Common motifs and topological effects in the protein folding transition state.

Through extensive experiment, simulation, and analysis of protein S6 (1RIS), we find that variations in nucleation and folding pathway between circular permutations are determined principally by the restraints of topology and specific nucleation, and affected by changes in chain entropy. Simulations also relate topological features to experimentally measured stabilities. Despite many sizable changes in phi values and the structure of the transition state ensemble that result from permutation, we observe a common theme: the critical nucleus in each of the mutants share a subset of residues that can be mapped to the critical nucleus residues of the wild-type. Circular permutations create new N and C termini, which are the location of the largest disruption of the folding nucleus, leading to a decrease in both phi values and the role in nucleation. Mutant nuclei are built around the wild-type nucleus but are biased towards different parts of the S6 structure depending on the topological and entropic changes induced by the location of the new N and C termini.

Nucleation and the transition state of the SH3 domain.

We present a verified computational model of the SH3 domain transition state (TS) ensemble. This model was built for three separate SH3 domains using experimental phi-values as structural constraints in all-atom protein folding simulations. While averaging over all conformations incorrectly considers non-TS conformations as transition states, quantifying structures as pre-TS, TS, and post-TS by measurement of their transmission coefficient ("probability to fold", or p(fold)) allows for rigorous conclusions regarding the structure of the folding nucleus and a full mechanistic analysis of the folding process. Through analysis of the TS, we observe a highly polarized nucleus in which many residues are solvent-exposed. Mechanistic analysis suggests the hydrophobic core forms largely after an early nucleation step. SH3 presents an ideal system for studying the nucleation-condensation mechanism and highlights the synergistic relationship between experiment and simulation in the study of protein folding.

Commitment and nucleation in the protein G transition state.

An accurate characterization of the transition state ensemble (TSE) is central to furthering our understanding of the protein folding reaction. We have extensively tested a recently reported method for studying a protein's TSE, utilizing phi-value data from protein engineering experiments and computational studies as restraints in all-atom Monte Carlo (MC) simulations. The validity of interpreting experimental phi-values as the fraction of native contacts made by a residue in the TSE was explored, revealing that this definition is unable to uniquely specify a TSE. The identification of protein G's second hairpin, in both pre and post-transition conformations demonstrates that high experimental phi-values do not guarantee a residue's importance in the TSE. An analysis of simulations based on structures restrained by experimental phi-values is necessary to yield this result, which is not obvious from a simplistic interpretation of individual phi-values. The TSE that we obtain corresponds to a single, specific nucleation event, characterized by six residues common to all three observed, convergent folding pathways. The same specific nucleus was independently identified from computational and experimental data, and "Conservation of Conservation" analysis in the protein G fold. When associated strictly with complete nucleus formation and concomitant chain collapse, folding is a well-defined two state event. Once the nucleus has formed, the folding reaction enters a slow relaxation process associated with side-chain packing and small, local backbone rearrangements. A detailed analysis of phi-values and their relationship to the transition state ensemble allows us to construct a unified theoretical model of protein G folding.

Geometric and physical considerations for realistic protein models.

Protein structure is generally conceptualized as the global arrangement or of smaller, local motifs of helices, sheets, and loops. These regular, recurring secondary structural elements have well understood and standardized definitions in terms of amino acid backbone geometry and the manner in which hydrogen bonding requirements are satisfied. Recently, "tube" models have been proposed to explain protein secondary structure in terms of the geometrically optimal packing of a featureless cylinder. However, atomically detailed simulations demonstrate that such packing considerations alone are insufficient for defining secondary structure; both excluded volume and hydrogen bonding must be explicitly modeled for helix formation. These results have fundamental implications for the construction and interpretation of realistic and meaningful biomacromolecular models.

Understanding ensemble protein folding at atomic detail.

It has long been known that a protein's amino acid sequence dictates its native structure. However, despite significant recent advances, an ensemble description of how a protein achieves its native conformation from random coil under physiologically relevant conditions remains incomplete. Here we present a detailed all-atom model with a transferable potential that is capable of ab initio folding of entire protein domains using only sequence information. The computational efficiency of this model allows us to perform thousands of microsecond-time scale-folding simulations of the engrailed homeodomain and to observe thousands of complete independent folding events. We apply a graph-theoretic analysis to this massive data set to elucidate which intermediates and intermediary states are common to many trajectories and thus important for the folding process. This method provides an atomically detailed and complete picture of a folding pathway at the ensemble level. The approach that we describe is quite general and could be used to study the folding of proteins on time scales orders of magnitude longer than currently possible.

