Effect of Proline Residues on Protein Folding

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 IVei...
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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 proline residues 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:s peptide isomer while still part of the native folded structure. The cis proline residue can alwavs be accommodated by small changes of the native conformation ( < 1 A root-mea”n-square deviation). For three of the four proline residues, Pro& Pro9 and Pro13. being in the r/is form is calculated to destabilize the folded conformation by less than 11 kcal/mol, suggesting that rapid folding to a stable native-like conformation can occur with either isomeric form. For one of these three, Pro13, the destabilization is onlv 1 kcal/mol, suggesting the existence of an alternative folded native conformation with Pro13 cis. The fourth proline residue, Pro& is calculated to destabilize the native conformation bv so much (33 kcai/mol) that it will block folding in the manner proposed bvc Brandts et al. (1975).

1. Introduction Proline residues are widely recognized as p1aving.a special role in the folding and unfolding transitions of glYobular protein molecules. This amino acid residue has a relativelvc high intrinsic probabilitv u (between 0-l and O-3, depending on the adjacent’ sequence) of existing as the cis rather than the tram peptide isomer, (Brandts et al.. 19’75: Grathwolhl & Withrich. 1976). whereas for other amino acids the probability is much smaller (less than 10D3: see Ramachandran & Rlitra. 1976). Because the interconversion of the two isomers is slow under normal conditions (1 to 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 proline residues 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 with bot’h the cis and tram isomeric forms. Onlv those unfolded molecules in which all the proline residues have the same isomkric form as in the native protein are assumed to fold directlv to the native conformation. Unfolded molecules with one or 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. 251 (H~L’~-~~~~fi/~l/OlOL’~1-13

$iW.OO/O

i” 1981 Academics Press Inc. (London) Ltd.

252

M.

LEVITT

isomers als in tlhe native conformat,ion. Thus, one expects that proteins containing proline residues should consist of a mixture of fast and slow folding molecules, as first obser~d for ribonuclealse (Garel Cc Baldwin. 1973.19T5 : Baldwin. 1978). Further studies (Schmid & Baldwin, 1978) led to the suggestion that not all proline residues in aI protein are essential, in that thev block rapid folding and that these 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 k favouring folding even the essential proline residues that slow ribonuclealse refolding can isomerize aft)er extensive and specific folding to a nativelike structure. This isomerization to the native isomeric form occurs significantlv more 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 other protjeiA ma\- behave like ribonuclease. Here conformational energy calculations on the refined X-ray structure of the protein bovine pancreatic trvpsin inhibitor (Huber et al., 1971 : Deisenhofer 6: Steigemann. 1974) are used to investigate the strain associated with the incorporation of incorrect proline isomers into the native conformation. Each of the four proline residues in BPT1-t is forced by constrained energy minimization from its native tram isomer to the incorrect cis isomer. The results indicate that isomerizing one of the proline residues, Pro13, in this way has a vervc small effect on the stabiMv . of the native conformation. increasing the total equilibrium potential energv bv only 1 kcal/mol. For two other proline residues, Pro2 and Pro9, the change in energv is less than 11 kcal/mol, suggesting that these proline residues could a’lso be incorporated as cis isomers during the folding of BPTI as observed by Cook et ~1. (1979). Onlv one proline residue, Pro& so destabilizes the native conformatlion (bv 33.3 kcal/mol) that, it should block rapid folding in the wax proposed 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 ho bans 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 the folded BPTT molecules should have proline residue Pro13 in the cis isomer giving rise to a slightlv c different native folded structure that might be detectable by nuclealr 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) the natjive conformation, in which all 4 proline residues have tram peptide isomers (torsion angle co = lso”), (b) the 4 native-like conformations in which each proline residue is forced in turn to have the his isomeric form (W = O”), and (c) the 2 conformations in which Pro2 and Pro9 are 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

253

bond angles

+

K,( 1 +cY-e (,q+S)!+

: torsion angles

--T E,(+e

4)

