interactions (mechanism of folding/contact free energies/range of interactions/monte Carlo)

Transcription

1 Proc. Nat. Acad. Sci. USA Vol. 72, No. 1, pp , October 1975 Cheistry Model of protein folding: Inclusion of short, ediu, and longrange interactions (echanis of folding/contact free energies/range of interactions/monte Carlo) SEIjI TANAKA* AND HAROLD A. SCHERAGAt Departent of Cheistry, Cornell University, Ithaca, Ne York Contributed by Harold A. Scheraga, July 3, 1975 ABSTRACT A hypothesis for protein folding is proposed, in hich the native structure is fored by a threestep echanis: (A) foration of ordered backbone structures by shortrange interactions, (B) foration of sall contact regions by ediurange interactions, and (C) association of the sall contact regions into the native structure by longrange interactions. Epirical interaction paraeters (free energy of foration of a contact) beteen ainoacid residues ere evaluated fro the frequency of contacts in the xray structures of native proteins. On the basis of this echanis, a Monte Carlo siulation of protein folding (ith an accopanying decrease in the total contact free energy) as carried out for bovine pancreatic trypsin inhibitor. The predicted threediensional structure is in fairly good agreeent ith the experiental one. In order to predict the threediensional structure of a protein, it is necessary to circuvent the ultipleiniu proble and overcoe the difficulties of treating the longrange interactions (1). For this purpose, a starting conforation as obtained fro epirical prediction algoriths, and then its total conforational energy as iniied (2). As an alternative approach, the conforations of the unfolded protein can be obtained by statistical echanical procedures involving only shortrange interactions,t and altered (to a iniufreeenergy structure) by a Monte Carlo procedure involving short, ediu, and longrange interactions. This paper describes a odel for protein folding, and the results obtained for bovine pancreatic trypsin inhibitor (BPTI) by a Monte Carlo siulation of the odel. A full description of the procedure and results ill be published elsehere. I. Hypothetical echanis of protein folding The folding of a polypeptide chain to the native structure of a protein in a given ediu is assued to occur in three steps (hich ay proceed siultaneously). (A) Because of shortrange interactions, orderedl backbone structures, such as ahelical, extended, and chainreversal conforations, are fored in a syste at equilibriu under given physical conditions. (B) When these physical conditions are changed, so as to introduce ediurange interactions, the equilibriu is shifted, and sall contact regions (defined in section II) are nucleated aong the residues both in the ordered and in the unordered structures. In this step, the ordered backbone structures fored in step A ay be rearranged to soe ex Abbreviation: BPTI, bovine pancreatic trypsin inhibitor. * Fro Kyoto University, t To ho requests for reprints should be addressed. *S. Tanaka and H. A. Scheraga, anuscript subitted. S. Tanaka and H. A. Scheraga, anuscripts to be subitted. The dihedral angles of, say, an ahelix are generally not the sae in every residue of an ahelical segent of a protein, nor are they assued to be in the Monte Carlo treatent used here. Therefore, e describe such structures as ordered rather than regular. 382 tent to for ore stable structures in these contact regions. (C) Finally, the sall contact regions fored in step B associate, in response to longrange interactions, possibly involving further sall rearrangeents of the structures fored in steps A and B. A statistical echanical treatent in ters of a onedinensional Ising odel, based on shortrange interactions, has been developed recentlyt to obtain the conforation of step A. Therefore, in this paper, e concentrate on the deonstration of the role of ediu and longrange interactions in steps B and C. II. Epirical interaction paraeters beteen aino acids of proteins fro xray data Contact regions (fored in steps B and C) arise fro ediu and longrange interactions beteen residues that approach each other. The solvent (ater) plays an iportant role in stabiliing such conforations. We describe specific local interactions as a contact beteen to groups, A and B, here the group ay be the hole residue, or the side chain and the backbone, or each ato of the residue. A specific local interaction is said to exist beteen groups A and B in ater if these groups are in contact or, ore quantitatively, if the distance beteen the, rab, satisfies the relation ra() + rb(w) < rab < r (W) + rb) + 2rH2o() [11 here ra(), rb() and rh2o() are the van der Waals radii of groups A, B, and a ater olecule, respectively [rh2o() is taken as 1.4 A]. The local interaction beteen A and B is neglected hen rab > ra'l + rb() + 2rH2OU ) I Infinite repulsion arises (excluded volue effect), hen rab < ra() + r(). The threediensional structure of a protein can be represented sybolically by the presence or absence of contacts beteen the ith and jth residues [1 < (i,j) < N and i <j, here N is the chainlength], hen account is taken of the chain connectivity. Fig. 1A shos such a contact ap for BPTI, based on its xray coordinates;" a contact is said to exist if at least one pair of atos (one ato in the ith and one in the jth residue) satisfies Eq. 1. The sae analysis, as in Fig. 1A, as ade for 25 proteins hose xray structures are knon. Fro these data, counts 11 Those of R. Huber, personal counication, already used in ref. 2. [2] [3]

