn incorporte unnturl mino cids into protein site-specificlly. This technique hs the dvntges over the conventionl mutgenesis techniques tht more precise chnges of steric nd chemicl properties of n mino cid cn be mde to optimize n enzyme s properties. Becuse smll structurl chnges cn be mde on n mino cid, the technique mkes possible more precise seprtion of different contributing forces to protein s stbility. This presents n excellent opportunity to study the detiled energetics of protein stbility problem. In collbortive study 17 of the stbility of bcteriophge T4 lysozyme with the Schultz s (University of Cliforni t Berkeley) group, we hve used moleculr dynmics simultions nd energetic nlyses to predict tht replcement of Leu t position 133 of the enzyme with n unnturl mino cid, S-2-mino- 3-cyclopentylpropnoic cid (Cpe) will better stbilize the enzyme thn substitutions of the Leu with 19 other nturl mino cids: prediction tht ws confirmed experimentlly. The most rigorous method for modeling protein stbility should be the free energy perturbtion method. 24 However, the time-consuming nture of free energy perturbtion clcultions prevents it from being used to ssess the effects of every muttions of n enzyme. Thus, it mkes sense to first use other computtionl less expensive pproches which provide qulittive suggestions on the muttions of n enzyme nd lter verify the results by free energy perturbtion clcultions or by experiments, s we hve done (moleculr dynmics nd computer grphics) in our previous study. 17 More recently, we hve developed two other computtionlly more efficient pproches: free energy derivtives nd PROFEC (Pictoril Representtion Of Free Energy Chnges- ), 28 which cn be used to suggest how lignds or mino cids could be modified to improve lignd binding ffinity or protein stbility. In free energy derivtives, one evlutes the prtil derivtives of the free energy with respect to prtil chrges, vn der Wls rdii, nd well depths t ech tom in the folded nd unfolded sttes (protein stbility) or bound nd free sttes of lignd (lignd-binding) nd evlutes the difference between these derivtives in the two sttes. It hs been shown tht free energy derivtives cn indicte how the properties (size nd chrge) of ech constituent tom of lignd should be modified to increse the lignd s binding ffinity. 26,27 In PROFEC, by verging over moleculr dynmics trjectories, contour mps re generted, which show how binding free energy or protein stbility chnges when dditionl prticles re dded ner the lignd or residue of protein. In test on benzmidine/trysin complex, it ws shown tht PROFEC is ble to reproduce the generl trend in binding free energies of benzmidine nlogs. 28 Below, we show combined ppliction of the free energy derivtives, PROFEC nd free energy perturbtion methods to the study of the stbility of the mutnt T4 lysozyme with Cpe t position 133. Both the free energy derivtives nd PROFEC suggest tht the enzyme s stbility my be further incresed by introducing vn der Wls group t C 2 position on the cyclopentyl ring of Cpe. The effects on the enzyme s stbility of four cndidte modifictions were investigted by the free energy perturbtion method. Respectively, they involve the introduction of, (i) methyl group t C 2 (Mcpe), (ii) tert-butyl group t C 2 (tbcpe), (iii) trifluoromethyl group t C 2 (FMcpe) nd (iv) cyclopropyl group between C 2 nd C 2 (Pcpe). The stereochemistry of introducing the groups in two different configurtions ws considered. We found tht the enzyme s stbility my be further incresed by the modifictions of Cpe=Mcpe or Cpe=Pcpe, but the methyl or the cyclopropyl group must be introduced in specific configurtion. This suggests tht the enzyme s stbility is sensitive to pcking interctions in the hydrophobic core. By nlyzing the contributions from different interctions nd from different residues to the clculted free energies, we were ble to rech comprehensive understnding of the moleculr bsis of these results. The nlyses lso led to some new suggestions to further increse the enzyme s stbility. The results of our simultions hve been forwrded to the Schultz s group nd, hopefully, will be subject to experimentl tests. METHODS Model, Prmeters, nd MD Simultions The structures of the mutnt T4 lysozyme with Cpe, Mcpe, tbcpe, FMcpe or Pcpe t position 133 were obtined by model building using stndrd geometries bsed on the coordintes of the wild-type T4 lysozyme from the Brookhven Protein Dt Bnk. 29 Ech structure is composed of two domins, i.e., the mino- nd crboxyl-terminl lobes, nd the

3 440 L. WANG ET AL. Fig. 1. Ribbon representtion of the structure of the T4 lysozyme with S-2-mino-3-cyclopentylpropnoic cid residue (Cpe) t position 133. Fig. 2. Definition of the nd configurtions using the exmple of Mcpe. ctive site cleft is between the two lobes. The unnturl mino cid residue 133 is locted in the hydrophobic core of the crboxyl-terminl lobe (Fig. 1), t the end of helix. For the simultions on the enzyme, n 18 Å of cp TIP3P wter 30 molecules centered round the C 2 tom of residue 133 ws used. To keep the whole system neutrl, 17 counterions (N or Cl ) were plced round residues 8, 14, 16, 19, 20, 35, 43, 47, 61, 65, 85, 96, 119, 124, 135, 147 nd 164. Only residues within the sphere nd the cp wter molecules re llowed to move in moleculr dynmics simultions. Ech system consists of bout 1600 protein toms (including the