Discerning the Structure and Energy of Multiple Transition States in Protein Folding using ψ-Analysis

AlphaFold2 knows some protein folding principles

AlphaFold2 (AF2) has revolutionized protein structure prediction. However, a common confusion lies in equating the protein structure prediction problem with the protein folding problem. The former provides a static structure, while the latter explains the dynamic folding pathway to that structure. We challenge the current status quo and advocate that AF2 has indeed learned some protein folding principles, despite being designed for structure prediction. AF2's high-dimensional parameters encode an imperfect biophysical scoring function. Typically, AF2 uses multiple sequence alignments (MSAs) to guide the search within a narrow region of its learned surface. In our study, we operate AF2 without MSAs or initial templates, forcing it to sample its entire energy landscape - more akin to an ab initio approach. Among over 7,000 proteins, a fraction fold using sequence alone, highlighting the smoothness of AF2's learned energy surface. Additionally, by combining recycling and iterative predictions, we discover multiple AF2 intermediate structures in good agreement with known experimental data. AF2 appears to follow a "local first, global later" folding mechanism. For designed proteins with more optimized local interactions, AF2's energy landscape is too smooth to detect intermediates even when it should. Our current work sheds new light on what AF2 has learned and opens exciting possibilities to advance our understanding of protein folding and for experimental discovery of folding intermediates.

Heterogeneity in Protein Folding and Unfolding Reactions

Proteins have dynamic structures that undergo chain motions on time scales spanning from picoseconds to seconds. Resolving the resultant conformational heterogeneity is essential for gaining accurate insight into fundamental mechanistic aspects of the protein folding reaction. The use of high-resolution structural probes, sensitive to population distributions, has begun to enable the resolution of site-specific conformational heterogeneity at different stages of the folding reaction. Different states populated during protein folding, including the unfolded state, collapsed intermediate states, and even the native state, are found to possess significant conformational heterogeneity. Heterogeneity in protein folding and unfolding reactions originates from the reduced cooperativity of various kinds of physicochemical interactions between various structural elements of a protein, and between a protein and solvent. Heterogeneity may arise because of functional or evolutionary constraints. Conformational substates within the unfolded state and the collapsed intermediates that exchange at rates slower than the subsequent folding steps give rise to heterogeneity on the protein folding pathways. Multiple folding pathways are likely to represent distinct sequences of structure formation. Insight into the nature of the energy barriers separating different conformational states populated during (un)folding can also be obtained by resolving heterogeneity.

Engineered Metal-Binding Sites to Probe Protein Folding Transition States: Psi Analysis

The formation of the transition state ensemble (TSE) represents the rate-limiting step in protein folding. The TSE is the least populated state on the pathway, and its characterization remains a challenge. Properties of the TSE can be inferred from the effects on folding and unfolding rates for various perturbations. A difficulty remains on how to translate these kinetic effects to structural properties of the TSE. Several factors can obscure the translation of point mutations in the frequently used method, "mutational Phi analysis." We take a complementary approach in "Psi analysis," employing rationally inserted metal binding sites designed to probe pairwise contacts in the TSE. These contacts can be confidently identified and used to construct structural models of the TSE. The method has been applied to multiple proteins and consistently produces a considerably more structured and native-like TSE than Phi analysis. This difference has significant implications to our understanding of protein folding mechanisms. Here we describe the application of the method and discuss how it can be used to study other conformational transitions such as binding.

Rational Design of Protein-Specific Folding Modifiers

Protein-folding can go wrong in vivo and in vitro, with significant consequences for the living organism and the pharmaceutical industry, respectively. Here we propose a design principle for small-peptide-based protein-specific folding modifiers. The principle is based on constructing a "xenonucleus", which is a prefolded peptide that mimics the folding nucleus of a protein. Using stopped-flow kinetics, NMR spectroscopy, Förster resonance energy transfer, single-molecule force measurements, and molecular dynamics simulations, we demonstrate that a xenonucleus can make the refolding of ubiquitin faster by 33 ± 5%, while variants of the same peptide have little or no effect. Our approach provides a novel method for constructing specific, genetically encodable folding catalysts for suitable proteins that have a well-defined contiguous folding nucleus.

