J. Mol. Biol. (1981) 145, 251-263

Effect of Proline Residues on Protein Folding

l&hCHAEL LEWIT,

Salk Institute, La Jolla. Calif., l’.S.A.and

IVeizmIann I astit u te. Rehovot, Israel?

(Rececived 6 LYay 1980)

C’onformat,ional energy calculations have been used to studs the role of the prolineresidues in the folding of bovine pancreatic trgpsin inhibitor. In the calculation.each of the four proline residues of this small protein is forced from the trans to cZ:speptide isomer while still part of the native folded structure. The cis proline residuecan alwavs be accommodated by small changes of the native conformation ( < 1 Aroot-mea”n-square deviation). For three of the four proline residues, Pro& Pro9 andPro13. being in the r/is form is calculated to destabilize the folded conformation byless than 11 kcal/mol, suggesting that rapid folding to a stable native-likeconformation can occur with either isomeric form. For one of these three, Pro13,the destabilization is onlv 1 kcal/mol, suggesting the existence of an alternativefolded native conformation with Pro13 cis. The fourth proline residue, Pro& iscalculated to destabilize the native conformation bv so much (33 kcai/mol) that itwill block folding in the manner proposed bv Brandts et al. (1975).c

1. Introduction

Proline residues are widely recognized as p1aving.a special role in the folding andunfolding transitions of glYobular protein molecules. This amino acid residue has arelativelv high intrinsic probabilitv (between 0-l and O-3, depending on thec uadjacent’ sequence) of existing as the cis rather than the tram peptide isomer,(Brandts et al.. 19’75: Grathwolhl & Withrich. 1976). whereas for other amino acidsthe probability is much smaller (less than 10D3: see Ramachandran & Rlitra. 1976).Because the interconversion of the two isomers is slow under normal conditions (1to 7 min for model peptides). with a barrier of approximately 20 kcal/mol between,the two forms. Brandts et al. (1975.1977) proposed that the existence of the prolineresidues in the wrong isomeric form would slow down protein folding. In this model.it is argued tha,t in the unfolded state of the protein the proline residues occur withbot’h the cis and tram isomeric forms. Onlv those unfolded molecules in which allthe proline residues have the same isomkric form as in the native protein areassumed to fold directlv to the native conformation. Unfolded molecules with oneor more prolines in the’incorrect isomeric form are assumed t/o fold only after first)undergoing the slow isomerization to the unfolded form with the same proline

t Author’s permanent address.

2 5 1

(H~L’~-~~~~fi/~l/OlOL’~1-13 $iW.OO/O i” 1981 Academics Press Inc. (London) Ltd.

252 M . L E V I T T

isomers als in tlhe native conformat,ion. Thus, one expects that proteins containingproline residues should consist of a mixture of fast and slow folding molecules, asfirst obser~d for ribonuclealse (Garel Cc Baldwin. 1973.19T5 : Baldwin. 1978).

Further studies (Schmid & Baldwin, 1978) led to the suggestion that not allproline residues in aI protein are essential, in that thev block rapid folding and thatthese non-essential proline residues can isomerize’ after folding has occurred.Subsequent experiments bv (rook et al. (1979) showed that under low-temperature.conditions st)ronglv favouring folding even the essential proline residues that slowkribonuclealse refolding can isomerize aft)er extensive and specific folding to a native-like structure. This isomerization to the native isomeric form occurs significantlvmore rapidlv (about XLfold) than in the unfolded state. In his theoretical analysis,.Creightjon (1978) indicates that’ manv large proline-containing prot,eins fold more.rapidlv than would be expected from Brandts’ model, suggesting that otherprotjeiA ma\- behave like ribonuclease.

Here conformational energy calculations on the refined X-ray structure of theprotein bovine pancreatic trvpsin inhibitor (Huber et al., 1971 : Deisenhofer 6:Steigemann. 1974) are used to investigate the strain associated with theincorporation of incorrect proline isomers into the native conformation. Each of thefour proline residues in BPT1-t is forced by constrained energy minimization fromits native tram isomer to the incorrect cis isomer. The results indicate thatisomerizing one of the proline residues, Pro13, in this way has a verv small effect oncthe stabiMv of the native conformation. increasing the total equilibrium potential.energv bv only 1 kcal/mol. For two other proline residues, Pro2 and Pro9, thechange in energv is less than 11 kcal/mol, suggesting that these proline residuescould a’lso be incorporated as cis isomers during the folding of BPTI as observed byCook et ~1. (1979). Onlv one proline residue, Pro& so destabilizes the nativeconformatlion (bv 33.3 kcal/mol) that, it should block rapid folding in the waxproposed bv Brandts et al. (1975). The results also indicate that int,eractions with.the surrounding atoms in t’he native folded conformation will accelerate the ~2:s hobans isomerization of Pro2 and Pro9 bv factors of 11,000 and 300, respectively.