counterions) nd bout 260 wter molecules. The cp wter molecules were kept from escping by wek repulsive potentil (1.5 kcl/mol) t the surfce of the dynmic sphere. Prior to free energy simultions, ech system ws energy minimized for 100 steps nd equilibrted for 10 ps by moleculr dynmics simultions. The unfolded stte of the enzyme ws represented by terminlly blocked dipeptide, Ace-X-NMe, in which Ace nd NMe re the cetyl nd N-methylmide groups respectively nd X is the unnturl mino cid residue. For exmple, for the enzyme with Cpe, it is Ace-Cpe-NMe. The bckbone of the dipeptide ws chosen to be in the extended stte( 180 f 0, 0 y 180 ). The side chin of X cn be in the g,t,org conformtions, which corresponds to c (N-C -C -C ) being centered round 60, 180, 60. We chose the conformtion t for ll our simultions in wter nd in vcuo, given tht the muttions of Cpe into Mcpe, tbcpe, Fmcpe, or Pcpe hppen fr from the bckbone on the cyclopentyl ring, nd thus, the results should not be sensitive to the side chin conformtion. For the simultions in wter, ech dipeptide ws plced t the center of box of Å 3 nd the rest of the box ws filled with TIP3P wter molecules under stndrd conditions. The number of wter molecules is bout 760. Mcpe, tbcpe, FMcpe nd Pcpe ech hve two different configurtions becuse the methyl, t-butyl, trifluoromethyl or cyclopropyl group my be t the sme or different side s the C tom (Fig. 2). Anlogous to the nomenclture of nomers of sugrs, we define the first s the configurtion nd the

4 CAN ONE PREDICT PROTEIN STABILITY? 441 TABLE I. The Chirlities of the Asymmetric Centers on the Cyclopentyl Ring of the Unnturl Amino Acids Configurtion Residue Mcpe C (R), C 2 (R) C (R), C 2 (S) tbcpe C (R), C 2 (R) C (R), C 2 (S) Fcpe C (R), C 2 (R) C (R), C 2 (S) Pcpe C (S), C 2 (R), C 2 (S) C (S), C 2 (S), C 2 (R) The chirlity of C is R for Mcpe, tbcpe, Fcpe nd S for Pcpe in the enzyme. R nd S re determined ccording to the Chn- Ingold-Prelog chirlity system. second s the configurtion. More rigorously, the configurtions cn be defined by the chirlities of ech symmetric toms on the ring ccording to the Chn-Ingold-Prelog system. The results re listed in Tble I. Note tht the chirlity of C is R for Mcpe, tbcpe, Fcpe nd S for Pcpe in the enzyme. This is the bsis for our definition of the chirlity of C 2 nd C 2 in the or configurtions. The sitution with the chirlity of C reversed hs not been considered becuse it is not the configurtion observed in the enzyme. All MD simultions nd energy minimiztions were performed with AMBER4.1 progrm 31 with the ll tom force field developed by Cornell et l. 32 The chrges, vn der Wls prmeters, equilibrium bond lengths, bond ngles nd dihedrls for the stndrd residues were tken from the AMBER4.1 dtbse. The vn der Wls prmeters nd the equilibrium bond lengths, bond ngles nd dihedrls of the unnturl mino cids re lso vilble in the AMBER4.1 dtbse. The tomic chrges of the unnturl mino cids were obtined by fitting with the RESP method 33 the electrosttic potentils of the terminlly-blocked dipeptide models, i.e., Ace-X- NMe, X Cpe, Mcpe, tbcpe, Fmcpe, or Pcpe. The electrosttic potentil of ech dipeptide model ws obtined by single point b initio quntum mechnicl clcultion with 6 31G* bsis set using Gussin on geometry generted by energy minimiztion with the AM1 method. In ech electrosttic fitting, the chrges of the toms of the peptide bckbone re constrined to the vlues given in the Cornell et l force field. Unless specified, the simultions were performed with time step of 2 fs with cutoff rdius of 8 Å. The bond lengths were constrined to their equilibrium vlues with the SHAKE lgorithm. 35 For ech simultion, the temperture ws controlled t 300K by coupling of the system to het bth. 36 For the simultions in wter, periodic boundry conditions were pplied nd the pressure ws controlled t 1 tm by djustment of the volume of the periodic box. 36 The interctions between the wter molecules were clculted by the SETTLE lgorithm 37 specificlly designed to speed up the clcultions on wter molecules, in which wter molecules undergo rigid body movements in moleculr dynmics simultions. Thermodynmic Cycles The following thermodynmic cycles were used to ssess the effect of ech chemicl modifiction of Cpe133 on the stbility of the mutnt T4 lysozyme: u=f g=u T4 m (f, w) T4 m (u, w) T4 m (u, g) m=m*,f m=m*,u m=m*,g T4 m* (f, w) T4 m* (u, w) T4 m* (u, g) * u=f * g=u (1) where T4 m stnds for the mutnt T4 lysozyme with Cpe133 nd T4 m * stnds for further modified mutnt with Mcpe, tbcpe, FMcpe or Pcpe t position 133 nd f, u, g, w refer to the folded, unfolded sttes of the enzyme, in gseous stte or in queous solution. The left nd right cycles were used to clculte, for the modifiction of T4 m =T4 m *, the chnges in the enzyme s stbility nd in the solubility of the unfolded stte of the enzyme. The reson for performing the ltter nlysis is tht protein folding cn be viewed s the result of desolvtion of its mino cid from wter into the protein interior nd pcking of the mino cids in the protein interior (see discussion section). Thus, the solubility difference in the unfolded stte provides the desolvtion contribution to the enzyme s stbility. Respectively, for T4 m nd T4 m *, u=f, * u=f re the folding free energies; g=u, * g=u re the solvtion free energies of the unfolded sttes of the enzymes. m=m*,f, m=m*,u nd m=m*,g represent the muttionl free energies for the modifiction of T4 m =T4 m * in the folded, unfolded sttes nd in the gs phse. Becuse free energy is stte function, the bove free energies re relted by the following equtions fold * u=f u=f solv * g=u g=u m=m*,f m=m*,u (2) m=m*,u m=m*,g (3) Here fold is the difference in folding free energy between T4 m * nd T4 m. It mesures the reltive stbility of T4 m nd T4 m *. solv is the difference in solvtion free energy of the unfolded sttes of T4 m * nd T4 m. Direct nd ccurte computtions of * u=f, u=f, * g=u, nd g=u re difficult due to the lrge chnges in free energy nd conformtions. Fortuntely, fold nd solv cn be expressed

