Calculation of protein conformation as an assembly of stable overlapping segments: Application to bovine pancreatic trypsin inhibitor

Transcription

1 Proc. Natl. Acad. Sci. USA Vol. 88, pp , May 1991 Biophysics Calculation of protein conformation as an assembly of stable overlapping segments: Application to bovine pancreatic trypsin inhibitor (conformational energy calculations/short-range interactions/build-up procedure/"conformon") ISTVAN SIMON*, LESLIE GLASSERt, AND HAROLD A. SCHERAGAt Baker Laboratory of Chemistry, Cornell University, Ithaca, NY Contributed by Harold A. Scheraga, January 4, 1991 ABSTRACT Conformations of bovine pancreatic trypsin inhibitor were calculated by assuming that the final structure as well as properly chosen overlapping segments thereof are simultaneously in low-energy (not necessarily the lowestenergy) conformational states. Therefore, the whole chain can be built up from building blocks whose conformations are determined primarily by short-range interactions. Our earlier buildup procedure was modified by taking account of a statistical analysis ofknown amino acid sequences that indicates that there is nonrandom pairing of amino acid residues in short segments along the chain, and by carrying out energy minimization on only these segments and on the whole chain [without minimizing the energies of intermediate-size segments (0-30 residues long)]. Results of this statistical analysis were used to determine the variable sizes of the overlapping oligopeptide building blocks used in the calculations; these varied from tripeptides to octapeptides, depending on the amino acid sequence. Successive stages of approximations were used to combine the low-energy conformations of these building blocks in order to keep the number of variables in the computations to a manageable size. The calculations led to a limited number of conformations of the protein (only two different groups, with very similar structure within each group), most residues of which were in the same conformational state as in the native structure. To overcome the large entropy difference between the unique native state and the ensemble of conformations constituting the unfolded states, the native conformation of a protein must correspond to a deep minimum in its conformational energy hypersurface. The whole conformational space available to the protein cannot possibly be explored within any reasonable amount of time, so that the success of refolding experiments implies that the minimum in the Gibbs free energy function which corresponds to the native state must be significantly deeper than any other minima attainable during the course of refolding. When the whole of conformational space is considered, however, there are so many minima (1) that there is no hope of finding the one minimum corresponding to the native conformation by attempting to examine all of them (). Therefore, the native conformation must be identified in a computationally feasible way that does not require comparison of the energies ofall the minimum-energy conformations. In this paper, we present a procedure that uses information only about the amino acid sequence and locations of the disulfide bonds of the protein and that results in a very limited number of conformations, which are close enough to the native one for application offurther refinement techniques The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C solely to indicate this fact. (1). This procedure has been applied to bovine pancreatic trypsin inhibitor (), a 58-residue protein. Designation of the Native Conformation We assume that the native conformation is not only the one of highest stability but also the one in which all properly chosen segments of the polypeptide chain are simultaneously in low-energy (not necessarily the lowest-energy) conformations (3). This implies that short-range interactions play a dominant role in determining the conformations of these segments (4). The number of low-energy conformations of an oligopeptide is usually several orders of magnitude smaller than the number of combinations constructed by combining the lowenergy conformations of the individual residues of which the oligopeptide is constituted. Since the common part of two overlapping segments must be in the same conformation in both of the overlapping oligopeptides (5), the number of conformations of the whole polypeptide chain in which most of the overlapping segments are simultaneously in a lowenergy conformation is rather limited (3). Such whole polypeptide conformations are designated as "conformons" [formerly called X-conformations (3)], and it has been suggested that, for properly defined segment sizes and energy ranges, the native conformation is the only conformon of the whole polypeptide chain (3); for short-chain proteins, this unique conformon would be the native conformation, but for long chains it would be the native conformation only of an independently folding domain. Thus, we search the conformational space for the conformon of the whole chain (defined by short-range interactions) and assume that it corresponds to the native conformation. On the other hand, we must keep in mind that, whereas short-range interactions dominate in determining the minimum-energy conformation corresponding to the conformon of the whole chain, long-range and protein-solvent interactions affect the stabilization free energy and contribute in determining the exact conformation of the protein; these additional interactions are incorporated by minimizing the energy of the whole structure (with inclusion of solvent and disulfide bonds) in the final stage of our procedure. Low-energy conformations of oligopeptides can be obtained by using a buildup procedure (6). Vdsquez and Scheraga (7, 8) built up the whole conformation from low-energy fragments by using a limited number of distance Abbreviation:, bovine pancreatic trypsin inhibitor. *On leave from: Institute of Enzymology, B.R.C., Hungarian Academy of Sciences, H-1518 Budapest, P.O. Box 7, Hungary ton leave from: Department of Chemistry, University of the Witwatersrand, Wits 050, South Africa tto whom reprint requests should be addressed. 3661