Energy Landscape of Ubiquitin Is Weakly Multidimensional

Single molecule pulling experiments report time-dependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to one-dimensional analytical models of the energy landscape, we can extract the hopping rates between the folded and unfolded states in two-state folders as well as the height and the location of the transition state (TS). Although this approach is remarkably insightful, there are cases for which the energy landscape is multidimensional (catch bonds being the most prominent). To assess if the unfolding energy landscape in small single domain proteins could be one-dimensional, we simulated force-induced unfolding of ubiquitin (Ub) using the coarse-grained self-organized polymer-side chain (SOP-SC) model. Brownian dynamics simulations using the SOP-SC model reveal that the Ub energy landscape is weakly multidimensional (WMD), governed predominantly by a single barrier. The unfolding pathway is confined to a narrow reaction pathway that could be described as diffusion in a quasi-1D X-dependent free energy profile. However, a granular analysis using the P_fold analysis, which does not assume any form for the reaction coordinate, shows that X alone does not account for the height and, more importantly, the location of the TS. The f-dependent TS location moves toward the folded state as f increases, in accord with the Hammond postulate. Our study shows that, in addition to analyzing the f-dependent hopping rates, the transition state ensemble must also be determined without resorting to X as a reaction coordinate to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD.

Mapping Distinct Sequences of Structure Formation Differentiating Multiple Folding Pathways of a Small Protein

To determine experimentally how the multiple folding pathways of a protein differ, in the order in which the structural parts are assembled, has been a long-standing challenge. To resolve whether structure formation during folding can progress in multiple ways, the complex folding landscape of monellin has been characterized, structurally and temporally, using the multisite time-resolved FRET methodology. After an initial heterogeneous polypeptide chain collapse, structure formation proceeds on parallel pathways. Kinetic analysis of the population evolution data across various protein segments provides a clear structural distinction between the parallel pathways. The analysis leads to a phenomenological model that describes how and when discrete segments acquire structure independently of each other in different subensembles of protein molecules. When averaged over all molecules, structure formation is seen to progress as α-helix formation, followed by core consolidation, then β-sheet formation, and last end-to-end distance compaction. Parts of the protein that are closer in the primary sequence acquire structure before parts separated by longer sequence.

Water as a Good Solvent for Unfolded Proteins: Folding and Collapse are Fundamentally Different

The argument that the hydrophobic effect is the primary effect driving the folding of globular proteins is nearly universally accepted (including by the authors). But does this view also imply that water is a "poor" solvent for the unfolded states of these same proteins? Here we argue that the answer is "no," that is, folding to a well-packed, extensively hydrogen-bonded native structure differs fundamentally from the nonspecific chain collapse that defines a poor solvent. Thus, the observation that a protein folds in water does not necessitate that water is a poor solvent for its unfolded state. Indeed, chain-solvent interactions that are marginally more favorable than nonspecific intrachain interactions are beneficial to protein function because they destabilize deleterious misfolded conformations and inter-chain interactions.

Extracting the Hidden Distributions Underlying the Mean Transition State Structures in Protein Folding

The inherent conflict between noncovalent interactions and the large conformational entropy of the polypeptide chain forces folding reactions and their mechanisms to deviate significantly from chemical reactions. Accordingly, measures of structure in the transition state ensemble (TSE) are strongly influenced by the underlying distributions of microscopic folding pathways that are challenging to discern experimentally. Here, we present a detailed analysis of 150,000 folding transition paths of five proteins at three different thermodynamic conditions from an experimentally consistent statistical mechanical model. We find that the underlying TSE structural distributions are rarely unimodal, and the average experimental measures arise from complex underlying distributions. Unfolding pathways also exhibit subtle differences from folding counterparts due to a combination of Hammond behavior and native-state movements. Local interactions and topological complexity, to a lesser extent, are found to determine pathway heterogeneity, underscoring the importance of the balance between local and nonlocal energetics in protein folding.

Structure-Based Prediction of Protein-Folding Transition Paths

We propose a general theory to describe the distribution of protein-folding transition paths. We show that transition paths follow a predictable sequence of high-free-energy transient states that are separated by free-energy barriers. Each transient state corresponds to the assembly of one or more discrete, cooperative units, which are determined directly from the native structure. We show that the transition state on a folding pathway is reached when a small number of critical contacts are formed between a specific set of substructures, after which folding proceeds downhill in free energy. This approach suggests a natural resolution for distinguishing parallel folding pathways and provides a simple means to predict the rate-limiting step in a folding reaction. Our theory identifies a common folding mechanism for proteins with diverse native structures and establishes general principles for the self-assembly of polymers with specific interactions.

Cooperative folding near the downhill limit determined with amino acid resolution by hydrogen exchange

The relationship between folding cooperativity and downhill, or barrier-free, folding of proteins under highly stabilizing conditions remains an unresolved topic, especially for proteins such as λ-repressor that fold on the microsecond timescale. Under aqueous conditions where downhill folding is most likely to occur, we measure the stability of multiple H bonds, using hydrogen exchange (HX) in a λYA variant that is suggested to be an incipient downhill folder having an extrapolated folding rate constant of 2 × 10(5) s(-1) and a stability of 7.4 kcal·mol(-1) at 298 K. At least one H bond on each of the three largest helices (α1, α3, and α4) breaks during a common unfolding event that reflects global denaturation. The use of HX enables us to both examine folding under highly stabilizing, native-like conditions and probe the pretransition state region for stable species without the need to initiate the folding reaction. The equivalence of the stability determined at zero and high denaturant indicates that any residual denatured state structure minimally affects the stability even under native conditions. Using our ψ analysis method along with mutational ϕ analysis, we find that the three aforementioned helices are all present in the folding transition state. Hence, the free energy surface has a sufficiently high barrier separating the denatured and native states that folding appears cooperative even under extremely stable and fast folding conditions.