(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 a. force-constants &, and K, and zero I-alues II” and 8” for everv tvpe of bond and bond angle. The first torsion angle term. which hinders free rotation about’ single (“4“ bonds and enforces tlhe planarit!v of peptide groups and 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 der Waals’ 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 onlvc one other atom) in-plane and also ensure that the amino acids remain as L-isomers. For example. in the group

the oxygen atom is kept in-plane bvL keeping t.he value of the improper torsion angle C”-X(‘4 close to 180’. The van der Waals’ interaction. which uses tlhe Lennard-?Jones ‘X-6” form. is parametrized bv I*‘. the separation at which the atom pair interacts most stronglv. and E. the strength of that interaction. Values of I*’ and E were obtained bvCI optimizing the fit between the calculated and experimental unit-cell dimensions of 28 hvdrocarbon. amide and amino acid 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, is designed to give linear chvdrogen bonds without requiring the computat~ionallv c more expensive elect:rostatic term usf?d on the crystals. This potential was shown to cause a smaller 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 the torsional potential 10[ 1 - cos (CO)]. that has a minimum value for cu = 0”. This is the”same tvpe 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 associated with 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 few badlv 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 tcl relax 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 on bonds) and 12 amide and peptide groups needed for accurate representation of hvdrogen .

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, method of’conjugate

1974). The minimization method used here. known as the

gradients (Hestenes & Stiefel, 19%). converges t,o a true minimum after

about 3OOO evaluations of the energy function for the 1581 variables of BPTI. The method of steepest descent,s used in some previous conformational energy calculations (Levitt & Lifson. 1969: Gelin Cyr Karplus, 1975) never converges, making any&a reliable comparison of energyc values impossible.

3. Results Seven distinct conformational energy minimizations of the X-ray conformation of BPTI were undertaken. In the first minimization. no constraints were used to alter the isomeric form of anv of the proline residues. The resulting all-trcbns conformation was close but n& identical to the crvst*al structure. with a O*6Ei A r.m.s. deviation of the main chain atoms from the refined X-rav structure (see Table 1). The corresponding r.m.s. deviation of the side-chain at’bms is larger at 141 A. The r.m.s. deviation of the exposed solvent accessible atoms (l-37 A) is substantiallv greater than that of the buried atoms (@61 A), indicating that the large r.m.s. ‘deviation mav be due to the omission of the hundreds of surround:ing solvent molecules and tie neglect of the other protein molecules in the BF’TI crvstal. The potential used here does, however, give a lower r.m.s. deviation for an isolated 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 fiirst minimization. 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 resulting equilibrium conformations are all within 1 A main chain r.m.s. devia)tion from the S-ray conformation. All have energies that are higher tlhan that’ of the all-tnxns mi&um. with increases in total energy (strain energy) that varv from onlb I kcal/‘mol for Pro13 tlo 33 kcal/mol for Pro% In the final two minimizations. alsb i

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

(‘onf’orma.tion (1) (2) (3) (1) (5) (6) (7)

Energy (kcal/mol) Total

deviations

Energyu contribution (kcal/mol) Bond

Angle

van der Torsion Was-1s’

H bond

r.m.s. deviation? from native no. 1 A (4) (4

A.411-fmn.s Proi cis Pro8 ch Pro9 ci.s Pro13 c,is Pro2 i n t Pro9 i n t

-t The r.m.s. deviation is of corresponding main chain atom positions of residues 2 to 56 relative tdo the S -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 to have isomeric forms intermediat,e between tmm and cis with the peptide torsion angle ct) = 90”. In both cases the intermediate form was more stable than t:he ck isomeric 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 the bond stretching and non-bonded van der Waals’ energv terms are least affected b\ proline isomerization. The bond angle bending and ‘torsional terms account for most 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 term ITaries less predictable. being leastfor Pro9 cis and most for Pro8 ~7:s. Detailed examination of the atomic co-ordinates expkns this in terms of an extra hvdrogen bond in Pro9 ctis between (:1u$W2 and one of the internal water molecules, *whereas

3’-

29cis

3

8-c/3

0

IO

20

30 Residue

40

50

number

FIG. 1 . The r.m .s. deviation of’ main chain atoms f’rom their positions in the all-kans equilibrium c~onf’ormation is plotted against the location of the residue along the polypeptide cbhain. The unbroken (bur\‘t’ s h o w s t he (+onventional r.m .s. (leviat ion of corresponding atomic posit ions. The broken curve shows 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 molecule and also changed their local conf’ormation : regions that shoti- only high values of the positional deviation have moved wit bout changing conformat ion.

