Mapping the interactions present in the transition state for unfolding/folding of FKBP12

Enhancing response of a protein conformational switch by using two disordered ligand binding domains

Introduction: Protein conformational switches are often constructed by fusing an input domain, which recognizes a target ligand, to an output domain that establishes a biological response. Prior designs have employed binding-induced folding of the input domain to drive a conformational change in the output domain. Adding a second input domain can in principle harvest additional binding energy for performing useful work. It is not obvious, however, how to fuse two binding domains to a single output domain such that folding of both binding domains combine to effect conformational change in the output domain. Methods: Here, we converted the ribonuclease barnase (Bn) to a switchable enzyme by duplicating a C-terminal portion of its sequence and appending it to its N-terminus, thereby establishing a native fold (OFF state) and a circularly permuted fold (ON state) that competed for the shared core in a mutually exclusive fashion. Two copies of FK506 binding protein (FKBP), both made unstable by the V24A mutation and one that had been circularly permuted, were inserted into the engineered barnase at the junctions between the shared and duplicated sequences. Results: Rapamycin-induced folding of FK506 binding protein stretched and unfolded the native fold of barnase via the mutually exclusive folding effect, and rapamycin-induced folding of permuted FK506 binding protein stabilized the permuted fold of barnase by the loop-closure entropy principle. These folding events complemented each other to turn on RNase function. The cytotoxic switching mechanism was validated in yeast and human cells, and in vitro with purified protein. Discussion: Thermodynamic modeling and experimental results revealed that the dual action of loop-closure entropy and mutually exclusive folding is analogous to an engine transmission in which loop-closure entropy acts as the low gear, providing efficient switching at low ligand concentrations, and mutually exclusive folding acts as the high gear to allow the switch to reach its maximum response at high ligand concentrations.

Protein folding problem: enigma, paradox, solution

The ability of protein chains to spontaneously form their three-dimensional structures is a long-standing mystery in molecular biology. The most conceptual aspect of this mystery is how the protein chain can find its native, "working" spatial structure (which, for not too big protein chains, corresponds to the global free energy minimum) in a biologically reasonable time, without exhaustive enumeration of all possible conformations, which would take billions of years. This is the so-called "Levinthal's paradox." In this review, we discuss the key ideas and discoveries leading to the current understanding of protein folding kinetics, including folding landscapes and funnels, free energy barriers at the folding/unfolding pathways, and the solution of Levinthal's paradox. A special role here is played by the "all-or-none" phase transition occurring at protein folding and unfolding and by the point of thermodynamic (and kinetic) equilibrium between the "native" and the "unfolded" phases of the protein chain (where the theory obtains the simplest form). The modern theory provides an understanding of key features of protein folding and, in good agreement with experiments, it (i) outlines the chain length-dependent range of protein folding times, (ii) predicts the observed maximal size of "foldable" proteins and domains. Besides, it predicts the maximal size of proteins and domains that fold under solely thermodynamic (rather than kinetic) control. Complementarily, a theoretical analysis of the number of possible protein folding patterns, performed at the level of formation and assembly of secondary structures, correctly outlines the upper limit of protein folding times.

De novo protein folding on computers. Benefits and challenges

There has been recent success in prediction of the three-dimensional folded native structures of proteins, most famously by the AlphaFold Algorithm running on Google's/Alphabet's DeepMind computer. However, this largely involves machine learning of protein structures and is not a de novo protein structure prediction method for predicting three-dimensional structures from amino acid residue sequences. A de novo approach would be based almost entirely on general principles of energy and entropy that govern protein folding energetics, and importantly do so without the use of the amino acid sequences and structural features of other proteins. Most consider that problem as still unsolved even though it has occupied leading scientists for decades. Many consider that it remains one of the major outstanding issues in modern science. There is crucial continuing help from experimental findings on protein unfolding and refolding in the laboratory, but only to a limited extent because many researchers consider that the speed by which real proteins folds themselves, often from milliseconds to minutes, is itself still not fully understood. This is unfortunate, because a practical solution to the problem would probably have a major effect on personalized medicine, the pharmaceutical industry, biotechnology, and nanotechnology, including for example "smaller" tasks such as better modeling of flexible "unfolded" regions of the SARS-COV-2 spike glycoprotein when interacting with its cell receptor, antibodies, and therapeutic agents. Some important ideas from earlier studies are given before moving on to lessons from periodic and aperiodic crystals, and a possible role for quantum phenomena. The conclusion is that better computation of entropy should be the priority, though that is presented guardedly.

Mutational Analysis of Protein Folding Transition States: Phi Values

The analysis of protein folding reactions by monitoring the kinetic effects of specifically designed single-point mutations, the so-termed phi-value analysis, has been a favorite technique to experimentally probe the mechanisms of protein folding. The idea behind phi-value analysis is that the effects that mutations have on the folding and unfolding rate constants report on the energetic/structural features of the folding transition state ensemble (TSE), which is the highest point in the free energy surface connecting the native and unfolded states, and thus the rate limiting step that ultimately defines the folding mechanism. For single-domain, two-state folding proteins, the general procedure to perform the phi-value analysis of protein folding is relatively simple to implement in the lab. Once the mutations have been produced and purified, the researcher needs to follow a few specific guidelines to perform the experiments and to analyze the data so produced. In this chapter, a step-by-step description of how to measure and interpret the effects induced by site-directed mutations on the folding and unfolding rate constants of a protein of interest is provided. Some possible solutions to the most typical problems that arise when performing phi-value analysis in the lab are also provided.

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.

