Protein Science (1995), 4:2247-2251. Cmbridge University Press. Printed in the USA. Copyright 1995 The Protein Society REVIEW Side-chin conformtionl entropy in protein folding ANDREW J. DOIG' AND MICHAEL J.E. STERNBERG' ' Deprtment of Biochemistry nd Applied Moleculr Biology, University of Mnchester Institute of Science nd Technology, Mnchester M6 lqd, United Kingdom Biomoleculr Modelling Lbortory, Imperil Cncer Reserch Fund, London WC2A 3PX, United Kingdom (RECEIVED July 24, 1995; ACCEPTED September 11, 1995) Abstrct An importnt, but often neglected, contribution to the thermodynmics of protein folding is the loss of entropy tht results from restricting the number of ccessible side-chin conformers in the ntive structure. Conformtionl entropy chnges cn be found by compring the number of ccessible rotmers in the unfolded nd folded sttes, or by estimting fusion entropies. Comprison of severl sets of results using different techniques shows tht the men conformtionl free energy chnge (TAS) is 1 kcl.mol-' per side chin or.5 kcl.mol-' per bond. Chnges in vibrtionl entropy pper to be negligible compred to the entropy chnge resulting from the loss of ccessible rotmers. Side-chin entropies cn help rtionlize -helix propensities, predict proteidinhibitor complex structures, nd ccount for the distribution of side chins on the protein surfce or interior. Keywords: conformtionl entropy; internl rottion; protein folding; protein stbility; side chin The mjor force opposing protein folding is loss of conformtionl entropy. A dynmic unfolded protein is ble to ccess vst number of conformtions. In prticulr, its side chins re smpling mny different rotmeric sttes. When protein folds, side chins tht re buried in the close-pcked protein core re generlly restricted to single conformtion. Even side chins tht remin exposed to solvent on the protein surfce cn be more restricted thn in the unfolded stte. Entropy is relted directly to the number of different conformtions prticulr stte cn dopt. This reduction in the number of side-chin rotmers tht re populted results in sizeble loss of entropy opposing protein folding. Side-chin conformtionl entropy is, of course, only one of the mny spects of the thermodynmics of protein stbility tht re generlly considered to be primrily entropic rther thn enthlpic. Probbly the best recognized nd most studied of these is the hydrophobic effect tht primrily results from the free- ~. "~ Reprint requests to: Andrew J. Doig, Deprtment of Biochemistry nd Applied Moleculr Biology, University of Mnchester Institute of Science nd Technology, P.O. Box 88, Mnchester M6 lqd, UK; e-mil: ndrew.doig@umist.c.uk. Abbrevitions: AScon,, chnge in entropy from decresing the number of energeticlly ccessible rotmers; AS,,b, loss of vibrtionl entropy; AS,,,,,,, totl entropy chnge from restricting side-chin motion (sum of AS,,,,, nd A&,); W, number of different conformtions dopted in the unfolded stte; u, symmetry number for rottion; p,, frctionl popultion of rotmer; ASfus, fusion (liquid + solid) entropy chnge. 2247 ing up of ordered wters when nonpolr groups re removed from solvent. Mny workers hve estblished scles for residue hydrophobicity. Indeed Cornette et l. (1987) cited 46 different scles. Another well-studied effect is disulfide bridge formtion. Mny workers ttribute the restriction in conformtionl freedom of the unfolded stte in the crosslinked chin compred to the uncrosslinked molecule s the min reson for the increse in protein stbility resulting from disulfide bridge. Recently, for exmple, Hrrison nd Sternberg (1994) showed tht entropic restriction in the unfolded stte provides good model for observed disulfide connectivity ptterns nd loop lengths in short sequences (<75 residues). However, Doig nd Willims (1991) proposed in ddition tht disulfides decrese the surfce re of the unfolded stte. This reduces the