Posttransition state desolvation of the hydrophobic core of the src-SH3 protein domain

The folding thermodynamics of the src-SH3 protein domain were characterized under refolding conditions through biased fully atomic molecular dynamics simulations with explicit solvent. The calculated free energy surfaces along several reaction coordinates revealed two barriers. The first, larger barrier was identified as the transition state barrier for folding, associated with the formation of the first hydrophobic sheet of the protein. phi values calculated from structures residing at the transition state barrier agree well with experimental phi values. The microscopic information obtained from our simulations allowed us to unambiguously assign intermediate phi values as the result of multiple folding pathways. The second, smaller barrier occurs later in the folding process and is associated with the cooperative expulsion of water molecules between the hydrophobic sheets of the protein. This posttransition state desolvation barrier cannot be observed through traditional folding experiments, but is found to be critical to the correct packing of the hydrophobic core in the final stages of folding. Hydrogen exchange and NMR experiments are suggested to probe this barrier.     

Dynamics, energetics, and structure in protein folding

For many decades, protein folding experimentalists have worked with no information about the time scales of relevant protein folding motions and without methods for estimating the height of folding barriers. Protein folding experiments have been interpreted using chemical models in which the folding process is characterized as a series of equilibria between two or more distinct states that interconvert with activated kinetics. Accordingly, the information to be extracted from experiments was circumscribed to apparent equilibrium constants and relative folding rates. Recent developments are changing this situation dramatically. The combination of fast-folding experiments with the development of analytical methods more closely connected to physical theory reveals that folding barriers in native conditions range from minimally high (approximately 14RT for the very slow folder AcP) to nonexistent. While slow-folding (i.e., > or = 1 ms) single-domain proteins are expected to fold in a two-state fashion, microsecond-folding proteins should exhibit complex behavior arising from crossing marginal or negligible folding barriers. This realization opens a realm of exciting opportunities for experimentalists. The free energy surface of a protein with a marginal (or no) barrier can be mapped using equilibrium experiments, which could resolve energetic factors from structural factors in folding. Kinetic experiments on these proteins provide the unique opportunity to measure folding dynamics directly. Furthermore, the complex distributions of time-dependent folding behaviors expected for these proteins might be accessible to single-molecule measurements. Here, we discuss some of these recent developments in protein folding, emphasizing aspects that can serve as a guide for experimentalists interested in exploiting this new avenue of research.     

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two‐state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non‐cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier‐less “downhill” folding, as well as for continuous “uphill” unfolding transitions, indicate that gradual non‐cooperative processes may be ubiquitous features on the free energy landscape of protein folding.     

Protein folding: matching theory and experiment.

The impact of folding funnels and folding simulations on the way experimentalists interpret results is examined. The image of the transition state has changed from a unique species that has a strained configuration, with a correspondingly high free energy, to a more ordinary folding intermediate, whose balance between limited conformational entropy and stabilizing contacts places it at the top of the free energy barrier. Evidence for a broad transition barrier comes from studies showing that mutations can change the position of the barrier. The main controversial issue now is whether populated folding intermediates are productive on-pathway intermediates or dead-end traps. Direct experimental evidence is needed. Theories suggesting that populated intermediates are trapped in a glasslike state are usually based on mechanisms which imply that trapping would only be extremely short-lived (e.g., nanoseconds) in water at 25 degrees C. There seems to be little experimental evidence for long-lived trapping in monomers, if folding aggregates are excluded. On the other hand, there is good evidence for kinetic trapping in dimers. alpha-Helix formation is currently the fastest known process in protein folding, and incipient helices are present at the start of folding. Fast helix formation has the effect of narrowing drastically the choice of folding routes. Thus helix formation can direct folding. It changes the folding metaphor from pouring liquid down a folding funnel to a train leaving a switchyard with only a few choices of exit tracks.     