Small Molecule-Induced Domain Swapping as a Mechanism for Controlling Protein Function and Assembly

Domain swapping is the process by which identical proteins exchange reciprocal segments to generate dimers. Here we introduce induced domain swapping (INDOS) as a mechanism for regulating protein function. INDOS employs a modular design consisting of the fusion of two proteins: a recognition protein that binds a triggering molecule, and a target protein that undergoes a domain swap in response to binding of the triggering ligand. The recognition protein (FK506 binding protein) is inserted into functionally-inactivated point mutants of two target proteins (staphylococcal nuclease and ribose binding protein). Binding of FK506 to the FKBP domain causes the target domain to first unfold, then refold via domain swap. The inactivating mutations become ‘swapped out’ in the dimer, increasing nuclease and ribose binding activities by 100-fold and 15-fold, respectively, restoring them to near wild-type values. INDOS is intended to convert an arbitrary protein into a functional switch, and is the first example of rational design in which a small molecule is used to trigger protein domain swapping and subsequent activation of biological function.

There and back again: Two views on the protein folding puzzle

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the "foldable" protein domains.

Characterization of protein folding by a Φ-value calculation with a statistical-mechanical model

The Φ-value analysis approach provides information about transition-state structures along the folding pathway of a protein by measuring the effects of an amino acid mutation on folding kinetics. Here we compared the theoretically calculated Φ values of 27 proteins with their experimentally observed Φ values; the theoretical values were calculated using a simple statistical-mechanical model of protein folding. The theoretically calculated Φ values reflected the corresponding experimentally observed Φ values with reasonable accuracy for many of the proteins, but not for all. The correlation between the theoretically calculated and experimentally observed Φ values strongly depends on whether the protein-folding mechanism assumed in the model holds true in real proteins. In other words, the correlation coefficient can be expected to illuminate the folding mechanisms of proteins, providing the answer to the question of which model more accurately describes protein folding: the framework model or the nucleation-condensation model. In addition, we tried to characterize protein folding with respect to various properties of each protein apart from the size and fold class, such as the free-energy profile, contact-order profile, and sensitivity to the parameters used in the Φ-value calculation. The results showed that any one of these properties alone was not enough to explain protein folding, although each one played a significant role in it. We have confirmed the importance of characterizing protein folding from various perspectives. Our findings have also highlighted that protein folding is highly variable and unique across different proteins, and this should be considered while pursuing a unified theory of protein folding.

Early steps in thermal unfolding of superoxide dismutase 1 are similar to the conformational changes associated with the ALS-associated A4V mutation

There are over 100 mutations in Cu/Zn superoxide dismutase (SOD1) that result in a subset of familial amyotrophic lateral sclerosis (fALS) cases. The hypothesis that dissociation of the dimer, misfolding of the monomer and subsequent aggregation of mutant SOD1 leads to fALS has been gaining support as an explanation for how these disparate missense mutations cause the same disease. These forms are only responsible for a fraction of the ALS cases; however, the rest are sporadic. Starting with a folded apo monomer, the species considered most likely to be involved in misfolding, we used high-temperature all-atom molecular dynamics simulations to explore the events of the wild-type protein unfolding through the denatured state. All simulations showed early loss of structure along the β5-β6 edge of the β-sandwich, supporting earlier findings of instability in this region. Transition state structures identified from the simulations are in good agreement with experiment, providing detailed, validated molecular models for this elusive state. Furthermore, we compare the process of thermal unfolding investigated here to that of the lethal A4V mutant-induced unfolding at physiological temperature and find that the pathways are very similar.

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.

A comparison of experimental and computational methods for mapping the interactions present in the transition state for folding of FKBP12

The folding pathway of FKBP12, a 107 residue α/β protein, has been characterised in detail using a combination of experimental and computational techniques. FKBP12 follows a two-state model of folding in which only the denatured and native states are significantly populated; no intermediate states are detected. The refolding rate constant in water is 4 s(-1) at 25 °C. Two different experimental strategies were employed for studying the transition state for folding. In the first case, a non-mutagenic approach was used and the unfolding and refolding of the wild-type protein measured as a function of experimental conditions such as temperature, denaturant, ligand and trifluoroethanol (TFE) concentration. These data suggest a compact transition state relative to the unfolded state with some 70% of the surface area buried. The ligand-binding site, whichis mainly formed by two long loops, is largely unstructured in the transition state. TFE experiments suggest that the α-helix may be formed in the transition state. The second experimental approach involved using protein engineering techniques with φ-value analysis. Residue-specific information on the structure and energetics of the transition state can be obtained by this method. 34 mutations were made at sites throughout the protein to probe the extent of secondary and tertiary structure in the transition state. In contrast to some other proteins of this size, no element of structure is fully formed in the transition state, instead, the transition state is similar to that found for smaller, single-domain proteins, such as chymotrypsin inhibitor 2 and the SH3 domainfrom α-spectrin. For FKBP12, the central three strands of the β-sheet (2, 4 and 5), comprise the most structured region of the transition state. In particular Val 101, which is one of the most highly buried residues and located in the middle of the central β-strand,makes approximately 60% of its native interactions. The outer β-strands, and the ends of the central β-strands are formed to a lesser degree. The short α-helix is largely unstructured in the transition state as are the loops. The data are consistent with a nucleation-condensation model of folding, the nucleus of which is formed by side chains within β-strands 2, 4 and 5 and the C-terminus of the α-helix. These residues are distant in the primary sequence, demonstrating the importance of tertiary interactions in the transition state. High-temperature molecular dynamic simulations on the unfoldingpathway of FKBP12 are in good agreement with the experimental results.

Golden triangle for folding rates of globular proteins

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured rates of spontaneous folding of single-domain globular proteins range from microseconds to hours: the difference (11 orders of magnitude) is akin to the difference between the life span of a mosquito and the age of the universe. Here, we show that physical theory with biological constraints outlines a "golden triangle" limiting the possible range of folding rates for single-domain globular proteins of various size and stability, and that the experimentally measured folding rates fall within this narrow triangle built without any adjustable parameters, filling it almost completely. In addition, the golden triangle predicts the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control. It also predicts the maximal allowed size of the "foldable" protein domains, and the size of domains found in known protein structures is in a good agreement with this limit.

