Experimental evidence for a frustrated energy landscape in a three-helix-bundle protein family

Diffusion Monte Carlo study on temporal evolution of entropy and free energy in nonequilibrium processes

A computational scheme to describe the temporal evolution of thermodynamic functions in stochastic nonequilibrium processes of isothermal classical systems is proposed on the basis of overdamped Langevin equation under given potential and temperature. In this scheme the associated Fokker-Planck-Smoluchowski equation for the probability density function is transformed into the imaginary-time Schrödinger equation with an effective Hamiltonian. The propagator for the time-dependent wave function is expressed in the framework of the path integral formalism, which can thus represent the dynamical behaviors of nonequilibrium molecular systems such as those conformational changes observed in protein folding and ligand docking. The present study then employs the diffusion Monte Carlo method to efficiently simulate the relaxation dynamics of wave function in terms of random walker distribution, which in the long-time limit reduces to the ground-state eigenfunction corresponding to the equilibrium Boltzmann distribution. Utilizing this classical-quantum correspondence, we can describe the relaxation processes of thermodynamic functions as an approach to the equilibrium state with the lowest free energy. Performing illustrative calculations for some prototypical model potentials, the temporal evolutions of enthalpy, entropy, and free energy of the classical systems are explicitly demonstrated. When the walkers initially start from a localized configuration in one- or two-dimensional harmonic or double well potential, the increase of entropy usually dominates the relaxation dynamics toward the equilibrium state. However, when they start from a broadened initial distribution or go into a steep valley of potential, the dynamics are driven by the decrease of enthalpy, thus causing the decrease of entropy associated with the spatial localization. In the cases of one- and two-dimensional asymmetric double well potentials with two minimal points and an energy barrier between them, we observe a nonequilibrium behavior that the system entropy first increases with the broadening of the initially localized walker distribution and then it begins to decrease along with the trapping at the global minimum of the potential, thus leading to the minimization of the free energy.

Structural origin of slow diffusion in protein folding

Experimental, theoretical, and computational studies of small proteins suggest that interresidue contacts not present in the folded structure play little or no role in the self-assembly mechanism. Non-native contacts can, however, influence folding kinetics by introducing additional local minima that slow diffusion over the global free-energy barrier between folded and unfolded states. Here, we combine single-molecule fluorescence with all-atom molecular dynamics simulations to discover the structural origin for the slow diffusion that markedly decreases the folding rate for a designed α-helical protein. Our experimental determination of transition path times and our analysis of the simulations point to non-native salt bridges between helices as the source, which provides a quantitative glimpse of how specific intramolecular interactions influence protein folding rates by altering dynamics and not activation free energies.

Protein misfolding occurs by slow diffusion across multiple barriers in a rough energy landscape

The timescale for the microscopic dynamics of proteins during conformational transitions is set by the intrachain diffusion coefficient, D. Despite the central role of protein misfolding and aggregation in many diseases, it has proven challenging to measure D for these processes because of their heterogeneity. We used single-molecule force spectroscopy to overcome these challenges and determine D for misfolding of the prion protein PrP. Observing directly the misfolding of individual dimers into minimal aggregates, we reconstructed the energy landscape governing nonnative structure formation. Remarkably, rather than displaying multiple pathways, as typically expected for aggregation, PrP dimers were funneled into a thermodynamically stable misfolded state along a single pathway containing several intermediates, one of which blocked native folding. Using Kramers' rate theory, D was found to be 1,000-fold slower for misfolding than for native folding, reflecting local roughening of the misfolding landscape, likely due to increased internal friction. The slow diffusion also led to much longer transit times for barrier crossing, allowing transition paths to be observed directly for the first time to our knowledge. These results open a new window onto the microscopic mechanisms governing protein misfolding.