256

ICI. LEVITT

in Pro8 cis a hvdrogen bond between TvrlOH and an internal water is lostI. The extra hvdrogen’bond cannot, form when FL9 is trans due to a close contact betlween the watler molecule and the ljeptide oxygen of Pro& The other conformations a,11 have essenGallv the same hvdrogen bonds as in the X-rayCI conformation (Deisenhofer CC Steigemann. 19j3) ’ . The main chain r.m.s. deviations of the four conformations with ~‘2:s proline residues va’rv from O-12 ,-I to O-56 A. with the smallest de\-iations associated with the smallest’strain energies (Table 1). The variation of this deviation with position of the residue along the polypeptide chain (Fig. 1) shows how the residue immediatelv preceding the isomerized proline moves more than the proline itself in all 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 and 5iH at the C-terminal of BPTI ari moved by the isomerization of Pro2. and residues 3% t’o -40 are moved b\- the isomerization of Pro13. The broken lines in Figure 1 sholbfthe r.Iy1.s. deviatlions’of the main chain interatomic contacts closer than -4 A for each resid*.le along the chain. This deviation indicates a change in local conformation and is insensitive tlo rigid body movements of the particular region. The isomerization of Pro2 causes almost no change in local main chain conformation., the isomerizations of Pro8 and Pro9 cause local conformational changes of residues 7 to 11. together with rigid body movements of manv other residues, and the isomerization of Pro13 causes iocal and global confor&ational changes of residues 11 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 the vicinity of the isomerized prolines. In the isomerization of Pro13, the two torsion angles Pro 13 or) and GM2 4 undergo a co-operative crankshaft-like movement thalt affects the position of the CO group of Glv12 most. This type of movement. in which the isomerization causes a \rerv local change of conformation. is alwavs possible when the proline residue is preceded bv a glvcine residue that has a + toLion angle value close to 180”. A different tvpi of &-operative movement occurs for the isomerization of Pro2 : the x1 iorsion angle of Argl changes bv 12t3” t o accommodate the change in cu without moving the guanidinium group ai the end of the 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 a simple crankshaft1 tvpe of iotion and it is accompanied bv large changes of man-k other Pro8 and Pr69 torsion angles (see Table 2). In thl isomerization of Prok which generates much greater strain than the other three proline isomerizations, t’here are no large clhanges in conformational angles that compensate for the change of Pro8 or) from 179” tlo - 40’. GM’, the residue preceding Pros. is anchored by\7 hvdrogen 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 were constrained to have isomeric states intermediat’e betNween tram and ris with thp peF)tide bond tlorsion angle w held close to 90”. This was done to see whether thle

EFFECT

OF

0

PKOLINE

RESIDUES

257

Pro 2

Pro 2 0

4

- Arg

Pro 2

lro 2 ,/

\

Arg

I

\

(b)

Arg i

FIG. 2. Stereoscopic drawings of the BPTI molecule in the vicinity of Pro2. Atom t!ypes are distinguished by their radius, with the radius increasing from H t>hrough 0, N and C to S. The drawings show (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 over the lef’t ‘halves of’ (a) and (b) and blink the eyes in alternation. c TABLE

2

lm-9& ch.cxnges in torsjon cr~~gks c/a irwd by isomerixation * ( ‘onfi,rmat ion

Torsion angle value (deg)

Angle Initial *

Xl x2

Pro9

x3

4 * X4

Pro9 ris

GM Pro8

x3

4 X l

x2

Pro9

x3

4 * cr) x4

Pro 13 cis

Glvl2 Prh3

4 w

Final

Change

l-i? 64 178

-54 -64 -1

163 128 180

156 178 - 3’; 3r> -64 131 161

122 -40 -44 31 -8 - 101 - 174 -165

34 138 71 68 40 37 55 34

- 163 15fi 2’; -37 3L’ -64 131 180 161

- 108 -61 -35 39 -28 -107 -179 13 -163

55 143 62 76 61 43 51 167 36

78 180

-82 - 3

- 160 177

2'7

Pro 9

(a)

Pro 8

(b)

(cl

1Pro

8

EFFECT

OF

PROLINE

RESIDUES

259

constraintIs of the protein matiris increase the rate of proline isomerization bv lowt~~~i~~g t I w bitrrier between C+S and trajis forms from the substantial value of 20 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 form were lower bya. 56 kcal/mol and 3.4 kcal/mol,, respectively, than the corresponding strain energies in the conformations with the cis isomeric form. These reductions in stJrain energy reduce the effective barrier between cis and trams forms and correspond to rate accelerations of 11,000 x for Pro2 and 300 x for Pro9 (calculated as 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 and 200 s - l, respectively. c