Even with nonnative interactions, the updated folding transition states of the homologs Proteins G & L are extensive and similar

Experimental and computational folding studies of Proteins L & G and NuG2 typically find that sequence differences determine which of the two hairpins is formed in the transition state ensemble (TSE). However, our recent work on Protein L finds that its TSE contains both hairpins, compelling a reassessment of the influence of sequence on the folding behavior of the other two homologs. We characterize the TSEs for Protein G and NuG2b, a triple mutant of NuG2, using ψ analysis, a method for identifying contacts in the TSE. All three homologs are found to share a common and near-native TSE topology with interactions between all four strands. However, the helical content varies in the TSE, being largely absent in Proteins G & L but partially present in NuG2b. The variability likely arises from competing propensities for the formation of nonnative β turns in the naturally occurring proteins, as observed in our TerItFix folding algorithm. All-atom folding simulations of NuG2b recapitulate the observed TSEs with four strands for 5 of 27 transition paths [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517-520]. Our data support the view that homologous proteins have similar folding mechanisms, even when nonnative interactions are present in the transition state. These findings emphasize the ongoing challenge of accurately characterizing and predicting TSEs, even for relatively simple proteins.

Evidence for the sequential folding mechanism in RNase H from an ensemble-based model

The number of distinct protein folding pathways starting from an unfolded ensemble, and hence, the folding mechanism is an intricate function of protein size, sequence complexity, and stability conditions. This has traditionally been a contentious issue particularly because of the ensemble nature of conventional experiments that can mask the complexity of the underlying folding landscape. Recent hydrogen-exchange experiments combined with mass spectrometry (HX-MS) reveal that the folding of RNase H proceeds in a hierarchical fashion with distinct intermediates and following a single discrete path. In our current work, we provide computational evidence for this unique folding mechanism by employing a structure-based statistical mechanical model. Upon calibrating the energetic terms of the model with equilibrium measurements, we predict multiple intermediate states in the folding of RNase H that closely resemble experimental observations. Remarkably, a simplified landscape representation adequately captures the folding complexity and predicts the possibility of a well-defined sequence of folding events. We supplement the statistical model study with both explicit solvent molecular simulations of the helical units and electrostatic calculations to provide structural and energetic insights into the early and late stages of RNase H folding that hint at the frustrated nature of its folding landscape.

Microsecond molecular dynamics simulation of guanidinium chloride induced unfolding of ubiquitin

All atom molecular dynamics simulations have been used to explore the atomic detail mechanism of guanidinium induced unfolding of the protein ubiquitin.

Simplified protein models: predicting folding pathways and structure using amino acid sequences

We demonstrate the ability of simultaneously determining a protein's folding pathway and structure using a properly formulated model without prior knowledge of the native structure. Our model employs a natural coordinate system for describing proteins and a search strategy inspired by the observation that real proteins fold in a sequential fashion by incrementally stabilizing nativelike substructures or "foldons." Comparable folding pathways and structures are obtained for the twelve proteins recently studied using atomistic molecular dynamics simulations [K. Lindorff-Larsen, S. Piana, R. O. Dror, D. E. Shaw, Science 334, 517 (2011)], with our calculations running several orders of magnitude faster. We find that nativelike propensities in the unfolded state do not necessarily determine the order of structure formation, a departure from a major conclusion of the molecular dynamics study. Instead, our results support a more expansive view wherein intrinsic local structural propensities may be enhanced or overridden in the folding process by environmental context. The success of our search strategy validates it as an expedient mechanism for folding both in silico and in vivo.

The loop hypothesis: contribution of early formed specific non-local interactions to the determination of protein folding pathways

The extremely fast and efficient folding transition (in seconds) of globular proteins led to the search for some unifying principles embedded in the physics of the folding polypeptides. Most of the proposed mechanisms highlight the role of local interactions that stabilize secondary structure elements or a folding nucleus as the starting point of the folding pathways, i.e., a "bottom-up" mechanism. Non-local interactions were assumed either to stabilize the nucleus or lead to the later steps of coalescence of the secondary structure elements. An alternative mechanism was proposed, an "up-down" mechanism in which it was assumed that folding starts with the formation of very few non-local interactions which form closed long loops at the initiation of folding. The possible biological advantage of this mechanism, the "loop hypothesis", is that the hydrophobic collapse is associated with ordered compactization which reduces the chance for degradation and misfolding. In the present review the experiments, simulations and theoretical consideration that either directly or indirectly support this mechanism are summarized. It is argued that experiments monitoring the time-dependent development of the formation of specifically targeted early-formed sub-domain structural elements, either long loops or secondary structure elements, are necessary. This can be achieved by the time-resolved FRET-based "double kinetics" method in combination with mutational studies. Yet, attempts to improve the time resolution of the folding initiation should be extended down to the sub-microsecond time regime in order to design experiments that would resolve the classes of proteins which first fold by local or non-local interactions.