2 366 Biophysics: Simon et al. constraints from simulated NMR spectra. In that approach, the low-energy conformations of all the constituent tetrapeptides were calculated independently of one another and then overlapped. Since the number of conformations of larger fragments built up from various combinations of these tetrapeptide conformations was exceedingly large, about 00 distance constraints (from simulated NMR spectra) were required to reduce the magnitude of the computational problem to select the final, native structure. In this paper, we modify the buildup procedure by introducing statistical information expressing the correlation between the types of residues that can exist at various positions along the chain; this information dictates the sizes of the fragments (which depend on the amino acid sequence) that should be used in the buildup procedure and obviates the previous need (7, 8) to introduce distance constraints. At the present stage of development of this modified procedure, however, the final results are not yet as good as those of refs. 7 and 8. Initial Screening of the Conformational Space We first considered the influence of neighboring residues on each other's conformations, without introducing correlations among the types of amino residues at this stage. For this purpose, we began with tripeptides as the initial building blocks. When the conformational energies of tripeptides (and, later, of larger oligopeptides) were calculated, their N and C termini were blocked with acetyl and methylamide groups, respectively. These blocking groups simulated the adjacent peptide groups within a protein. The total energy was calculated with the ECEPP/ potential (Empirical Conformational Energy Program for Peptides; refs. 9-11) together with the SUMSL minimizer (Secant Unconstrained Minimization Solver; ref. 1). All backbone and side-chain dihedral angles were varied in the minimization. At the oligopeptide stage, no solvent effects were included in the calculation because, at this stage, it was not known which residues were exposed to solvent. In the final stage, when the conformational energy of the whole molecule was calculated and minimized, the solvation free energy of its constituent groups, proportional to the water-accessible surface area, was included in the total energy (13) with an average penalty of 0.05 kcal/(mol A) for both polar and nonpolar groups (14). Unless noted otherwise, two conformations of a residue were considered to be the same if their backbone dihedral angles fell in the same region of the map, as defined by the conformational code of Zimmerman et al. (15) [which divides the map into 16 regions], and the first side-chain dihedral angles, X1, were in the same rotational isomeric state, g+, g-, or t. The conformational energies were minimized for sequential tripeptides, starting at the N terminus of, as follows. All of the low-energy conformations of the terminally blocked tripeptide RPD were calculated first, by combining all lowenergy conformations (16) of the single terminally blocked amino acid residues R, P, and D that fell within a 3.0-kcal/mol range of the global minimum; all single residues differing only in X' (j> 1) were replaced by the lowest-energy one in each set. All tripeptide conformations with minimized energies less than 8 kcal/mol above the global minimum were retained. These energy ranges were chosen in order to retain a manageable number of conformations. To minimize the low-energy conformations of the next overlapping tripeptide, PDF, not as an isolated one but as one whose conformation reflects the presence of the preceding residue R, the full list of low-energy conformations of RPD was reduced by selecting only the lowest-energy conformations (within the 8-kcal/mol range) of RPD for which the PD Proc. Natl. Acad. Sci. USA 88 (1991) dipeptide conformations differed from each other (i.e., in 4, q1, XI), irrespective of the conformation of residue R. These selected PD dipeptide conformations were combined with all of the low-energy conformations of the next residue, F. With this overlapping new tripeptide, the whole of the above procedure was repeated. The process was then repeated for each successive overlapping tripeptide of the whole polypeptide chain. An 8-kcal/mol cutoff was used for tripeptides that did not contain half-cystine, C, whereas a higher, 10-kcal/mol cutoff was used for those that did contain C, because of the extra constraining covalent bond that can compensate for higher conformational energies. It is important to note that, when the conformations of the second tripeptide, PDF, were calculated, the lowest-energy