It is concluded that only 230/6 of unfolded BPTI molecules should refold slowly,in contrast to the 600/;, expected from Brandts model. In addition? about 5% of thefolded BPTT molecules should have proline residue Pro13 in the cis isomer givingrise to a slightlv different native folded structure that might be detectable bycnuclealr magnetic resonance or other spectroscopic methods.

2. Conformational Energy Calculations

A ctonformational energy function of the empirical type used before (Levit,t 8r Lifson? 1969 :Levitt, 1974.1978) is used here to calculate the equilibrium conformation energies of (a) thenatjive conformation, in which all 4 proline residues have tram peptide isomers (torsion angleco = lso”), (b) the 4 native-like conformations in which each proline residue is forced in turnto have the his isomeric form (W = O”), and (c) the 2 conformations in which Pro2 and Pro9are forced tlo have an intermediat!e isomeric form (W = 90”).

The energv is calculated as a sum of terms representing bonds, bond angles, torsion angles,improper torsion angles, van der Waals’ intleractions and hvdrogen bonds:*

t Abbrevia.tions used : BPTI. bovine pancreatic trypsin inhibitlor : r.m.s.. root-mea,n-square.

EFFE(“I‘ O F IWOLISE RESII>I_‘ES 2 5 3

bond angles

+ : K,( 1 +cY-e (,q+S)!+ -T E,(+e 4)-torsion angles (4, $1 pairs

improper torsions

+ \‘-non-bonded pairs

+ z Ej(rl)p -2(,.5/r)6j. exp ( -B2/02).0.. . H pairs

The bond and bond angle functjions a,re parametrized bv force-constants &, and K, and zeroa.I-alues II” and 8” for everv tvpe of bond and bond angle. The first torsion angle term. whichhinders free rotation about’ single (“4“ bonds and enforces tlhe planarit!v of peptide groupsand aromatic rings, is parametrized bv a barrier height %K,, a periodic& ?j and a phase 6.The second torsion angle term is included to allow for the effect 011 the (4: 4) angles of every,residue of the near-neighbour non-bonded interactions tIhat are excluded from the van derWaals’ and hvdropen bond terms (see below 1. This special potential has minima of depths of-& kcal/mol and 2 kcal/mol at (4. 4) values of ( - 75’. 0’) and ( -60”. 150”). respectivelv. The*third torsion angle term allows for the improper torsion angles needed to keep side atoms(atoms connected to onlv one other atom) in-plane and also ensure that the amino acidscremain as L-isomers. For example. in the group

the oxygen atom is kept in-plane bv keeping t.he value of the improper torsion angle C”-X-L(‘4 close to 180’.

The van der Waals’ interaction. which uses tlhe Lennard-?Jones ‘X-6” form. isparametrized bv I*‘. the separation at which the atom pair interacts most stronglv. and E. thestrength of that interaction. Values of I*’ and E were obtained bv optimizing the fit betweenCIthe calculated and experimental unit-cell dimensions of 28 hvdrocarbon. amide and aminoacid cmstals using a well-established procedure (Warshel & Li’fson, 1970: Hagler it al., 1974:Lifson”et al.. 1979: Lifson & Levitt. 1979. and unpublished results). The special hvdrogen-”bonding term. which acts between all pairs of oxygen and peptide hydrogen atoms, isdesigned to give linear hvdrogenc bonds without requiring the computat~ionallv morecexpensive elect:rostatic term usf?d on the crystals. This potential was shown to cause asmaller delTiation from the S-rav structure of BPTI than the electrostatic term (Levitt,198(I) and is parametrized with ,a’ = I.7 A. 6 = 5 kcaljmol. and CT = W. The van der Waals’and hvdrogen bond interactlions are calculated between all atom pairs closer together than.the sum of the van der Waals’ radii plus 2 A and separated bv more than 3 bonds along the”covalent st!ructure.