Atomic-level description of ubiquitin folding

Equilibrium molecular dynamics simulations, in which proteins spontaneously and repeatedly fold and unfold, have recently been used to help elucidate the mechanistic principles that underlie the folding of fast-folding proteins. The extent to which the conclusions drawn from the analysis of such proteins, which fold on the microsecond timescale, apply to the millisecond or slower folding of naturally occurring proteins is, however, unclear. As a first attempt to address this outstanding issue, we examine here the folding of ubiquitin, a 76-residue-long protein found in all eukaryotes that is known experimentally to fold on a millisecond timescale. Ubiquitin folding has been the subject of many experimental studies, but its slow folding rate has made it difficult to observe and characterize the folding process through all-atom molecular dynamics simulations. Here we determine the mechanism, thermodynamics, and kinetics of ubiquitin folding through equilibrium atomistic simulations. The picture emerging from the simulations is in agreement with a view of ubiquitin folding suggested from previous experiments. Our findings related to the folding of ubiquitin are also consistent, for the most part, with the folding principles derived from the simulation of fast-folding proteins, suggesting that these principles may be applicable to a wider range of proteins.

Analyses of the effects of all ubiquitin point mutants on yeast growth rate

The amino acid sequence of a protein governs its function. We used bulk competition and focused deep sequencing to investigate the effects of all ubiquitin point mutants on yeast growth rate. Many aspects of ubiquitin function have been carefully studied, which enabled interpretation of our growth analyses in light of a rich structural, biophysical and biochemical knowledge base. In one highly sensitive cluster on the surface of ubiquitin, almost every amino acid substitution caused growth defects. In contrast, the opposite face tolerated virtually all possible substitutions. Surface locations between these two faces exhibited intermediate mutational tolerance. The sensitive face corresponds to the known interface for many binding partners. Across all surface positions, we observe a strong correlation between burial at structurally characterized interfaces and the number of amino acid substitutions compatible with robust growth. This result indicates that binding is a dominant determinant of ubiquitin function. In the solvent-inaccessible core of ubiquitin, all positions tolerated a limited number of substitutions, with hydrophobic amino acids especially interchangeable. Some mutations null for yeast growth were previously shown to populate folded conformations indicating that, for these mutants, subtle changes to conformation caused functional defects. The most sensitive region to mutation within the core was located near the C-terminus that is a focal binding site for many critical binding partners. These results indicate that core mutations may frequently cause functional defects through subtle disturbances to structure or dynamics.

De novo prediction of protein folding pathways and structure using the principle of sequential stabilization

Motivated by the relationship between the folding mechanism and the native structure, we develop a unified approach for predicting folding pathways and tertiary structure using only the primary sequence as input. Simulations begin from a realistic unfolded state devoid of secondary structure and use a chain representation lacking explicit side chains, rendering the simulations many orders of magnitude faster than molecular dynamics simulations. The multiple round nature of the algorithm mimics the authentic folding process and tests the effectiveness of sequential stabilization (SS) as a search strategy wherein 2° structural elements add onto existing structures in a process of progressive learning and stabilization of structure found in prior rounds of folding. Because no a priori knowledge is used, we can identify kinetically significant non-native interactions and intermediates, sometimes generated by only two mutations, while the evolution of contact matrices is often consistent with experiments. Moreover, structure prediction improves substantially by incorporating information from prior rounds. The success of our simple, homology-free approach affirms the validity of our description of the primary determinants of folding pathways and structure, and the effectiveness of SS as a search strategy.

Visualizing transient protein-folding intermediates by tryptophan-scanning mutagenesis

To understand how proteins fold, assemble and function, it is necessary to characterize the structure and dynamics of each state they adopt during their lifetime. Experimental characterization of the transient states of proteins remains a major challenge because high-resolution structural techniques, including NMR and X-ray crystallography, cannot be directly applied to study short-lived protein states. To circumvent this limitation, we show that transient states during protein folding can be characterized by measuring the fluorescence of tryptophan residues, introduced at many solvent-exposed positions to determine whether each position is native-like, denatured-like or non-native-like in the intermediate state. We use this approach to characterize a late-folding-intermediate state of the small globular mammalian protein ubiquitin, and we show the presence of productive non-native interactions that suggest a 'flycatcher' mechanism of concerted binding and folding.