conformation was not necessarily the known globalminimum one of the isolated tripeptide PDF. This is because we used only those initial PD conformations which appeared among the low-energy conformations of the first tripeptide, RPD, and this ensemble of PD conformations reflects the influence of the residue R. Some of the conformations of isolated PDF might have lower energies than those computed here but, when the PD portion is combined with R, they would have higher energies than the 8-kcal/mol cutoff for RPD. The cutoff level was measured with respect to the minimum of this modified set of PDF conformations (influenced by residue R), rather than from the global minimum of isolated PDF, and a range of energies (8-10 kcal/mol), smaller than that used previously (7, 8), was enough to retain the native conformations of all tripeptides. By using this overlapping procedure, all successive tripeptides, up to the C-terminal one, feel the influence of all of the preceding residues. When all of the tripeptides of the polypeptide chain had been generated in this manner-i.e., when the C-terminal tripeptide, GGA, was reached-we had retained about 10 to 10,000 conformations with an average of about 1000 for each tripeptide. At this point, without carrying out any further energy calculations, we introduced the following screening process in the reverse direction to reduce the number of conformations even further. From the low-energy conformations of the C-terminal tripeptide, GGA, the different conformations of the dipeptide GG (reflecting the influence of the preceding residues and of the C-terminal residue A) were selected by the same criterion as that used for PD in the forward chain generation. Moving backward from the C terminus to the N terminus, we retained only those conformations of the preceding tripeptide, CGG, for which the conformation of the GG dipeptide portion appeared in the set of low-energy conformations of the GGA tripeptide, irrespective of the conformation of residue A. With the new, reduced list for tripeptide CGG, the backward selection (based on overlapping tripeptides) was continued until the N-terminal tripeptide, RPD, was reached. At the end of this backward selection, an average of about 300 conformations of each tripeptide remained, with the number varying from about 10 to 3000; the native conformation of each tripeptide [in terms of the code of Zimmerman et al. (15)] still appeared in each ensemble. Introduction of Statistical Information: Identification of Low-Energy Building Blocks In order to build up the conformon of the whole protein from low-energy conformations of smaller segments, we must first determine the sizes of the low-energy segments (to be built from the foregoing tripeptides) that will serve as the building blocks. For this purpose, we next introduced the use of statistical information about regularities in amino acid sequences.

3 Biophysics: Simon et A It has been shown that short-range regularities (nonrandomness) exist in the amino acid sequences of proteins, and that these regularities lead to certain structural features (17-19). Recently, the range of these regularities, measured by the nonrandomness of amino acid pairing (or the correlation between the types of residues) as a function of the separation between two residues in an amino acid sequence, has been determined (0). If it is assumed that the range of nonrandom pairing reflects the separation within which the residues influence each other's conformations significantly, the lengths of the overlapping segments (building blocks) that simultaneously must be in low-energy conformations are found to vary from tripeptides to octapeptides, depending on the amino acid sequences of the relevant segments (0). To obtain these building blocks, we combined the foregoing reduced set of tripeptide conformations into larger segments. The sizes chosen for these building blocks reflect the separation distances for nonrandom pairing of the residues, as found from a large protein sequence data base (0). For example, the N-terminal sequence of is RPDF- CLEPPY... Starting with R at position i, there are nonrandom correlations of R with P at position i + 1, with D at position i +, with F at position i + 3, and with C at position i + 4, but the correlation becomes random with residue L at position i + 5; therefore, the first building block is RPDFC. The remaining building blocks, selected by this criterion, are each shifted along the chain by at least one residue and are ilhimctretaa crhermntieqilv in Pip 1 To IIemrnntrate how the Proc. Natd. Acad. Sci. USA 88 (1991) 3663 tripeptide conformations of the previous reduced set for RPD, PDF, and DFC were combined (with no further screening at this point) to form the pentapeptide; the energies of all of these conformations of RPDFC were then minimized with respect to all backbone and side-chain dihedral angles [the starting values of Xi, forj > 1, were the lowest-energy ones for single residues (16) for the given backbone conformation]. It was observed that, after the earlier screening at the tripeptide level, it was possible to retain the native conformations of the building blocks with a lower energy cutoffthan 8-10 kcal/mol. Thus, a 5-kcal/mol cutoff was chosen in the energy minimization for each building block that did not include half-cystine, while a 7-kcal/mol cutoffwas chosen for those having half-cystine. Only