Protein folding: the free energy surface

Quantitative models and experiments are revealing how the folding free energy surface of a protein is sculpted by sequence and environment. The sometimes conflicting demands of folding, structure and function determine which folding pathways, if any, dominate. Recent advances include experimental estimates of diffusive barrier-crossing times, the observation of ultrafast folders amenable to full-atom simulation, the use of thermodynamic tuning and nonconservative mutations to probe 'hidden' parts of the free energy surface, and a complete microscopic theory of folding.     

Protein folding pathways and kinetics: molecular dynamics simulations of beta-strand motifs

The folding pathways and the kinetic properties for three different types of off-lattice four-strand antiparallel beta-strand protein models interacting via a hybrid Go-type potential have been investigated using discontinuous molecular dynamics simulations. The kinetic study of protein folding was conducted by temperature quenching from a denatured or random coil state to a native state. The progress parameters used in the kinetic study include the squared radius of gyration R(2)(g), the fraction of native contacts within the protein as a whole Q, and between specific strands Q(ab). In the time series of folding, the denatured proteins undergo a conformational change toward the native state. The model proteins exhibit a variety of kinetic folding pathways that include a fast-track folding pathway without passing through an intermediate and multiple pathways with trapping into more than one intermediate. The kinetic folding behavior of the beta-strand proteins strongly depends on the native-state geometry of the model proteins and the size of the bias gap g, an artificial measure of a model protein's preference for its native state.     

Characterization of the nucleation step and folding of a collagen triple-helix peptide

Peptide T1-892 is a triple-helical peptide designed to include two distinct domains: a C-terminal (Gly-Pro-Hyp)(4) sequence, together with an N-terminal 18-residue sequence from the alpha1(I) chain of type I collagen. Folding experiments of T1-892 using CD spectroscopy were carried out at varying concentrations and temperatures, and fitting of kinetic models to the data was used to obtain information about the folding mechanism and to derive rate constants. Proposed models include a heterogeneous population of monomers with respect to cis-trans isomerization and a third-order folding reaction from competent monomer to the triple helix. Fitting results support a nucleation domain composed of all or most of the (Gly-Pro-Hyp)(4) sequence, which must be in trans form before the monomer is competent to initiate triple-helix formation. The folding of competent monomer to a triple helix is best described by an all-or-none third-order reaction. The temperature dependence of the third-order rate constant indicates a negative activation energy and provides information about the thermodynamics of the trimerization step. These CD studies complement NMR studies carried out on the same peptide at high concentrations, illustrating how the rate-limiting folding step is affected by changes in concentration. This sequence preference of repeating Gly-Pro-Hyp units for the initiation of triple-helix formation in peptide T1-892 may be related to features in the triple-helix folding of collagens.     

Roles of beta-turns in protein folding: from peptide models to protein engineering

Reverse turns are a major class of protein secondary structure; they represent sites of chain reversal and thus sites where the globular character of a protein is created. It has been speculated for many years that turns may nucleate the formation of structure in protein folding, as their propensity to occur will favor the approximation of their flanking regions and their general tendency to be hydrophilic will favor their disposition at the solvent-accessible surface. Reverse turns are local features, and it is therefore not surprising that their structural properties have been extensively studied using peptide models. In this article, we review research on peptide models of turns to test the hypothesis that the propensities of turns to form in short peptides will relate to the roles of corresponding sequences in protein folding. Turns with significant stability as isolated entities should actively promote the folding of a protein, and by contrast, turn sequences that merely allow the chain to adopt conformations required for chain reversal are predicted to be passive in the folding mechanism. We discuss results of protein engineering studies of the roles of turn residues in folding mechanisms. Factors that correlate with the importance of turns in folding indeed include their intrinsic stability, as well as their topological context and their participation in hydrophobic networks within the protein's structure.     

Protein energy landscape exploration with structure-based models

Exploring the multi-dimensional energy landscape of a large protein in detail is a computational challenge. Such investigations may include analysis of multiple folding pathways, rate constants for important conformational transitions, locating intermediate states populated during folding, estimating energetic and entropic barriers that separate populated basins, and visualising a high-dimensional surface. The complexity of the landscape can be simplified through coarse-grained structure-based models (SBMs). These widely used coarse-grained representations of proteins provide a minimalist approximation to the free energy landscape, which subsumes the folding behaviour of many single-domain proteins. Here we describe the combination of SBMs with discrete path sampling (DPS), and show how this approach can provide details of the landscape and folding pathways. Combining SBMs and DPS provides an efficient framework for sampling the protein free energy landscape and for calculating various kinetic and thermodynamic quantities.     