5 442 L. WANG ET AL. through Eqution 2 nd Eqution 3 s the differences of m=m*,f, m=m*,u, nd m=m*,g, which cn be redily clculted by the free energy perturbtion method in moleculr dynmics simultions. In the following, we use X=Y to represent the modifiction of residue X to residue Y, either in vcuo, in wter, or in the enzyme. Here X, Y cn be Cpe, Mcpe, tbcpe, Fcpe or Pcpe. For the modifiction in the enzyme, it refers to the modifiction t position 133. For the modifiction in vcuo nd in wter, it refers to the modifiction in the dipeptide model described bove. Free Energy Simultions In this study, the thermodynmic integrtion 24,38 method, which llows decomposition of the totl free energy into electrosttic, vn der Wls, bond, bond ngle nd dihedrl ngle contributions, ws used to clculte the free energies. In the method, for the trnsformtion of one thermodynmic stte into nother, coupling prmeter is introduced nd the Hmiltonins of the two sttes re defined s H 0 ( 0) nd H 1 ( 1). The totl free energy chnge for the trnsformtion is expressed s the following integrl H( )/ 8 d (4) where 7 H( )/ 8 is n ensemble verge t. In prctice, the integrl is clculted by the trpezoidl integrtion method, in which number of evenlyspced windows with different vlues rnging from 0 to 1 re chosen nd t ech window, 7 H( )/ 8 is clculted by verging over moleculr dynmics trjectories. For the enzyme stbility problem, we ssume tht the kinetic energy contribution cn be neglected, is pproximted by i 7 V( )/ 8 i (5) where i is the vlue of the ith window nd is the intervl between successive windows. V is the potentil function tht describes the tomic interctions in the system. It hs the following form in the force field of Cornell et l. 32 V bonds K r (r r eq ) 2 ngles K ( eq ) 2 V n dihedrls 2 [1 cos (n )] i j 1 A ij R B ij 12 ij R ij 6 2 i j q i q j R ij (6) where the five terms represent the bond, bond ngle, dihedrl, vn der Wls nd electrosttic interctions respectively. A ij nd B ij re clculted bsed on the following equtions: A ij ij R* 12 6 ij, B ij 2 ij R* ij (7) ij ( * i * j ) 1/2, R ij R* i R* j (8) The four modifictions for which the free energy chnges were clculted re illustrted in Figure 3. The free energy chnge of Mcpe=tBcpe cn be obtined in two wys, either in one step, or in two steps vi Cpe=Mcpe nd Mcpe =tbcpe. The onestep clcultion involves lrge structurl chnge wheres the two-step clcultion involves two smller structurl chnges. Since the error of free energy simultion is much less for smller structurl chnges, in ddition to the fct tht the result of Cpe=Mcpe is required, we did the clcultion in two steps. For Cpe=Mcpe, Mcpe=tBcpe, nd Cpe=Fcpe, the single topology method ws used, in which the two moleculr sttes re represented in one topology structure nd during the free energy clcultions, the prmeters of the molecule re grdully chnged from those corresponding to one stte to nother. As n exmple, in Cpe=Mcpe, the prmeters of one hydrogen tom t C 2 is chnged into tht of crbon nd the three dummy toms re chnged into rel hydrogens. For Cpe=Pcpe, the dul topology method ws used, in which the two sttes corresponding to 0 nd 1 coexist but do not interct with ech other. The Hmiltonin of the system is expressed s liner combintion of the two sttes, H( ) H 1 (1 ) H 0 nd by chnging, the reltive contribution of ech stte is chnged nd the molecule is trnsformed from one into nother. In the clcultions with the single topology method, the contributions to free energy due to chnge of bond length needs to be included 39,40 becuse s hydrogen is replced by crbon (Cpe=Mcpe nd Mcpe=tBcpe) or fluorine tom (Cpe=Fcpe), the bond length of C H will be chnged into tht of C C or C F. These contributions were clculted by the potentil of men force (PMF) lgorithm. 39 As hs been pointed out, since the free energy contributions from intrperturbed group my not lwys be negligible, 19 we included ll the intr-perturbed group contributions in our clcultions. The clculted free energies were decomposed by the procedure employed in previous studies from this lbortory. 5,18,41 Bsiclly, t ech, V( )/ is decomposed into contributions from vrious interctions (such s electrosttic, Vn der Wls, bonds, bond ngles nd dihedrl ngles) or from different groups nd their integrls over give the contributions from ech component. The decomposition is possible becuse V( )/ cn be expressed s sum of contributions from different interctions or from different groups.

6 CAN ONE PREDICT PROTEIN STABILITY? 443 Fig. 3. The structurl chnges in the free energy perturbtion simultions of the four modifictions. The single topology method ws used for Cpe=Mcpe (), Mcpe=tBcpe (b) nd Cpe=Fcpe (c). The dul topology method ws used for Cpe=Pcpe (d).