structures having energies below the cutoffs were retained as building blocks for further buildup. When the C terminus was reached, with an accumulation of a few hundred to hundreds of thousands of oligopeptide conformations, the same backward selection (with no energy minimization) as was described for the tripeptides was applied; in this backward screening, the degree of overlap shown in Fig. 1 was used. This screening resulted in to 10,000 conformations per oligopeptide, with the retention of the native conformation of each building block. Buildup of Chain with Low-Energy Building Blocks: Use of Disulfide Loops second building block was obtained, we note that, for P taken To proceed further, it was necessary to invoke additional as residue i, there is a random correlation with the next three chemical information to limit the number of conformations residues, D, F, and C (0); likewise for D with respect to F retained during the construction of the whole molecule; this C, and L; however, the same logic, applied to F as residue i information was the locations of the disulfide-bonded loops. yields the hexapeptide FCLEPP. Therefore, these two oli- We began the build-up with the N terminus of the smallest gopeptides (RPDFC and FCLEPP), rather than the nonapep- disulfide-bonded loop, Cys30-Cys51 (actually from Gly8 to tide RPDFCLEPP, were considered as building blocks be- Arg53 to avoid splitting a building block, and then truncating cause R is correlated up to C but not beyond. back to Cys3-Cys51). Further reduction of the ensembles of The building blocks were assembled by again starting at t building blocks was achieved by considering the nondegen- N terminus ofthe protein. Forexample, forrpdfc, all ofthe erate minima-i.e., by selecting only one (lowest-energy) side-chain conformation for the given backbone conformal tion (1) [according to the code of Zimmerman et al. (15)] for each residue in the building blocks. 1+1 l In order to combine the ensembles of building blocks in all 1.4+' combinations [based on the conformational letter code (15)] according to the overlaps in Fig. 1 to form larger segments, 1-H-H the dihedral angles of the overlapping residues in the two Ill,, building blocks were averaged (since the conformations being averaged were similar, no change occurred in the conforma- Hl l H tional letter code). For values close to 1800, however, the Hll l llldeviations 4 from 1800 were averaged. This procedure of come+1-91 l bination (without energy minimization) resulted in 3000 dif- F-H-I ferent backbone conformations (including the native) for the segment between residues 30 and 51. HlH Of these 3000 conformations, only 47 had a separation FH-Ibetween the two sulfur atoms of <10 A. The choice of 10 A l+hl lllwas a compromise between 5 A, for which no conformations were found, and 13 A, for which too many remained, espelhl llcially when combined with later fragments. With the io-a cutoff, the native backbone conformation of the Cys30-Cys51 loop was lost, but several backbone conformations (very similar to the corresponding part of the native protein) were l-hl lllretained. Energy minimization with a disulfide loop-closing H potential [without constraints on the (q5, f) dihedral angles] H was not applied at this stage because it might have shifted the conformational codes (15), thereby destroying the building FIG. 1. The sizes of the segments that were used as stable blocks and preventing further implementation ofthe essential building blocks in the buildup procedure, and their distribution along feature of this modified buildup procedure (the simultaneous the polypeptide chain of. The residues of the C-terminal existence of all the building blocks of the whole chain in tripeptide, G, G and A, are in random pairing with the preceding low-energy conformations). In the final stage of the proceresidues (0); therefore, this figure shows segments only up to dure, however, after the whole structure was built, energy residue 55. minimization (with a disulfide loop-closing potential) was

4 3664 Biophysics: Simon et al. applied, and the conformational codes were allowed to change. Among these 47 conformations, there were only different conformations for the nonapeptide from residues 30 to 38, which is the C-terminal portion of a second loop, the one involving Cys'4 and Cys38. These two nonapeptide conformations were combined, successively, with the building blocks of Fig. 1, moving toward the N terminus of Cys'4 to form the Cys14-Cys38 segment. Of the resulting =500 conformations of the segment, only 49 had a separation distance between the sulfur atoms of <10 A. Combination of the 47 conformations of segment and the 49 conformations of segment resulted in 136 backbone conformations for the portion of the polypeptide. These conformations were extended in both directions with the building blocks of Fig. 1, resulting in >4000 conformations of the 5-55 portion of the chain; only 8 of these, which had a separation distance between the sulfur atoms of Cys5 and Cys55 within the 10-A limit, were retained. Consideration of the Side Chains of the Building Blocks In each of the 8 backbone structures of the 5-55 segment, the side chains were attached in all possible combinations (with respect to X1); however, we retained only those sidechain conformations (i.e., values of X1) that were found earlier for the residues in the respective building blocks [the values