A "Link-Psi" strategy using crosslinking indicates that the folding transition state of ubiquitin is not very malleable

Using a combined crosslinking-ψ analysis strategy, we examine whether the structural content of the transition state of ubiquitin can be altered. A synthetic dichloroacetone crosslink is first introduced across two β strands. Whether the structural content in the transition state ensemble has shifted towards the region containing the crosslink is probed by remeasuring the ψ value at another region (ψ identifies the degree to which an inserted bi-Histidine metal ion binding site is formed in the transition state). For sites around the periphery of the obligate transition state nucleus, we find that the resulting changes in ψ values are near or at our detection limit, thereby indicating that the structural content of the transition state has not measurably changed upon crosslinking. This work demonstrates the utility of the simultaneous application of crosslinking and ψ-analysis for examining potential transition state heterogeneity in globular proteins.

The folding transition state of protein L is extensive with nonnative interactions (and not small and polarized)

Progress in understanding protein folding relies heavily upon an interplay between experiment and theory. In particular, readily interpretable experimental data that can be meaningfully compared to simulations are required. According to standard mutational ϕ analysis, the transition state for Protein L contains only a single hairpin. However, we demonstrate here using ψ analysis with engineered metal ion binding sites that the transition state is extensive, containing the entire four-stranded β sheet. Underreporting of the structural content of the transition state by ϕ analysis also occurs for acyl phosphatase [Pandit, A. D., Jha, A., Freed, K. F. & Sosnick, T. R., (2006). Small proteins fold through transition states with native-like topologies. J. Mol. Biol.361, 755-770], ubiquitin [Sosnick, T. R., Dothager, R. S. & Krantz, B. A., (2004). Differences in the folding transition state of ubiquitin indicated by ϕ and ψ analyses. Proc. Natl Acad. Sci. USA 101, 17377-17382] and BdpA [Baxa, M., Freed, K. F. & Sosnick, T. R., (2008). Quantifying the structural requirements of the folding transition state of protein A and other systems. J. Mol. Biol.381, 1362-1381]. The carboxy-terminal hairpin in the transition state of Protein L is found to be nonnative, a significant result that agrees with our Protein Data Bank-based backbone sampling and all-atom simulations. The nonnative character partially explains the failure of accepted experimental and native-centric computational approaches to adequately describe the transition state. Hence, caution is required even when an apparent agreement exists between experiment and theory, thus highlighting the importance of having alternative methods for characterizing transition states.

Overview of protein folding mechanisms: experimental and theoretical approaches to probing energy landscapes

We present an overview of the current experimental and theoretical approaches to studying protein folding mechanisms, set against current models of the folding energy landscape. We describe how stability and folding kinetics can be determined experimentally and how this data can be interpreted in terms of the characteristic features of various models from the simplest two-state pathway to a multi-state mechanism. We summarize the pros and cons of a range of spectroscopic methods for measuring folding rates and present a theoretical framework, coupled with protein engineering approaches, for elucidating folding mechanisms and structural features of folding transition states. A series of case studies are used to show how experimental kinetic data can be interpreted in the context of non-native interactions, populated intermediates, parallel folding pathways, and sequential transition states. We also show how computational methods now allow transient species of high energy, such as folding transition states, to be modeled on the basis of experimental Φ-value analysis derived from the effects of point mutations on folding kinetics.

Modeling large regions in proteins: applications to loops, termini, and folding

Template-based methods for predicting protein structure provide models for a significant portion of the protein but often contain insertions or chain ends (InsEnds) of indeterminate conformation. The local structure prediction "problem" entails modeling the InsEnds onto the rest of the protein. A well-known limit involves predicting loops of ≤12 residues in crystal structures. However, InsEnds may contain as many as ~50 amino acids, and the template-based model of the protein itself may be imperfect. To address these challenges, we present a free modeling method for predicting the local structure of loops and large InsEnds in both crystal structures and template-based models. The approach uses single amino acid torsional angle "pivot" moves of the protein backbone with a C(β) level representation. Nevertheless, our accuracy for loops is comparable to existing methods. We also apply a more stringent test, the blind structure prediction and refinement categories of the CASP9 tournament, where we improve the quality of several homology based models by modeling InsEnds as long as 45 amino acids, sizes generally inaccessible to existing loop prediction methods. Our approach ranks as one of the best in the CASP9 refinement category that involves improving template-based models so that they can function as molecular replacement models to solve the phase problem for crystallographic structure determination.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

A comprehensive multidimensional-embedded, one-dimensional reaction coordinate for protein unfolding/folding