size of the hydrophobic effect nd cuses enthlpic stbiliztion nd entropic destbiliztion of the folded stte when disulfide is present. Experimentl evidence tht could distinguish these two models remins inconclusive (Betz, 1993). In contrst to these effects, the conformtionl nd vibrtionl entropy of both min chin nd side chin hve been fr less well chrcterized. Here we re interested in the chnge in entropy occurring during folding. When protein folds, entropic effects from chnging its configurtion cn rise from two sources: First, there will be chnge in the number of conformtions (essentilly rotmers) populted (AScon,). Figure l shows chnge in AS,,,,, s rotmer is restricted from three conformtions to one. Second, the width of n llowed potentil en-
2248 A. J. Doig nd M. J. E, Sternberg 9 c K Chi Angle Chi Angle ssconfig = &onf + &ib Fig. 1. Chnges in the configurtionl entropy (A.Scon,,g) of side chin rise from two sources: reduction in the number of rotmers populted (AS,,,,) nd the restriction of torsionl vibrtions bout n energy minimum (AS[,,h). Outside the ccessible rnge of x ngles, the energy is very high nd unknown. ergy well might nrrow in close-pcked folded protein. This corresponds to the bond being restricted to smller rnge of dihedrl ngles nd results in loss of vibrtionl entropy (ASvlb; Fig. 1). This is torsionl vibrtion bout covlent bond xis. The sum of both these effects is configurtionl en- tropy (Asconfig = Ascon, + ASu;b). Krplus et l. (1987) used moleculr dynmics simultions to estimte vibrtionl nd conformtionl entropy during folding. They suggested tht, lthough the mgnitude of bsolute vibrtionl entropy is nerly n order of mgnitude lrger thn conformtionl entropy, the most importnt chnge on folding is in conformtionl entropy. Although ttempts to dissect the reltive mgnitudes of different thermodynmic effects hve been criticized s not formlly correct (Mrk& vn Gunsteren, 1994), it remins helpful in understnding protein stbility to estimte these individul contributions (Boresch et l., 1994). In this rticle, we review the renewed interest in estimting side- chin conformtionl entropy. Rottble side-chin x ngles tht cn be restricted in protein folding re numbered ccording to convention (IUPAC-IUB Commission on Biochemicl Nomenclture, 1969, 197). Chnges in side-chin conformtionl entropy on folding (herefter bbrevited AS,.,,,,) were first discussed nerly 3 yers go (Nkmethy et l., 1966). In recent yers, there hs been much renewed interest in this re. In the lst five yers, number of ppers hve been published tht mke estimtes of AS,,,,, by independent methods. Here we discuss ech of these methods nd compre their results. This llows us to drw some generl conclusions on the size nd importnce of ASco,,,. Side-chin conformtionl entropy from the Boltzmnn eqution The most strightforwrd method uses the Boltzmnn eqution (Eqution 1) directly to clculte entropy: W is the number of different conformtions dopted in the unfolded stte. This cn be tken to be 3 for ech sp3-sp3 single bond (Novotny et l., 1989; Krystek et l., 1993) if it is ssumed tht ech rotmer is populted eqully in the unfolded stte (i.e., ech bond is 33% guche+, 33% guche-, nd 33% trns) nd tht the conformtionl entropy of the folded stte is zero (i.e., 1% in single rotmer). The simplest method is therefore to estimte AS,,,,, s -R In 3 (-2.2 c1.k-l mol-') per rottble bond (Novotny et l., 1989). The symmetry bout the bond xis (u) must lso be considered. For exmple, the bond to the romtic ring in Phe (x2) hs twofold symmetry, becuse n identicl stte is reched if this bond is rotted by 18". The entropy in the folded stte is thus R In 2, insted of zero (R In l), nd AS,.,,,, for this bond is therefore smller. Similrly, x2 of Tyr, x2 of Asp, nd x3 of Glu lso hve twofold symmetry nd hence reduced vlue of As,.,,,,. A more sophisticted pproch is to tke into ccount tht