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.

Ligand-switchable substrates for a ubiquitin-proteasome system

Cellular maintenance of protein homeostasis is essential for normal cellular function. The ubiquitin-proteasome system (UPS) plays a central role in processing cellular proteins destined for degradation, but little is currently known about how misfolded cytosolic proteins are recognized by protein quality control machinery and targeted to the UPS for degradation in mammalian cells. Destabilizing domains (DDs) are small protein domains that are unstable and degraded in the absence of ligand, but whose stability is rescued by binding to a high affinity cell-permeable ligand. In the work presented here, we investigate the biophysical properties and cellular fates of a panel of FKBP12 mutants displaying a range of stabilities when expressed in mammalian cells. Our findings correlate observed cellular instability to both the propensity of the protein domain to unfold in vitro and the extent of ubiquitination of the protein in the non-permissive (ligand-free) state. We propose a model in which removal of stabilizing ligand causes the DD to unfold and be rapidly ubiquitinated by the UPS for degradation at the proteasome. The conditional nature of DD stability allows a rapid and non-perturbing switch from stable protein to unstable UPS substrate unlike other methods currently used to interrogate protein quality control, providing tunable control of degradation rates.

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.

Folding intermediate and folding nucleus for I-->N and U-->I-->N transitions in apomyoglobin: contributions by conserved and nonconserved residues

Kinetic investigation on the wild-type apomyoglobin and its 12 mutants with substitutions of hydrophobic residues by Ala was performed using stopped-flow fluorescence. Characteristics of the kinetic intermediate I and the folding nucleus were derived solely from kinetic data, namely, the slow-phase folding rate constants and the burst-phase amplitudes of Trp fluorescence intensity. This allowed us to pioneer the phi-analysis for apomyoglobin. As shown, these mutations drastically destabilized the native state N and produced minor (for conserved residues of G, H helices) or even negligible (for nonconserved residues of B, C, D, E helices) destabilizing effect on the state I. On the other hand, conserved residues of A, G, H helices made a smaller contribution to stability of the folding nucleus at the rate-limiting I-->N transition than nonconserved residues of B, D, E helices. Thus, conserved side chains of the A-, G-, H-residues become involved in the folding nucleus before crossing the main barrier, whereas nonconserved side chains of the B-, D-, E-residues join the nucleus in the course of the I-->N transition.

Temperature-induced unfolding of epidermal growth factor (EGF): insight from molecular dynamics simulation

Thermal disruption of protein structure and function is a potentially powerful therapeutic vehicle. With the emerging nanoparticle-targeting and femtosecond laser technology, it is possible to deliver heating locally to specific molecules. It is therefore important to understand how fast a protein can unfold or lose its function at high temperatures, such as near the water boiling point. In this study, the thermal damage of EGF was investigated by combining the replica exchange (136 replicas) and conventional molecular dynamics simulations. The REMD simulation was employed to rigorously explore the free-energy landscape of EGF unfolding. Interestingly, besides the native and unfolded states, we also observed a distinct molten globule (MG) state that retained substantial amount of native contacts. Based on the understanding that which the unfolding of EGF is a three-state process, we have examined the unfolding kinetics of EGF (N-->MG and MG-->D) with multiple 20-ns conventional MD simulations. The Arrhenius prefactors and activation energy barriers determined from the simulation are within the range of previously studied proteins. In contrast to the thermal damage of cells and tissues which take place on the time scale of seconds to hours at relatively low temperatures, the denaturation of proteins occur in nanoseconds when the temperature of heat bath approaches the boiling point.

Unfolding simulations reveal the mechanism of extreme unfolding cooperativity in the kinetically stable alpha-lytic protease

Kinetically stable proteins, those whose stability is derived from their slow unfolding kinetics and not thermodynamics, are examples of evolution's best attempts at suppressing unfolding. Especially in highly proteolytic environments, both partially and fully unfolded proteins face potential inactivation through degradation and/or aggregation, hence, slowing unfolding can greatly extend a protein's functional lifetime. The prokaryotic serine protease α-lytic protease (αLP) has done just that, as its unfolding is both very slow (t_1/2 ∼1 year) and so cooperative that partial unfolding is negligible, providing a functional advantage over its thermodynamically stable homologs, such as trypsin. Previous studies have identified regions of the domain interface as critical to αLP unfolding, though a complete description of the unfolding pathway is missing. In order to identify the αLP unfolding pathway and the mechanism for its extreme cooperativity, we performed high temperature molecular dynamics unfolding simulations of both αLP and trypsin. The simulated αLP unfolding pathway produces a robust transition state ensemble consistent with prior biochemical experiments and clearly shows that unfolding proceeds through a preferential disruption of the domain interface. Through a novel method of calculating unfolding cooperativity, we show that αLP unfolds extremely cooperatively while trypsin unfolds gradually. Finally, by examining the behavior of both domain interfaces, we propose a model for the differential unfolding cooperativity of αLP and trypsin involving three key regions that differ between the kinetically stable and thermodynamically stable classes of serine proteases.