of Xi (j > 1) were taken from the lowest-energy conformations (for the given X1) of each single residue (16)]. This selection procedure resulted in >300 conformations, but most of them were very similar in the backbone codes of Zimmerman et al. (15) and in the rotational isomeric states of X1 of their side chains. These conformations essentially fell into only two different groups, reflecting the two different conformations for residues We selected 0 structures of segment 5-55 randomly (10 from each group), and combined them with the N-terminal building blocks of Fig. 1 and the original C-terminal tripeptides (the C-terminal residues, G, G, and A being noncorrelated with the preceding residues). The terminal oligopeptides, especially the C-terminal tripeptide GGA, exhibited great flexibility-i.e., hundreds of conformations could be fitted to the rest of the molecule. Therefore, we combined 10 randomly selected conformations of each of the N- and C-terminal oligopeptides with the 0 randomly selected conformations of segment 5-55 to produce 000 conformations of the whole molecule; 60 of these 000 conformations, chosen randomly from the two groups (more from the group with lower energy), were selected for further consideration. Energy Minimization of the Whole Molecule Once the energies of the building blocks of Fig. 1 had been minimized, no further energy minimization had been applied up to this point; the combination of the building blocks, thus far, involved only selective screening. Now, the energies [including a pseudopotential (9-11) to form the disulfide bonds] of the 60 selected conformations of the whole molecule were minimized without solvation; only 4 of these 60 conformations had energies <104 kcal/mol (this high cutoff reflected high-energy local minima). Only 8 of these 4 had different conformations of the whole molecule, the remaining differences being only in the conformations of the N- and C-terminal blocking groups. The energies of these 8 conformations were minimized again, but now including the solvation free energy (13, 14); this reminimization required about 30 times more computational time but resulted only in some reordering of the conformational energies with very little conformational change. Proc. Natl. Acad. Sci. USA 88 (1991) The whole procedure resulted in two different families of conformations. Within each of these two conformational families, the structures differed only in the conformations of the terminal parts or in the side-chain conformations, but their backbones were very similar. Results and Discussion The lowest-energy structures of each of the two different conformational families were compared with the x-ray structure of native (), using the coordinate set 5PTI from the Brookhaven Data Bank (3, 4). Both calculated conformations are much less compact than the x-ray structure. The two loops, from Cys'4 to Cys38 and from Cys30 to Cys51, appear to be similar to those in the native structure, although the Cys14-Cys38 loop is slightly less twisted and the Cys30- Cys5' loop is more planar in the calculated conformations. The relative placements of the segments have been less accurately established. For example, the overlapping part of the two loops, the nonapeptide 30-38, was one of the central elements of our calculation procedure. When the nonapeptide from one of the families of the whole molecule is optimally superimposed on the corresponding portion of the x-ray structure, the rms deviation of the backbone atoms is <1 A (the nonapeptide from the other family is not as good); however, when the whole molecule is superimposed on the x-ray structure, these central nonapeptides lie far from one another, with a rms distance of 1oA. This demonstrates that when two structures are not sufficiently similar, the rms deviation can be a very misleading measure of agreement because a single parameter cannot distinguish between, on the one hand, two completely different structures and, on the other, two structures consisting of very similar segments that are poorly placed with respect to each other. Therefore, at the present stage of the development of our procedure (where our results are mainly of conceptual interest), we use only the conformational codes of Zimmerman et al. (15), rather than the rms deviation or a more detailed differential geometric comparison (5), for comparing two conformations. This type of comparison not only illustrates the conformational differences but also indicates whether the differences are distributed evenly or are confined to a few positions along the 14 F AC la BE F F IEC E ICI F 'Ft ' F' F F E F*: B F C A C F C LAj IEj F F DJLI E C F 15 9 D F D C C E E E C A A A A A* G D F D C C E E E C C A A A A* E D FD C C E E E C A A A A A* G I EiiDii Ei C CIrA ia*e G G G A C D IF IB' E A C D F: IEi FiE IA*I L..J C'C'L A E A* F A C D [m] FCI A C A A A A A A A* C* D G LIJ B: E AA A A A A A WrB B F*? A LAJ A J [AJ J JA J LJ IAI C* E G FIG.. Backbone conformational codes (15) of the residues. First row, structure 1; second row, standard-geometry version (7, 8) of the x-ray structure; and third row, structure. The boxes with full lines enclose identical conformational codes, whereas the boxes with broken lines enclose immediately adjacent conformational codes (15). The question marks arise because dihedral angle 4 of residue 1 and dihedral angle 4i of residue 58 are not defined in the x-ray structure.