7 444 L. WANG ET AL. Free Energy Derivtives The prtil derivtives of free energy with respect to the nonbonded interction prmeters, q i, i nd R i *, were clculted by the following equtions: 26,27 / q i 7 j q j /( R ij )8 1/q i 7V coul (i)8 (9) / i 7 j [1/(2 i )] ij [(R* ij /R ij ) 12 2(R* ij /R ij ) 6 ]8 / R* i [1/(2 i )] 7V L J (i)8 (10) 7 j ij (12/R* ij )[(R* ij /R ij ) 12 (R* ij /R ij ) 6 ]8 (11) where 7V coul (i)8 nd 7V L-J (i)8 re the men Coulombic nd Lennrd-Jones interction energies of the ith tom with the rest of the system. The sign nd the mgnitude of these derivtives reflect the tendencies of the free energy chnges upon chnging the tomic properties of the ith tom. To nlyze the effects of these chnges on protein s stbility, ccording to Eqution 2, these free energy derivtives need to be clculted for both the folded nd the unfolded sttes of the protein nd their difference is used to indicte the stbility chnge of the protein. According to the definition of the derivtives, these clculted stbility chnges cn be viewed s the stbility chnges of the protein upon infinitesiml chnges of the prmeters of the ith tom. The clcultions of the free energy derivtives cn be performed for ll toms of interest in the protein. Often, ll the derivtives cn be ssumed to be independent, nd cn thus be clculted simultneously during one single moleculr dynmics simultion. Pictoril Representtion of Free Energy Chnges (PROFEC) The bsic ide of the PROFEC method 28 is to generte contour mp round residue of protein or lignd, which cn indicte how the protein s stbility or the binding ffinity of the lignd will chnge when dditionl prticles re dded ner the residue or the lignd. The contour mp is obtined by introducing test prticles on the grid points in the vicinity of the residue or the lignd nd evluting the insertion free energies of the test prticles on the grid points from the moleculr dynmics simultion. To nlyze protein s stbility, similrly, ccording to Eqution 2, two contour mps for the folded nd the unfolded sttes of the protein hve to be generted nd their difference mp is used to indicte the stbility chnge of the protein for introducing prticles round the residue of interest. A detiled discussion of PROFEC method cn be found in Reference 28. Here, we only briefly describe the method nd list the computtionl procedures. The position nd orienttion of the grid is defined using one tom of the residue of interest to indicte the origin of the grid, second tom to define the x-xis, nd third tom to define the xy-plne. The z-xis cn be generted by the cross product of the unit vectors of x nd y xes. In this study, C 2 of residue 133 ws used s the origin of the grid. The two hydrogens ttched to C 2 were used to define the x-xis nd the xy-plne. The free energy cost of dding Lennrd-Jones prticle t specific grid point ws clculted by 28 (i, j, k) RT ln 7exp ( V(i, j, k)/rt8 0 (12) where i, j nd k indicte grid point reltive to the three toms of residue 133. (i,j,k) is the chnge in free energy resulting from the ddition of the Lennrd-Jones prticle. V(i, j, k) is the vn der Wls interction energy between the prticle nd the surrounding toms, which include only the toms from residues other thn residue 133 nd the solvent toms. The prmeters of the Lennrd-Jones prticle re R* 2.0 Å nd 0.15 kcl/mol, which re close to the vn der Wls prmeters of tetrhedrl crbon tom. The electrosttic contributions for introducing prticles t the grid points cn be exmined by clculting the derivtive of free energy with respect to chrge t ech grid point. However, it is more useful to clculte the derivtive ssuming tht Lennrd- Jones prticle is first plced t tht grid point. This weights the clculted free energy derivtives by how fvorble stericlly it is to hve n tom t tht point. According to the formul of umbrell smpling, the electrosttic contribution to the free energy is given by 28 3dG(i, j, k) dq 4 LJ (i,j,k) 7 (i, j, k) exp ( V(i, j, k)/rt8 0 7exp ( V(i, j, k)/rt8 0 (13) where (i, j, k) is the electrosttic potentil t ech grid point. [...] LJ(i,j,k) indictes tht the derivtive is clculted ssuming tht Lennrd-Jones prticle is dded t point i, j, k. In prctice, the contour mp generted by insertion of Lennrd-Jones prticles cn be colored ccording to the free energy derivtives of the electrosttic contributions. This cn be used to suggest how lignd chrge distribution should be chnged to improve protein s stbility. RESULTS Free Energy Derivtives nd PROFEC The free energy derivtives with respect to VDW rdius (R*) of eight hydrogen toms on the cyclopentyl ring of Cpe were clculted (Tble II). The

8 CAN ONE PREDICT PROTEIN STABILITY? 445 Atom TABLE II. The Free Energy Derivtives of Cpe (kcl/mol) dg/dr*, prot dg/dr*, soln Protsoln Comments HD Pro- HD Pro- HE Pro- HE Pro- HE Pro- HE Pro- HD Pro- HD Pro- The free energy derivtives were obtined by 300 ps MD simultions in the enzyme nd in wter. TABLE III. The Free Energy Chnges of Cpe 8 Mcpe In Vcuo, Wter, nd the Enzyme (kcl/mol) Medium Config. Time Forwrd Bckwrd Averge Protein 164 ps Protein 324 ps Protein 488 ps Protein 164 ps Protein 324 ps Wter 164 ps Wter 324 ps Wter 504 ps Wter 324 ps Vcuo 324 ps Vcuo 644 ps Vcuo 324 ps The time for the forwrd or bckwrd chnge. Ech window hs 2 ps/2 ps for equilibrtion nd smpling. 164, 324, 504, nd 644 ps hve 41, 81, 126, nd 161 windows respectively. 