An all-atom structure-based potential for proteins: bridging minimal models with all-atom empirical forcefields

Protein dynamics take place on many time and length scales. Coarse-grained structure-based (Go) models utilize the funneled energy landscape theory of protein folding to provide an understanding of both long time and long length scale dynamics. All-atom empirical forcefields with explicit solvent can elucidate our understanding of short time dynamics with high energetic and structural resolution. Thus, structure-based models with atomic details included can be used to bridge our understanding between these two approaches. We report on the robustness of folding mechanisms in one such all-atom model. Results for the B domain of Protein A, the SH3 domain of C-Src Kinase, and Chymotrypsin Inhibitor 2 are reported. The interplay between side chain packing and backbone folding is explored. We also compare this model to a C(alpha) structure-based model and an all-atom empirical forcefield. Key findings include: (1) backbone collapse is accompanied by partial side chain packing in a cooperative transition and residual side chain packing occurs gradually with decreasing temperature, (2) folding mechanisms are robust to variations of the energetic parameters, (3) protein folding free-energy barriers can be manipulated through parametric modifications, (4) the global folding mechanisms in a C(alpha) model and the all-atom model agree, although differences can be attributed to energetic heterogeneity in the all-atom model, and (5) proline residues have significant effects on folding mechanisms, independent of isomerization effects. Because this structure-based model has atomic resolution, this work lays the foundation for future studies to probe the contributions of specific energetic factors on protein folding and function.     

Characterization of Folding Cores in the Cyclophilin A-Cyclosporin A Complex

Determining the folding core of a protein yields information about its folding process and dynamics. The experimental procedures for identifying the amino acids that make up the folding core include hydrogen-deuterium exchange and Φ-value analysis and can be expensive and time consuming. Because of this, there is a desire to improve upon existing methods for determining protein folding cores theoretically. We have obtained HDX data for the complex of cyclophilin A with the immunosuppressant cyclosporin A. We compare these data, as well as literature values for uncomplexed cyclophilin A, to theoretical predictions using a combination of rigidity analysis and coarse-grained simulations of protein motion. We find that in this case, the most specific prediction of folding cores comes from a combined approach that models the rigidity of the protein using the first software suite and the dynamics of the protein using the froda tool.     

Experimental study of the protein folding landscape: unfolding reactions in cytochrome c.

Hydrogen exchange results for cytochrome c have been interpreted in terms of transient hydrogen bond-breaking reactions that include large unfolding reactions and small fluctuational distortions. The differential sensitivity of these opening reactions to denaturant, temperature, and protein stability makes it possible to distinguish the different opening reactions and to characterize their structural and thermodynamic parameters. The partially unfolded forms (PUFs) observed are few and discrete, evidently because they are produced by the reversible unfolding of the protein's several intrinsically cooperative secondary structural elements. The PUFs are robust, evidently because the structural elements do not change over a wide range of conditions. The discrete nature of the PUFs and their small number is as expected for classical folding intermediates but not for theoretically derived folding models apparently because the simplified non-protein models usually analyzed in theoretical studies encompass only a single cooperative unit rather than multiple separable units.     

Coarse-grained models of protein folding: toy models or predictive tools?

Coarse-grained models are emerging as a practical alternative to all-atom simulations for the characterization of protein folding mechanisms over long time scales. While a decade ago minimalist toy models were mainly designed to test general hypotheses on the principles regulating protein folding, the latest coarse-grained models are increasingly realistic and can be used to characterize quantitatively the detailed folding mechanism of specific proteins. The ability of such models to reproduce the essential features of folding dynamics suggests that each single atomic degree of freedom is not by itself particularly relevant to folding and supports a statistical mechanical approach to characterize folding transitions. When combined with more refined models and with experimental studies, the systematic investigation of protein systems and complexes using coarse-grained models can advance our theoretical understanding of the actual organizing principles that emerge from the complex network of interactions among protein atomic constituents.     

Structural details,pathways, and energetics of unfolding apomyoglobin

Protein folding is often difficult to characterize experimentally because of the transience of intermediate states, and the complexity of the protein-solvent system. Atomistic simulations, which could provide more detailed information, have had to employ highly simplified models or high temperatures, to cope with the long time scales of unfolding; direct simulation of folding is even more problematic. We report a fully atomistic simulation of the acid-induced unfolding of apomyoglobin in which the protonation of acidic side-chains to simulate low pH is sufficient to induce unfolding at room temperature with no added biasing forces or other unusual conditions; and the trajectory is validated by comparison to experimental characterization of intermediate states. Novel insights provided by their analysis include: characterization of a dry swollen globule state forming a barrier to initial unfolding or final folding; observation of cooperativity in secondary and tertiary structure formation and its explanation in terms of dielectric environments; and structural details of the intermediate and the completely unfolded states. These insights involve time scales and levels of structural detail that are presently beyond the range of experiment, but come within reach through the simulation methods described here. An implicit solvation model is used to analyze the energetics of protein folding at various pH and ionic strength values, and a reasonable estimate of folding free energy is obtained. Electrostatic interactions are found to disfavor folding.     