The proline residues were forced from the native tram isomer to the cis form bv thetorsional potential 10[ 1 - cos (CO)]. that has a minimum value for cu = 0”. This is the”sametvpe of potential that is normallv. . used to keep peptide bonds planar and trans (i.e.cc) = 1 fw”).

The energv function described above can be used to calculate the energv value associatedwith the arrangement of atoms in the native or anv other conformation. &fortunately, this’simple procedure will not give energy I-alues At can be meaningfullv compared: a fewbadlv placed atoms can give rise to ajrbitrarilv large changes in energ\:. Instead. we must1*com;,are the energies of equilibrium conformations obtained after minimizing the energy tclrelax all excess strain. Here we minimize with respect to all the 1581 Cartesian co-ordinates,of the molecular system that comprised 51C5 protein atoms (including the hydrogen atoms onamide and peptide groups needed for accurate representation of hvdrogen bonds) and 12.

254 %I. L E V I T T

atoms of‘ the 4 buried water molecules observed in the refined BPTI S-ray structure(D&en hofer & Wigemann, 1974). The minimization method used here. known as themethod of’conjugate gradients (Hestenes & Stiefel, 19%). converges t,o a true minimum afterabout 3OOO evaluations of the energy function for the 1581 variables of BPTI. The method ofsteepest descent,s used in some previous conformational energy calculations (Levitt & Lifson.1969: Gelin Cyr Karplus, 1975) never converges, making any reliable comparison of energy&a cvalues impossible.

3. Results

Seven distinct conformational energy minimizations of the X-ray conformationof BPTI were undertaken. In the first minimization. no constraints were used toalter the isomeric form of anv of the proline residues. The resulting all-trcbnsconformation was close but n& identical to the crvst*al structure. with a O*6Ei Ar.m.s. deviation of the main chain atoms from the refined X-rav structure (seeTable 1). The corresponding r.m.s. deviation of the side-chain at’bms is larger at141 A. The r.m.s. deviation of the exposed solvent accessible atoms (l-37 A) issubstantiallv greater than that of the buried atoms (@61 A), indicating that thelarge r.m.s. ‘deviation mav be due to the omission of the hundreds of surround:ingsolvent molecules and tie neglect of the other protein molecules in the BF’TIcrvstal. The potential used here does, however, give a lower r.m.s. deviation for anisolated protein molecule A vacua than do the other potentials tested (Levitt,1980).

In the next follr minimizations. all starting from the end-point of the fiirstminimization. each of the four BPTI proline residues (at positions 2. 8, 9 and 13)was forced in turn from the native trans form to the cis form. The resultingequilibrium conformations are all within 1 A main chain r.m.s. devia)tion from theS-ray conformation. All have energies that are higher tlhan that’ of the all-tnxnsmi&um. with increases in total energy (strain energy) that varv from onlbI kcal/‘mol for Pro13 tlo 33 kcal/mol for Pro% In the final two minimizations. alsbi

Energy contdwtio~cs and root-rnea’n-.sqI(cr,.e deviations

Energy contribution (kcal/mol)r.m.s. deviation?

Energy u from(kcal/mol) van der native no. 1

(‘onf’orma.tion Total Bond Angle Torsion Was-1s’ H bond (4)A (4

( 1 ) A.411-fmn.s(2) Proi cis(3) Pro8 ch(1) Pro9 ci.s(5) Pro13 c,is(6) Pro2 int(7) Pro9 int

-t The r.m.s. deviation is of corresponding main chain atom positions of residues 2 to 56 relative tdo theS -rav or all-/raw ( 1) conformation. respectivelv.

z be energies for cwdormations (2) to (7) aEe given relative to those of’ conf’ormation (1).

EFFECT O F P K O L I S E KESIDVES 255

starting from tne end-poim of’the first minimization. Pro2 and Pro9 wer~‘e forced tohave isomeric forms intermediat,e between tmm and cis with the peptide torsionangle ct) = 90”. In both cases the intermediate form was more stable than t:he ckisomeric form as the 20 kcal/mol intrinsic barrier tlo isomerization is not included.

