The early folding kinetics of apomyoglobin.

The folding pathway of apomyoglobin has been experimentally shown to have early kinetic intermediates involving the A, B, G, and H helices. The earliest detected kinetic events occur on a ns to micros time scale. We show that the early folding kinetics of apomyoglobin may be understood as the association of nascent helices through a network of diffusion-collision-coalescence steps G + H <--> GH + A <--> AGH + B <--> ABGH obtained by solving the diffusion-collision model in a chemical kinetics approximation. Our reproduction of the experimental results indicates that the model is a useful way to analyze folding data. One prediction from our fit is that the nascent A and H helices should be relatively more helix-like before coalescence than the other apomyoglobin helices.     

Brownian dynamics simulation of protein folding: a study of the diffusion-collision model

The dynamic aspects of protein folding are described by a series of diffusion-collision steps involving structural units (microdomains) of various sizes that combine to form the protein in its native state. A method is introduced for obtaining the rate constants for the basic diffusion-collision step by use of Brownian dynamics. The method is applied to an investigation of the folding dynamics of two α-helices connected by a flexible (random-coil) polypeptide chain. The results of this full three-dimensional treatment are compared with simplified model calculations for the diffusion-collision step. Of particular interest are the nature of the collision dynamics and the role of the intervening peptide chain.     

Reinterpretation of GCN4-p1 folding kinetics: partial helix formation precedes dimerization in coiled coil folding.

The folding of coiled coil peptides has traditionally been interpreted in terms of native dimer and unfolded monomers. Calculations using AGADIR and experimental studies of fragments suggest that the monomers of the coiled coil peptide, GCN4-p1, contain significant residual helical structure. A simple model based on diffusion-collision theory predicts not only the measured folding rate within an order of magnitude, but also predicts remarkably well the effect of alanine to glyXcine mutations. We suggest that intrinsic helix stability is a major determinant of the folding rate of the GCN4 coiled coil.     

The building block folding model and the kinetics of protein folding.

Here we show that qualitatively, the building blocks folding model accounts for three-state versus the two-state protein folding. Additionally, it is consistent with the faster versus slower folding rates of the two-state proteins. Specifically, we illustrate that the building blocks size, their mode of associations in the native structure, the number of ways they can combinatorially assemble, their population times and the way they are split in the iterative, step-by-step structural dissection which yields the anatomy trees, explain a broad range of folding rates. We further show that proteins with similar general topologies may have different folding pathways, and hence different folding rates. On the other hand, the effect of mutations resembles that of changes in conditions, shifting the population times and hence the energy landscapes. Hence, together with the secondary structure type and the extent of local versus non-local interactions, a coherent, consistent rationale for folding kinetics can be outlined, in agreement with experimental results. Given the native structure of a protein, these guidelines enable a qualitative prediction of the folding kinetics. We further describe these in the context of the protein folding energy landscape. Quantitatively, in principle, the diffusion-collision model for the building block association can be used. However, the folding rates of the building blocks and traps in their formation and association, need to be considered.     

Are residues in a protein folding nucleus evolutionarily conserved?

Protein is the working molecule of the cell, and evolution is the hallmark of life. It is important to understand how protein folding and evolution influence each other. Several studies correlating experimental measurement of residue participation in folding nucleus and sequence conservation have reached different conclusions. These studies are based on assessment of sequence conservation at folding nucleus sites using entropy or relative entropy measurement derived from multiple sequence alignment. Here we report analysis of conservation of folding nucleus using an evolutionary model alternative to entropy-based approaches. We employ a continuous time Markov model of codon substitution to distinguish mutation fixed by evolution and mutation fixed by chance. This model takes into account bias in codon frequency, bias-favoring transition over transversion, as well as explicit phylogenetic information. We measure selection pressure using the ratio omega of synonymous versus non-synonymous substitution at individual residue site. The omega-values are estimated using the PAML method, a maximum-likelihood estimator. Our results show that there is little correlation between the extent of kinetic participation in protein folding nucleus as measured by experimental phi-value and selection pressure as measured by omega-value. In addition, two randomization tests failed to show that folding nucleus residues are significantly more conserved than the whole protein, or the median omega value of all residues in the protein. These results suggest that at the level of codon substitution, there is no indication that folding nucleus residues are significantly more conserved than other residues. We further reconstruct candidate ancestral residues of the folding nucleus and suggest possible test tube mutation studies for testing folding behavior of ancient folding nucleus.     