Energy barriers, cooperativity, and hidden intermediates in the folding of small proteins

Current theoretical views of the folding process of small proteins (< approximately 100 amino acids) postulate that the landscape of potential mean force (PMF) for the formation of the native state has a funnel shape and that the free energy barrier to folding arises from the chain configurational entropy only. However, recent theoretical studies on the formation of hydrophobic clusters with explicit water suggest that a barrier should exist on the PMF of folding, consistent with the fact that protein folding generally involves a large positive activation enthalpy at room temperature. In addition, high-resolution structural studies of the hidden partially unfolded intermediates have revealed the existence of non-native interactions, suggesting that the correction of the non-native interactions during folding should also lead to barriers on PMF. To explore the effect of a PMF barrier on the folding behavior of proteins, we modified Zwanzig's model for protein folding with an uphill landscape of PMF for the formation of transition states. We found that the modified model for short peptide segments can satisfy the thermodynamic and kinetic criteria for an apparently two-state folding. Since the Levinthal paradox can be solved by a stepwise folding of short peptide segments, a landscape of PMF with a locally uphill search for the transition state and cooperative stabilization of folding intermediates/native state is able to explain the available experimental results for small proteins. We speculate that the existence of cooperative hidden folding intermediates in small proteins could be the consequence of the highly specific structures of the native state, which are selected by evolution to perform specific functions and fold in a biologically meaningful time scale.     

Evidence for sequential barriers and obligatory intermediates in apparent two-state protein folding

Many small proteins fold fast and without detectable intermediates. This is frequently taken as evidence against the importance of partially folded states, which often transiently accumulate during folding of larger proteins. To get insight into the properties of free energy barriers in protein folding we analyzed experimental data from 23 proteins that were reported to show non-linear activation free-energy relationships. These non-linearities are generally interpreted in terms of broad transition barrier regions with a large number of energetically similar states. Our results argue against the presence of a single broad barrier region. They rather indicate that the non-linearities are caused by sequential folding pathways with consecutive distinct barriers and a few obligatory high-energy intermediates. In contrast to a broad barrier model the sequential model gives a consistent picture of the folding barriers for different variants of the same protein and when folding of a single protein is analyzed under different solvent conditions. The sequential model is also able to explain changes from linear to non-linear free energy relationships and from apparent two-state folding to folding through populated intermediates upon single point mutations or changes in the experimental conditions. These results suggest that the apparent discrepancy between two-state and multi-state folding originates in the relative stability of the intermediates, which argues for the importance of partially folded states in protein folding.     

Ultrafast events in the folding of ferrocytochrome c

Laser flash photolysis and stopped-flow methods have been used to study the dynamic events in the micro- to millisecond time bin in the refolding of horse ferrocytochrome c in the full range of guanidine hydrochloride concentration at pH 12.8 (+/-0.1), 22 degrees C. Under the absolute refolding condition, the earliest relaxation time of the unfolded protein chain is less than 1 micros. The chain then undergoes diffusive dynamics-mediated contraction and expansion, in which intrapolypeptide ligands make transient contacts with the heme iron, giving rise to two distinct kinetic phases of approximately 0.4 and approximately 3 micros. Under moderate to absolute refolding conditions, the rates of these processes show little dependence on the denaturant concentration, indicating the absence of structural element in the incipient or the relaxed state. Chain expansion and contraction events continue until the polypeptide finds a stable and supportive transition state. The crossing of this transition barrier, which rate-limits the folding of alkaline ferrocytochrome c, is characterized by a stopped-flow measured time constant of approximately 3 ms in aqueous solvent. Observed kinetics thus implicate no submillisecond folding structure. The folding kinetics is effectively two state in which the unfolded polypeptide first relaxes to an unstructured chain and then crosses over a late rate-limiting barrier to achieve the native conformation. The experimentally observed rates as a function of guanidine hydrochloride concentration have been simulated by numerically calculated microscopic rates of a simple kinetic model that captures the essential features of folding.     