the rotmers in the unfolded stte re not eqully populted. Figure 1 shows three conformtions ccessible in the unfolded stte with different energies. A stte with higher energy will be populted less often. Nkmethy et l. (1966) nd Finkelstein nd Jnin (1989) used Eqution 1, with Ws 2-3 for ech rottble bond. A more ccurte pproch is to use Eqution 2, where pi is the frctionl popultion of ech rotmer stte i in the unfolded stte. The popultions of ech rotmer in the unfolded stte cnnot yet be observed directly. Insted, Pickett nd Sternberg (1993) ssumed tht the conformtions dopted by side chins in protein crystl structures re representtive of unfolded conformtions. The distribution of side-chin rotmers t interior positions of -helices is unusul, however, so they were excluded. The results of their survey were used to determine AS,,,,, using Eqution 2. It ws necessry to correct some residues for symmetry (discussed bove) nd they dded term for groups tht showed essentilly free rottion in the unfolded stte, restricted by hydrogen bonding when buried. Their results re given in Tble 1. Abgyn nd Totrov (1994) used similr pproch, finding pi for ll x1 nd x2 ngles by surveying 161 dissimilr protein domins. Additionl terms were dded for x3 nd x4 rottions nd symmetry corrections were mde. Their results re given in Tble 1. Koehl nd Delrue (1994) found pi for ech rottble bond in the folded stte by clculting the energy of ech rotmer. The energies were clculted for different conformtions of nerby rotmers nd weighted by how often ech neighboring conformtion ws dopted. The entropy of the unfolded stte ws found using Eqution 1, where W is the number of possible
~ - Side-chin con formtionl entropy in protein folding 2249 Tble 1. Chnges in side-chin conformtionl entropy (TAS) on protein folding t 3 K (kcl.rnol") TAsconf" Number Pickett Abgyn Koehl Cremer X nd nd nd Blber nd Lee Residue ngles Sternberg Totrov Delrue et l. Rose l. et Men TASfu$ Hydrophobicity' Al -.42 Arg 4-2.3-2.13-1.21-2.13-1.88 1.37 Asn 2-1.57 -.81 -.75 -.99-1.3-1.24.82 ASP 2-1.25 -.61 -.65 -.6 -.78-1.37 1.5 CYS 2 -.55-1.14 -.63-1.6 -.85 -.65-1.34 Gln 3-2.1 1-2.2-1.29-1.51-1.73-1.91.3 Glu 3-1.81-1.65-1.31-1.6-1.46-2.4.87 GIY His 2 -.96 -.99 -.92 -.89-1. -.95-1.64 -.18 Ile 2 -.89 -.75 -.94 -.79 -.67 -.52 -.76 -.83-2.46 Leu 2 -.78 -.75 -.94 -.69 -.58 -.49 -.71 -.83-2.32 LYS 4-1.94-2.21-1.63-1.76-1.89-3.5 1.35 Met 3-1.61-1.53-1.24-1.53-1.37-1.46-1.54-1.68 Phe 2 -.58 -.58 -.65 -.61 -.87e -.42 -.62 -.93-2.44 Pro -.3 -.6 -.98 Ser 2-1.71 -.43-1.19-1.1-1.11 -.89.5 Thr 2-1.63-1.12 -.57 -.99-1.8 -.73 -.35 Trp 2 -.97 -.97-1.14 -.88-1.16 -.82 -.99-1.88-3.7 TYr 3 -.98 -.99-1.76' -1.7 -.83-1.13-1.35-1.31 Vl 1 -.51 -.5 -.62 -.46 -.42 -.4 -.43 -.15-1.66 Totl 41-21.88-19.94-16.29-18.92 Men 2.5-1.9-1. -.81 -.95 Absolute TSd -13.7-5.6-4.2-7.8-6.4-4.5-2.6-2.7-9.3-4.4-3.1-4.4-5.6-1.3-87.3-4.37 References: Pickett nd Sternberg (1993); Abgyn nd Totrov (1994); Koehl nd Delrue (1994); Blber et l. (1994); Cremer nd Rose (1994); Lee et l. (1994). Sternberg nd Chickos (1994). Fuchere nd Plisk (1983). Doig et l. (1993). Corrected for symmetry. rotmers for ech side chin in the rotmer librry of Tuffery et l. (1991). The difference between these quntities gives AS,.,, (Tble 1). Cremer nd Rose (1994) used n cetyl-(al),-x-(al)5- NMe peptide in nonhelicl stte s model for n unfolded protein nd found the rotmer popultions of residue X by Monte Crlo simultions for eight residues. Blber et l. (1994) surveyed the popultions of x1 nd x2 in nonhelicl structure for seven residues. Tble 1 gives these results t 3 K nd the men vlues of TAS, for ech residue. Ech of these cn be compred to the hydrophobicity of the side chins (Fuchere & Plisk, 1983), given reltive to Gly. It is seen tht side-chin conformtionl entropy is close to hydrophobicity in mgnitude nd hence importnce in protein stbility. The men vlue of