The goal of the Dynameomics project is to perform, store, and analyze molecular dynamics simulations of representative proteins, of all known globular folds, in their native state and along their unfolding pathways. To analyze unfolding simulations, the location of the protein along the unfolding reaction coordinate (RXN) must be determined. Properties such as the fraction of native contacts and radius of gyration are often used; however, there is an issue regarding degeneracy with these properties, as native and nonnative species can overlap. Here, we used 15 physical properties of the protein to construct a multidimensional-embedded, one-dimensional RXN coordinate that faithfully captures the complex nature of unfolding. The unfolding RXN coordinates for 188 proteins (1534 simulations and 22.9 mus in explicit water) were calculated. Native, transition, intermediate, and denatured states were readily identified with the use of this RXN coordinate. A global native ensemble based on the native-state properties of the 188 proteins was created. This ensemble was shown to be effective for calculating RXN coordinates for folds outside the initial 188 targets. These RXN coordinates enable, high-throughput assignment of conformational states, which represents an important step in comparing protein properties across fold space as well as characterizing the unfolding of individual proteins.

Protein structure prediction enhanced with evolutionary diversity: SPEED

For naturally occurring proteins, similar sequence implies similar structure. Consequently, multiple sequence alignments (MSAs) often are used in template-based modeling of protein structure and have been incorporated into fragment-based assembly methods. Our previous homology-free structure prediction study introduced an algorithm that mimics the folding pathway by coupling the formation of secondary and tertiary structure. Moves in the Monte Carlo procedure involve only a change in a single pair of phi,psi backbone dihedral angles that are obtained from a Protein Data Bank-based distribution appropriate for each amino acid, conditional on the type and conformation of the flanking residues. We improve this method by using MSAs to enrich the sampling distribution, but in a manner that does not require structural knowledge of any protein sequence (i.e., not homologous fragment insertion). In combination with other tools, including clustering and refinement, the accuracies of the predicted secondary and tertiary structures are substantially improved and a global and position-resolved measure of confidence is introduced for the accuracy of the predictions. Performance of the method in the Critical Assessment of Structure Prediction (CASP8) is discussed.

Kinetics and reaction coordinates of the reassembly of protein fragments via forward flux sampling

We studied the mechanism of the reassembly and folding process of two fragments of a split lattice protein by using forward flux sampling (FFS). Our results confirmed previous thermodynamics and kinetics analyses that suggested that the disruption of the critical core (of an unsplit protein that folds by a nucleation mechanism) plays a key role in the reassembly mechanism of the split system. For several split systems derived from a parent 48-mer model, we estimated the reaction coordinates in terms of collective variables by using the FFS least-square estimation method and found that the reassembly transition is best described by a combination of the total number of native contacts, the number of interchain native contacts, and the total conformational energy of the split system. We also analyzed the transition path ensemble obtained from FFS simulations using the estimated reaction coordinates as order parameters to identify the microscopic features that differentiate the reassembly of the different split systems studied. We found that in the fastest folding split system, a balanced distribution of the original-core amino acids (of the unsplit system) between protein fragments propitiates interchain interactions at early stages of the folding process. Only this system exhibits a different reassembly mechanism from that of the unsplit protein, involving the formation of a different folding nucleus. In the slowest folding system, the concentration of the folding nucleus in one fragment causes its early prefolding, whereas the second fragment tends to remain as a detached random coil. We also show that the reassembly rate can be either increased or decreased by tuning interchain cooperativeness via the introduction of a single point mutation that either strengthens or weakens one of the native interchain contacts (prevalent in the transition state ensemble).

Protein vivisection reveals elusive intermediates in folding

Although most folding intermediates escape detection, their characterization is crucial to the elucidation of folding mechanisms. Here, we outline a powerful strategy to populate partially unfolded intermediates: A buried aliphatic residue is substituted with a charged residue (e.g., Leu-->Glu(-)) to destabilize and unfold a specific region of the protein. We applied this strategy to ubiquitin, reversibly trapping a folding intermediate in which the beta5-strand is unfolded. The intermediate refolds to a native-like structure upon charge neutralization under mildly acidic conditions. Characterization of the trapped intermediate using NMR and hydrogen exchange methods identifies a second folding intermediate and reveals the order and free energies of the two major folding events on the native side of the rate-limiting step. This general strategy may be combined with other methods and have broad applications in the study of protein folding and other reactions that require trapping of high-energy states.

