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Molecular Picture of Folding of a Small Protein

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Molecular Picture of Folding of a Small Protein Proc. Natl. Acad. Sci. USA Vol. 95, pp. 1562–1567, February 1998 Biophysics Molecular picture of folding of a small ayb protein FELIX B. SHEINERMAN AND CHARLES L. BROOKS III* Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, CA 92037 Communicated by H. A. Scheraga, Cornell University, Ithaca, NY, December 12, 1997 (received for review May 2, 1997) ABSTRACT We characterize, at the atomic level, the unstructured fragments of polypeptide chains), thus the use of mechanism and thermodynamics of folding of a small ayb this force field to study protein conformational transitions protein. The thermodynamically significant states of segment under native conditions seems appropriate. Furthermore, we B1 of streptococcal protein G (GB1) are probed by using the make no a priori assumption about the nature of the folding statistical mechanical methods of importance sampling and process but build a database of conformations for starting molecular dynamics. From a thermodynamic standpoint, fold- points in our free energy sampling by considering high- ing commences with overall collapse, accompanied by forma- temperature unfolding trajectories of the protein in solution. tion of ;35% of the native structure. Specific contacts form at We demonstrate that our procedure is resilient to the choice the loci experimentally inferred to be structured early in of a different subset of initial conditions, and we verify the folding kinetics studies. Our study reveals that these initially convergence of our sampling within the set of initial conditions structured regions are not spatially adjacent. As folding that we have used. Our calculations produce models that progresses, fluid-like nonlocal native contacts form, with conform with experimental findings, providing a demonstra- many contacts forming and breaking as the structure searches tion of the insight into folding phenomenon that may be gained for the native conformation. Although the a-helix forms early, through consideration of detailed theoretical models. the b-sheet forms concomitantly with the overall topology. Often protein folding studies, experimental and theoretical, Water is present in the protein core up to a late stage of focus on a single protein as a paradigm. Helical proteins have folding, lubricating conformational transitions during the been particularly well studied in this vein, and our earlier work search process. Once 80% of the native contacts have formed, on an all-helical protein has demonstrated the successful water is squeezed from the protein interior and the structure application of simulations to explore the folding landscape for descends into the native manifold. Examination of the onset of this class of molecules (8, 9). In the present work, we explore side-chain mobility within our model indicates side-chain the folding mechanism of an ayb protein, providing an im- motion is most closely linked to the overall volume of the portant, and hitherto less well understood, paradigm. Our protein and no sharp order–disorder transition appears to theoretical study complements the elegant experiments of occur. Exploration of models for hydrogen deuterium ex- Fersht and coworkers (10, 11) on the folding of chymotrypsin change show qualitative agreement with equilibrium measure- inhibitor 2, another ayb protein. Insight into the thermody- ment of hydrogenydeuterium protection factors. namics of folding and the molecular picture provided by our study extend beyond the scope of previous theoretical studies The protein folding problem—understanding how a polypep- on ayb proteins (12). tide chain reaches its native conformation—is a long-standing challenge in molecular biophysics. There has been a significant Models and Methods effort to develop a theoretical basis for this phenomenon in recent years (1–3). Theoretical models of protein folding are Segment B1 of streptococcal protein G (GB1), the protein on based on analogy with better-studied physical phenomena, which we focus our present efforts, is a 56-residue single- e.g., spin glasses and polymer physics, and on simulations domain protein that is stable in isolation. NMR (13) and x-ray b involving highly simplified representations of protein energet- (14) structure determinations reveal a four-stranded -sheet a ics and structure. These studies have suggested a general packed against an -helix. GB1 contains no proline residues, framework for understanding the folding process. However, disulfide bridges, or prosthetic groups. It is therefore expected ayb direct testing of this framework and a compelling demonstra- to exhibit general features of folding for small proteins. tion of its relevance to real proteins has not been realized. To generate the free energy surfaces used to study the Furthermore, despite significant advances in experimental folding of GB1, we first characterized the native state of the methodologies (4–6), a complete and unambiguous descrip- protein. Two native simulations (2 ns and 1 ns) were performed tion of folding at the atomic