Autonomously folding protein fragments reveal differences in the energy landscapes of homologous RNases H

An important approach to understanding how a protein sequence encodes its energy landscape is to compare proteins with different sequences that fold to the same general native structure. In this work, we compare E. coli and T. thermophilus homologs of the protein RNase H. Using protein fragments, we create equilibrium mimics of two different potential partially-folded intermediates (I(core) and I(core+1)) hypothesized to be present on the energy landscapes of these two proteins. We observe that both T. thermophilus RNase H (ttRNH) fragments are folded and have distinct stabilities, indicating that both regions are capable of autonomous folding and that both intermediates are present as local minima on the ttRNH energy landscape. In contrast, the two E. coli RNase H (ecRNH) fragments have very similar stabilities, suggesting that the presence of additional residues in the I(core+1) fragment does not affect the folding or structure as compared to I(core). NMR experiments provide additional evidence that only the I(core) intermediate is populated by ecRNH. This is one of the biggest differences that has been observed between the energy landscapes of these two proteins. Additionally, we used a FRET experiment in the background of full-length ttRNH to specifically monitor the formation of the I(core+1) intermediate. We determine that the ttRNH I(core+1) intermediate is likely the intermediate populated prior to the rate-limiting barrier to global folding, in contrast to E. coli RNase H for which I(core) is the folding intermediate. This result provides new insight into the nature of the rate-limiting barrier for the folding of RNase H.

Dependence of internal friction on folding mechanism

An outstanding challenge in protein folding is understanding the origin of "internal friction" in folding dynamics, experimentally identified from the dependence of folding rates on solvent viscosity. A possible origin suggested by simulation is the crossing of local torsion barriers. However, it was unclear why internal friction varied from protein to protein or for different folding barriers of the same protein. Using all-atom simulations with variable solvent viscosity, in conjunction with transition-path sampling to obtain reaction rates and analysis via Markov state models, we are able to determine the internal friction in the folding of several peptides and miniproteins. In agreement with experiment, we find that the folding events with greatest internal friction are those that mainly involve helix formation, while hairpin formation exhibits little or no evidence of friction. Via a careful analysis of folding transition paths, we show that internal friction arises when torsion angle changes are an important part of the folding mechanism near the folding free energy barrier. These results suggest an explanation for the variation of internal friction effects from protein to protein and across the energy landscape of the same protein.

The roughness of the protein energy landscape results in anomalous diffusion of the polypeptide backbone

Recombination of photolysed protein disulfide bonds confirms subdiffusional backbone motion and measures the roughness of the protein's energy landscape.

Towards the free energy landscape for catalysis in mammalian nitric oxide synthases

The general requirement for conformational sampling in biological electron transfer reactions catalysed by multi-domain redox systems has been emphasized in recent years. Crucially, we lack insight into the extent of the conformational space explored and the nature of the energy landscapes associated with these reactions. The nitric oxide synthases (NOS) produce the signalling molecule NO through a series of complex electron transfer reactions. There is accumulating evidence that protein domain dynamics and calmodulin binding are implicated in regulating electron flow from NADPH, through the FAD and FMN cofactors, to the haem oxygenase domain, where NO is generated. Simple models based on static crystal structures of the isolated reductase domain have suggested a role for large-scale motions of the FMN-binding domain in shuttling electrons from the reductase domain to the oxygenase domain. However, detailed insight into the higher-order domain architecture and dynamic structural transitions in NOS enzymes during enzyme turnover is lacking. In this review, we discuss the recent advances made towards mapping the catalytic free energy landscapes of NOS enzymes through integration of both structural techniques (e.g. cryo-electron microscopy) and biophysical techniques (e.g. pulsed-electron paramagnetic resonance). The general picture that emerges from these experiments is that NOS enzymes exist in an equilibrium of conformations, comprising a 'rugged' or 'frustrated' energy landscape, with a key regulatory role for calmodulin in driving vectorial electron transfer by altering the conformational equilibrium. A detailed understanding of these landscapes may provide new opportunities for discovery of isoform-specific inhibitors that bind at the dynamic interfaces of these multi-dimensional energy landscapes.

Evolution, energy landscapes and the paradoxes of protein folding

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signaling a beautiful confluence of genomics and chemical physics.

Mechanistic studies of the biogenesis and folding of outer membrane proteins in vitro and in vivo: what have we learned to date?

