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Ankyrin (ANK) repeat proteins are coded by tandem occurrences of patterns with around 33 amino acids. They often mediate protein–protein interactions in a diversity of biological systems. These proteins have an elongated non-globular shape and often display complex folding mechanisms. This work investigates the energy landscape of representative proteins of this class made up of 3, 4 and 6 ANK repeats using the energy-landscape visualisation method (ELViM). By combining biased and unbiased coarse-grained molecular dynamics AWSEM simulations that sample conformations along the folding trajectories with the ELViM structure-based phase space, one finds a three-dimensional representation of the globally funnelled energy surface. In this representation, it is possible to delineate distinct folding pathways. We show that ELViMs can project, in a natural way, the intricacies of the highly dimensional energy landscapes encoded by the highly symmetric ankyrin repeat proteins into useful low-dimensional representations. These projections can discriminate between multiplicities of specific parallel folding mechanisms that otherwise can be hidden in oversimplified depictions. M.N.S. was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq; Grant 130147/2020-6). This research was supported by the Center for Theoretical Biological Physics sponsored by the NSF (Grant PHY-2019745). A.B.O. acknowledges the Robert A. Welch Postdoctoral Fellow program. P.G.W. is also supported by the D.R. Bullard-Welch Chair at Rice University (Grant C-0016). V.B.P.L. was supported by CNPq (Grant 310017/2020-3) and FAPESP (Grants 2019/22540-3 and 2018/18668-1). D.U.F. is a CONICET researcher and is supported by Grant PICT2016/1467, UBACYT, and NASA Astrobiology Institute-Enigma (Grant 80NSSC18M0093).

Conformational sampling of biomolecules using molecular dynamics simulations often produces large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE) that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as the prior, it can directly acknowledge the multi-basin nature of protein folding free-energy landscape. To make the model end-to-end differentialble, we use a Gumbel-softmax distribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outer in the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis (TICA).

Native mass spectrometry (MS) is a powerful means for studying macromolecular protein assemblies, including accessing activated states. However, much remains to be understood about what governs which regions of the protein (un)folding funnel, which can be explored by activation of protein ions in a vacuum. Here, we examine the trajectory that Cu/Zn superoxide dismutase (SOD1) dimers take over the unfolding and dissociation free energy landscape in a vacuum. We examined wild-type SOD1 and six disease-related point mutants by using tandem MS and ion-mobility MS as a function of collisional activation. For six of the seven SOD1 variants, increasing activation prompted dimers to transition through two unfolding events and dissociate symmetrically into monomers with (as near as possible) equal charges. The exception was G37R, which proceeded only through the first unfolding transition and displayed a much higher abundance of asymmetric products. Supported by the observation that ejected asymmetric G37R monomers were more compact than symmetric G37R ones, we localized this effect to the formation of a gas-phase salt bridge in the first activated conformation. To examine the data quantitatively, we applied Arrhenius-type analysis to estimate the barriers on the corresponding free energy landscape. This reveals a heightening of the barrier to unfolding in G37R by >5 kJ/mol-1 over the other variants, consistent with expectations for the strength of a salt bridge. Our work demonstrates weaknesses in the simple general framework for understanding protein complex dissociation in a vacuum and highlights the importance of individual residues, their local environment, and specific interactions in governing product formation.

Folding funnel is the essential concept of the free energy landscape for ordered proteins. How does this concept apply to intrinsically disordered proteins (IDPs)? Here, we address this fundamental question through the explicit characterization of the free energy landscapes of the representative α-helical (HP-35) and β-sheet (WW domain) proteins and of an IDP (pKID) that folds upon binding to its partner (KIX). We demonstrate that HP-35 and WW domain indeed exhibit the steep folding funnel: the landscape slope for these proteins is ca. −50 kcal/mol, meaning that the free energy decreases by ~5 kcal/mol upon the formation of 10% native contacts. On the other hand, the landscape of pKID is funneled but considerably shallower (slope of −24 kcal/mol), which explains why pKID is disordered in free environments. Upon binding to KIX, the landscape of pKID now becomes significantly steep (slope of −54 kcal/mol), which enables otherwise disordered pKID to fold. We also show that it is the pKID–KIX intermolecular interactions originating from hydrophobic residues that mainly confer the steep folding funnel. The present work not only provides the quantitative characterization of the protein folding free energy landscape, but also establishes the usefulness of the folding funnel concept to IDPs.