Metal binding kinetics of bi-histidine sites used in psi analysis: evidence of high-energy protein folding intermediates

The zinc-specific fluorophore, Zinpyr-1, is used in competition assays to determine the kinetic and thermodynamic parameters of Zn2+ binding to engineered bi-histidine sites located in ubiquitin and the B domain of protein A (BdpA). These binding sites are used in psi analysis studies to investigate structure formation in the folding transition state identified by the change in folding rate upon addition of metal ions. For ubiquitin, the on-rate binding constant and binding affinity for a site located along an alpha-helix are measured to be approximately 10(7) M-1 s-1 and 3 microM, respectively. For a site located across two beta-strands, the metal binding affinity was too weak to measure in the dye competition assays (Kd > 55 microM). The equilibrium-determined values for the Zn2+-induced stabilization of ubiquitin and BdpA match the values derived from changes in the global folding and unfolding rates. Therefore, metal ion binding is in fast equilibrium during the transit over the free energy barrier. Accordingly, the folding rate must be slower than the product of the fractional population of a high-energy intermediate with the metal site formed and the metal binding on-rate constant. The known folding rate of 20 s-1 at 1.5 M guanidinium chloride in 400 microM Zn2+ provides an upper bound for the stability of such intermediates (DeltaG(U-I) < 4 kcal/mol). These results support a view of the apparent two-state protein folding reaction surface as a fast pre-equilibrium between the denatured state and a series of high-energy species. The net folding rate is a product of the equilibrium constant of the highest-energy species and a transmission rate. For ubiquitin, we estimate the transmission rate to be approximately 10(4) s-1. Implications for the role of unfolded chain diffusion on folding rates and barrier heights are discussed.

The nucleation mechanism of protein folding: a survey of computer simulation studies

The nucleation mechanism of protein folding, originally proposed by Baldwin in the early 1970s, was firstly observed by Shakhnovich and co-workers two decades later in the context of Monte Carlo simulations of a simple lattice model. At about the same time the extensive use of φ-value analysis provided the first experimental evidence that the folding of Chymotrypsin-inhibitor 2, a small single-domain protein, which folds with two-state kinetics, is also driven by a nucleation mechanism. Since then, the nucleation mechanism is generally considered the most common form of folding mechanism amongst two-state proteins. However, recent experimental data has put forward the idea that this may not necessarily be so, since the accuracy of the experimentally determined φ values, which are used to identify the critical (i.e. nucleating) residues, is typically poor. Here, we provide a survey of in silico results on the nucleation mechanism, ranging from simple lattice Monte Carlo to more sophisticated off-lattice molecular dynamics simulations, and discuss them in light of experimental data.

Psi-constrained simulations of protein folding transition states: implications for calculating

Psi-analysis has been used to identify interresidue contacts in the transition state ensemble (TSE) of ubiquitin and other proteins. The magnitude of psi depends on the degree to which an inserted bihistidine (biHis) metal ion binding site is formed in the TSE. A psi equal to zero or one indicates that the biHis site is absent or fully native-like, respectively, while a fractional psi implies that in the TSE, the biHis site recovers only part of the binding-induced stabilization of the native state. All-atom Langevin dynamics simulations of the TSE are performed with restrictions imposed only on the distances between the pairs of residues with experimentally determined psi of unity. When a site with a fractional psi lies adjacent to a site with psi = 1, the fractional psi generally signifies that the "fractional site" has a distorted geometry in the TSE. When a fractional site is distal to the sites with psi = 1, however, the histidines sample configurations in which the site is absent. The simulations indicate that the psi = 1 sites by themselves can be used to generate a well-defined TSE having near-native topology. values calculated from the TS simulations exhibit mixed agreement with the experimental values. The origin and implication of the disparities are discussed.

Effect of interdomain linker length on an antagonistic folding-unfolding equilibrium between two protein domains

Fusion of one protein domain with another is a common event in both evolution and protein engineering experiments. When insertion is at an internal site (e.g., a surface loop or turn), as opposed to one of the termini, conformational strain can be introduced into both domains. Strain is manifested by an antagonistic folding-unfolding equilibrium between the two domains, which we previously showed can be parameterized by a coupling free-energy term (DeltaG(X)). The extent of strain is predicted to depend primarily on the ratio of the N-to-C distance of the guest protein to the distance between ends of the surface loop in the host protein. Here, we test that hypothesis by inserting ubiquitin (Ub) into the bacterial ribonuclease barnase (Bn), using peptide linkers from zero to 10 amino acids each. DeltaG(X) values are determined by measuring the extent to which Co(2+) binding to an engineered site on the Ub domain destabilizes the Bn domain. All-atom, unforced Langevin dynamics simulations are employed to gain structural insight into the mechanism of mechanically induced unfolding. Experimental and computational results find that the two domains are structurally and energetically uncoupled when linkers are long and that DeltaG(X) increases with decreasing linker length. When the linkers are fewer than two amino acids, strain is so great that one domain unfolds the other. However, the protein is able to refold as dimers and higher-order oligomers. The likely mechanism is a three-dimensional domain swap of the Bn domain, which relieves conformational strain. The simulations suggest that an effective route to mechanical unfolding begins with disruption of the hydrophobic core of Bn near the Ub insertion site.