Proteins, synthesized as linear polymers of amino acids, fold up into compact native states, burying their hydrophobic amino acids into their interiors. Protein folding minimizes the non-specific interactions that unfolded protein chains can make, which include aggregation with other proteins and degradation by proteases. Unfortunately, even in the native state, proteins can partially unfold, opening up regions of their structure and making these adverse events possible. Some proteins, particularly those in harsh environments full of proteases, have evolved to virtually eliminate partial unfolding, significantly reducing their rate of degradation. This elimination of partial unfolding is termed “cooperative,” because unfolding is an all-or-none process. One class of proteins has diverged into two families, one bacterial and highly cooperative and the other animal and non-cooperative. We have used detailed simulations of unfolding for members of each family, α-lytic protease (bacterial) and trypsin (animal) to understand the unfolding pathways of each and the mechanism for the differential unfolding cooperativity. Our results explain prior biochemical experiments, reproduce the large difference in unfolding cooperativity between the families, and point to the interface between α-lytic protease's two domains as essential to establishing unfolding cooperativity. As seen in an unrelated protein family, generation of a cooperative domain interface may be a common evolutionary response for ensuring the highest protein stability.

Dynameomics: a consensus view of the protein unfolding/folding transition state ensemble across a diverse set of protein folds

The Dynameomics project aims to simulate a representative sample of all globular protein metafolds under both native and unfolding conditions. We have identified protein unfolding transition state (TS) ensembles from multiple molecular dynamics simulations of high-temperature unfolding in 183 structurally distinct proteins. These data can be used to study individual proteins and individual protein metafolds and to mine for TS structural features common across all proteins. Separating the TS structures into four different fold classes (all proteins, all-alpha, all-beta, and mixed alpha/beta and alpha +beta) resulted in no significant difference in the overall protein properties. The residues with the most contacts in the native state lost the most contacts in the TS ensemble. On average, residues beginning in an alpha-helix maintained more structure in the TS ensemble than did residues starting in beta-strands or any other conformation. The metafolds studied here represent 67% of all known protein structures, and this is, to our knowledge, the largest, most comprehensive study of the protein folding/unfolding TS ensemble to date. One might have expected broad distributions in the average global properties of the TS relative to the native state, indicating variability in the amount of structure present in the TS. Instead, the average global properties converged with low standard deviations across metafolds, suggesting that there are general rules governing the structure and properties of the TS.

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.

Identifying critical residues in protein folding: Insights from phi-value and P(fold) analysis

We apply a simulational proxy of the phi-value analysis and perform extensive mutagenesis experiments to identify the nucleating residues in the folding "reactions" of two small lattice Go polymers with different native geometries. Our findings show that for the more complex native fold (i.e., the one that is rich in nonlocal, long-range bonds), mutation of the residues that form the folding nucleus leads to a considerably larger increase in the folding time than the corresponding mutations in the geometry that is predominantly local. These results are compared to data obtained from an accurate analysis based on the reaction coordinate folding probability P(fold) and on structural clustering methods. Our study reveals a complex picture of the transition state ensemble. For both protein models, the transition state ensemble is rather heterogeneous and splits up into structurally different populations. For the more complex geometry the identified subpopulations are actually structurally disjoint. For the less complex native geometry we found a broad transition state with microscopic heterogeneity. These findings suggest that the existence of multiple transition state structures may be linked to the geometric complexity of the native fold. For both geometries, the identification of the folding nucleus via the P(fold) analysis agrees with the identification of the folding nucleus carried out with the phi-value analysis. For the most complex geometry, however, the applied methodologies give more consistent results than for the more local geometry. The study of the transition state structure reveals that the nucleus residues are not necessarily fully native in the transition state. Indeed, it is only for the more complex geometry that two of the five critical residues show a considerably high probability of having all its native bonds formed in the transition state. Therefore, one concludes that, in general, the phi-value correlates with the acceleration/deceleration of folding induced by mutation, rather than with the degree of nativeness of the transition state, and that the "traditional" interpretation of phi-values may provide a more realistic picture of the structure of the transition state only for more complex native geometries.

How general is the nucleation-condensation mechanism?

We investigate the structures of the major folding transition states of nine proteins by correlation of published Phi-values with inter-residue contact maps. Combined with previous studies on six proteins, the analysis suggests that at least 10 of the 15 small globular proteins fold via a nucleation-condensation mechanism with a concurrent build-up of secondary and tertiary structure contacts, but a structural consolidation that is clearly nonuniformly distributed over the molecule and most intense in a single structural region suggesting the occurrence of a single folding nucleus. However, on average helix- and sheet-forming residues show somewhat larger Phi-values in the major transition state, suggesting that secondary structure formation is one important driving force in the nucleation-condensation in many proteins and that secondary-structure forming residues tend to be more prominent in folding nuclei. We synthesize the combined information on these 10 of 15 proteins into a unified nucleation-condensation mechanism which also accounts for effects described by the framework, hydrophobic collapse, zipper, and funnel models.

The dual histidine motif in the active site of Pin1 has a structural rather than catalytic role

The catalytic domain of the peptidyl-prolyl cis/ trans isomerase Pin1 is a member of the FKBP superfold family. Within its active site are two highly conserved histidine residues, H59 and H157. Despite their sequence conservation in parvulin PPIase domains, the role of these histidine residues remains unclear. Our previous work (Behrsin et al. (2007) J. Mol. Biol. 365, 1143- 1162.) was consistent with a model where one or both histidines had critical roles in a hydrogen bonding network in the active site. Here, we test this model by looking at the effect of mutations to H59 and H157 on Pin1 function, activity, and protein stability. Using a yeast complementation assay, we show that both H59 and H157 can be mutated to non-hydrogen bonding residues and still support viability. Surprisingly, a nonfunctional H59L mutation can be rescued by a mutation of H157, to leucine. This double mutation (H59L/H157L) also had about 5-fold greater isomerase activity than the H59L mutation with a phosphorylated substrate. Structural analyses suggest that rescue of function and activity results from partial rescue of protein stability. Our findings indicate that H59 and H157 are not required for hydrogen bonding within the active site, and in contrast to the active site C113, they do not participate directly in catalysis. Instead, we suggest these histidines play a key role in domain structure or stability.