Nucleation‐based prediction of the protein folding rate and its correlation with the folding nucleus size

The problem of protein self‐organization is in the focus of current molecular biology studies. Although the general principles are understood, many details remain unclear. Specifically, protein folding rates are of interest because they dictate the rate of protein aggregation which underlies many human diseases. Here we offer predictions of protein folding rates and their correlation with folding nucleus sizes. We calculated free energies of the transition state and sizes of folding nuclei for 84 proteins and peptides whose other parameters were measured at the point of thermodynamic equilibrium between their unfolded and native states. We used the dynamic programming method where each residue was considered to be either as folded as in its native state or completely disordered. The calculated and measured folding rates showed a good correlation at the temperature mid‐transition point (the correlation coefficient was 0.75). Also, we pioneered in demonstrating a moderate (‐0.57) correlation coefficient between the calculated sizes of folding nuclei and the folding rates. Predictions made by different methods were compared. The established good correlation between the estimated free energy barrier and the experimentally found folding rate of each studied protein/peptide indicates that our model gives reliable results for the considered data set. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Protein folding mechanisms and the multidimensional folding funnel

An important idea that emerges from the energy landscape theory of protein folding is that subtle global features of the protein landscape can profoundly affect the apparent mechanism of folding. The relationship between various characteristic temperatures in the phase diagrams and landmarks in the folding funnel at fixed temperatures can be used to classify different folding behaviors. The one-dimensional picture of a folding funnel classifies folding kinetics into four basic scenarios, depending on the relative location of the thermodynamic barrier and the glass transition as a function of a single-order parameter. However, the folding mechanism may not always be quantitatively described by a single-order parameter. Several other order parameters, such as degree of secondary structure formation, collapse and topological order, are needed to establish the connection between minimalist models and proteins in the laboratory. In this article we describe a simple multidimensional funnel based on two-order parameters that measure the degree of collapse and topological order. The appearance of several different “mechanisms” is illustrated by analyzing lattice models with different potentials and sequences with different degrees of design. In most cases, the two-dimensional analysis leads to a classification of mechanisms totally in keeping with the one-dimensional scheme, but a topologically distinct scenario of fast folding with traps also emerges. The nature of traps depends on the relative location of the glass transition surface and the thermodynamic barrier in the multidimensional funnel. Proteins 32:136–158, 1998. © 1998 Wiley-Liss, Inc.     

Desolvation is a likely origin of robust enthalpic barriers to protein folding

Experimental data from global analyses of temperature (T) and denaturant dependence of the folding rates of small proteins led to an intrinsic enthalpic folding barrier hypothesis: to a good approximation, the T-dependence of folding rate under constant native stability conditions is Arrhenius. Furthermore, for a given protein, the slope of isostability folding rate versus 1/T is essentially independent of native stability. This hypothesis implies a simple relationship between chevron and Eyring plots of folding that is easily discernible when both sets of rates are expressed as functions of native stability. Using experimental data in the literature, we verify the predicted chevron-Eyring relationship for 14 proteins and determine their intrinsic enthalpic folding barriers, which vary approximately from 15 kcal/mol to 40 kcal/mol for different proteins. These enthalpic barriers do not appear to correlate with folding rates, but they exhibit correlation with equilibrium unfolding enthalpy at room temperature. Intrinsic enthalpic barriers with similarly high magnitudes apply as well to at least two cases of peptide-peptide and peptide-protein association, suggesting that these barriers are a hallmark of certain general and fundamental kinetic processes during folding and binding. Using a class of explicit-chain C(alpha) protein models with constant elementary enthalpic desolvation barriers between C(alpha) positions, we show that small microscopic pairwise desolvation barriers, which are a direct consequence of the particulate nature of water, can act cooperatively to give rise to a significant overall enthalpic barrier to folding. This theoretical finding provides a physical rationalization for the high intrinsic enthalpic barriers in protein folding energetics. Ramifications of entropy-enthalpy compensation in hydrophobic association for the height of enthalpic desolvation barrier are discussed.     