Mimicking the folding pathway to improve homology-free protein structure prediction

Since the demonstration that the sequence of a protein encodes its structure, the prediction of structure from sequence remains an outstanding problem that impacts numerous scientific disciplines, including many genome projects. By iteratively fixing secondary structure assignments of residues during Monte Carlo simulations of folding, our coarse-grained model without information concerning homology or explicit side chains can outperform current homology-based secondary structure prediction methods for many proteins. The computationally rapid algorithm using only single (phi,psi) dihedral angle moves also generates tertiary structures of accuracy comparable with existing all-atom methods for many small proteins, particularly those with low homology. Hence, given appropriate search strategies and scoring functions, reduced representations can be used for accurately predicting secondary structure and providing 3D structures, thereby increasing the size of proteins approachable by homology-free methods and the accuracy of template methods that depend on a high-quality input secondary structure.

What have we learned from the studies of two-state folders, and what are the unanswered questions about two-state protein folding?

Small proteins with globular structures often fold by simple all-or-none mechanisms, both in an equilibrium and a kinetic sense, despite the very large number of partly folded conformations available. This type of 'two-state' folding will be discussed in terms of experimental tests, underlying molecular mechanisms, and limits to two-state behavior. Factors that appear to be important for two-state folding include topology (sequence distance of contacts in the native structure), molecular cooperativity and local energy distribution. Because their local stability distributions and cooperativities can be dissected and analyzed separately from topological features, recent studies of the folding of symmetric proteins will be discussed as a means to better understand the origins of two-state folding.

Principal determinants leading to transition state formation of a protein-protein complex, orientation trumps side-chain interactions

The binding transition state (TS) is the rate-limiting step for transient molecular interactions. This important step in the molecular recognition process, however, is largely understood only at a qualitative level. To establish a more quantitative picture of the TS structure, we exploit a set of biophysical techniques that have provided major insights in protein folding applications. As a model system representing the large class of "weakly charged" protein-protein interactions, we examine the binding of a variety of human growth hormone (hGH) variants to the human growth hormone receptor (hGHR) and the human prolactin receptor (hPRLR). hGH variants were chosen to probe different features of the TS structure, based on their highly reengineered interfaces. Both Eyring and urea (m value) analyses suggest that the majority of binding surface burial occurs after TS. A comprehensive phi analysis showed that individual hGH interface residues do not contribute energetically to the stability of the TS, but there is a TS "hot spot" in the receptor. Zinc dependence studies that take advantage of an endogenous tetracoordinated interfacial metal binding demonstrate that surfaces of the molecules have attained a high orientational complementarity by the time the TS is reached. The model that best fits these data are that a "knobs-into-holes" process precisely aligns the two molecular interfaces in forming the TS structure. Surprisingly, most of the thermodynamic character of the binding reaction is focused in the fine-tuning process occurring after TS.

Probing the folding transition state of ubiquitin mutants by temperature-jump-induced downhill unfolding

Crucial to revealing mechanistic details of protein folding is a characterization of the transition state ensemble and its structural dynamics. To probe the transition state of ubiquitin thermal unfolding, we examine unfolding dynamics and kinetics of wild-type and mutant ubiquitin using time-resolved nonlinear infrared spectroscopy after a nanosecond temperature jump. We observe spectral changes on two different time scales. A fast nonexponential microsecond phase is attributed to downhill unfolding from the transition state region, which is induced by a shift of the barrier due to the rapid temperature change. Slow millisecond changes arise from thermally activated folding and unfolding kinetics. Mutants that stabilize or destabilize beta strands III-V lead to a decreased or increased amplitude of the microsecond phase, indicating that the disruption or weakening of these strands occurs in the transition state. Unfolding features from microseconds to milliseconds can be explained by temperature-dependent changes of a two-dimensional free energy surface constructed by the native contacts between beta strands of the protein. In addition, the results support the possibility of an intermediate state in thermal unfolding.

Quantifying the structural requirements of the folding transition state of protein A and other systems

The B-domain of protein A is a small three-helix bundle that has been the subject of considerable experimental and theoretical investigation. Nevertheless, a unified view of the structure of the transition-state ensemble (TSE) is still lacking. To characterize the TSE of this surprisingly challenging protein, we apply a combination of psi analysis (which probes the role of specific side-chain to side-chain contacts) and kinetic H/D amide isotope effects (which measures hydrogen-bond content), building upon previous studies using mutational phi analysis (which probes the energetic influence of side-chain substitutions). The second helix is folded in the TSE, while helix formation appears just at the carboxy and amino termini of the first and third helices, respectively. The experimental data suggest a homogenous yet plastic TS with a native-like topology. This study generalizes our earlier conclusion, based on two larger alpha/beta proteins, that the TSEs of most small proteins achieve approximately 70% of their native state's relative contact order. This high percentage limits the degree of possible TS heterogeneity and requires a reevaluation of the structural content of the TSE of other proteins, especially when they are characterized as small or polarized.