Capillarity-like growth of protein folding nuclei

A full structural description of transition state ensembles in protein folding includes the specificity of the ordered residues composing the folding nucleus as well as spatial density. To our knowledge, the spatial properties of the folding nucleus and interface of specific nuclei have yet to receive significant attention. We analyze folding routes predicted by a variational model in terms of a generalized formalism of the capillarity scaling theory that assumes the volume of the folded core of the nucleus grows with chain length as V(f) approximately N(3nu). For 27 two-state proteins studied, the scaling exponent nu ranges from 0.2 to 0.45 with an average of 0.33. This average value corresponds to packing of rigid objects, although generally the effective monomer size in the folded core is larger than the corresponding volume per particle in the native-state ensemble. That is, on average, the folded core of the nucleus is found to be relatively diffuse. We also study the growth of the folding nucleus and interface along the folding route in terms of the density or packing fraction. The evolution of the folded core and interface regions can be classified into three patterns of growth depending on how the growth of the folded core is balanced by changes in density of the interface. Finally, we quantify the diffuse versus polarized structure of the critical nucleus through direct calculation of the packing fraction of the folded core and interface regions. Our results support the general picture of describing protein folding as the capillarity-like growth of folding nuclei.

Microscopic reversibility of protein folding in molecular dynamics simulations of the engrailed homeodomain

The principle of microscopic reversibility states that at equilibrium the number of molecules entering a state by a given path must equal those exiting the state via the same path under identical conditions or, in structural terms, that the conformations along the two pathways are the same. There has been some indirect evidence indicating that protein folding is such a process, but there have been few conclusive findings. In this study, we performed molecular dynamics simulations of an ultrafast unfolding and folding protein at its melting temperature to observe, on an atom-by-atom basis, the pathways the protein followed as it unfolded and folded within a continuous trajectory. In a total of 0.67 micros of simulation in water, we found six transient denaturing events near the melting temperature (323 and 330 K) and an additional refolding event following a previously identified unfolding event at a high temperature (373 K). In each case, unfolding and refolding transition state ensembles were identified, and they agreed well with experiment on the basis of a comparison of S and Phi values. On the basis of several structural properties, these 13 transition state ensembles agreed very well with each other and with four previously identified transition states from high-temperature denaturing simulations. Thus, not only were the unfolding and refolding transition states part of the same ensemble, but in five of the seven cases, the pathway the protein took as it unfolded was nearly identical to the subsequent refolding pathway. These events provide compelling evidence that protein folding is a microscopically reversible process. In the other two cases, the folding and unfolding transition states were remarkably similar to each other but the paths deviated.

Loop-closure principles in protein folding

Simple theoretical concepts and models have been helpful to understand the folding rates and routes of single-domain proteins. As reviewed in this article, a physical principle that appears to underly these models is loop closure.

Transition states in protein folding kinetics: modeling phi-values of small beta-sheet proteins

Small single-domain proteins often exhibit only a single free-energy barrier, or transition state, between the denatured and the native state. The folding kinetics of these proteins is usually explored via mutational analysis. A central question is which structural information on the transition state can be derived from the mutational data. In this article, we model and structurally interpret mutational Phi-values for two small beta-sheet proteins, the PIN and the FBP WW domains. The native structure of these WW domains comprises two beta-hairpins that form a three-stranded beta-sheet. In our model, we assume that the transition state consists of two conformations in which either one of the hairpins is formed. Such a transition state has been recently observed in molecular dynamics folding-unfolding simulations of a small designed three-stranded beta-sheet protein. We obtain good agreement with the experimental data 1), by splitting up the mutation-induced free-energy changes into terms for the two hairpins and for the small hydrophobic core of the proteins; and 2), by fitting a single parameter, the relative degree to which hairpins 1 and 2 are formed in the transition state. The model helps us to understand how mutations affect the folding kinetics of WW domains, and captures also negative Phi-values that have been difficult to interpret.

A directed approach for engineering conditional protein stability using biologically silent small molecules

The ability to regulate the function of specific proteins using cell-permeable molecules can be a powerful method for interrogating biological systems. To bring this type of "chemical genetic" control to a wide range of proteins, we recently developed an experimental system in which the stability of a small protein domain expressed in mammalian cells depends on the presence of a high affinity ligand. This ligand-dependent stability is conferred to any fused partner protein. The FK506- and rapamycin-binding protein (FKBP12) has been the subject of extensive biophysical analyses, including both kinetic and thermodynamic studies of the wild-type protein as well as dozens of mutants. The goal of this study was to determine if the thermodynamic stabilities (DeltaDeltaG(U-F)) of various amino acid substitutions within a given protein are predictive for engineering additional ligand-dependent destabilizing domains. We used FKBP12 as a model system and found that in vitro thermodynamic stability correlates weakly with intracellular degradation rates of the mutants and that the ability of a given mutation to destabilize the protein is context-dependent. We evaluated several new FKBP12 ligands for their ability to stabilize these mutants and found that a cell-permeable molecule called Shield-1 is the most effective stabilizing ligand. We then performed an unbiased microarray analysis of NIH3T3 cells treated with various concentrations of Shield-1. These studies show that Shield-1 does not elicit appreciable cellular responses.