TAS,,,f per residue is -.95 kcl.mol-'; the men vlue of TAS, per rottble x ngle is -.46 kcl.mo1-'. The greement between the results for vrious groups is best for nonpolr residues, becuse the tretment of side chins involved in hydrogen bonds vried. Some vrition lso rises from ssigning different number of llowed rotmers to ech X ngle nd in the tretment of the folded stte. Ech of these scles correltes well with ny other; the lest-squres correltion coefficients when ech scle is plotted ginst ech other vry from.73 to.99 (not shown). Absolute entropies As mentioned bove, ech of these methods hs ssumed tht the potentil energy well for ech rotmer hs sme width in the unfolded nd folded sttes (i.e., ASuib = ; Fig. 1). It is possible, however, tht the well is nrrower in the folded stte, restricting the bond to smller rnge of dihedrl ngles nd hence giving lrger AS,,, (i.e., AS,, < ). At the opposite extreme, we cn consider the thermodynmic chnges when motion stops completely nd bond is fixed t the bse of one well. This gives the mximum possible entropy chnge for restricting side chins nd is the bsolute entropy (i.e., entropy chnge upon cooling to bsolute zero). These mximum possible entropy chnges hve been clculted by Doig et l. (1993) (Tble 1). is =4 times lrger thn ASconf by this method, but the different sets of results correlte well. (The correltion coefficients when the bsolute entropy is plotted ginst ech of the scles of ASConfvries from.76 to.95.) This suggests tht only ~ 25% of the bsolute entropy of side chin is lost when protein folds. The reminder is retined in the form of torsionl vibrtion. Suib clculted by Krplus et l. (1987) is lrger thn the Suib of Doig et l. (1993) becuse the former work considered degrees of freedom in ddition to just dihedrl ngle rottion, such s bond ngle vrition nd lrger scle motions.
225 A.J. Doig nd M.J.E. Sternberg Lee et l. (1994) clculted side-chin entropies for residue X in helix (Al),-X-(Al), by three methods. First, they found using the Eqution 2, determining pi by clculting the energy s ech dihedrl ngle is vried (Tble 1). Second, they clculted Svlb by two methods to find the totl Sconfin. Svib ws found by ssuming tht the torsionl vibrtion is simple hrmonic oscilltor, or by integrting the Hmiltonin for the vibrtion with terms for kinetic nd potentil energies. The sum of S,,, nd Svib gives Sconirn for side chin on the surfce of n -helix. They concluded tht the frequency of ech torsionl oscilltion does not chnge when n internl rottion is restricted (i.e., ASuih = ), justifying using chnges in conformtionl entropy s the totl chnge in configurtionl entropy. Entropies of fusion The core of protein is s close pcked s n orgnic crystl (Richrds, 1977). Entropies of fusion of orgnic compounds cn thus be used s model for entropy chnges in protein folding. Nicholls et l. (1991) nd Serle nd Willims (1992) found TAS,,, to be -.4 to -.8 kcl.mol-' per rotor t 3 K by considering fusion entropies of series of n-lknes, lkyl crboxylic cids, nd 2-methyl ketones, consistent with other results. Sternberg nd Chickos (1994) estimted side-chin entropy by extending n empiricl pproch developed to model fusion entropy for smll orgnic molecules. They clculted TAS,.o,,jfor 17 residue side chins (Tble 1). The fusion entropy scle correltes well with ech of the other scles listed in Tble 1 nd, importntly, gives results of the sme mgnitude. This confirms tht tking the totl AS,,,, s purely AS,,, is good ssumption. The reminder pproch A finl pproch to AS,,, is to find ech of the other terms tht contribute to protein stbility nd ttribute the difference from the experimentl entropy chnge on folding to AS,,,. Privlov nd Mkhtdze (1993) estimted TAS,,,J to be -3. kcl.mo1" per residue t 3 K nd Freire et l. (1993) found TAS,,, to be -.9 kcl.mo1" per residue in this wy. The errors in this method re perhps lrger