2 Cheistry: Tanaka and Scheraga Proc. Nat. Acad. Sci. USA 72 (1975) 383 r LLI Ld Ld : cn FIG. 1. Contact aps of BPTI for (A) consideration of all atos, and (B) ith side chains and backbone treated as spheres (see text). The solid, hatched, and open squares in the vertical and horiontal runs outside the triangle designate aino acids ith highly nonpolar side chains (Cys, ile, Leu, Met, Phe, Trp, Tyr, Val, Ala, Pro), those ith eakly nonpolar or eakly polar side chains (Asn, Gln, Gly, Ser, Thr), and those ith highly polar side chains (Arg, Asp, Glu, His, Lys), respectively. The solid and hatched squares ithin the triangle (in A) designate contact beteen to highly nonpolar side chains, and beteen any other to side chains, respectively. The nuerals in the squares (in B) sho the su for the various types of contact, here a side chainside chain contact is designated by 1, a backbonebackbone contact by 2, and a side chainbackbone or backboneside chain contact by 4 (a coplete contact beteen to residues is indicated by 11, hich is the su of ); every su indicates a unique type of contact. Contacts fro i to i + 1, i + 2, i + 3, or i + 4 ere oitted fro these diagras in order to focus attention on the ediu and longrange interactions, and to obtain the longrange interaction paraeters. ere ade of the nuber of ties an aino acid, Ak, of the type k had no contacts, and of the nuber of ties, Akl, that to residues Ak and Al ere in contact. We then defined an epirical equilibriu constant, KM,. and its associated free energy, AGCM, for foration of the coplex AM, for contact beteen the side chains of all ainoacid residues except glycine. For glycine, e took the full residue, and evaluated its contact free energies ith the other 19 side chains and glycine; glycine also served as a prototype of the backbone for nonglycine residues. A ore detailed description, including the nuerical values of AGCM, ill be reported elsehere. The values of AGCM are used to copute the total contact free energy of any conforation of a protein that is generated by the Monte Carlo procedure (and does not have hardsphere overlaps). III. Prediction of threediensional structure by a Monte Carlo procedure A. Siplified Model of Protein Chain. Backbone conforations ere alays generated fro standard (3) bond lengths, bond angles, and planar trans peptide groups. Hoever, hardsphere overlaps ere checked and epirical contact free energies ere evaluated by representing the backbone NHCHCO group and the 2 sidechain R groups by spheres of given (van der Waals) radii. The effectiveness of such a spherical representation ay be seen by coparing the contact aps of Fig. 1A and 1B. B. Siulation of Hypothetical Mechanis of Protein Folding by a Monte Carlo Procedure. Since our interest in this paper is priarily the deonstration of the effectiveness of the Monte Carlo procedure for introducing ediu and longrange interactions, e ill consider only steps B and C of the folding echanis, and obtain an initial ordered conforation fro the xray structure of BPTI, instead of fro step A.J It should be ephasied that, in contrast to our earlier procedure (2), the result of step A is not given in ters of values of X and A but in ters of sybols designating the conforational states [helical (h), extended (e), and other (c)] (see Fig. 2). Since conforations are selected randoly fro these regions (see belo), and a residue never oves out of the region assigned in step A, regular helical or extended sequences ill occur rarely. Further, as deonstrated in ref. 2, hile the starting conforation has correct shortrange order, it lacks the proper ediu and longrange interactions, and hence does not reseble the native protein. C 12 6 _ 6 12 R Helical(hon R I I Other State (c) Region 18 IZovrvs~xxrIX e ri A/, #i (NCa) FIG. 2. Helical (h), extended (e), and other (c) state regions, in ters of hich the conforation of each residue is specified in step A.

3 384 Cheistry: Tanaka and Scheraga Proc. Nat. Acad. Sci. USA 72 (1975) (B) (C) (D ireo o6 I: I J U OE OF ITERATION FIG. 3. Change in free energy due to foration of contacts beteen residues of BPTI in steps B and C. The abscissa should be ultiplied by 15 conforations in step B, and by 4 conforations in step C. In step B, e ake a rando conforniational change by randoly selecting the nuber of residues to vary, and their positions in the chain, and then altering the conforations of these residues randoly (i) ithin the hole of their on conforational regions; these conforational changes are repeated (1 ties in this study). The resulting loest freeenergy conforation is altered as above, but no () restricted to the region 1,4 < 3; these conforational changes are repeated (5 ties, here). Thus, one iteration of step B consisted of 15 conforational deforations in this study. Various types of rando conforational deforations are la 2c 3 4F l\ *\ \ \BI. n Jr a ID l I iib2 U >~~~~~~~~~~~~ _ ~~~f \~~~~~ 5S 5 OJW\ I I I I ji I I cr FIG. 4. Changes in the contact aps of BPTI during step B. The nubers in the squares have the sae eaning as in Fig. 1B. The shorterrange contacts are oitted.