The influence of intrinsic folding mechanism of an unfolded protein on the coupled folding-binding process during target recognition

Intrinsically disordered proteins (IDPs) are extensively involved in dynamic signaling processes which require a high association rate and a high dissociation rate for rapid binding/unbinding events and at the same time a sufficient high affinity for specific recognition. Although the coupled folding-binding processes of IDPs have been extensively studied, it is still impossible to predict whether an unfolded protein is suitable for molecular signaling via coupled folding-binding. In this work, we studied the interplay between intrinsic folding mechanisms and coupled folding-binding process for unfolded proteins through molecular dynamics simulations. We first studied the folding process of three representative IDPs with different folded structures, that is, c-Myb, AF9, and E3 rRNase. We found the folding free energy landscapes of IDPs are downhill or show low barriers. To further study the influence of intrinsic folding mechanism on the binding process, we modulated the folding mechanism of barnase via circular permutation and simulated the coupled folding-binding process between unfolded barnase permutant and folded barstar. Although folding of barnase was coupled to target binding, the binding kinetics was significantly affected by the intrinsic folding free energy barrier, where reducing the folding free energy barrier enhances binding rate up to two orders of magnitude. This accelerating effect is different from previous results which reflect the effect of structure flexibility on binding kinetics. Our results suggest that coupling the folding of an unfolded protein with no/low folding free energy barrier with its target binding may provide a way to achieve high specificity and rapid binding/unbinding kinetics simultaneously.     

Chevron behavior and isostable enthalpic barriers in protein folding: successes and limitations of simple Gō-like modeling

It has been demonstrated that a "near-Levinthal" cooperative mechanism, whereby the common Gō interaction scheme is augmented by an extra favorability for the native state as a whole, can lead to apparent two-state folding/unfolding kinetics over a broad range of native stabilities in lattice models of proteins. Here such a mechanism is shown to be generalizable to a simplified continuum (off-lattice) Langevin dynamics model with a Calpha protein chain representation, with the resulting chevron plots exhibiting an extended quasilinear regime reminiscent of that of apparent two-state real proteins. Similarly high degrees of cooperativity are possible in Gō-like continuum models with rudimentary pairwise desolvation barriers as well. In these models, cooperativity increases with increasing desolvation barrier height, suggesting strongly that two-state-like folding/unfolding kinetics would be achievable when the pairwise desolvation barrier becomes sufficiently high. Besides cooperativity, another generic folding property of interest that has emerged from published experiments on several apparent two-state proteins is that their folding relaxation under constant native stability (isostability) conditions is essentially Arrhenius, entailing high intrinsic enthalpic folding barriers of approximately 17-30 kcal/mol. Based on a new analysis of published data on barnase, here we propose that a similar property should also apply to a certain class of non-two-state proteins that fold with chevron rollovers. However, several continuum Gō-like constructs considered here fail to predict any significant intrinsic enthalpic folding barrier under isostability conditions; thus the physical origin of such barriers in real proteins remains to be elucidated.     

分子内分子伴侣--Pro肽在蛋白质折叠中的作用

在体内,许多蛋白质,如很多胞外蛋白酶、某些多肽激素等都以含前导肽的前体形式合成,前导肽在蛋白质折叠中具有分子伴侣的功能。为了与一般意义上的分子伴侣相区别,人们将对蛋白质折叠有帮助的前导肽称为分子内分子伴侣,分子内分子伴侣帮助蛋白质在折叠过程中克服高的能量障碍,某些蛋白质的分子内分子伴侣甚至促进其在氧化性折叠中二硫键的正确配对。     