The different contributions to the calculated energv (see Table 1) show how thebond stretching and non-bonded van der Waals’ energv terms are least affected b\proline isomerization. The bond angle bending and ‘torsional terms account formost of t’he energv increase in the three most strained conformations (ProZ Pro&and Pro9 his). TlZs happens as the localized change of the proline CC) angle bv 18c)”causes a localized strain in the polvpeptide backbone. The hvdrogen bond termITaries less predictable. being leastfor Pro9 cis and most for Pro8 ~7:s. Detailedexamination of the atomic co-ordinates expkns this in terms of an extra hvdrogenbond in Pro9 ctis between (:1u$W2 and one of the internal water molecules, *whereas

3’- 29cis

3 8-c/3

0 IO 20 30 4 0 50

Residue number

FIG. 1 . The r.m .s. deviation of’ main chain atoms f’rom their positions in the all-kans equilibriumc~onf’ormation is plotted against the location of the residue along the polypeptide cbhain. The unbroken(bur\‘t’ shows t he (+onventional r.m .s. (leviat ion of corresponding atomic posit ions. The broken curveshows the r.m.s. deviation of’ corresponding interatomic distances defined as

*\where “ii and rij x-e the distances between main chain atoms i and j in the confi>rmat’ions compared.Regions that show high values of’ both deviations have both moved relat’ive to the rest of the moleculeand also changed their local conf’ormation : regions that shoti- only high values of the positional deviationhave moved wit bout changing conformat ion.

256 ICI. LEVITT

in Pro8 cis a hvdrogen bond between TvrlOH and an internal water is lostI. Theextra hvdrogen’bond cannot, form when FL9 is trans due to a close contact betlweenthe watler molecule and the ljeptide oxygen of Pro& The other conformations a,11have essenGallv the same hvdrogen bonds as in the X-ray conformationCI(Deisenhofer CC Steigemann. ’ .19j3)

The main chain r.m.s. deviations of the four conformations with ~‘2:s prolineresidues va’rv from O-12 ,-I to O-56 A. with the smallest de\-iations associated withthe smallest’strain energies (Table 1). The variation of this deviation with positionof the residue along the polypeptide chain (Fig. 1) shows how the residueimmediatelv preceding the isomerized proline moves more than the proline itself inall cases except Pro8 cis. Other significant movements (greater than 05 A r.m.s.)involve residues that, a,re spatiallv close to the site of isomerization. Residues 57 and5iH at the C-terminal of BPTI ari moved by the isomerization of Pro2. and residues3% t’o -40 are moved b\- the isomerization of Pro13. The broken lines in Figure 1 sholbf-the r.Iy1.s. deviatlions’of the main chain interatomic contacts closer than -4 A for eachresid*.le along the chain. This deviation indicates a change in local conformation andis insensitive tlo rigid body movements of the particular region. The isomerizationof Pro2 causes almost no change in local main chain conformation. the,isomerizations of Pro8 and Pro9 cause local conformational changes of residues 7 to11. together with rigid body movements of manv other residues, and theisomerization of Pro13 causes iocal and global confor&ational changes of residues11 t/o 15 and 38 to 39. Global conformation changes in which a part, of the protein(not necessarilv a single segment of the polypeptide chain) moves as a rigid hod\occur easilv il; the Cartesian co-ordinates used here and cause onk small changes.(less than i(v) in t.he main chain torsion angles.

The stereoscopic drawings in Figures 2 and 3 show ‘the conformation in thevicinity of the isomerized prolines. In the isomerization of Pro13, the two torsionangles Pro 13 or) and GM2 4 undergo a co-operative crankshaft-like movement thaltaffects the position of the CO group of Glv12 most. This type of movement. in whichthe isomerization causes a \rerv local change of conformation. is alwavs possiblewhen the proline residue is preceded bv a glvcine residue that has a + toLion anglevalue close to 180”. A different tvpi of &-operative movement occurs for theisomerization of Pro2 : the x1 iorsion angle of Argl changes bv 12t3” t oaccommodate the change in cu without moving the guanidinium group ai the end ofthe arginine side-chain. In the isomerization of Pro9 the change in Pro9 ~1) from 1801”to 13” is compensated for bv a change of Pro8 $ from 156” to -61”. This is not asimple crankshaft1 tvpe of iotion and it is accompanied bv large changes of man-kother Pro8 and Pr69 torsion angles (see Table 2). In thl isomerization of Prokwhich generates much greater strain than the other three proline isomerizations,t’here are no large clhanges in conformational angles that compensate for the changeof Pro8 or) from 179” tlo - 40’. GM’, the residue preceding Pros. is anchored by\7hvdrogen bonds t/o both itIs ma.in chain and side-chain and cannot move easik&stead. Pro8 and Pro9 both move without anv major change in torsion angles:

In two of the equilibrium conformations ge’nerated here, Pro2 and Pro9 wereconstrained to have isomeric states intermediat’e betNween tram and ris with thppeF)tide bond tlorsion angle w held close to 90”. This was done to see whether thle

EFFECT OF PKOLINE RESIDUES 2 5 7

Pro 20

Pro 20

4- Arg

Pro 2,/

lro 2

(b)\Arg i

\Arg I

FIG. 2. Stereoscopic drawings of the BPTI molecule in the vicinity of Pro2. Atom t!ypes aredistinguished by their radius, with the radius increasing from H t>hrough 0, N and C to S. The drawingsshow (a) the native all-trans equilibrium conformation and (b) the Pro2 c,is equilibrium conformation.One wav to see the small conformational changes more clearlv is to place the stereoscopic viewer overthe lef’t ‘halves of’ (a) and (b) and blink the eyes in alternation.c

T A B L E 2

lm-9& ch.cxnges in torsjon cr~~gks c/a irwd by isomerixation*

( ‘onfi,rmat ion Angle Torsion angle value (deg)

Initial Final Change

* l-i?64

178

- 5 4- 6 4

- 1

122- 4 0- 4 4

3 1-8

- 101- 174- 1 6 5- 108

- 6 1- 3 5

3 9-28

- 1 0 7- 1 7 9

1 3- 1 6 3

1631281 8 0

1 5 61782'7

- 3’;3r>

- 6 41 3 11 6 1

3 4138

7 16 84 03 75 53 4

- 16315fi

2’;-37

3L’- 6 4

1 3 11 8 01 6 1

5 5143627 66 14 35 1

1673 6

78 -82 - 1 6 0180 - 3 177

X l

x2

x3

4

*

X4

Pro9

Pro9 ris GMPro8

x3

4X l

x2

x3

4*cr)

Pro9

x4

4Pro 13 cis Glvl2Prh3 w

(a)

(b)

(cl

Pro 9

Pro 8 1Pro 8

EFFECT OF PROLINE RESIDUES 259

constraintIs of the protein matiris increase the rate of proline isomerization bvlowt~~~i~~g t I w bitrrier between C+S and trajis forms from the substantial value of20 kcal/mol found for model compounds free in solution (see Brandts et al., 1975).The strain energies calculated for Pro2 and Pro9 in the intermediate isomeric formwere lower by 56 kcal/mol and 3.4 kcal/mol, respectively, than the correspondinga. ,strain energies in the conformations with the cis isomeric form. These reductions instJrain energy reduce the effective barrier between cis and trams forms andcorrespond to rate accelerations of 11,000 x for Pro2 and 300 x for Pro9 (calculatedas exp [ - AE/kT], where k is Boltzmanris constant of O*OOZ kcal/mol per Kelvin,and T is the absolute temperature), giving isomerization rates of about 2 s-l and200 s - l, respectively.c

4. Discussion

These energy calculations have shown that each of the four proline residues inBPTI can be forced from the tram to the cis peptide isomer with r.m.s. main chaindeviations of less than 1 A from the native X-ray conformation (Huber et al., 1971;Deisenhofer & Steigemann, 1974). Furthermore, the destabilization of the nativeconformation caused by this isomerization is 1 kcal/mol for one proline residue(Prol3), less than 11 kcal/mol for two others (Pro2 and Pro9) and 33 kcal/mol foranother (Pro@. The constraints of the native conformation serve to accelerate therates of c.& to trams isomerization of Pro2 and Pro9 by reducing the energy barrier1between the two forms by between 5% and 3.4 kcal/mol (accelerations of 11,000 xand 300 x , respectively). The protein effectively catalyses the isomerizationreaction bv applying a couple to the u angle. Such steric strain, which is not easilygeneratedior a normal substrate (Warshel & Levitt, 1976), can be generated here asboth ends of the polypeptide chain containing the CC) angle (the “substrate”) arecovalently bonded to the rest of the protein (the “enzyme”).