4. Discussion These energy calculations have shown that each of the four proline residues in BPTI can be forced from the tram to the cis peptide isomer with r.m.s. main chain deviations of less than 1 A from the native X-ray conformation (Huber et al., 1971; Deisenhofer & Steigemann, 1974). Furthermore, the destabilization of the native conformation 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 for another (Pro@. The constraints of the native conformation serve to accelerate the rates of c.& to trams isomerization of Pro2 and Pro9 by reducing the energy barrier1 between the two forms by between 5% and 3.4 kcal/mol (accelerations of 11,000 x and 300 x , respectively). The protein effectively catalyses the isomerization reaction bv applying a couple to the u angle. Such steric strain, which is not easily generatedior a normal substrate (Warshel & Levitt, 1976), can be generated here as both ends of the polypeptide chain containing the CC) angle (the “substrate”) are covalently bonded to the rest of the protein (the “enzyme”). The results also show how proline isomerization can occur easily even when the proline residue is part of a native folded conformation : The 4 torsion angle of the residue preceding the isomerized proline residue changes by 180” to compensate for the 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 the native protein conformation and the residue preceding the proline residue. In particular, the CO group and the side-chain must be free to move without disruption of the native conformation. The approximations involved in the present calculations are extensive bultl should have a small effect on the strain energies for the following reasons. (a) The conformational energy function has been empirically fitted to the properties of small molecules and then applied to proteins. These energy parameters were tested on 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. Thle atom types are distinguished as explained in the legend to Fig. 2. The drawings show (a) the native alltrans equilibrium conformation, (b) the Pro8 CCY conformation, (c) the Pro9 cis conformation, and (d) the Pro 13 ~1:a conformat ion.

260

M. LEVITT

f’rom th S-ra~ structuw than other available parameters (Levitt, 1980). (b) The neglected solvent effects are likelv to cancel out in the subtraction of energy values used to get the strain energv of proline isomerization as the conformational changes are generallv too small (less than 1 ,% r.m.s. deviation) to affect the structure of the solvent surrounding the protein. When Pro8 is isomerized to cis, its side-chain does become more exposed to solvent so that inclusion of solvent effects would further destabilize this already verv unstable cis form. Solvent interactions may be expected to weaken the hvdrogen bonds between pairs of protein atoms ‘by providing alternative hvdrogen-bonding partners. The most significant changes in hvdrogen bonding caused by proline isomerization are the loss of the TirlOH . . . water interaction in Pro8 ~2:s and the additional Glu70. . . water interaction in Pro9 ~5s. It is notable that both cases involve aI protein. . . water hvdrogen bond, although onlv four water molecules are included in the calculation. Including a’ more realistic shell of water molecules should have little effect on the energies of these protein. . . water hydrogen bonds. (c) The neglected vibrational entropy and other thermal effects can be estimated only by much more timeconsuming calculations impossible with present-day computing facilities. As with the solvent effects, thermal effects will cancel out in the calculation of relative strain energies : the frequencies of vibration of the protein are expected to be similar in native-like conformations with either the tram or cis proline isomers. (d) T:he conformations computed here might be only local minima with energies above those of other minima not found. Such local minima are more likely to exist in conformations with incorrect proline isomers as these conformations are further from the X-rav conformation: we can regard the present values of the strain energv ad as being upped- limits. It must) be emphasized that the use of convergent energy minimization in the present studs eliminates the most) unreliable feature of ;,revious attempts to calculate strain energies in macromolecules : the problem of comparing energy values that are far above minimum values due to lack of convergence. Here the energy values that are compared in the calculation of the strain energy are within MKH ‘kcal/mol of the true value at the particular minimum. The results obtained here on the isomerization of proline residues in the folded native conformation of BPTI have clea#r implication for the folding transition of this protein molecule. Brandts’ model must now be modified to allow for the existence of three types of proline residues in globular proteins. Type I proline residues can isomerize as freelv when incorporated in the native protein conformation as when in solution (Pro13 in BPTI). Tvpe II proline residues destabilize the native conformation when in the w incorrect isomeric form but not suf’ficientlv to block folding to a native-like conformation, in which thev then more rapidlvc isomerize to the correct form (Pro2 and Pro9 in BPTI). C Type III proline residues destabilize the native conformation so much when thev” are in the incorrect isomeric form that folding to a native-like conformation is blocked unless the proline residue has the correct isomeric form (Pro8 in BPTI).