Kinetic barriers and the role of topology in protein and RNA folding

This review compares the folding behavior of proteins and RNAs. Topics covered include the role of topology in the determination of folding rates, major folding events including collapse, properties of denatured states, pathway heterogeneity, and the influence of the mode of initiation on the folding pathway.     

Diverse pathways of oxidative folding of disulfide proteins: underlying causes and folding models

The pathway of oxidative folding of disulfide proteins exhibits a high degree of diversity, which is manifested mainly by distinct structural heterogeneity and diverse rearrangement pathways of folding intermediates. During the past two decades, the scope of this diversity has widened through studies of more than 30 disulfide-rich proteins by various laboratories. A more comprehensive landscape of the mechanism of protein oxidative folding has emerged. This review will cover three themes. (1) Elaboration of the scope of diversity of disulfide folding pathways, including the two opposite extreme models, represented by bovine pancreatic trypsin inhibitor (BPTI) and hirudin. (2) Demonstration of experimental evidence accounting for the underlying mechanism of the folding diversity. (3) Discussion of the convergence between the extreme models of oxidative folding and models of conventional conformational folding (framework model, hydrophobic collapse model).     

Taming the complexity of protein folding

Protein folding is an important problem in structural biology with significant medical implications, particularly for misfolding disorders like Alzheimer's disease. Solving the folding problem will ultimately require a combination of theory and experiment, with theoretical models providing a comprehensive view of folding and experiments grounding these models in reality. Here we review progress towards this goal over the past decade, with an emphasis on recent theoretical advances that are empowering chemically detailed models of folding and the new results these technologies are providing. In particular, we discuss new insights made possible by Markov state models (MSMs), including the role of non-native contacts and the hub-like character of protein folded states.     

Recent advances in the development and application of implicit solvent models in biomolecule simulations

Advances have recently been made in the development of implicit solvent methodologies and their application to the modeling of biomolecules, particularly with regard to generalized Born approaches, dielectric screening function formulations and models based on solvent-accessible surface areas. Interesting new developments include more refined non-polar solvation energy estimators, and implicit methods for modeling low-dielectric and heterogeneous environments such as membrane systems. These have been successfully applied to molecular dynamics simulations, the scoring of protein conformations, and the calculation of binding affinities and folding free energy landscapes.     

Computational methods for generating models of denatured and partially folded proteins

Partially folded and denatured proteins can give important insights into protein folding, misfolding, and aggregation. Such non-native states of proteins are however very difficult to characterise in detail as they are dynamic, heterogeneous systems comprising of ensembles of interconverting conformers. This article describes methods that produce models for non-native proteins in atomic detail. A variety of molecular dynamics based protocols are discussed together with some recent procedures that include restraints from experimental data. These models provide an important framework for interpreting experimental data from studies of non-native states using nuclear magnetic resonance spectroscopy, fluorescence, circular dichroism, and small angle scattering techniques.     

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.     

Desolvation Barrier Effects Are a Likely Contributor to the Remarkable Diversity in the Folding Rates of Small Proteins

The variation in folding rate among single-domain natural proteins is tremendous, but common models with explicit representations of the protein chain are either demonstrably insufficient or unclear as to their capability for rationalizing the experimental diversity in folding rates. In view of the critical role of water exclusion in cooperative folding, we apply native-centric, coarse-grained chain modeling with elementary desolvation barriers to investigate solvation effects on folding rates. For a set of 13 proteins, folding rates simulated with desolvation barriers cover ∼ 4.6 orders of magnitude, spanning a range essentially identical to that observed experimentally. In contrast, folding rates simulated without desolvation barriers cover only ∼ 2.2 orders of magnitude. Following a Hammond-like trend, the folding transition-state ensemble (TSE) of a protein model with desolvation barriers generally has a higher average number of native contacts and is structurally more specific, that is, less diffused, than the TSE of the corresponding model without desolvation barriers. Folding is generally significantly slower in models with desolvation barriers because of their higher overall macroscopic folding barriers as well as slower conformational diffusion speeds in the TSE that are ≈ 1/50 times those in models without desolvation barriers. Nonetheless, the average root-mean-square deviation between the TSE and the native conformation is often similar in the two modeling approaches, a finding suggestive of a more robust structural requirement for the folding rate-limiting step. The increased folding rate diversity in models with desolvation barriers originates from the tendency of these microscopic barriers to cause more heightening of the overall macroscopic folding free-energy barriers for proteins with more nonlocal native contacts than those with fewer such contacts. Thus, the enhancement of folding cooperativity by solvation effects is seen as positively correlated with a protein's native topological complexity.