A kinetically trapped intermediate of FK506 binding protein forms in vitro: Chaperone machinery dominates protein folding in vivo

We have characterised the stability, binding and enzymatic properties of three human FK506 binding proteins (FKBP-12) differing only by the length and sequence of their N-terminus. One construct has a short hexa-his tag (6H-FKBP12); the second longer fusion protein (6HL-FKBP12) contains an additional thrombin protease cleavage site; the third has the long fusion tag removed and is essentially native FKBP-12 (cFKBP12). The proteins were purified both under native conditions and also using a refolding protocol. All three natively purified proteins have, within experimental error, the same peptidyl-prolyl isomerase (PPIase) activity (k(cat)/K(m) approximately 1 x 10(6)M(-1)s(-1)), and bind a natural inhibitor, rapamycin, with the same high affinity (K(d) approximately 6 nM). However, refolding of the protein containing the longer tag in vitro results in reduced PPIase activity (the k(cat)/K(m) was reduced from 1 x 10(6)M(-1)s(-1) to 0.81 x 10(6)M(-1)s(-1)) and a 6-fold affinity loss for rapamycin. Addition of both the long and short N-terminal his-tags slows the refolding kinetics of FKBP-12. However, the shorter his-tagged fusion protein regains fully native activity (> or =95%) while the longer regains only approximately 80-85% of native activity. Equilibrium urea denaturation titrations, isothermal titration calorimetry (ITC), analytical gel-filtration, and fluorescence binding data show that this loss of activity is not due to gross misfolding events, but is rather caused by the formation of a stable but subtly misfolded protein that has reduced peptidyl-prolyl isomerase (PPIase) activity and reduced affinity for rapamycin. The difference in behaviour between the in vitro refolded and native forms is due to the dominant role of the cellular chaperone/folding machinery.

Key Role of Coulombic Interactions for the Folding Transition State of the Cold Shock Protein

The cold shock protein CspB shows a five-stranded beta-sheet structure, and it folds rapidly via a native-like transition state. A previous Phi value analysis showed that most of the residues with Phi values close to one reside in strand beta1, and two of them, Lys5 and Lys7 are partially exposed charged residues. To elucidate how coulombic interactions of these two residues contribute to the energetic organisation of the folding transition state we performed comparative folding experiments in the presence of an ionic denaturant (guanidinium chloride) and a non-ionic denaturant (urea) and a double-mutant analysis. Lys5 contributes 6.6 kJ mol(-1) to the stability of the transition state, and half of it originates from screenable coulombic interactions. Lys7 contributes 5.3 kJ mol(-1), and 3.4 kJ mol(-1) of it are screened by salt. In the folded protein Lys7 interacts with Asp25, and the screenable coulombic interaction between these two residues is fully formed in the transition state. This suggests that long-range coulombic interactions such as those originating from Lys5 and Lys7 of CspB can be important for organizing and stabilizing native-like structure early in protein folding.

Transition-states in protein folding kinetics: the structural interpretation of Phi values

Phi values are experimental measures of the effects of mutations on the folding kinetics of a protein. A central question is what structural information Phi values give about the transition-state of folding. Traditionally, a Phi value is interpreted as representing the "nativeness" of a mutated residue in the transition-state. However, this interpretation is often problematic. We present here a better structural interpretation of Phi values for mutations within a given helix. Our interpretation is based on a simple physical model that distinguishes between secondary and tertiary free energy contributions of helical residues. From a linear fit of the model to experimental data, we obtain two structural parameters: the extent of helix formation in the transition-state, and the nativeness of tertiary interactions in the transition-state. We apply the model to all proteins with well-characterized helices for which more than 10 Phi values are available: protein A, CI2, and protein L. The model is simple to apply to experimental data, captures nonclassical Phi values <0 or >1 in these helices, and explains how different mutations at a given site can lead to different Phi values.

Similarity and difference in the unfolding of thermophilic and mesophilic cold shock proteins studied by molecular dynamics simulations

Molecular dynamics simulations were performed to unfold a homologous pair of thermophilic and mesophilic cold shock proteins at high temperatures. The two proteins differ in just 11 of 66 residues and have very similar structures with a closed five-stranded antiparallel beta-barrel. A long flexible loop connects the N-terminal side of the barrel, formed by three strands (beta1-beta3), with the C-terminal side, formed by two strands (beta4-beta5). The two proteins were found to follow the same unfolding pathway, but with the thermophilic protein showing much slower unfolding. Unfolding started with the melting of C-terminal strands, leading to exposure of the hydrophobic core. Subsequent melting of beta3 and the beta-hairpin formed by the first two strands then resulted in unfolding of the whole protein. The slower unfolding of the thermophilic protein could be attributed to ion pair formation of Arg-3 with Glu-46, Glu-21, and the C-terminal. These ion pairs were also found to be important for the difference in folding stability between the pair of proteins. Thus electrostatic interactions appear to play similar roles in the difference in folding stability and kinetics between the pair of proteins.

Phi-analysis of the folding of the B domain of protein A using multiple optical probes

We examined the co-operativity of ultra-fast folding of a protein and whether the Phi-value analysis of its transition state depended on the location of the optical probe. We incorporated in turn a tryptophan residue into each of the three helices of the B domain of Protein A. Each Trp mutant of the three-helix bundle protein was used as a pseudo-wild-type parent for Phi-analysis in which the intrinsic Trp fluorescence probed the formation of each helix during the transition state. Apart from local effects in the immediate vicinity of the probe, the three separate sets of Phi-values were in excellent agreement, demonstrating the overall co-operativity of folding and the robustness of the Phi-analysis. The transition state of folding of Protein A contains the second helix being well formed with many stabilizing tertiary hydrophobic interactions. In contrast, the first and the third helices are more poorly structured in the transition state. The mechanism of folding thus involves the concurrent formation of secondary and tertiary interactions, and is towards the nucleation-condensation extreme in the nucleation-condensation-framework continuum of mechanism, with helix 2 being the nucleus. We provide an error analysis of Phi-values derived purely from the kinetics of two-state chevron plots.