Research into the mechanisms by which proteins fold into their native structures has been on-going since the work of Anfinsen in the 1960s. Since that time, the folding mechanisms of small, water-soluble proteins have been well characterised. By contrast, progress in understanding the biogenesis and folding mechanisms of integral membrane proteins has lagged significantly because of the need to create a membrane mimetic environment for folding studies in vitro and the difficulties in finding suitable conditions in which reversible folding can be achieved. Improved knowledge of the factors that promote membrane protein folding and disfavour aggregation now allows studies of folding into lipid bilayers in vitro to be performed. Consequently, mechanistic details and structural information about membrane protein folding are now emerging at an ever increasing pace. Using the panoply of methods developed for studies of the folding of water-soluble proteins. This review summarises current knowledge of the mechanisms of outer membrane protein biogenesis and folding into lipid bilayers in vivo and in vitro and discusses the experimental techniques utilised to gain this information. The emerging knowledge is beginning to allow comparisons to be made between the folding of membrane proteins with current understanding of the mechanisms of folding of water-soluble proteins.

The role of high-dimensional diffusive search, stabilization, and frustration in protein folding

Proteins are polymeric molecules with many degrees of conformational freedom whose internal energetic interactions are typically screened to small distances. Therefore, in the high-dimensional conformation space of a protein, the energy landscape is locally relatively flat, in contrast to low-dimensional representations, where, because of the induced entropic contribution to the full free energy, it appears funnel-like. Proteins explore the conformation space by searching these flat subspaces to find a narrow energetic alley that we call a hypergutter and then explore the next, lower-dimensional, subspace. Such a framework provides an effective representation of the energy landscape and folding kinetics that does justice to the essential characteristic of high-dimensionality of the search-space. It also illuminates the important role of nonnative interactions in defining folding pathways. This principle is here illustrated using a coarse-grained model of a family of three-helix bundle proteins whose conformations, once secondary structure has formed, can be defined by six rotational degrees of freedom. Two folding mechanisms are possible, one of which involves an intermediate. The stabilization of intermediate subspaces (or states in low-dimensional projection) in protein folding can either speed up or slow down the folding rate depending on the amount of native and nonnative contacts made in those subspaces. The folding rate increases due to reduced-dimension pathways arising from the mere presence of intermediate states, but decreases if the contacts in the intermediate are very stable and introduce sizeable topological or energetic frustration that needs to be overcome. Remarkably, the hypergutter framework, although depending on just a few physically meaningful parameters, can reproduce all the types of experimentally observed curvature in chevron plots for realizations of this fold.

Interplay between partner and ligand facilitates the folding and binding of an intrinsically disordered protein

Protein-protein interactions are at the heart of regulatory and signaling processes in the cell. In many interactions, one or both proteins are disordered before association. However, this disorder in the unbound state does not prevent many of these proteins folding to a well-defined, ordered structure in the bound state. Here we examine a typical system, where a small disordered protein (PUMA, p53 upregulated modulator of apoptosis) folds to an α-helix when bound to a groove on the surface of a folded protein (MCL-1, induced myeloid leukemia cell differentiation protein). We follow the association of these proteins using rapid-mixing stopped flow, and examine how the kinetic behavior is perturbed by denaturant and carefully chosen mutations. We demonstrate the utility of methods developed for the study of monomeric protein folding, including β-Tanford values, Leffler α, Φ-value analysis, and coarse-grained simulations, and propose a self-consistent mechanism for binding. Folding of the disordered protein before binding does not appear to be required and few, if any, specific interactions are required to commit to association. The majority of PUMA folding occurs after the transition state, in the presence of MCL-1. We also examine the role of the side chains of folded MCL-1 that make up the binding groove and find that many favor equilibrium binding but, surprisingly, inhibit the association process.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has, therefore, been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase-space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs/PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, a 1 ms Anton MD simulation of the bovine pancreatic trypsin inhibitor protein, and an optical tweezer force probe trajectory of an RNA hairpin.