488 ps: 41 windows for the electrosttic contribution nd 81 windows for the VDW contribution. configurtions of the hydrogens re either pro- or pro-. Anlogous to the definition of pro-r or pro-s in the Chn-Ingold-Prelog chirlity system, the pro- or pro- configurtion of hydrogen mens tht if the hydrogen is replced by group such s methyl, the cyclopentyl ring will be in or configurtion s defined bove. From Tble III, one sees tht the free energy derivtives of HD12 (pro- ), HE12 (pro- ), HE21 (pro- ), nd HD22 (pro- ) re negtive, indicting tht introducing some VDW group lrger thn hydrogen on either one of these sites my stbilize the protein. In this study, we focused our nlyses round CE2 where HE21 is ttched becuse the free energy derivtive of HE21 is the lowest. The PROFEC contour of zero VDW potentil with C 2 of Cpe s the origin is shown in Figure 4. Interestingly, the contour hs the shpe of vse; its mouth fces the cvity nd its neck embrces C 2. The contour grees with the free energy derivtives in tht there is much more spce for introducing group t HE21 (negtive derivtives) thn t HE22 (positive derivtives). A nturl proposl is the introduction of methyl group t HE21 in the configurtion. Figure 5 shows the superimposition of methyl group t HE21 nd t HE22. Obviously, the methyl group introduced t HE21 cn fit very well in the cvity while the methyl group introduced t HE22 will collide with the wll of the vse belly. Another proposl tht my efficiently utilize the spce round the vse neck is the introduction of cyclopropyl group round C 2 nd C 2, in which the introduced cyclopropyl group will fce the cvity or the belly of the vse in the or configurtions respectively. Superimposing of the cyclopropyl group in either the or the configurtion in the contour (Figure 6) seems cceptble. (It is noted tht since the rdius of the test prticle for generting the PROFEC contour is 2.0 Å, lrger thn the hydrogen rdius of 1.5 Å, slight protrusion of hydrogen tom outside the contour should not give high VDW energy.) However, it is not obvious in the superimposed structures which configurtion is more stble. Especilly, becuse the introduced cyclopropyl group in both configurtions re on the edge of the zero VDW contour, the predictions of the contour my be less ccurte thn the cses when the introduced group is considerbly inside the contour (s in -Mcpe) or fr outside the contour (s in -Mcpe). Supplementry to the PROFEC results, we hve performed two 100 ps MD simultions on the -Pcpe nd the -Pcpe mutnts nd clculted the verge interction energies between the CH 2 of the cyclopropyl group with the rest of the systems. The verge interction energies re kcl/mol nd kcl/mol, respectively, for the nd the configurtions. Therefore, it ppers tht the configurtion is likely to be more stble thn the configurtion. For other modifictions, we my lso consider the introduction of some negtively chrged group becuse the electrosttic potentil on the contour is positive. CF3 seems to be good cndidte becuse it is smll nd the fluorine toms hve considerble prtil negtive chrges. All these cndidte modifictions will be studied by free energy simultions discussed below. Free Energy Perturbtion Clcultions Cpe=Mcpe We hve clculted the free energy chnges for introducing methyl group in the (t HE21) nd (t HE22) configurtions in vcuo, in wter nd in the T4 lysozyme. The results re listed in Tble III. One sees tht the hystereses of the clculted free energies re generlly less thn 0.5 kcl/mol nd the results re not sensitive to simultion time. Going from 164 ps to 324 ps for the forwrd nd bckwrd chnges, the verge in the enzyme nd in wter differs by only 0.6 kcl/mol. This indictes tht good convergence of the results hs been chieved.

9 446 L. WANG ET AL. Fig. 4. The PROFEC contour centered t C 2 of Cpe. The MD simultions in the enzyme nd in wter re both 100 ps. The trjectories were recorded every 0.25 ps. The contour is the difference mp of the verge grid potentils in the enzyme nd in wter. Fig. 5. The superimposed structures of methyl group in the configurtion t HE21 () nd in the configurtion t HE22 (b) in the PROFEC contour of Cpe. Becuse the verge in wter fluctutes round 0.8 kcl/mol with different lengths of simultion time, 0.8 kcl/mol is tken s the estimted verge in wter. In greement with the predictions of the free energy derivtives nd PROFEC, Cpe= -Mcpe is indeed found to be more fvorble thn Cpe= - Mcpe. Bsed on the clculted free energies, Cpe= - Mcpe will stbilize the enzyme by 1.9 kcl/mol while Cpe= -Mcpe will destbilize the enzyme by 0.4 kcl/mol (Tble XIII). The solvtion free energy of Ace-Mcpe-NMe is estimted to be less thn tht of Ace-Cpe-NMe by 0.5 kcl/mol (Tble XIII), in greement with the fct tht methylcyclopentne is less soluble thn cyclopentne by 0.4 to 0.8 kcl/mol. 42,43 The free energy chnges for Cpe= -Mcpe nd Cpe= -Mcpe re similr in wter nd in vcuo. The reson should be tht C is fr from the methyl group so tht lthough for -Mcpe nd -Mcpe, correspondingly, hydrogen tom nd C H 2 group fce the methyl group on the ring, the interction energy is similr. According to the free energy derivtives nd PROFEC contour, the free energy chnges of Cpe= - Mcpe nd Cpe= -Mcpe in the enzyme should hve lrge difference in VDW components. This is lso