A framework for describing topological frustration in models of protein folding

In a natively folded protein of moderate or larger size, the protein backbone may weave through itself in complex ways, raising questions about what sequence of events might have to occur in order for the protein to reach its native configuration from the unfolded state. A mathematical framework is presented here for describing the notion of a topological folding barrier, which occurs when a protein chain must pass through a hole or opening, formed by other regions of the protein structure. Different folding pathways encounter different numbers of such barriers and therefore different degrees of frustration. A dynamic programming algorithm finds the optimal theoretical folding path and minimal degree of frustration for a protein based on its natively folded configuration. Calculations over a database of protein structures provide insights into questions such as whether the path of minimal frustration might tend to favor folding from one or from many sites of folding nucleation, or whether proteins favor folding around the N terminus, thereby providing support for the hypothesis that proteins fold co-translationally. The computational methods are applied to a multi-disulfide bonded protein, with computational findings that are consistent with the experimentally observed folding pathway. Attention is drawn to certain complex protein folds for which the computational method suggests there may be a preferred site of nucleation or where folding is likely to proceed through a relatively well-defined pathway or intermediate. The computational analyses lead to testable models for protein folding.     

Apparent two-state tendamistat folding is a sequential process along a defined route

The small all-beta-sheet protein tendamistat folds and unfolds rapidly in apparent two-state reactions. Kinetic measurements of two tendamistat variants under various solvent conditions reveal, however, that folding occurs in at least two sequential steps through a metastable obligatory intermediate. Depending on the solvent conditions either step can become rate limiting. The activation parameters indicate that the first step represents an enthalpic barrier whereas the second step is an entropic barrier at 25 degrees C. Our results suggest that initial non-specific collapse precedes formation of native secondary and tertiary structure in tendamistat folding. This points at a distinct route in tendamistat folding and indicates that partially folded metastable intermediates might play an important role in the mechanism of apparent two-state folding.     

The folding landscape of an alpha-lytic protease variant reveals the role of a conserved beta-hairpin in the development of kinetic stability

Most secreted bacterial proteases, including alpha-lytic protease (alphaLP), are synthesized with covalently attached pro regions necessary for their folding. The alphaLP folding landscape revealed that its pro region, a potent folding catalyst, is required to circumvent an extremely large folding free energy of activation that appears to be a consequence of its unique unfolding transition. Remarkably, the alphaLP native state is thermodynamically unstable; a large unfolding free energy barrier is solely responsible for the persistence of its native state. Although alphaLP folding is well characterized, the structural origins of its remarkable folding mechanism remain unclear. A conserved beta-hairpin in the C-terminal domain was identified as a structural element whose formation and positioning may contribute to the large folding free energy barrier. In this article, we characterize the folding of an alphaLP variant with a more favorable beta-hairpin turn conformation (alphaLP(beta-turn)). Indeed, alphaLP(beta-turn) pro region-catalyzed folding is faster than that for alphaLP. However, instead of accelerating spontaneous folding, alphaLP(beta-turn) actually unfolds more slowly than alphaLP. Our data support a model where the beta-hairpin is formed early, but its packing with a loop in the N-terminal domain happens late in the folding reaction. This tight packing at the domain interface enhances the kinetic stability of alphaLP(beta-turn), to nearly the same degree as the change between alphaLP and a faster folding homolog. However, alphaLP(beta-turn) has impaired proteolytic activity that negates the beneficial folding properties of this variant. This study demonstrates the evolutionary limitations imposed by the simultaneous optimization of folding and functional properties.     

Engineering strand-specific DNA nicking enzymes from the type IIS restriction endonucleases BsaI, BsmBI, and BsmAI

To determine the extent to which protein folding rates and free energy landscapes have been shaped by natural selection, we have examined the folding kinetics of five proteins generated using computational design methods and, hence, never exposed to natural selection. Four of these proteins are complete computer-generated redesigns of naturally occurring structures and the fifth protein, called Top7, has a computer-generated fold not yet observed in nature. We find that three of the four redesigned proteins fold much faster than their naturally occurring counterparts. While natural selection thus does not appear to operate on protein folding rates, the majority of the designed proteins unfold considerably faster than their naturally occurring counterparts, suggesting possible selection for a high free energy barrier to unfolding. In contrast to almost all naturally occurring proteins of less than 100 residues but consistent with simple computational models, the folding energy landscape for Top7 appears to be quite complex, suggesting the smooth energy landscapes and highly cooperative folding transitions observed for small naturally occurring proteins may also reflect the workings of natural selection.     