Molecular origins of internal friction effects on protein-folding rates

Recent experiments on protein folding dynamics have revealed strong evidence for internal friction effects. That is, observed relaxation times are not simply proportional to the solvent viscosity as might be expected if the solvent were the only source of friction. However, a molecular interpretation of this remarkable phenomenon is currently lacking. Here, we use all-atom simulations of peptide and protein folding in explicit solvent, to probe the origin of the unusual viscosity dependence. We find that an important contribution to this effect, explaining the viscosity dependence of helix formation and the folding of a helix-containing protein, is the insensitivity of torsion angle isomerization to solvent friction. The influence of this landscape roughness can, in turn, be quantitatively explained by a rate theory including memory friction. This insensitivity of local barrier crossing to solvent friction is expected to contribute to the viscosity dependence of folding rates in larger proteins.

Folding of fourteen small proteins with a residue-specific force field and replica-exchange molecular dynamics

Ab initio protein folding via physical-based all-atom simulation is still quite challenging. Using a recently developed residue-specific force field (RSFF1) in explicit solvent, we are able to fold a diverse set of 14 model proteins. The obtained structural features of unfolded state are in good agreement with previous observations. The replica-exchange molecular dynamics simulation is found to be efficient, resulting in multiple folding events for each protein. Transition path time is found to be significantly reduced under elevated temperature.

Quantifying the Sources of Kinetic Frustration in Folding Simulations of Small Proteins

Experiments and atomistic simulations of polypeptides have revealed structural intermediates that promote or inhibit conformational transitions to the native state during folding. We invoke a concept of “kinetic frustration” to quantify the prevalence and impact of these behaviors on folding rates within a large set of atomistic simulation data for 10 fast-folding proteins, where each protein’s conformational space is represented as a Markov state model of conformational transitions. Our graph theoretic approach addresses what conformational features correlate with folding inhibition and therefore permits comparison among features within a single protein network and also more generally between proteins. Nonnative contacts and nonnative secondary structure formation can thus be quantitatively implicated in inhibiting folding for several of the tested peptides.

The folding of a family of three-helix bundle proteins: spectrin R15 has a robust folding nucleus, unlike its homologous neighbours

Three homologous spectrin domains have remarkably different folding characteristics. We have previously shown that the slow-folding R16 and R17 spectrin domains can be altered to resemble the fast folding R15, in terms of speed of folding (and unfolding), landscape roughness and folding mechanism, simply by substituting five residues in the core. Here we show that, by contrast, R15 cannot be engineered to resemble R16 and R17. It is possible to engineer a slow-folding version of R15, but our analysis shows that this protein neither has a rougher energy landscape nor does change its folding mechanism. Quite remarkably, R15 appears to be a rare example of a protein with a folding nucleus that does not change in position or in size when its folding nucleus is disrupted. Thus, while two members of this protein family are remarkably plastic, the third has apparently a restricted folding landscape.

Understanding the mechanism of proteasome 20S core particle gating

The 20S core particle proteasome is a molecular machine playing an important role in cellular function by degrading protein substrates that no longer are required or that have become damaged. Regulation of proteasome activity occurs, in part, through a gating mechanism controlling the sizes of pores at the top and bottom ends of the symmetric proteasome barrel and restricting access to catalytic sites sequestered in the lumen of the structure. Although atomic resolution models of both open and closed states of the proteasome have been elucidated, the mechanism by which gates exchange between these states remains to be understood. Here, this is investigated by using magnetization transfer NMR spectroscopy focusing on the 20S proteasome core particle from Thermoplasma acidophilum. We show from viscosity-dependent proteasome gating kinetics that frictional forces originating from random solvent motions are critical for driving the gating process. Notably, a small effective hydrodynamic radius (EHR; <4Å) is obtained, providing a picture in which gate exchange proceeds through many steps involving only very small segment sizes. A small EHR further suggests that the kinetics of gate interconversion will not be affected appreciably by large viscogens, such as macromolecules found in the cell, so long as they are inert. Indeed, measurements in cell lysate reveal that the gate interconversion rate decreases only slightly, demonstrating that controlled studies in vitro provide an excellent starting point for understanding regulation of 20S core particle function in complex, biologically relevant environments.

Transient non-native helix formation during the folding of β-lactoglobulin

In ideal proteins, only native interactions are stabilized step-by-step in a smooth funnel-like energy landscape. In real proteins, however, the transient formation of non-native structures is frequently observed. In this review, the transient formation of non-native structures is described using the non-native helix formation during the folding of β-lactoglobulin as a prominent example. Although β-lactoglobulin is a predominantly β-sheet protein, it has been shown to form non-native helices during the early stage of folding. The location of non-native helices, their stabilization mechanism, and their role in the folding reaction are discussed.