becuse they require the ccurte estimtion of ll other terms. Applictions Considertion of side-chin conformtionl entropies cn help rtionlize some spects of protein structure. There is tendency for residues with lrger vlues of AS,,, to remin on the protein surfce, where they will hve higher entropy thn if they were buried (Doig et l., 1993; Pickett & Sternberg, 1993). Shkhnovich nd Finkelstein (1989) rgued tht the rtedetermining step in protein folding is finding the correct sidechin rotmers. A residue on the surfce of folded protein cn be restricted in side-chin motion, though generlly to lesser extent thn when it is buried. Cremer nd Rose (1992, 1994) clculted sidechin entropies on the surfce of -helices, using Eqution 2, where pi is found by Monte Crlo simultion, nd showed tht these correlte well with experimentlly mesured helix preferences for eight nonpolr residues. Blber et l. (1994) repeted this work for x 1 nd x2 for ll 2 mino cids, finding p, by surveying helices in crystl structures, nd found somewht weker correltion between AS,,, nd helix preference. They rgued tht lthough side-chin conformtionl entropy goes some wy to rtionlize helix propensities, other fctors lso ply role (principlly the hydrophobic effect). Totrov nd Abgyn (1994) incorported side-chin entropy effects into n lgorithm used to predict the structure of proteidntibody complex. Jckson nd Sternberg (1995) explored the inclusion of them to distinguish correctly from incorrectly docked proteidinhibitor complexes. Future pplictions of this work my include helping to understnd the effects of point muttions on protein stbility nd in ssessing correctly from incorrectly folded protein structures. Conclusion Comprison of ech of these methods llows one to drw some generl conclusions on the mgnitude nd importnce of chnges in side-chin conformtionl entropy. If the nomlous results of Privlov nd Mkhtdze (1993) re discounted, consensus is reched tht the cost of restricting side-chin motion (TAS,.,,,) is =-1 kcl.mo1" per residue in protein folding or =-OS kcl.rnol-l per rotmer. It is thus of considerble importnce in protein stbility. The excellent greement for AS,,, per side chin mesured by severl methods, using both empiricl nd theoreticl pproches, suggests tht the shpe of ech conformtionl well is indeed similr in the folded nd unfolded sttes. In the folded stte, rottble x ngle is merely restricted to fewer (often one) sttes. Chnges in vibrtionl entropy cn thus be sfely ignored (i.e., AStmth = ; ASconltX = AS,,,) nd only 225% of the bsolute side-chin entropy is lost on buril in folded protein. Acknowledgments We thnk Dudley Willims, Mrk Serle, nd Trevor Cremer for helpful discussions. A.J.D. thnks the BBSRC, the Royl Society, nd the Nuffield Foundtion for finncil support. References Abgyn R, Totrov M. 1994. Bised probbility Monte-Crlo conformtionl serches nd electrosttic clcultions for peptides nd proteins. J Mol Bi/235:983-12. Betz SF. 1993. Disulfide bonds nd the stbility of globulr proteins. Protein Sci2:1551-1558. Blber M, Zhng XJ, Lindstrom JD, Pepiot SD, Bse WA, Mtthews BW. 1994. Determintion of -helix propensity within the context of folded protein-sites 44 nd 131 in bcteriophge-t4 lysozyme. J Mol Biof 23.5:6-624. Boresch S, Archontis G, Krplus M. 1994. Free-energy simultions-the mening of the individul contributions from component nlysis. Proteins Struct Funct Genet 29-33. Cornette JL, Cese KB, Mrglit H, Spouge JL, Berzofsky JA, DeLisi C. 1987. Hydrophobicity scles nd computtionl techniques for detecting mphipthic structures in proteins. JMo/ Bio/ /95:659-685. Cremer TP, Rose GD. 1992. Side-chin entropy opposes lph-helix formtion but rtionlizes experimentlly determined helix-forming propensities. Proc Not1 Acd Sci USA 895937-5941. Cremer TP, Rose GD. 1994. -Helix-forming propensities in peptides nd proteins. Proteins Struct Funct Genet /9:85-97. Doig AJ, Grdner M, Serle MS. Willims DH. 1993. Thermodynmics of side chin internl rottions-effects on protein structure nd stbility. In: Angeletti RH, ed. Techniques in protein chemistry IV. London: AC- demic Press. pp 557-566. Doig AJ, Willims DH. 1991. Is the hydrophobic effect stbilizing or de-