Transient excited states in proteins can be accurately probed from temperature dependence of amide proton (1HN) chemical shifts displaying significant curvatures. Characterizing these near-native alternative states is of high therapeutic relevance in conformational diseases wherein missense mutations promote structural instability that leads to conformational heterogeneity. Extending the structure-function paradigm from physiology to pathology, we recently reported the solution NMR structure and dynamics of a severe congenital cataract variant, G57W of human γS-crystallin (abbreviated as γS-G57W) which is resistant towards crystallization. In an endeavour to explore the functional consequences of this mutation, here we report for the first time, native state conformational ruggedness in human γS-G57W as compared to its wild-type counterpart from residue resolved nonlinear temperature dependence of backbone 1HN chemical shifts using solution NMR spectroscopy. Our calculations suggest that the simulated chemical shift curvatures are indicative of low energy excited states within 2–4 kcal mol−1 from the native state. Residues accessing alternative conformations populate the N-terminal domain of γS-G57W more than its C-terminal counterpart. Collectively, curvatures retaining native state ensemble on mild denaturation suggest that the free energy landscape in human γS-G57W at the bottom of the folding funnel is sufficiently robust and malleable against such perturbations. Overall, this critical study highlights the functional aspects of such structural malleability promoting infantile cataracts as a global health risk marker.

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

Practically proteins perform their functions exposed to various molecules (macro/micro) of different shapes, sizes, and high concentrations. In such conditions, proteins fold through various intermediate states to execute their type of functions. There are various in vitro studies that showed that proteins yield intermediate states (either pre-molten globule, PMG or molten globules, MG) in changing environments (pH, temperature, and co-solute). Here, we investigate that myoglobin (Mb) yields two intermediate states in the presence of polyethylene glycol, PEG (4 kDa molecular weight) at two different concentrations. These intermediates were characterized by various spectroscopic techniques, further; we demonstrated that these changes in the structure of the protein were due to soft interactions which were confirmed by isothermal titration calorimetric and computational studies. Besides, in silico (molecular dynamic simulations) studies were exploited to know the atomic-level details of the protein which are useful to comprehend the functional characteristics of the bio-molecule with structural change and to study atomic motions and inter-atomic interactions in the bio-molecular systems. This is the first time that two intermediates (MG and PMG state) in the protein (Mb) at two different concentrations in the presence of solo size of PEG are yielded. This study shows folding of a protein does not follow a singular and specific pathway but occurs through routes down a folding funnel more like rain flowing down a funnel, hence foresees the energy landscape theory. Moreover, the study provides the significance of crowding concentrations in the cellular organism.

The N-terminal domain of L9 (NTL9) is a 56-residue mixed α-β protein that lacks disulfides, does not bind cofactors, and folds reversibly. NTL9 has been widely used as a model system for experimental and computational studies of protein folding and for investigations of the unfolded state. The role of side-chain interactions in the folding of NTL9 is probed by mutational analysis. ϕ-values, which represent the ratio of the change in the log of the folding rate upon mutation to the change in the log of the equilibrium constant for folding, are reported for 25 point mutations and 15 double mutants. All ϕ-values are small, with an average over all sites probed of only 0.19 and a largest value of 0.4. The effect of modulating unfolded-state interactions is studied by measuring ϕ-values in second- site mutants and under solvent conditions that perturb unfolded-state energetics in a defined way. Neither of these alterations significantly affects the distribution of ϕ-values. The results, combined with those of earlier studies that probe the role of hydrogen-bond formation in folding and the burial of surface area, reveal that the transition state for folding contains extensive backbone structure and buries a significant fraction of hydrophobic surface area, but lacks well developed side-chain-side-chain interactions. The folding transition state for NTL9 does not contain a specific “nucleus” consisting of a few key residues; rather, it involves extensive backbone hydrogen bonding and partially formed structure delocalized over almost the entire domain. The potential generality of these observations is discussed.

Native mass spectrometry (MS) is a powerful means for studying macromolecular protein assemblies, including accessing activated states. However, much remains to be understood about what governs which regions of the protein (un)folding funnel are explored by activation of protein ions in vacuum. Here we examine the trajectory that dimeric Cu/Zn superoxide dismutase (SOD1) dimers take over the unfolding and dissociation free energy landscape in vacuum. We examined wild-type SOD1 and six disease-related point-mutants by using tandem MS and ion-mobility MS (MS/MS-IMMS) coupled with increasing collisional activation potentials. For six of the seven SOD1 variants, increasing activation promoted dimers to transition through two unfolding events to access three gas-phase conformers before dissociating symmetrically into monomers with (as near as possible) equal charges. The exception was G37R, which proceeded only through the first unfolding transition, and displayed a much higher abundance of asymmetric products. We localise this effect to the formation of a new salt-bridge in the first activated conformation. To examine the data quantitatively, we generated a model of SOD1 gas phase unfolding and dissociation, and applied Arrhenius-type analysis to estimate the barriers on the corresponding free energy landscape. This reveals an increase in the barrier height to unfolding in G37R to be >5 kJ/mol-1 higher than for the other variants, consistent with expectations for the strength of a salt-bridge. Our work demonstrates the importance of bond formation during the unfolding of proteins in vacuum, and provides a framework for comparing quantitatively the free energy landscape they explore upon activation.