Energetic frustrations in protein folding at residue resolution: a homologous simulation study of Im9 proteins

Energetic frustration is becoming an important topic for understanding the mechanisms of protein folding, which is a long-standing big biological problem usually investigated by the free energy landscape theory. Despite the significant advances in probing the effects of folding frustrations on the overall features of protein folding pathways and folding intermediates, detailed characterizations of folding frustrations at an atomic or residue level are still lacking. In addition, how and to what extent folding frustrations interact with protein topology in determining folding mechanisms remains unclear. In this paper, we tried to understand energetic frustrations in the context of protein topology structures or native-contact networks by comparing the energetic frustrations of five homologous Im9 alpha-helix proteins that share very similar topology structures but have a single hydrophilic-to-hydrophobic mutual mutation. The folding simulations were performed using a coarse-grained Gō-like model, while non-native hydrophobic interactions were introduced as energetic frustrations using a Lennard-Jones potential function. Energetic frustrations were then examined at residue level based on φ-value analyses of the transition state ensemble structures and mapped back to native-contact networks. Our calculations show that energetic frustrations have highly heterogeneous influences on the folding of the four helices of the examined structures depending on the local environment of the frustration centers. Also, the closer the introduced frustration is to the center of the native-contact network, the larger the changes in the protein folding. Our findings add a new dimension to the understanding of protein folding the topology determination in that energetic frustrations works closely with native-contact networks to affect the protein folding.

Assessment of local friction in protein folding dynamics using a helix cross-linker

Internal friction arising from local steric hindrance and/or the excluded volume effect plays an important role in controlling not only the dynamics of protein folding but also conformational transitions occurring within the native state potential well. However, experimental assessment of such local friction is difficult because it does not manifest itself as an independent experimental observable. Herein, we demonstrate, using the miniprotein trp-cage as a testbed, that it is possible to selectively increase the local mass density in a protein and hence the magnitude of local friction, thus making its effect directly measurable via folding kinetic studies. Specifically, we show that when a helix cross-linker, m-xylene, is placed near the most congested region of the trp-cage it leads to a significant decrease in both the folding rate (by a factor of 3.8) and unfolding rate (by a factor of 2.5 at 35 °C) but has little effect on protein stability. Thus, these results, in conjunction with those obtained with another cross-linked trp-cage and two uncross-linked variants, demonstrate the feasibility of using a nonperturbing cross-linker to help quantify the effect of internal friction. In addition, we estimate that a m-xylene cross-linker could lead to an increase in the roughness of the folding energy landscape by as much as 0.4-1.0k(B)T.

Visualizing side chains of invisible protein conformers by solution NMR

Sparsely populated and transiently formed protein conformers can play key roles in many biochemical processes. Understanding the structure function paradigm requires, therefore, an atomic-resolution description of these rare states. However, they are difficult to study because they cannot be observed using standard biophysical techniques. In the past decade, NMR methods have been developed for structural studies of these elusive conformers, focusing primarily on backbone (1)H, (15)N and (13)C nuclei. Here we extend the methodology to include side chains by developing a (13)C-based chemical exchange saturation transfer experiment for the assignment of side-chain aliphatic (13)C chemical shifts in uniformly (13)C labeled proteins. A pair of applications is provided, involving the folding of β-sheet Fyn SH3 and α-helical FF domains. Over 96% and 89% of the side-chain (13)C chemical shifts for excited states corresponding to the unfolded conformation of the Fyn SH3 domain and a folding intermediate of the FF domain, respectively, have been obtained, providing insight into side-chain packing and dynamics.

How well does a funneled energy landscape capture the folding mechanism of spectrin domains?