10 CAN ONE PREDICT PROTEIN STABILITY? 447 Fig. 6. The superimposed structures of cyclopropyl group introduced t C 2 nd C 2 in the configurtion () nd in the configurtion (b) in the PROFEC contour of Cpe. TABLE IV. The Contributions of Different Interctions to the Free Energies of Cpe 8 Mcpe (kcl/mol) Medium Config. EL VDW BADH CORC Totl Protein Protein Wter Vcuo The results re the verges of the forwrd nd bckwrd chnges. In protein: from the 324 ps simultions. In wter: the verge of the 164 ps, 324 ps, nd 504 ps simultions. In vcuo: from the 644 ps simultion. confirmed by decomposing the clculted free energies into contributions from different interctions (Tble IV). The free energies re decomposed into the electrosttic, Vn der Wls, bond, ngle nd dihedrl (BADH) contributions nd the correction term due to chnge of bond length (CORC). The CORC term is the work needed for stretching the bond length of C H to tht of C C in the simultions (Fig. 3). It reflects the interctions of the methyl group with the rest of the Mcpe residue nd the environment. 39 For Cpe=Mcpe in the enzyme, the difference in the CORC term should minly reflect the difference in the interctions of the methyl group with the protein. Clerly, for Cpe= Mcpe nd Cpe= -Mcpe in the enzyme, the mjor differences in free energy components re in the VDW nd CORC terms: the VDW term of Cpe= -Mcpe is less thn tht of Cpe= -Mcpe by 1.3 kcl/mol; the CORC term of Cpe= -Mcpe is less thn tht of Cpe= -Mcpe by 0.8 kcl/mol. Together, they ccount for 95% of the stbility difference between the -Mcpe nd -Mcpe mutnts. The VDW term of Cpe= -Mcpe in the enzyme is lso much smller tht those in wter nd in vcuo, suggesting of n extr stbiliztion in the enzyme. The CORC term of Cpe= -Mcpe in the enzyme is much higher thn other cses, indicting tht the resistnce of introducing the methyl group in the configurtion in the enzyme is much lrger. To understnd the structurl bsis for the energetic differences, we hve decomposed the free energies into residue contributions (Tble V). The locl structures round -Mcpe nd -Mcpe re shown in Figure 7. From Tble V, one sees tht number of residues mke considerble contributions to the free energies, but interestingly, for Cpe= -Mcpe nd Cpe= -Mcpe in the enzyme, the mjor differences re in just three residues, i.e., Met102, Ser117 nd Mcpe133. Met102 contributes 0.1 kcl/mol to Cpe= -Mcpe nd 2.0 kcl/mol to Cpe= -Mcpe; Ser117 contributes 0.8 kcl/mol to Cpe= -Mcpe nd 0.2 kcl/mol to Cpe= -Mcpe; Mcpe 133 contributes 1.1 kcl to Cpe= -Mcpe nd 0.4 kcl/mol to Cpe= -Mcpe. Counting the contributions of only these three residues, -Mcpe mutnt will be more stble thn -Mcpe mutnt by 1.6 kcl/mol, over 2/3 of the stbility difference when ll contributions re included (2.2 kcl/mol, Tble XIII). In the structures (Fig. 7), the methyl group of -Mcpe is close to the

11 448 L. WANG ET AL. TABLE V. The Group Contributions to the Free Energies of Cpe 8 Mcpe (kcl/mol) Contributions Groups T4 lysozyme Met Phe Ser Leu Asn Mcpe Al Trp Phe Vl Wter Totl Ace-Mcpe-NMe Ace 0.42 Mcpe 0.32 NMe 0.25 Wter 0.08 Totl 0.65 The results for the protein were obtined by 164 ps forwrd simultion. The results for the dipeptide were obtined by 324 ps forwrd simultion. side chin of Met102; the methyl group of -Mcpe is close to the side chin of Ser117. This explins the positive contributions of Met102 to Cpe= -Mcpe nd of Ser117 to Cpe= -Mcpe. It lso indictes tht Met102 nd Ser117 hve considerble contributions to the PROFEC contour centered round C 2. The free energy contribution of -Mcpe133 is lower thn tht of -Mcpe133 by 0.7 kcl/mol. This difference my come from the difference in the CORC term, which, s we pointed out, is relted to inter-residue interctions nd the difference in the intr-residue interctions. Since the CORC term of Cpe= -Mcpe is 0.8 kcl/mol lower thn tht of Cpe= -Mcpe in the enzyme (Tble IV), the intr-residue contributions of -Mcpe133 nd -Mcpe133 ctully differs by only 0.1 kcl/mol. Thus, we cn ttribute the stbility difference of -Mcpe nd -Mcpe mutnts minly to their interctions with Met102 nd Ser117. However, we should point out tht lthough other residues re not crucil for determining the stbility difference of the -Mcpe nd -Mcpe mutnts, they re importnt to the stbilities of both mutnts becuse it is esy to see tht without their contributions, the stbilities of both mutnts will be reduced. Exmining the superimposed structures of -Mcpe nd -Mcpe in the PROFEC contour (Fig. 5) nd the ctul structures (Fig. 7) when the methyl group is introduced, one sees tht the superimposed nd the ctul -Mcpe structures re drsticlly different while the superimposed nd the ctul -Mcpe structures re similr. The methyl group of -Mcpe ctully points to the vse mouth (Fig. 7) insted of to the belly (Fig.5). This cn be seen more clerly by compring the structures of Cpe, -Mcpe nd -Mcpe in the protein (Fig. 9). In -Mcpe, the cyclopentyl ring hs similr conformtion s Cpe nd the methyl group fits nicely into the hydrophobic cvity. -Mcpe hs the methyl group in similr position s in -Mcpe, but the cyclopentyl ring hs repuckered in order to point the methyl group into the cvity. This lrge conformtionl chnge is most likely driven by the strong VDW repulsion from Met102 to -Mcpe. The contributions of wter to the free energies of Cpe= -Mcpe nd Cpe= -Mcpe in the enzyme re smll. The reson is tht Mcpe133 is buried in the hydrophobic core of the crboxyl lobe of the enzyme, fr wy from wter. The smll contribution from wter to the free energy of Cpe= -Mcpe in wter my look unusul. Agin, we cll the ttention to the CORC term, which is included in the contribution of Mcpe but is relted to wter-mcpe interctions. The free energy contributions from the flnking residues of Mcpe in the enzyme (Asn132 nd Al134) nd in wter (Ace nd NMe) re similr. This indictes tht the free energy results re not sensitive to the bckbone nd the side-chin conformtions round Mcpe, becuse in the enzyme, Asn132-Mcpe133- Al134 is in the helicl stte with the g side chin conformtion, while Ace-Mcpe-NMe is in the extended stte with the t side chin