Side-chin conformtionl entropy in protein folding 225 I stbilizing in proteins? The contribution of disulfide bonds to protein stbility. J Mol Biol 217:389-398. Fuchere JL, Plisk V. 1983. Hydrophobic prmeters n of mino-cid sidechins from the prtitioning of N-cetyl-mino-cid mides. Eur JMed Chem Chim Ther 18:369-375. Finkelstein AV, Jnin J. 1989. The price of lost freedom-entropy of bimoleculr complex-formtion. Protein Eng 3: 1-3. Fre~re E, Hynie DT, Xie D. 1993. Moleculr-bsis of coopertivity in protein-folding. 4. CORE-A generl coopertive folding model. Proreins Srrrrct Funct Gene1 17: 1 I 1-123. Hrrison PM, Sternberg MJE. 1994. Anlysis nd clssifiction of disulfide connectivity in proteins -The entropic effect of cross-linkge. J Mol Biol 244:448-463. IUPAC-IUB Commission on Biochemicl Nomenclture. 1969, 197. Abbrevitions nd symbols for the description of the conformtion of polypeptide chins. Tenttive rules. Biochemistry 9:3471-3479. Jckson KM, Sternberg MJE. 1995. A continuum model for protein-protein interctions: Appliction to the docking problem. J Mol Biol 25: 258-27.5. Krplus M, lchiye T, Pettitt BM. 1987. Configurtionl entropy of ntive proteins. Biophys J 52:183-185. Koehl P, Delrue M. 1994. Appliction of self-consistent men-field theory to predict protein side-chins conformtion nd estimte their conformtionl entropy. J Mol Biol 239:249-275. Kryhtek S, Stouch T, Novotny J. 1993. Affinity nd specificity ofserine endopeptidse protein inhibitor interctions-empiricl free-energy clcultlons bsed on X-ry crystllogrphic structures. J Mol Biol234: 66 1-679. 1.ec KH, Xie D, Frcire E, Amzel I.M. 1994. Estimtion of chnges in sidechin configurtionl entropy in binding nd folding-generl methods nd ppliction to helix formtlon. Proterns Struct Funcl Gene1 258-84. Mrk AE, vn Gunsteren WF. 1994. Decomposition of the free-energy of system in terms of specific interctions-implictions for theoreticl nd experimentl studies. J Mol Biol24:167-176. Nemethy G, Lech SJ, Scherg HA. 1966. The influence of mino cid side chins on the free energy of helix-coil trnsitions. J Phys Chem 7: 998-14. Nicholls A, Shrp KA, Honig B. 1991. Protein folding nd ssocition- Insights from the interfcil nd thermodynmic properties of hydrocrbons. Proleins Strucl Funcl Gener 1/:281-296. Novotny J, Bruccoleri RE, Sul FA. 1989. On the ttribution of bindingenergy in ntigen-ntibody complexcs Mcpc-63, Dl.3, nd Hyhel-5. B/ochemistry 28:4735-4749. Pickett SD, Sternberz MJE. 1993. Empiricl scle of side-chin conformtionl entropy in protein folding. J Mol Bid 23/:825-839. Privlov PL, Mkhtdze GI. 1993. Contribution of hydrtion to proteinfolding thermodynmics. 2. The entropy nd Gibbs energy of hydrtion. J Mol Biol232:66-679. Rlchrd5 FM. 1977. Ares, volumes, pcking nd protein structure. Annu Rev Biophys Bioeng 6: I5 I - 176. Serle MS, Willims DH. 1992. The cost of conformtionl ordcr-entropy chnge5 in moleculr ssocitions. JAm Chem Soc 1/4:169-1697. Shkhnovich El, Finkelstein AV. 1989. Theory of coopertive trnsitions in protein molecules. 1. Why denturtion of globulr protein is 1st-order phse-trnsition. Biopolymers 28:1667-168. Sternberg MJE, Chickos JS. 1994. Protein side-chin conformtionl entropy derived from fusion dt-comprison with other empiricl scles. Protein Eng 7:149-155. Totrov M, Abgyn R. 1994. Detiled b-initio prediction of lysozymentibody complex with 1.6 ngstrom ccurcy. Nture Slruct Biol 4: 259-263. Tuffcry P, Etchebest C, Hzout S, Lvery K. 1991. A new pproch to the rpid determintion of protein side-chin conformtions. J BiotnolSrruct Dyn 8:1267-1289.