Three structurally similar domains from α-spectrin have been shown to fold very differently. First, there is a contrast in the folding mechanism, as probed by Φ-value analysis, between the R15 domain and the R16 and R17 domains. Second, there are very different contributions from internal friction to folding: the folding rate of the R15 domain was found to be inversely proportional to solvent viscosity, showing no apparent frictional contribution from the protein, but in the other two domains, a large internal friction component was evident. Non-native misdocking of helices has been suggested to be responsible for this phenomenon. Here, I study the folding of these three proteins with minimalist coarse-grained models based on a funneled energy landscape. Remarkably, I find that, despite the absence of non-native interactions, the differences in folding mechanism of the domains are well captured by the model, and the agreement of the Φ-values with experiment is fairly good. On the other hand, within the context of this model, there are no significant differences in diffusion coefficient along the chosen folding coordinate, and the model cannot explain the large differences in folding rates between the proteins found experimentally. These results are nonetheless consistent with the expectations from the energy landscape perspective of protein folding, namely, that the folding mechanism is primarily determined by the native-like interactions present in the Gō-like model, with missing non-native interactions being required to explain the differences in "internal friction" seen in experiment.

Single-molecule fluorescence probes dynamics of barrier crossing

Kramers developed the theory on how chemical reaction rates are influenced by the viscosity of the medium. At the viscosity of water, the kinetics of unimolecular reactions are described by diffusion of a Brownian particle over a free-energy barrier separating reactants and products. For reactions in solution this famous theory extended Eyring's transition state theory, and is widely applied in physics, chemistry and biology, including to reactions as complex as protein folding. Because the diffusion coefficient of Kramers' theory is determined by the dynamics in the sparsely populated region of the barrier top, its properties have not been directly measured for any molecular system. Here we show that the Kramers diffusion coefficient and free-energy barrier can be characterized by measuring the temperature- and viscosity-dependence of the transition path time for protein folding. The transition path is the small fraction of an equilibrium trajectory for a single molecule when the free-energy barrier separating two states is actually crossed. Its duration, the transition path time, can now be determined from photon trajectories for single protein molecules undergoing folding/unfolding transitions. Our finding of a long transition path time with an unusually small solvent viscosity dependence suggests that internal friction as well as solvent friction determine the Kramers diffusion coefficient for α-helical proteins, as opposed to a breakdown of his theory, which occurs for many small-molecule reactions. It is noteworthy that the new and fundamental information concerning Kramers' theory and the dynamics of barrier crossings obtained here come from experiments on a protein rather than a much simpler chemical or physical system.

Native contacts determine protein folding mechanisms in atomistic simulations

The recent availability of long equilibrium simulations of protein folding in atomistic detail for more than 10 proteins allows us to identify the key interactions driving folding. We find that the collective fraction of native amino acid contacts, Q, captures remarkably well the transition states for all the proteins with a folding free energy barrier. Going beyond this global picture, we devise two different measures to quantify the importance of individual interresidue contacts in the folding mechanism: (i) the log-ratio of lifetimes of contacts during folding transition paths and in the unfolded state and (ii) a Bayesian measure of how predictive the formation of each contact is for being on a transition path. Both of these measures indicate that native, or near-native, contacts are important for determining mechanism, as might be expected. More remarkably, however, we found that for almost all the proteins, with the designed protein α3D being a notable exception, nonnative contacts play no significant part in determining folding mechanisms.

Membrane proteins can have high kinetic stability

Approximately 10% of water-soluble proteins are considered kinetically stable with unfolding half-lives in the range of weeks to millenia. These proteins only rarely sample the unfolded state and may never unfold on their respective biological time scales. It is still not known whether membrane proteins can be kinetically stable, however. Here we examine the subunit dissociation rate of the trimeric membrane enzyme, diacylglycerol kinase, from Escherichia coli as a proxy for complete unfolding. We find that dissociation occurs with a half-life of at least several weeks, demonstrating that membrane proteins can remain locked in a folded state for long periods of time. These results reveal that evolution can use kinetic stability to regulate the biological function of membrane proteins, as it can for soluble proteins. Moreover, it appears that the generation of kinetic stability could be a viable target for membrane protein engineering efforts.