The results also show how proline isomerization can occur easily even when theproline residue is part of a native folded conformation : The 4 torsion angle of theresidue preceding the isomerized proline residue changes by 180” to compensate forthe 180” change in the CI) torsion angle of the proline itself. The ease of this in sitar

isomerization depends on the number and strength of the interactions between thenative protein conformation and the residue preceding the proline residue. Inparticular, the CO group and the side-chain must be free to move withoutdisruption of the native conformation.

The approximations involved in the present calculations are extensive bultlshould have a small effect on the strain energies for the following reasons. (a) Theconformational energy function has been empirically fitted to the properties ofsmall molecules and then applied to proteins. These energy parameters were testedon the native X-ray conformation of BPTI and found to cause a smaller deviation

FIG. 3. Stereoscopic drawings of the BPTI molecule in the vicinity of proline residues 8,9 and 13. Thleatom types are distinguished as explained in the legend to Fig. 2. The drawings show (a) the native all-trans equilibrium conformation, (b) the Pro8 CCY conformation, (c) the Pro9 cis conformation, and (d) thePro 13 ~1:a conformat ion.

260 M. LEVITT

f’rom th S-ra~ structuw than other available parameters (Levitt, 1980). (b) Theneglected solvent effects are likelv to cancel out in the subtraction of energy valuesused to get the strain energv of proline isomerization as the conformational changesare generallv too small (less than 1 ,% r.m.s. deviation) to affect the structure of thesolvent surrounding the protein. When Pro8 is isomerized to cis, its side-chain doesbecome more exposed to solvent so that inclusion of solvent effects would furtherdestabilize this already verv unstable cis form. Solvent interactions may beexpected to weaken the hvdrogen bonds between pairs of protein atoms ‘byproviding alternative hvdrogen-bonding partners. The most significant changes inhvdrogen bonding caused by proline isomerization are the loss of theTirlOH . . . water interaction in Pro8 ~2:s and the additional Glu70. . . waterinteraction in Pro9 ~5s. It is notable that both cases involve aI protein. . . waterhvdrogen bond, although onlv four water molecules are included in the calculation.Including a’ more realistic shell of water molecules should have little effect on theenergies of these protein. . . water hydrogen bonds. (c) The neglected vibrationalentropy and other thermal effects can be estimated only by much more time-consuming calculations impossible with present-day computing facilities. As withthe solvent effects, thermal effects will cancel out in the calculation of relativestrain energies : the frequencies of vibration of the protein are expected to be similarin native-like conformations with either the tram or cis proline isomers. (d) T:heconformations computed here might be only local minima with energies abovethose of other minima not found. Such local minima are more likely to exist inconformations with incorrect proline isomers as these conformations are furtherfrom the X-rav conformation: we can regard the present values of the strain energvas being upped- limits.

ad

It must) be emphasized that the use of convergent energy minimization in thepresent studs eliminates the most) unreliable feature of ;,revious attempts tocalculate strain energies in macromolecules : the problem of comparing energyvalues that are far above minimum values due to lack of convergence. Here theenergy values that are compared in the calculation of the strain energy are withinMKH ‘kcal/mol of the true value at the particular minimum.

The results obtained here on the isomerization of proline residues in the foldednative conformation of BPTI have clea#r implication for the folding transition of thisprotein molecule. Brandts’ model must now be modified to allow for the existenceof three types of proline residues in globular proteins.

Type I proline residues can isomerize as freelv when incorporated in thenative protein conformation as when in solution (Pro13 in BPTI).Tvpe II proline residues destabilize the native conformation when in thewincorrect isomeric form but not suf’ficientlv to block folding to a native-likeconformation, in which thev then more rapidlv isomerize to the correct form(Pro2 and Pro9 in BPTI). C

c

Type III proline residues destabilize the native conformation so much whenthev are in the incorrect isomeric form that folding to a native-like”conformation is blocked unless the proline residue has the correct isomericform (Pro8 in BPTI).

EF’FE:(‘T OF PICOIJXE ItESII)L?ES 2 6 1

The (+~ssification of a particular proline residue into one of the three classesdepends on two factors: the strain energv associated with the non-native isomerand the stabilitJv of the folded na,tive-lik’c conformation, The energies calculatedhere are ill VCZCU’O enthalpies that give only a rough guide to the actual strain freeenergies. For a proline residue tlo be type’ II rather than type III, this strain freeenergv must) not) exceed the st)abilization energy of the folded intermediate. Here it’is asAmed that! calculated strain energies of l&s than about 12 kcal/mol are smallemq$~ to allow stable native-like intermediates to be formed. This threshold valuewill depend on the condit!ions under which folding occurs: if the native form isstlrongly favoured. a type 111 proline residue could be changed to type II, and if thenatjive iorm is onlv weakI\- favoured, a tape II proline residue could be changed toc c ct’vpe I I I ..