conformtion. The ltter observtion is understndble becuse the methyl group of Mcpe is enough fr wy from the bckbone of the peptide. Cpe=tBcpe The purpose of this modifiction is to ccess the size limit for introducing group t C 2 which is stbilizing to the enzyme. As hs been discussed, to minimize the error, the clcultion ws performed in two steps, i.e., Cpe=Mcpe nd Mcpe=tBcpe. The results of the first step hs been described nd the results of the second step re listed in Tble VI. It is expected tht the results for Mcpe= -tbcpe nd Mcpe= -tbcpe in wter nd in vcuo re similr; therefore, only the configurtion ws considered for simultions in wter nd in vcuo. For the simultions in the enzyme nd in wter, with 164 ps for the forwrd nd bckwrd chnges, the hystereses of the clculted free energies re quite smll ( 0.5 kcl/mol ). On the other hnd, for the simultions in vcuo, much longer time is required to reduce the hysteresis to close to 0.5 kcl/ mol. However, the trend is very cler. Both -Mcpe= -tbcpe nd -Mcpe= -tbcpe will gretly destbilize the enzyme. The former will destbilize the protein by 2.6 kcl/mol while the ltter will destbilize the protein by 4.9 kcl/mol (Tble XIII). Agin, the configurtion is more stble thn the configurtion. Adding the results of Cpe=Mcpe, for

12 CAN ONE PREDICT PROTEIN STABILITY? 449 TABLE VI. The Free Energy Chnges for Mcpe 8 tbcpe In Vcuo, Wter, nd the Enzyme (kcl/mol) Medium Config. Time Forwrd Bckwrd Averge Protein 164 ps Protein 164 ps Wter 164 ps Vcuo 810 ps Vcuo 1.61 ns ps: see Tble III. 810 nd 1610 ps (1.61 ns): 81 nd 161 windows, 5 ps/5 ps for equilibrtion nd smpling. Fig. 7. The locl structures in the enzyme round -Mcpe () nd -Mcpe (b). Ech structure is n verge over 100 snpshots from 100 ps simultion. TABLE VII. The Contributions of Different Interctions to the Free Energies of Mcpe 8 tbcpe (kcl/mol) Medium Config. EL VDW BADH CORC Totl Protein Protein Wter Vcuo The results re the verges of the forwrd nd bckwrd chnges. In protein nd wter: from the 164 ps simultions. In vcuo: from the 1.61 ns simultion. Cpe= -tbcpe nd Cpe= -tbcpe, the stbility of the enzyme will be decresed by 0.4 nd 5.3 kcl/mol respectively. Thus, the enzyme stbility gined by Cpe= -Mcpe is completely offset by -Mcpe= tbcpe, while the instbility introduced by Cpe= - Mcpe is further enlrged by -Mcpe= -tbcpe. The solvtion free energy of Ace-tBcpe-NMe is estimted to be less thn tht of Ace-Mcpe-NMe by 3.1 kcl/ mol. There is no experimentl dt for comprison, but since the contribution of CH 3 group ws estimted to be bout 0.8 kcl/mol, 42 the result seems to be resonble.

13 450 L. WANG ET AL. TABLE VIII. The Free Energy Chnges for Cpe 8 Fcpe In Vcuo, Wter, nd the Enzyme (kcl/mol) Medium Config. Time Forwrd Bckwrd Averge Protein 324 ps Wter 328 ps Vcuo 486 ps ps: see Tble III. 328 ps: 41 windows for the electrosttic contribution nd 41 windows for the VDW contribution, 2 ps/2 ps for equilibrtion nd smpling. 486 ps: 81 windows, 3 ps/3 ps for equilibrtion nd smpling. For the simultion in wter, the time step is 1 fs. Obviously, introducing three extr methyl group on Mcpe is too much to stbilize the enzyme. Listed in Tble VII re the free energy components of the clculted free energies. Compring the results in the enzyme nd in wter, one sees tht both the EL nd VDW terms of Mcpe=tBcpe ( nd ) inthe enzyme re much higher thn tht in wter, suggesting of high energy interctions in the protein. We cn lso see tht the VDW nd CORC terms of -Mcpe= -tbcpe re smller thn those of -Mcpe= -tbcpe. Since this modifiction will not increse the stbility of the enzyme, we did not perform further decomposition nlyses. TABLE IX. The Contributions of Different Interctions to the Free Energies of Cpe 8 Fcpe (kcl/mol) Medium Config. EL VDW BADH CORC Totl Protein Wter Vcuo The results re the verges of the forwrd nd bckwrd chnges of the simultions listed in Tble VIII. Cpe=FMcpe The solubility of perfluorocrbon in wter is generlly lower thn tht of the hydrocrbon from which it is derived, while the solubility of orgnic compounds contining both hydrogen nd fluorine decreses with the number of fluorine toms. 42,44 This incresed hydrophobicity of fluorocrbons compred to hydrocrbons my be utilized to improve the enzyme s stbility becuse replcing severl hydrogens with fluorines my decrese the solubility of the unfolded stte nd becuse the electrosttic potentil on the PROFEC zero VDW contour is positive, plcing more negtively chrged group ner there could stbilize the protein. We hve clculted the free energy chnges of Cpe= -FMcpe in vcuo, in wter, nd in the enzyme (Tble VIII). We hve only studied Cpe= -FMcpe becuse -FMcpe is expected to hve much less fvorble VDW interctions in the enzyme thn -FMcpe. For the simultions in wter, we found tht due to the highly polr chrcter of the CF 3 group, time step of 1 fs nd the electrosttic decoupling scheme 45 hd to be used to void SHAKE filures nd to reduce the hysteresis of the free energy result. Similr problem ws not observed in the simultions in the enzyme nd in vcuo with 2 fs time step. Unfortuntely, the estimted stbility of the enzyme with -FMcpe is found to be 0.6 kcl/mol less thn tht of the enzyme with Cpe (Tble XIII). Therefore, introducing the CF 3 group on Cpe does not improve the stbility of the enzyme. The clculted solvtion free energy difference between Ace- FMcpe-NMe nd Ace-Cpe-NMe is 0.04 kcl/mol, indicting tht solvtion free energy of the unfolded stte chnges little with the introduction of the CF 3 group. Since Ace-Cpe-NMe is more soluble thn Ace-Mcpe-NMe by 0.5 kcl/mol (Tble