Frustration-induced protein intrinsic disorder

Spontaneous folding into a specific native structure is the most important property of protein to perform their biological functions within organisms. Spontaneous folding is understood on the basis of an energy landscape picture based on the minimum frustration principle. Therefore, frustration seemingly only leads to protein functional disorder. However, frustration has recently been suggested to have a function in allosteric regulation. Functional frustration has the possibility to be a key to our deeper understanding of protein function. To explore another functional frustration, we theoretically examined structural frustration, which is designed to induce intrinsic disorder of a protein and its function through the coupled folding and binding. We extended the Wako-Saitô-Muñoz-Eaton model to take into account a frustration effect. With the model, we analyzed the binding part of neuron-restrictive silencer factor and showed that designed structural frustration in it induces intrinsic disorder. Furthermore, we showed that the folding and the binding are cooperative in interacting with a target protein. The cooperativity enables an intrinsically disordered protein to exhibit a sharp switch-like folding response to binding chemical potential change. Through this switch-like response, the structural frustration may contribute to the regulation function of interprotein interaction of the intrinsically disordered protein.

Internal friction in enzyme reactions

The empirical concept of internal friction was introduced 20 years ago. This review summarizes the results of experimental and theoretical studies that help to uncover the nature of internal friction. After the history of the concept, we describe the experimental challenges in measuring and interpreting internal friction based on the viscosity dependence of enzyme reactions. We also present speculations about the structural background of this viscosity dependence. Finally, some models about the relationship between the energy landscape and internal friction are outlined. Alternative concepts regarding the viscosity dependence of enzyme reactions are also discussed.

Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy

Theory, simulations and experimental results have suggested an important role of internal friction in the kinetics of protein folding. Recent experiments on spectrin domains provided the first evidence for a pronounced contribution of internal friction in proteins that fold on the millisecond timescale. However, it has remained unclear how this contribution is distributed along the reaction and what influence it has on the folding dynamics. Here we use a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, microfluidic mixing and denaturant- and viscosity-dependent protein-folding kinetics to probe internal friction in the unfolded state and at the early and late transition states of slow- and fast-folding spectrin domains. We find that the internal friction affecting the folding rates of spectrin domains is highly localized to the early transition state, suggesting an important role of rather specific interactions in the rate-limiting conformational changes.

Take home lessons from studies of related proteins

The 'Fold Approach' involves a detailed analysis of the folding of several topologically, structurally and/or evolutionarily related proteins. Such studies can reveal determinants of the folding mechanism beyond the gross topology, and can dissect the residues required for folding from those required for stability or function. While this approach has not yet matured to the point where we can predict the native conformation of any polypeptide chain in silico, it has been able to highlight, amongst others, the specific residues that are responsible for nucleation, pathway malleability, kinetic intermediates, chain knotting, internal friction and Paracelsus switches. Some of the most interesting discoveries have resulted from the attempt to explain differences between homologues.

Slow, reversible, coupled folding and binding of the spectrin tetramerization domain

Many intrinsically disordered proteins (IDPs) are significantly unstructured under physiological conditions. A number of these IDPs have been shown to undergo coupled folding and binding reactions whereby they can gain structure upon association with an appropriate partner protein. In general, these systems display weaker binding affinities than do systems with association between completely structured domains, with micromolar K(d) values appearing typical. One such system is the association between α- and β-spectrin, where two partially structured, incomplete domains associate to form a fully structured, three-helix bundle, the spectrin tetramerization domain. Here, we use this model system to demonstrate a method for fitting association and dissociation kinetic traces where, using typical biophysical concentrations, the association reactions are expected to be highly reversible. We elucidate the unusually slow, two-state kinetics of spectrin assembly in solution. The advantages of studying kinetics in this regime include the potential for gaining equilibrium constants as well as rate constants, and for performing experiments with low protein concentrations. We suggest that this approach would be particularly appropriate for high-throughput mutational analysis of two-state reversible binding processes.

The dominant folding route minimizes backbone distortion in SH3

Energetic frustration in protein folding is minimized by evolution to create a smooth and robust energy landscape. As a result the geometry of the native structure provides key constraints that shape protein folding mechanisms. Chain connectivity in particular has been identified as an essential component for realistic behavior of protein folding models. We study the quantitative balance of energetic and geometrical influences on the folding of SH3 in a structure-based model with minimal energetic frustration. A decomposition of the two-dimensional free energy landscape for the folding reaction into relevant energy and entropy contributions reveals that the entropy of the chain is not responsible for the folding mechanism. Instead the preferred folding route through the transition state arises from a cooperative energetic effect. Off-pathway structures are penalized by excess distortion in local backbone configurations and contact pair distances. This energy cost is a new ingredient in the malleable balance of interactions that controls the choice of routes during protein folding.