Comparing the folding and misfolding energy landscapes of phosphoglycerate kinase

Partitioning of polypeptides between protein folding and amyloid formation is of outstanding pathophysiological importance. Using yeast phosphoglycerate kinase as model, here we identify the features of the energy landscape that decide the fate of the protein: folding or amyloidogenesis. Structure formation was initiated from the acid-unfolded state, and monitored by fluorescence from 10 ms to 20 days. Solvent conditions were gradually shifted between folding and amyloidogenesis, and the properties of the energy landscape governing structure formation were reconstructed. A gradual transition of the energy landscape between folding and amyloid formation was observed. In the early steps of both folding and misfolding, the protein searches through a hierarchically structured energy landscape to form a molten globule in a few seconds. Depending on the conditions, this intermediate either folds to the native state in a few minutes, or forms amyloid fibers in several days. As conditions are changed from folding to misfolding, the barrier separating the molten globule and native states increases, although the barrier to the amyloid does not change. In the meantime, the native state also becomes more unstable and the amyloid more stable. We conclude that the lower region of the energy landscape determines the final protein structure.     

Proteome Folding Kinetics Is Limited by Protein Halflife

How heterogeneous are proteome folding timescales and what physical principles, if any, dictate its limits? We answer this by predicting copy number weighted folding speed distribution – using the native topology – for E.coli and Yeast proteome. E.coli and Yeast proteomes yield very similar distributions with average folding times of 100 milliseconds and 170 milliseconds, respectively. The topology-based folding time distribution is well described by a diffusion-drift mutation model on a flat-fitness landscape in free energy barrier between two boundaries: i) the lowest barrier height determined by the upper limit of folding speed and ii) the highest barrier height governed by the lower speed limit of folding. While the fastest time scale of the distribution is near the experimentally measured speed limit of 1 microsecond (typical of barrier-less folders), we find the slowest folding time to be around seconds (8 seconds for Yeast distribution), approximately an order of magnitude less than the fastest halflife (approximately 2 minutes) in the Yeast proteome. This separation of timescale implies even the fastest degrading protein will have moderately high (96%) probability of folding before degradation. The overall agreement with the flat-fitness landscape model further hints that proteome folding times did not undergo additional major selection pressures – to make proteins fold faster – other than the primary requirement to “sufficiently beat the clock” against its lifetime. Direct comparison between the predicted folding time and experimentally measured halflife further shows 99% of the proteome have a folding time less than their corresponding lifetime. These two findings together suggest that proteome folding kinetics may be bounded by protein halflife.     

Burst-phase expansion of native protein prior to global unfolding in SDS

Although numerous studies have been directed at understanding early folding events through the characterization of folding intermediates, there are few reports on the very late folding events, i.e. on the events taking place on the native side of the folding barrier and on alternative conformations of the folded state. To shed further light on these issues, we have characterized by protein engineering the structure of an expanded but native-like intermediate that accumulates transiently in the unfolding reaction of the small protein S6 in the presence of SDS. The results show that the SDS micelles attack the native protein in the dead-time of the denaturation experiment, causing an expansion of the hydrophobic core prior to the major unfolding transition. We distinguish two forms of the unfolding intermediate that are correlated with the micellar structure. With spherical micelles, the expansion is seen mainly as a weakening of the interactions which anchor the two alpha-helices to the core of the S6 structure. With cylindrical micelles, prevalent at higher SDS concentrations, the expansion is more global and produces a species which closely resembles the transition-state structure for unfolding in GdmCl. Despite the highly weakened core, the micelle-associated intermediate displays cooperative unfolding, indicating a significant structural plasticity of the species on the native side of the folding barrier in the presence of SDS.