Diffusion-collision model study of misfolding in a four-helix bundle protein.

Proteins with complex folding kinetics will be susceptible to misfolding at some stage in the folding process. We simulate this problem by using the diffusion-collision model to study non-native kinetic intermediate misfolding in a four-helix bundle protein. We find a limit on the size of the pairwise hydrophobic area loss in non-native intermediates, such that burying above this limit creates long-lasting non-native kinetic intermediates that would disrupt folding and prevent formation of the native state. Our study of misfolding suggests a method for limiting the production of misfolded kinetic intermediates for helical proteins and could, perhaps, lead to more efficient production of proteins in bulk.     

Folding kinetics of designer proteins. Application of the diffusion-collision model to a de novo designed four-helix bundle.

A folding algorithm is described, based on the diffusion-collision model, combining static and dynamic calculational methods. The algorithm is applied to predict the basic structure and schematic folding pathways of an artificial four-helix bundle.     

On the Prediction of Folding Nuclei in Globular Proteins

An approach to predicting folding nuclei in globular proteins with known three-dimensional structures is proposed. This approach is based on the pinpointing of the lowest saddle points on the barrier between the unfolded state and native structure on the free-energy landscape of a protein chain; the proposed technique uses the dynamic programming method. A comparison of calculation results with experimental data on the folding nuclei of 21 proteins shows that the model provides good Φ value predictions for protein structures determined by X-ray analysis and, less successfully, in structures determined by nuclear magnetic resonance. Consideration of the whole ensemble of transition states provides a better prediction of folding nuclei than consideration of only transition states with lowest free energies. In addition, we predict the location of folding nuclei in three-dimensional structures of some proteins whose folding kinetics is being studied, but there is no experimental evidence concerning their folding nuclei.     

Preorganized secondary structure as an important determinant of fast protein folding

The folding and unfolding kinetics of the B-domain of staphylococcal protein A, a small three-helix bundle protein, were probed by NMR. The lineshape of a single histidine resonance was fit as a function of denaturant to give folding and unfolding rate constants. The B-domain folds extremely rapidly in a two-state manner, with a folding rate constant of 120,000 s-1, making it one of the fastest-folding proteins known. Diffusion-collision theory predicts folding and unfolding rate constants that are in good agreement with the experimental values. The apparent rate constant as a function of denaturant ('chevron plot') is predicted within an order of magnitude. Our results are consistent with a model whereby fast-folding proteins utilize a diffusion-collision mechanism, with the preorganization of one or more elements of secondary structure in the unfolded protein.     

Transient, highly populated, building blocks folding model

Protein folding is a hierarchical event, in which transiently formed local structural elements assemble to yield the native conformation. In principle, multiple paths glide down the energy landscape, but, in practice, only a few of the paths are highly traveled. Here, the literature is reviewed in this light, and, particularly, a hierarchical, building block protein-folding model is presented, putting it in the context of a broad range of experimental and theoretical results published over the past few years. The model is based on two premises: First, although the local building block elements may be unstable, they nevertheless have higher population times than all alternate conformations; and, second, protein folding progresses through a combinatorial assembly of these elements. Through the binding of the most favorable building block conformers, there is a redistribution of the conformers in solution, propagating the protein-folding reaction. We describe the algorithm, and illustrate its usefulness, then we focus on its utility in assigning simple vs complex folding pathways, on chaperonin-assisted folding, on its relevance to domain-swapping processes, and on its relevance and relationship to disconnectivity graphs and tree diagrams. Considering protein folding as initiating from local transient structural elements is consistent with available experimental and theoretical results. Here, we have shown that, early in the folding process, sequential interactions are likely to take place, even if the final native fold is a complex, nonsequential one. Such a route is favorable kinetically and entropically. Through the construction of anatomy trees, the model enables derivation of the major folding pathways and their bumps, and qualitatively explains the kinetics of protein folding.     