EF’FE:(‘T

OF PICOIJXE

ItESII)L?ES

261

The (+~ssification of a particular proline residue into one of the three classes depends on two factors: the strain energv associated with the non-native isomer and the stabilitJv of the folded na,tive-lik’c conformation, The energies calculated here are ill VCZCU’O enthalpies that give only a rough guide to the actual strain free energies. For a proline residue tlo be type’ II rather than type III, this strain free energv 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 small emq$~ to allow stable native-like intermediates to be formed. This threshold value will depend on the condit!ions under which folding occurs: if the native form is stlrongly favoured. a type 111 proline residue could be changed to type II, and if the natjive iorm is onlvc weakI\-c favoured, a tape II proline residue could be changed to c t’vpe III. . The existence of these different types of proline residues can be used together with thcl known a,verage probabilit,\: of’ proline isomerization in solution (0% trans and 0*2 cis) to calcuMe what fraciion of unfolded BPTI molecules should refold Iapidly. For this, we assume that tlvpe I proline residues have no effect on the rate of folding, that at most one type i-1 proline residue can be incorporated into the folded conformation as the incorrect isomer, and that type III proline residues must have the correct isomeric form for rapid folding. Unfolded BPTI would now consist) of the following fractions of rapidly folding molecules : (a) Those molecules tlhat. have all four tram proline residues giGes (0+$)4 = Ml. (b) Those molecules with cis isomers for eit!her .Pro2. Pro9 or Pro13 gives 3 x 0*2 x (~8)~ = O-31. (c) Those molec’ules with Pro13 his and. in a!ddition, either Pro2 or Pro9 cis, gives 2 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 priline residues are of tlvl)e 111 and block rapid folding unless they a,re tram isomers, the tjotjall fraction of ;al’idlvc folding molecules is (0=8)4 = 0=&l ani the total fraction that I Creighton (1977) has observed that lQO to 20; of unfolded refold 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 & Baldwin japer) also found that onlva. 2Fi”/6 of a sligl& modified form of 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 first demonstrat)ed for ribonuclease $arel & Baldwin, 1973, 1975) and then invoked to explain 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 six proteins each with at least two proline residues show no slow-folding fraction on the time-scale of his measurements (slower than 1 min). The existence of a type I proline residue in BPTI raises the possibility of two distlinct 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 this isomerization and the lower intrinsic stabiliby of the cis iso;ner (also 1 kcal/mol). o n e w o u l d expectI !jc&, (exp [ - ~//CT]) o f c native BPTI molecules at room temperature to have an alternative conformation with Pro13 cis. The transition between these two hypothetical native states would be slow due to the high intrinsic barrier of proline isomerization and the existence of the minor species ma,y be detectable by nuclear magnetic resonance or other spectroscopic methods. Tape I proline residlies that can occur in the native state as either tran.s or cl:s isorLers mav be of genera1 funct,ional significance in that thev serve to define two distinct and slowly.’ interconverting conformational states of the native folded protein. KlecentIly. Mat/es cf crl. (NW) detected aI metastable form of native BPTT that shows changes in the nuclear magnetic: resonance of residues 21? 23, 32, 45, 48 and 52. 1-n the present st,udy . onlv the Pro9 cis conformation involves changes of the interatomic conta& of Aese residues but further studs is needed to check whethe the other changes in this form would have been det’ected. The conformations with Pro2 cis or Pr613 cis would not be expected to cause the wide-spread changes observed experimentally (see Fig. 1). Convergent energy minimization of an entire protein conformation introduced here has several other applications including : (a) calculation of conformational changes caused bv substrate binding. (b) Calculation of the strain energy and conformatiional pe’.turbations associated with other more general perturbations of the native structure (for example, alternative disulphide bridges as in BPTI folding intermediates, see Preighton. 1977). (c) Generation of conformations of proteins that are homologous to LI protein of known conformatlion (for example. I generate the conformation of trypsin from that of chymotrypsin). All these applications require the power of the convergent1 energy minimization method to make sufficiently large changes 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 and constructive 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. 76,615’76161. 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 g Ciarel, 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.

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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.

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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.

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