Do proteins with similar folds have similar transition state structures? A diffuse transition state of the 169 residue apoflavodoxin

Apoflavodoxin from Anabaena PCC 7119 is a 169 residue globular protein of known structure and energetics. Here, we present a comprehensive Phi-value analysis to characterize the structure of its transition state. A total of 34 non-disruptive mutations are made throughout the structure and a range of Phi-values from zero to one are observed. In addition, a small set of eight aliphatic small-to-large mutations have been introduced in the hydrophobic core of the protein and they have been analyzed to investigate the feasibility of stabilizing the unfolding transition state by creating new non-native interactions. We find that the transition state of apoflavodoxin (so far the largest protein subjected to Phi-analysis) is diffuse and that it can be stabilized by unspecific hydrophobic interactions that can speed up the folding reaction. The data gathered on the apoflavodoxin transition state are compared with results from experimental studies in other proteins to revisit the relationship between the native state topology and transition state structure.

The contribution of the residues from the main hydrophobic core of ribonuclease A to its pressure-folding transition state

The role of hydrophobic interactions established by the residues that belong to the main hydrophobic core of ribonuclease A in its pressure-folding transition state was investigated using the Phi-value method. The folding kinetics was studied using pressure-jump techniques both in the pressurization and depressurization directions. The ratio between the folding activation volume and the reaction volume (beta p-value), which is an index of the compactness or degree of solvation of the transition state, was calculated. All the positions analyzed presented fractional Phi f-values, and the lowest were those corresponding to the most critical positions for the ribonuclease A stability. The structure of the transition state of the hydrophobic core of ribonuclease A, from the point of view of formed interactions, is a relatively, uniformly expanded form of the folded structure with a mean Phi f-value of 0.43. This places it halfway between the folded and unfolded states. On the other hand, for the variants, the average of beta p-values is 0.4, suggesting a transition state that is 40% native-like. Altogether the results suggest that the pressure-folding transition state of ribonuclease A looks like a collapsed globule with some secondary structure and a weakened hydrophobic core. A good correlation was found between the Phi f-values and the Deltabeta p-values. Although the nature of the transition state inferred from pressure-induced folding studies and the results of the protein engineering method have been reported to be consistent for other proteins, to the best of our knowledge this is the first direct comparison using a set of mutants.

The folding pathway of spectrin R17 from experiment and simulation: using experimentally validated MD simulations to characterize States hinted at by experiment

We present an experimental and computational analysis of the folding pathway of the 17th domain of chicken brain alpha-spectrin, R17. Wild-type R17 folds in a two-state manner and the chevron plot (plot of the logarithm of the observed rate constant against concentration of urea) shows essentially linear folding and unfolding arms. A number of mutant proteins, however, show a change in slope of the unfolding arm at high concentration of denaturant, hinting at complexity in the folding landscape. Through a combination of mutational studies and high temperature molecular dynamics simulations we show that the folding of R17 can be described by a model with two sequential transition states separated by an intermediate species. The rate limiting transition state for folding in water has been characterized both through experimental Phi-value analysis and by simulation. In contrast, a detailed analysis of the transition state predicted to dominate under highly denaturing conditions is only possible by simulation.

Thermal unfolding simulations of a multimeric protein--transition state and unfolding pathways

The folding of an oligomeric protein poses an extra challenge to the folding problem because the protein not only has to fold correctly; it has to avoid nonproductive aggregation. We have carried out over 100 molecular dynamics simulations using an implicit solvation model at different temperatures to study the unfolding of one of the smallest known tetramers, p53 tetramerization domain (p53tet). We found that unfolding started with disruption of the native tetrameric hydrophobic core. The transition state for the tetramer to dimer transition was characterized as a diverse ensemble of different structures using Phi value analysis in quantitative agreement with experimental data. Despite the diversity, the ensemble was still native-like with common features such as partially exposed tetramer hydrophobic core and shifts in the dimer-dimer arrangements. After passing the transition state, the secondary and tertiary structures continued to unfold until the primary dimers broke free. The free dimer had little secondary structure left and the final free monomers were random-coil like. Both the transition states and the unfolding pathways from these trajectories were very diverse, in agreement with the new view of protein folding. The multiple simulations showed that the folding of p53tet is a mixture of the framework and nucleation-condensation mechanisms and the folding is coupled to the complex formation. We have also calculated the entropy and effective energy for the different states along the unfolding pathway and found that the tetramerization is stabilized by hydrophobic interactions.

Experimental investigation of the frequency and substitution dependence of negative phi-values in two-state proteins

Negative phi-values, which arise, for example, when a mutation stabilizes the folding transition state while destabilizing the native state, have been the focus of significant theoretical interest. Here we survey the experimental folding kinetics literature to ascertain the frequency with which negative phi-values occur in two-state proteins and describe the detailed experimental characterization of a negative phi-value previously reported to be among the most statistically significant. We find that, while almost 9% of more than 500 reported phi-values (from a set of 16, well-characterized two-state proteins) fall below zero, many of these do not represent statistically significant observations. For example, only 6% of the phi-values for which estimates of precision are available fall even one reported "error bar" below zero, and only 4% are simultaneously negative, significant at this level and associated with free energy changes at or above 2.5 kJ/mol (below which phi-value analysis is widely considered unreliable). Moreover, given the asymmetric distribution of phi-values around zero and given that reported error bars may significantly underestimate true confidence intervals, the actual number of negative phi-values may be much smaller still. We have also performed detailed characterization of one of the most statistically significant negative phi-values reported in the literature to date, the V55F mutant of FynSH3. We find that substitution of the wild-type valine to other hydrophobic residues often increases folding rates without significantly altering folding free energy. This in turn leads to poorly defined phi-values, some of which are formally negative but only one or two of which fall statistically significantly below zero. In contrast, substitution to polar residues significantly destabilizes both the transition and native states, generally producing small but statistically significant positive phi-values of approximately 0.1. Thus, unlike other previously characterized phi-values, the negative phi-value associated with position 55 of the FynSH3 domain appears to be strongly dependent on the substitution employed to measure it, suggesting that subtlety will be required in order to develop a theoretical model of such behavior.