Statistical analyses of protein folding rates from the view of quantum transition

Understanding protein folding rate is the primary key to unlock the fundamental physics underlying protein structure and its folding mechanism.Especially,the temperature dependence of the folding rate remains unsolved in the literature.Starting from the assumption that protein folding is an event of quantum transition between molecular conformations,we calculated the folding rate for all two-state proteins in a database and studied their temperature dependencies.The non-Arrhenius temperature relation for 16 proteins,whose experimental data had previously been available,was successfully interpreted by comparing the Arrhenius plot with the first-principle calculation.A statistical formula for the prediction of two-state protein folding rate was proposed based on quantum folding theory.The statistical comparisons of the folding rates for 65 two-state proteins were carried out,and the theoretical vs.experimental correlation coefficient was 0.73.Moreover,the maximum and the minimum folding rates given by the theory were consistent with the experimental results.     

Folding propensities of synthetic peptide fragments covering the entire sequence of phage 434 Cro protein.

The phage 434 Cro protein, the N-terminal domain of its repressor (R1-69) and that of phage lambda (lambda6-85) constitute a group of small, monomeric, single-domain folding units consisting of five helices with striking structural similarity. The intrinsic helix stabilities in lambda6-85 have been correlated to its rapid folding behavior, and a residual hydrophobic cluster found in R1-69 in 7 M urea has been proposed as a folding initiation site. To understand the early events in the folding of 434 Cro, and for comparison with R1-69 and lambda6-85, we examined the conformational behavior of five peptides covering the entire 434 Cro sequence in water, 40% (by volume) TFE/water, and 7 M urea solutions using CD and NMR. Each peptide corresponds to a helix and adjacent residues as identified in the native 434 Cro NMR and crystal structures. All are soluble and monomeric in the solution conditions examined except for the peptide corresponding to the 434 Cro helix 4, which has low water solubility. Helix formation is observed for the 434 Cro helix 1 and helix 2 peptides in water, for all the peptides in 40% TFE and for none in 7 M urea. NMR data indicate that the helix limits in the peptides are similar to those in the native protein helices. The number of side-chain NOEs in water and TFE correlates with the helix content, and essentially none are observed in 7 M urea for any peptide, except that for helix 5, where a hydrophobic cluster may be present. The low intrinsic folding propensities of the five helices could account for the observed stability and folding behavior of 434 Cro and is, at least qualitatively, in accord with the results of the recently described diffusion-collision model incorporating intrinsic helix propensities.     

Diffusion-collision of foldons elucidates the kinetic effects of point mutations and suggests control strategies of the folding process of helical proteins

In this article we use mutation studies as a benchmark for a minimal model of the folding process of helical proteins. The model ascribes a pivotal role to the collisional dynamics of a few crucial residues (foldons) and predicts the folding rates by exploiting information drawn from the protein sequence. We show that our model rationalizes the effects of point mutations on the kinetics of folding. The folding times of two proteins and their mutants are predicted. Stability and location of foldons have a critical role as the determinants of protein folding. This allows us to elucidate two main mechanisms for the kinetic effects of mutations. First, it turns out that the mutations eliciting the most notable effects alter protein stability through stabilization or destabilization of the foldons. Secondly, the folding rate is affected via a modification of the foldon topology by those mutations that lead to the birth or death of foldons. The few mispredicted folding rates of some mutants hint at the limits of the current version of the folding model proposed in the present article. The performance of our folding model declines in case the mutated residues are subject to strong long-range forces. That foldons are the critical targets of mutation studies has notable implications for design strategies and is of particular interest to address the issue of the kinetic regulation of single proteins in the general context of the overall dynamics of the interactome.     