Folding of the four-helix bundle FF domain from a compact on-pathway intermediate state is governed predominantly by water motion

Friction plays a critical role in protein folding. Frictional forces originating from random solvent and protein fluctuations both retard motion along the folding pathway and activate protein molecules to cross free energy barriers. Studies of friction thus may provide insights into the driving forces underlying protein conformational dynamics. However, the molecular origin of friction in protein folding remains poorly understood because, with the exception of the native conformer, there generally is little detailed structural information on the other states participating in the folding process. Here, we study the folding of the four-helix bundle FF domain that proceeds via a transiently formed, sparsely populated compact on-pathway folding intermediate whose structure was elucidated previously. Because the intermediate is stabilized by both native and nonnative interactions, friction in the folding transition between intermediate and folded states is expected to arise from intrachain reorganization in the protein. However, the viscosity dependencies of rates of folding from or unfolding to the intermediate, as established by relaxation dispersion NMR spectroscopy, clearly indicate that contributions from internal friction are small relative to those from solvent, so solvent frictional forces drive the folding process. Our results emphasize the importance of solvent dynamics in mediating the interconversion between protein configurations, even those that are highly compact, and in equilibrium folding/unfolding fluctuations in general.

Predictions from an Ising-like Statistical Mechanical Model on the Dynamic and Thermodynamic Effects of Protein Surface Electrostatics

Charged residues on the surface of a protein are known hot-spots for post-translational modification, protein/ligand-binding, and tuning conformational stabilities. Recent experimental evidence points to the fact that surface electrostatics can also modulate thermodynamic barriers and hence folding mechanisms. To probe for this behavior across different proteins, we develop a novel version of the Wako-Saitô-Muñoz-Eaton (WSME) model in which we include an electrostatic potential term in the energy function while simplifying the treatment of solvation free energy. Both of the energy terms are obtained by quantitatively fitting the model to differential scanning calorimetry (DSC) experiments that carry critical information on the protein partition function. We characterize four sets of structural/functional homologues (HEWL/BLA, CspB, engrailed, α-spectrin) either by fitting the experimental data of a single domain in the homologous set and predicting the conformational behavior of the rest with the same set of parameters or by performing semiblind predictions. The model with the added electrostatic term is able to successfully reproduce the order of thermodynamic stabilities and relaxation rates of most of the homologues. In parallel, we predict diverse conformational features including a wide range of thermodynamic barriers (∼9-40 kJ/mol), broad native ensembles in helical proteins, structured unfolded states and intermediates, rugged folding landscapes, and further provide an independent protein-specific estimate of the folding speed limit at 298 K (1/(7-300 μs)). Our results are evidence that protein surface electrostatics can be tailored to not only engineer stabilities but also folding mechanisms and the ruggedness of the underlying landscape.

Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy

The dimensions of unfolded and intrinsically disordered proteins are highly dependent on their amino acid composition and solution conditions, especially salt and denaturant concentration. However, the quantitative implications of this behavior have remained unclear, largely because the effective theta-state, the central reference point for the underlying polymer collapse transition, has eluded experimental determination. Here, we used single-molecule fluorescence spectroscopy and two-focus correlation spectroscopy to determine the theta points for six different proteins. While the scaling exponents of all proteins converge to 0.62 ± 0.03 at high denaturant concentrations, as expected for a polymer in good solvent, the scaling regime in water strongly depends on sequence composition. The resulting average scaling exponent of 0.46 ± 0.05 for the four foldable protein sequences in our study suggests that the aqueous cellular milieu is close to effective theta conditions for unfolded proteins. In contrast, two intrinsically disordered proteins do not reach the Θ-point under any of our solvent conditions, which may reflect the optimization of their expanded state for the interactions with cellular partners. Sequence analyses based on our results imply that foldable sequences with more compact unfolded states are a more recent result of protein evolution.