level has yet to emerge. These as a reference point for the folding study (15). From an analysis points motivate the current theoretical studies to explore the of these native simulations, the properties characteristic of the folding thermodynamics of a small protein with molecular naive basin were defined. Fifty-four side-chain contacts, simulations. formed between residues not adjacent in sequence and present We attempt, in this study, to address some of the issues for more than two-thirds of each simulation, were identified as underlying a more accurate energetic description of folding, on ‘‘native contacts’’ and used to define a reaction coordinate: the one hand, and a more complete atomic description, on the 1 other, by using a full-atomic model of the solvated protein with O p~i!F1 2 G empirically derived interaction forces. The empirical force ~1 1 exp$20@d~i! 2 6.75#%! r 5 , field we use, CHARMM (7), has been developed to represent O p~i! equilibrium properties of both native proteins and peptides (or for characterization of the progress of folding. In this expres- The publication costs of this article were defrayed in part by page charge sion, d(i) is the distance between centers of geometry of side payment. This article must therefore be hereby marked ‘‘advertisement’’ in chains forming contact i, and p(i) is the weight of the ith accordance with 18 U.S.C. §1734 solely to indicate this fact. © 1998 by The National Academy of Sciences 0027-8424y98y951562-6$2.00y0 *To whom reprint requests should be addressed. e-mail: brooks@ PNAS is available online at http:yywww.pnas.org. scripps.edu. 1562 Downloaded by guest on September 29, 2021 Biophysics: Sheinerman and Brooks Proc. Natl. Acad. Sci. USA 95 (1998) 1563 contact. The probability of a given side-chain contact being formed in the native state is defined on the basis of the fraction of time the contact is present in the native trajectories and ranges between 66% and 100% [@ i, 0.66 , p(i) , 1.0]. We note that this choice of reaction coordinate clearly distinguishes between native and nonnative protein conformations, a nec- essary condition for any reaction coordinate. Furthermore, it provides us with the ability to make direct connections with simpler lattice-based and analytical models of protein folding and with experimental data on interresidue distance contacts. Three high-temperature unfolding simulations at a temper- ature of 400 K were used to generate a database of initial conditions. Although such a database is certainly not encom- passing of all conformational states accessible to the protein as it folds, particularly in the most nonnative conformational regions, we believe it provides a representative ensemble of configurations. Alternative methods of generating nonnative conformations might be imagined, and we address one such method briefly below. However, if the alternative approaches produce conformations that, when solvated, are of very high r energy, these nonrepresentative conformations will never FIG. 1. Free energy surfaces along the reaction coordinate (defined by the number of native contacts) (Inset) and as a function of achieve proper equilibration in the time period of sampling r and Rg (the radius of gyration). Contours are drawn every 0.5 accessible for calculations of this sort. The database generated kcalymol. from the unfolding simulations was partitioned into ‘‘bins’’ along the reaction coordinate r. The conformations in each of energy landscape in regions of conformational space that are these bins were clustered, resulting in a total of 76 clusters, and of intermediate compactness and ‘‘nativeness.’’ the cluster centers served as initial conditions for our free All molecular dynamics simulations were carried out with energy sampling. The database was clustered on the basis of the CHARMM package (7), using a polar hydrogen parameter the content of native contacts, native hydrogen bonds, and the set (TOPH19yPARAM19) and the TIP3P water model (20). solvation energy, by using a hierarchical scheme as described The protein was solvated in a truncated octahedron con- (9). The cluster centers were resolvated in a preequilibrated structed from a box that was 62 Å on a side. Corresponding y volume of water (at 298 K and 1 g ml) and then further periodic boundary conditions were applied. Dynamics were equilibrated for 20 ps. These final structures were used as propagated with a time step of 0.002 ps. X–H bonds were fixed initial conditions for importance sampling (16). with the SHAKE algorithm (21). Nonbonded interactions were Importance sampling was performed with a harmonic bias- r processed by using a list updated every 25 steps (22). Trun- ing potential defined along the reaction coordinate . The cation of nonbonded interactions was done at 11 Å with a list biasing potential force constant was chosen to yield an energy y 5 extending to 12.5 Å. Temperature was maintained at 298 K by change of 0.6 kcal mol (kBT at 298 K; 1 cal 4.184 J) when r reassigning individual atomic velocity components from a the coordinate was displaced half the bin width from the Gaussian distribution if the average temperature drifted out- center.
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