Identification of the minimal protein-folding nucleus through loop-entropy perturbations.

To explore the plasticity and structural constraints of the protein-folding nucleus we have constructed through circular permutation four topological variants of the ribosomal protein S6. In effect, these topological variants represent entropy mutants with maintained spatial contacts. The proteins were characterized at two complementary levels of detail: by phi-value analysis estimating the extent of contact formation in the transition-state ensemble and by Hammond analysis measuring the site-specific growth of the folding nucleus. The results show that, although the loop-entropy alterations markedly influence the appearance and structural location of the folding nucleus, it retains a common motif of one helix docking against two strands. This nucleation motif is built around a shared subset of side chains in the center of the hydrophobic core but extends in different directions of the S6 structure following the permutant-specific differences in local loop entropies. The adjustment of the critical folding nucleus to alterations in loop entropies is reflected by a direct correlation between the phi-value change and the accompanying change in local sequence separation.

On the origin and highly likely completeness of single-domain protein structures.

The size and origin of the protein fold universe is of fundamental and practical importance. Analyzing randomly generated, compact sticky homopolypeptide conformations constructed in generic simplified and all-atom protein models, all have similar folds in the library of solved structures, the Protein Data Bank, and conversely, all compact, single-domain protein structures in the Protein Data Bank have structural analogues in the compact model set. Thus, both sets are highly likely complete, with the protein fold universe arising from compact conformations of hydrogen-bonded, secondary structures. Because side chains are represented by their Cbeta atoms, these results also suggest that the observed protein folds are insensitive to the details of side-chain packing. Sequence specificity enters both in fine-tuning the structure and thermodynamically stabilizing a given fold with respect to the set of alternatives. Scanning the models against a three-dimensional active-site library, close geometric matches are frequently found. Thus, the presence of active-site-like geometries also seems to be a consequence of the packing of compact, secondary structural elements. These results have significant implications for the evolution of protein structure and function.

High-resolution protein folding with a transferable potential.

A generalized computational method for folding proteins with a fully transferable potential and geometrically realistic all-atom model is presented and tested on seven helix bundle proteins. The protocol, which includes graph-theoretical analysis of the ensemble of resulting folded conformations, was systematically applied and consistently produced structure predictions of approximately 3 A without any knowledge of the native state. To measure and understand the significance of the results, extensive control simulations were conducted. Graph theoretic analysis provides a means for systematically identifying the native fold and provides physical insight, conceptually linking the results to modern theoretical views of protein folding. In addition to presenting a method for prediction of structure and folding mechanism, our model suggests that an accurate all-atom amino acid representation coupled with a physically reasonable atomic interaction potential and hydrogen bonding are essential features for a realistic protein model.

CoC: a database of universally conserved residues in protein folds.

UNLABELLED: The conservatism of conservatism (CoC) database presents statistically analyzed information about the conservation of residue positions in folds across protein families. AVAILABILITY: On the web at http://kulibin.mit.edu/coc/

Simulation, experiment, and evolution: understanding nucleation in protein S6 folding.

In this study, we explore nucleation and the transition state ensemble of the ribosomal protein S6 using a Monte Carlo (MC) Go model in conjunction with restraints from experiment. The results are analyzed in the context of extensive experimental and evolutionary data. The roles of individual residues in the folding nucleus are identified, and the order of events in the S6 folding mechanism is explored in detail. Interpretation of our results agrees with, and extends the utility of, experiments that shift phi-values by modulating denaturant concentration and presents strong evidence for the realism of the mechanistic details in our MC Go model and the structural interpretation of experimental phi-values. We also observe plasticity in the contacts of the hydrophobic core that support the specific nucleus. For S6, which binds to RNA and protein after folding, this plasticity may result from the conformational flexibility required to achieve biological function. These results present a theoretical and conceptual picture that is relevant in understanding the mechanism of nucleation in protein folding.