The existence of these different types of proline residues can be used togetherwith thcl known a,verage probabilit,\: of’ proline isomerization in solution (0% transand 0*2 cis) to calcuMe what fraciion of unfolded BPTI molecules should refoldIapidly. For this, we assume that tlvpe I proline residues have no effect on the rateof folding, that at most one type i-1 proline residue can be incorporated into thefolded conformation as the incorrect isomer, and that type III proline residuesmust have the correct isomeric form for rapid folding. Unfolded BPTI would nowconsist) of the following fractions of rapidly folding molecules : (a) Those moleculestlhat. have all four tram proline residues giGes (0+$)4 = Ml. (b) Those molecules withcis isomers for eit!her .Pro2. Pro9 or Pro13 gives 3 x 0*2 x (~8)~ = O-31. (c) Thosemolec’ules with Pro13 his and. in a!ddition, either Pro2 or Pro9 cis, gives2 x (o*q’ x (0-H)’ = OG. The total fraction of molecules that fold rapidly is:t~hert~fore, 04 1 + O-3 1 + 0-05 = w i . and the total fraction that fold sloffiv is

1 - o*ii = O-23. For Brand& model (Brandts et al., 19T5), in which all four prilineresidues are of tlvl)e 111 and block rapid folding unless they a,re tram isomers, thetjotjall fraction of ;al’idlv folding molecules is (0=8)4 = 0=&l ani the total fraction thatc

I Creighton (1977) has observed that lQO to 20; of unfoldedrefold ilicorrectllv t/o give incorrect disulphide bridges under

proline isome&ation should be rate-limiting, in agreement>b calculated here. In their detailed study, Jullien & Baldwinjaper) also found that onlv 2Fi”/6 of a sligl& modified form ofa.

BPTI is slow folding.It. is of interest to speculate on tlhe generality of these results on BPTI. The

lkwomenon of species of slowly- and rapidlv refolding protein molecules was firstdemonstrat)ed for ribonuclease $arel & Baldwin, 1973, 1975) and then invoked toexplain the two-step folding observed for other proteins (Brandts et al., 1975 : Pohl.1976 : Hagerman. 197’7). For ribonuclease it now seems likelv that in the slow:folding fraction incorrect proline isomers are incorporated’ and then rapidly

isomerized to the correct native isomeric form (Cook et al., 1979). (“reighton (1986)has used his low-temperature urea gradient electrophoresis method to show that sixproteins each with at least two proline residues show no slow-folding fraction on thetime-scale of his measurements (slower than 1 min).

The existence of a type I proline residue in BPTI raises the possibility of twodistlinct slowly inteT~~on\~e~~tiIlg folded struct,ures, one witlh Pro13 tram and the

262 M. LEVITT

other with Pro13 cis. From the 1 kcal/mol strain energv calculated for thisisomerization and the lower intrinsic stabiliby of the cis iso;ner (also 1 kcal/mol).one would expectI !jc&, (exp [ - ~//CT]) o f c native BPTI molecules at roomtemperature to have an alternative conformation with Pro13 cis. The transitionbetween these two hypothetical native states would be slow due to the highintrinsic barrier of proline isomerization and the existence of the minor species ma,ybe detectable by nuclear magnetic resonance or other spectroscopic methods. TapeI proline residlies that can occur in the native state as either tran.s or cl:s isorLersmav be of genera1 funct,ional significance in that thev serve to define two distinctand slowly interconverting conformational states of the native folded protein..’KlecentIly. Mat/es cf crl. (NW) detected aI metastable form of native BPTT that showschanges in the nuclear magnetic: resonance of residues 21? 23, 32, 45, 48 and 52. 1-nthe present st,udy . onlv the Pro9 cis conformation involves changes of theinteratomic conta& of Aese residues but further studs is needed to check whethethe other changes in this form would have been det’ected. The conformations withPro2 cis or Pr613 cis would not be expected to cause the wide-spread changesobserved experimentally (see Fig. 1).