5 polypeptide chain. Such a comparison is given in Fig.. For both groups of calculated conformations, about two-thirds of the residues are in the same conformational code region as in the standard-geometry version (7, 8) of the x-ray structure. Moreover, in structure no., half of the residues with incorrect backbone conformations are located at the two ends of the chain, which are more flexible than the interior of the chain. While such good agreement of conformational status (15) is encouraging, it should be recalled that a perfectprediction model [albeit only a 5-state one (6), compared to the 16-state one of Zimmerman et al. (15)] led to a poor structure (6); however, further refinements by procedures outlined in ref. I can improve the structure. Conclusions Biophysics: Simon et A Polypeptides with special, naturally selected amino acid sequences adopt unique, native conformations that have lower free energy than does the unfolded state. Therefore, when we attempt to solve the protein-folding problem, we must consider only those polypeptides having these special, naturally selected sequences. It therefore makes sense to incorporate the special features of naturally selected sequences in calculations ofprotein conformation. This was the basis for modifying the buildup procedure by selection of the sizes of the overlapping building blocks based on nonrandom correlations of amino acid sequences, from which the whole molecule was built. The whole procedure is based on the premise that shortrange interactions determine which of the minimum-energy structures correspond to the conformon, which is assumed to be the native structure. It is believed that chain-folding initiation sites (CFISs) are formed in various parts of the unfolded polypeptide chain in response to short-range interactions (7-9), and that further folding around these CFISs is also dominated by short-range interactions. In fact, CFISs have been shown to exist in short peptide fragments (9). It is further assumed that long-range and protein-solvent interactions only enhance the stability of the folded structure. The use of energy minimization (with inclusion of solvent and disulfide bonds) in the final stage of the procedure conforms to the collapse phenomenon discussed by Chan and Dill (30). Polypeptide sequences that do not lead to a single structure whose free energy is significantly lower than that ofany other accessible conformation may be presumed to be unsuitable from a biological point of view, so that natural selection will not retain such amino acid sequences. The procedure presented in this paper has taken advantage of this presumed natural selection to obtain a unique or, perhaps, a limited number of conformations for a polypeptide with selected amino acid sequences in which the overlapping building blocks are simultaneously in low-energy conformations. We thank K. D. Gibson, A. Nayeem, G. Ndmethy, M. R. Pincus, S. Rackovsky, and M. VAsquez for helpful comments on the manuscript. This work was supported by research grants from the National Institute of General Medical Sciences of the National Institutes of Health (GM1431) and from the National Science Foundation (DMB ). Support was also received from the National Foundation for Cancer Research and from the U.S.-Hungary International Cooperative Science Program (NSF-INT88-75). Support from the Hungarian Academy of Sciences (OTKA 318) is also Proc. Natl. Acad. Sci. USA 88 (1991) 3665 acknowledged. The computations were carried out at the Cornell National Supercomputer Facility, a resource of the Cornell Center for Theory and Simulation in Science and Engineering, which receives major funding from the National Science Foundation and the IBM Corporation, with additional support from New York State and members of the Corporate Research Institute. 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