XIII), Ace- FMcpe-NMe will be more soluble thn Ace-Mcpe- NMe by 0.5 kcl/mol. This is resonble estimte becuse trifluoromethne is more soluble thn methne by 1.2 kcl/mol 42 nd for Ace-FMcpe-NMe nd Ace-Mcpe-NMe, the solvtion free energy difference should be less. To understnd why Cpe= -FMcpe is not stbilizing, we clculted the free energy components from different interctions for the free energy chnges (Tble IX). The BADH nd CORC terms re similr for the simultions in the enzyme nd in wter. The VDW term of Cpe= -FMcpe in the enzyme is bout 0.9 kcl/mol higher thn tht in wter. But the EL term of Cpe= -FMcpe in the enzyme is only 0.3 kcl/mol lower thn tht in wter, indicting tht the introduction of the CF 3 group does not gin much electrosttic stbiliztion in the enzyme s we hoped. The reson my be tht the fvorble electrosttic interction between the negtively chrged fluorine toms nd the protein is offset by the unfvorble electrosttic interction between positively chrged crbon tom nd the protein. Compring the results of Cpe= -FMcpe in wter nd in vcuo, the EL term of the former is 1.8 kcl/mol lower, but its VDW term is 1.8 kcl/mol higher. This compenstion explins why the solvtion free energy of Ace-Cpe-NMe nd Ace-FMcpe-NMe re similr. Cpe=Pcpe We hve done the clcultions in vcuo for both the nd the configurtions of Pcpe becuse it is not obvious tht the results will be similr to those found for Mcpe. For -Mcpe nd -Mcpe in vcuo, s discussed, respectively, the methyl group will fce the hydrogen nd the C H 2 on the C tom, but becuse the methyl group is fr wy from the C H 2, the free energies for introducing the methyl group in the two configurtions were found to be similr. This my be not true for -Pcpe nd -Pcpe becuse the cyclopropyl group is closer to the C tom nd whether it fces the hydrogen ( -Pcpe) or the C H 2

14 CAN ONE PREDICT PROTEIN STABILITY? 451 TABLE X. The Free Energy Chnges of Cpe 8 Pcpe In Vcuo, Wter, nd the Enzyme (kcl/mol) Medium Config. Time Forwrd Bckwrd Averge Protein 164 ps Protein 324 ps Protein 164 ps Protein 324 ps Wter 328 ps Wter 488 ps Wter 808 ps Vcuo 324 ps Vcuo 324 ps , 324, 328 nd 488 ps: see Tble III nd Tble VIII. 808 ps: 41 windows for the electrosttic contribution nd 161 windows for the VDW contribution, 2 ps/2 ps for equilibrtion nd smpling. ( -Pcpe) on the C tom my mke difference energeticlly. From Tble X, one sees tht the clculted free energy chnges for Cpe= -Pcpe nd Cpe= -Pcpe in vcuo re only slightly different. Therefore, for the simultions in wter, we only performed the clcultions for -Pcpe. For the simultions in the enzyme, the clcultions were performed on both -Pcpe nd -Pcpe. The hystereses of the clculted free energies for this modifiction re higher thn previous cses, especilly in the simultions in the enzyme. The reson my be tht there is considerble strin energy in the cyclopropyl ring which prevents quick equilibrtion of the system. This is demonstrted by the simultions in wter: it tkes 488 ps for the forwrd nd bckwrd chnges to reduce the hysteresis to below 0.4 kcl/mol. To reduce the hystereses of the clcultions in the enzyme, longer time my be required. However, the reltive stbility of the -Pcpe nd -Pcpe mutnts is very cler from the 164 ps clcultion nd the stbility difference of two mutnts does not chnge much when 324 ps for the forwrd nd bckwrd chnges is used (3.5 kcl/mol for 164 ps vs. 3.0 kcl/mol for 324 ps). Using the results of 324 ps for the forwrd nd bckwrd chnges in the enzyme nd 808 ps for the forwrd nd bckwrd chnges in wter, Cpe= -Pcpe will decrese the stbility of the enzyme by 1.1 kcl/mol nd Cpe= -Pcpe will increse the stbility of the enzyme by 2.0 kcl/mol (Tble XIII). This is in contrst with the Cpe=Mcpe modifiction, in which the -Mcpe mutnt is more stble thn the -Mcpe mutnt. This trend is congruent with the verge interction energies between the CH 2 of the cyclopropyl group with the rest of the systems in the -Pcpe nd -Pcpe mutnts. But it is only prtilly in greement with the PROFEC results which suggest tht both Cpe= -Pcpe nd Cpe= -Pcpe my be stbilizing. The solvtion free energy of Ace-Pcpe- NMe is estimted to be less thn tht of Ace-Cpe- TABLE XI. The Contributions of Different Interctions to the Free Energies of Cpe 8 Pcpe (kcl/mol) Medium Config. EL VDW Totl Protein Protein Wter Vcuo The results re the verges of the forwrd nd bckwrd chnges. In protein: from the 324 ps simultions. In wter: from the 808 ps simultion. In vcuo: from the 324 ps simultion. TABLE XII. The Group Contributions to the Free Energies of Cpe 8 Pcpe (kcl/mol) Contributions Groups T4 lysozyme Met Phe Ser Leu Leu Al Asn Pcpe Al Trp Phe Vl Wter Totl Ace-Pcpe-NMe Ace 0.52 Pcpe 0.39 NMe 0.40 Wter 0.08 Totl 0.59 For the simultion procedures, see Tble V. NMe by 0.9 kcl/mol (Tble XIII). The reson my be tht due to the high strin energy in the cyclopropyl ring, Pcpe is more polr thn Cpe (the RESP chrges of the CH 2 of the cyclopropyl group re: C: 0.44; H: 0.17). To further nlyze the free energy clcultions, we hve determined the contributions to the free energies from different interctions s well s from different residues (Tbles XI nd XII). The locl structures round Pcpe 133 re shown in Figure 8. Becuse the dul topology method ws used in the free energy clcultions, there re no CORC nd BADH contributions to the free energies. From Tble XI, one sees tht the VDW nd EL terms of Cpe= - Pcpe in the enzyme re both much lower thn those of Cpe= -Pcpe in the enzyme. But the mjor difference is in the VDW term. The VDW nd EL terms of Cpe= -Pcpe in the enzyme re lso lower thn those