Convergent energy minimization of an entire protein conformation introducedhere has several other applications including : (a) calculation of conformationalchanges caused bv substrate binding. (b) Calculation of the strain energy andconformatiional pe’.turbations associated with other more general perturbations ofthe native structure (for example, alternative disulphide bridges as in BPTI foldingintermediates, see Preighton. 1977). (c) Generation of conformations of proteinsthat are homologous to LI protein of known conformatlion (for example. generate theIconformation of trypsin from that of chymotrypsin). All these applications requirethe power of the convergent1 energy minimization method to make sufficiently largechanges of conformation while still converging to a well-defined energy valie.*

1 am gratef’ul to Drs R. L. Baldwin and T. E. Creighton for tIheir encouragement andconstructive criticism. This research was supported by a Sational Science Foundation awa:rd(PclM-7808029).

REFEREXES

Baldwin, R. L. (1978). Tre~uh Biochem. Sci. 3, 66-68.Brandts, J. F., Halvorson, H. R. &, Brennan, M. (1975). Biochemistry, 14, 4953-4963.Brandts, J. F.. Brennan. M. & Lin, L.-N. (1977). Proc. Xat. Acad. Sci., LS.A. 74, 417%

3181.Cook, K. H., Schmid, F. X. & Baldwin, R. L. (1979). Proc. Sat. Acad. Sci., WLl. 76,615’7-

6161.Creighton. T. E. (1977). J. i’)/lol. Riol. 113, 295-312.(‘reighton, T. E. (1978). J. lkfol. RioZ. 125, 401-406.(‘reighton, T. E. (1980). J. Mol. Riol. 137, 61-80.Deisenhofer, J. KT Steigemann, N7. (1974). Acta CrystaZEogr. sect. R, 31, 238-250.(iarel, J.-R. 81 Baldwin, R. L. (1973). hoc. Nat. Acad. Sci., V.S.A . 70, 3347-3351 gCiarel, J.-R. & Baldwin, R. L. (1975). J. Mol. Biol. 94, 61 l-620.Gelin, B. R. & Karplus, I!& (1975). hoc. Nat. Acad. Sci., W!z?.A. 72, 2002-2006.(bathwohl, 0. & Wiithrich. K. (1976). Riopolymers, 15, 20252041.Hagerman, I? J. (1977). Riopolymers, 16, 731-747.Hagler, A. T., Huler, E. Cc; Lifson, S. (1974). J. Amer. Them. Sot. 96, 5319-5326.,

EFFE(“I‘ OF PROLISE RESIDUES 263

Hwt,enw IhI. 1-L LY! Stiefid. E. (1952). J. lTCes. Hw. Starldards, 49, 409-436.Huller, IX., Kukla, II.. Ruhlmann, A. & Steie;emann, W. (1971). Cold Sprilzg Harbor Symt~.1

Quad. Hid. 36. l-H-150.Jullien, M. C! Baldwin, R. L. (1980). J. Mol. Viol. 145. 2G-280.Levitt, IM. (1971). J. Mol. Rio!. 82, 393420.Levitt, Al. (1978). Proc. Xat. Acad. Sci., C’.S.A. 75, 640-644.Levit’t, M. (1980). III Proth Foldijjg (Jaenicke. R., ed.), ~1’. 17-39, Elsevier/SortI>-Holland.

Amsterdam.Levitt!, hl. CV Lifson. S. (1969). J. Mol. H,iol. 46, 269-279.Lifson, S. CYI Levitt. 11. (1979). Camp. Chem. 3, 49-50.Lifson, S.. Hagler. A. T. 2k Dauber, 1’. (1979). J. Amer. Chem. Sot. 101, 5lLk5121.Pohl, F. &I. (1970). FERS Letters, 65, 293-296.Ramachandran. G. S. Sz Mitra, A. K. (1976). J. Mol. Riol. 107, M-92.Schmid. I’. S. A Baldwin, R. L. (1978). Proc. Sat. Acad. Sci., TUS.A. 75, 4764-4768.States, D. ,J.. Dolwon. V. M.. Karplus, Nl. & Freighton, T. E. (1980). Natwe (Lolldoz). 286,

630-632.Warshel. ;I. & Levitt. M. (1976). J. Mol. Rio/. 103, 227-249.Warshel. A. & Lifson. S. (1970). J. Churl. Phys. 53, 582-594.