Mechanism of induced folding: Both folding before binding and binding before folding can be realized in staphylococcal nuclease mutants

A considerable number of functional proteins are unstructured under physiological condition. These "intrinsically disordered" proteins exhibit induced folding when they bind their targets. The induced folding comprises two elementary processes: folding and binding. Two mechanisms are possible for the induced folding: either folding before binding or binding before folding. We found that these two mechanisms can be distinguished by the target-concentration dependence of folding kinetics. We also created two types of mutants of staphylococcal nuclease showing the different inhibitor-concentration dependence of induced folding kinetics. One mutant obeys the scheme of binding before folding, while the other the folding before binding. This is the first experimental evidence demonstrating that both mechanisms are realized for a single protein. Binding before folding is possible, when the protein lacks essential nonlocal interaction to stabilize the native conformation. The results cast light on the protein folding mechanism involved in the intrinsically disordered proteins.     

Protein folding: simple models for a complex process

Twenty-eight years after its original publication, the diffusion-collision model has successfully been applied to describe the folding kinetics of two proteins with the same native structure but different sequences (Islam et al., this issue of Structure). The calculations show the relative importance of the primary and tertiary structure on the sequence of events and folding. For both proteins, the model suggests parallel folding pathways, a finding which has wide implications for the interpretations of experiments.     

Minimalist protein model as a diagnostic tool for misfolding and aggregation

We propose a realistic coarse-grained protein model and a technique to "anchor" the model to available experimental data. We apply this procedure to characterize the effect of multiple mutations on the folding mechanism of protein S6. We show that the mutation of a few "gatekeeper" residues triggers significant changes on the folding landscape of S6. These results suggest that gatekeeper residues control the flexibility of critical regions of S6, that in turn regulates the delicate balance between folding and aggregation. Although obtained with a minimalist protein model, these results are fully consistent with experimental evidence and offer a clue to understand the interplay between folding and aggregation in protein S6.     

A comprehensive database of verified experimental data on protein folding kinetics

Insights into protein folding rely increasingly on the synergy between experimental and theoretical approaches. Developing successful computational models requires access to experimental data of sufficient quantity and high quality. We compiled folding rate constants for what initially appeared to be 184 proteins from 15 published collections/web databases. To generate the highest confidence in the dataset, we verified the reported lnk_f value and exact experimental construct and conditions from the original experimental report(s). The resulting comprehensive database of 126 verified entries, ACPro, will serve as a freely accessible resource ( https://www.ats.amherst.edu/protein/ ) for the protein folding community to enable confident testing of predictive models. In addition, we provide a streamlined submission form for researchers to add new folding kinetics results, requiring specification of all the relevant experimental information according to the standards proposed in 2005 by the protein folding consortium organized by Plaxco. As the number and diversity of proteins whose folding kinetics are studied expands, our curated database will enable efficient and confident incorporation of new experimental results into a standardized collection. This database will support a more robust symbiosis between experiment and theory, leading ultimately to more rapid and accurate insights into protein folding, stability, and dynamics.     

Gatekeepers in the ribosomal protein s6: thermodynamics, kinetics, and folding pathways revealed by a minimalist protein model

We investigate the effect of structural gatekeepers on the folding of the ribosomal protein S6. Folding thermodynamics and early refolding kinetics are studied for this system utilizing computer simulations of a minimalist protein model. When gatekeepers are eliminated, the thermodynamic signature of a folding intermediate emerges, and a marked decrease in folding efficiency is observed. We explain the prerequisites that determine the "strength" of a given gatekeeper. The investigated gatekeepers are found to have distinct functions, and to guide the folding and time-dependent packing of non-overlapping secondary structure elements in the protein. Gatekeepers avoid kinetic traps during folding by favoring the formation of "productive topologies" on the way to the native state. The trends in folding rates in the presence/absence of gatekeepers observed for our minimalist model of S6 are in very good agreement with experimental data on this protein.