4 5 _,_ Cheistry: Tanaka and Scheraga Proc. Nat. Acad. Sci. USA 72 (1975) 385 a] C D D c C,) C co) 3 O: Cn C' L 2 C2 1 3 _ Cf) cj_ 4 ~~~~~I 1 4 so 1o FIG. 5. Sae as Fig. 4, but for step C. produced in step Bi, typically (a) local deforations of the chain ithout a large change of shape of the hole olecule, and (b) drastic changes in the overall shape of the protein. Hoever, only the deforations of type a effectively serve to for sall local contact regions in the chain. The sall conforational changes of step Bfl are ade to stabi

5 386 Cheistry: Tanaka and Scheraga lie the contact regions fored in step BI. Since large rings have a loer probability of foration than ediusie rings in a polyer chain, deforations of type b are not effective in bringing contact regions together (longrange order) in step B, even though such deforations are included in this step; i.e., the rare occurrences of contacts of longrange order are altered by the ore stable contacts of ediurange order. At the end of step B (i and ii), local contact regions of ediurange order are fored, ithout yet achieving overall globularity. In step C, drastic conforational changes are produced as follos. First, e randoly select a region (a given sequence of residues) to be varied, then randoly choose the nuber of residues to vary, and their positions, ithin the region, and finally e alter the conforations of these residues randoly ithin their on conforational doains (Fig. 2). Because of the regional conforational changes, soe of the local contact regions fored in step B ay rearrange, but the predoinant effect is to bring these contact regions together (longrange order). By restricting these conforational changes to local regions, the contacts of longrange order are favored ithout an increase in free energy that ould arise fro the destruction of the local contact regions fored in step B. In brief, the chain as represented as a sequence of sybols h, (, and c (the siulated result fro step A). Then the folloing Monte Carlo siulation as carried out. Chain conforations ere generated randoly, as described in step Bi, until one as found ith no hardsphere overlaps (Eq. 3). Then, the procedure described above for step B as folloed, alays checking for absence of hardsphere overlaps. When a conforation ith no overlaps as found, the free energy for all pair contacts as coputed, using the paraeters entioned in section II. If this free energy as larger than that of the previous conforation, the latest conforational change as unfavorable (and as discarded), and the conforational changes of step B ere started again fro the previous conforation. If the ne conforational changes gave a loer free energy than that of the previous conforation, the ne one as retained as the starting conforation for further conforational changes in step B. This procedure as repeated until the free energy could not be loered by an additional 1, applications of step B. Proc. Nat. Acad. Sci. USA 72 (1975) Then, the process as continued by application of step C, again until the free energy could not be loered by an additional 1, applications of step C. IV. Results and discussion Fig. 3 shos the change in free energy of contact foration in steps B and C, starting ith the xray (siulated step A) structure of BPTI. A horiontal line. indicates that highfreeenergy conforational changes ere generated (and discarded) in these iterations. The conforational changes, corresponding to the free energies of Fig. 3, are illustrated in Figs. 4 and 5 for steps B and C, respectively. To assess the predictive results, the final one (C6 of Fig. 5) should be copared to Fig. 1 (the native structure). It can be seen that the ain features of the native structure (indicated by IVII in Fig. 1B) are reproduced in regions IVII in C6 of Fig. 5. This agreeent is fairly good, especially if one takes into consideration the fact that e did not use a disulfide loopclosing function, as as used previously (2) to obtain globularity, and the fact that values of 4 and 4' ere not specified precisely initially, as previously (2). The ost iportant iplication of these results is that the threestep echanis of protein folding is necessary, because a rando conforational change in the hole olecule can lead only to sall contact regions ithin about ten residues, due to local ediurange interactions (in step B), as seen in Fig. 4. The introduction of rando conforational changes, that are restricted to a liited nuber of residues (in step C), is required to produce large conforational changes and the globular for of the protein, in hich the local contact regions of longrange order (ore than about 1 residues apart fro each other) are fored. This ork as supported by grants fro the National Institutes of Health and fro the National Science Foundation. 1. Scheraga, H. A. (1974) in Peptides, Polypeptides and Proteins, eds. Blout, E. R., Bovey, F. A., Goodan, M. & Lotan, N. (John Wiley, Ne York), pp Burgess, A. W. & Scheraga, H. A. (1975) Proc. Nat. Acad. Sci. USA 72, Moany, F. A., McGuire, R. F., Burgess, A. W. & Scheraga, H. A. (1975) J. Phys. Che., in press.