Loss of protein structure stability as a major causative factor in monogenic disease

The most common cause of monogenic disease is a single base DNA variant resulting in an amino acid substitution. In a previous study, we observed that a high fraction of these substitutions appear to result in reduction of stability of the corresponding protein structure. We have now investigated this phenomenon more fully. A set of structural effects, such as reduction in hydrophobic area, overpacking, backbone strain, and loss of electrostatic interactions, is used to represent the impact of single residue mutations on protein stability. A support vector machine (SVM) was trained on a set of mutations causative of disease, and a control set of non-disease causing mutations. In jack-knifed testing, the method identifies 74% of disease mutations, with a false positive rate of 15%. Evaluation of a set of in vitro mutagenesis data with the SVM established that the majority of disease mutations affect protein stability by 1 to 3 kcal/mol. The method's effective distinction between disease and non-disease variants, strongly supports the hypothesis that loss of protein stability is a major factor contributing to monogenic disease.

Proteins QSAR with Markov average electrostatic potentials

Classic physicochemical and topological indices have been largely used in small molecules QSAR but less in proteins QSAR. In this study, a Markov model is used to calculate, for the first time, average electrostatic potentials xik for an indirect interaction between aminoacids placed at topologic distances k within a given protein backbone. The short-term average stochastic potential xi1 for 53 Arc repressor mutants was used to model the effect of Alanine scanning on thermal stability. The Arc repressor is a model protein of relevance for biochemical studies on bioorganics and medicinal chemistry. A linear discriminant analysis model developed correctly classified 43 out of 53, 81.1% of proteins according to their thermal stability. More specifically, the model classified 20/28, 71.4% of proteins with near wild-type stability and 23/25, 92.0% of proteins with reduced stability. Moreover, predictability in cross-validation procedures was of 81.0%. Expansion of the electrostatic potential in the series xi0, xi1, xi2, and xi3, justified the use of the abrupt truncation approach, being the overall accuracy >70.0% for xi0 but equal for xi1, xi2, and xi3. The xi1 model compared favorably with respect to others based on D-Fire potential, surface area, volume, partition coefficient, and molar refractivity, with less than 77.0% of accuracy [Ramos de Armas, R.; González-Díaz, H.; Molina, R.; Uriarte, E. Protein Struct. Func. Bioinf.2004, 56, 715]. The xi1 model also has more tractable interpretation than others based on Markovian negentropies and stochastic moments. Finally, the model is notably simpler than the two models based on quadratic and linear indices. Both models, reported by Marrero-Ponce et al., use four-to-five time more descriptors. Introduction of average stochastic potentials may be useful for QSAR applications; having xik amenable physical interpretation and being very effective.

Simulation and experiment conspire to reveal cryptic intermediates and a slide from the nucleation-condensation to framework mechanism of folding

There is a change from three-state to two-state kinetics of folding across the homeodomain superfamily of proteins as the mechanism slides from framework to nucleation-condensation. The tendency for framework folding in this family correlates with inherent helical propensity. The cellular myeloblastis protein (c-Myb) falls in the mechanistic transition region. An earlier, preliminary report of protein engineering experiments and molecular dynamics simulations (MD) showed that the folding mechanism for this protein has aspects of both the nucleation-condensation and framework models. In the more in-depth analysis of the MD trajectories presented here, we find that folding may be attributed to both of these mechanisms in different regions of the protein. The folding of the loop, middle helix, and turn is best described by nucleation-condensation, whereas folding of the N and C-terminal helices may be described by the framework model. Experimentally, c-Myb folds by apparent two-state kinetics, but the MD simulations predict that the kinetics hide a high-energy intermediate. We stabilized this hypothetical folding intermediate by deleting a residue (P174) in the loop between its second and third helices, and the mutant intermediate is long-lived in the simulations. Equilibrium and kinetic experiments demonstrate that folding of the DeltaP174 mutant is indeed three-state. The presence and shape of the intermediate observed in the simulations were confirmed by small angle X-ray scattering experiments.

How well can simulation predict protein folding kinetics and thermodynamics?

Simulation of protein folding has come a long way in five years. Notably, new quantitative comparisons with experiments for small, rapidly folding proteins have become possible. As the only way to validate simulation methodology, this achievement marks a significant advance. Here, we detail these recent achievements and ask whether simulations have indeed rendered quantitative predictions in several areas, including protein folding kinetics, thermodynamics, and physics-based methods for structure prediction. We conclude by looking to the future of such comparisons between simulations and experiments.

The Structure of the Major Transition State for Folding of an FF Domain from Experiment and Simulation

We have analysed the transition state of folding of the four-helix FF domain from HYPA/FBP11 by high-resolution experiment and simulation as part of a continuing effort to understand the principles of folding and the refinement of predictive methods. The major transition state for folding was subjected to a Phi-value analysis utilising 50 mutants. The transition state contained a nucleus for folding centred around the end of helix 1 (H1) and the beginning of helix 2 (H2). Secondary structure in this region was fully formed (PhiF=0.9-1) and tertiary interactions were well developed. Interactions in the distal part of the native structure were weak (PhiF=0-0.2). The hydrophobic core and other parts of the protein displayed intermediate Phi-values, suggesting that interactions coalesce as the end of H1 and beginning of H2 are in the process of being formed. The distribution of Phi-values resembled that of barnase, which folds via an intermediate, rather than that of CI2 which folds by a concerted nucleation-condensation mechanism. The overall picture of the transition state structure identified in molecular dynamics simulations is in qualitative agreement, with the turn connecting H1 and H2 being formed, a loosened core, and H4 partially unfolded and detached from the core. There are some differences in the details and interpretation of specific Phi-values.