A complete description of the pathways and mechanisms of protein folding requires a detailed structural and energetic characterization of the conformational ensemble along the entire folding reaction coordinate. Simulations can provide this level of insight for small proteins. In contrast, with the exception of hydrogen exchange, which does not monitor folding directly, experimental studies of protein folding have not yielded such structural and energetic detail. NMR can provide residue specific atomic level structural information, but its implementation in protein folding studies using chemical or temperature perturbation is problematic. Here we present a highly detailed structural and energetic map of the entire folding landscape of the leucine-rich repeat protein, pp32 (Anp32), obtained by combining pressure-dependent site-specific 1H-15N HSQC data with coarse-grained molecular dynamics simulations. The results obtained using this equilibrium approach demonstrate that the main barrier to folding of pp32 is quite broad and lies near the unfolded state, with structure apparent only in the C-terminal region. Significant deviation from two-state unfolding under pressure reveals an intermediate on the folded side of the main barrier in which the N-terminal region is disordered. A nonlinear temperature dependence of the population of this intermediate suggests a large heat capacity change associated with its formation. The combination of pressure, which favors the population of folding intermediates relative to chemical denaturants; NMR, which allows their observation; and constrained structure-based simulations yield unparalleled insight into protein folding mechanisms.

Using hydrodynamic description of protein folding, the process of the first-passage folding of ubiquitin has been studied. Since a large number of folding trajectories were required to obtain converged folding flows, a coarse-grained representation of the protein in the form of a C-bead Gō-model was employed, and discrete molecular dynamics was used to perform simulations. It has been found that the free energy surface has a maximum width in the transition state region, so that the densities of folding flows (probability fluxes) decrease to minimum when the system passes through the transition state. There are indications that the increasing number of different protein conformations in the transition state region compared with those in the neighboring regions of semi-compact and native-like states is responsible for the present phenomena. It has also been shown that if the free energy is projected onto a single reaction coordinate, the low populations of the transition states can be compensated by the increasing number of states, which can lead to a considerable decrease or even disappearance of the free energy barrier in the transition state.

Intermediate states in protein folding may slow folding, and sometimes can provide a starting point for aggregation. Recently, the FBP28 WW domain of the formin-binding protein was used as a model for a computational study of the origin and prevention of intermediate-state formation, and local hydrophobic interactions of Leu26 were implicated. Here, we combine new simulations over a broad temperature range with experimental temperature-jump data to study this site in more detail. We replace Leu26 by Asp26 or Trp26 to alter the folding scenario from three-state folding toward two-state or downhill folding at temperatures below the melting point, whereas the wild type shows two-state behavior only near its melting temperature. We offer an explanation of this behavior mainly in terms of principles of hydrophobic interactions.

Protein folding is the process that a protein molecule transforms from the linear polymer of peptides to a three-dimensional native structure with specific biological function. By now, the protein folding problem has been studied for more than 50 years and already became a broad and active research field. To answer the 58th question raised by Science in 2005, in this article we briefly reviewed the background and research history of the protein folding problem, and introduced the progresses of protein folding prediction research from four aspects: the protein folding process prediction (protein folding simulation), the folding process related parameter prediction, the protein folding result prediction (protein structure prediction), and the folding result related parameter prediction. The studies on the protein folding problem began in the 60s of 20th century, with the efforts to seek a solution to the paradox that a protein can actually form a native 3D structure in only several seconds but the time scale estimated by a thermodynamic ergodic hypothesis would be longer than the age of universe. Computer simulation is an important approach for protein folding study. The protein models can be classified into 3 categories: lattice model, off-lattice model and all-atom model. The current knowledge about protein folding mechanism is based on the concept of folding funnel on a free-energy landscape, and the current opinion is that the protein folding mechanism is not unique for the whole protein universe and that there may exist a continuum between the two extreme ends of hierarchical folding and nucleation folding scenarios. The hardware for protein folding simulation was becoming more powerful; distributed systems (e.g, Folding@home), special-purpose machines (e.g, ANTON), and GPU-based platforms have been developed for protein folding simulation. Meanwhile, the folding simulation software was continuously enhanced. An important issue in protein folding simulation is to overcome the local energy barrier to find the global energy minimum; several approaches such as replica-exchange, multi-scale modeling and Modeling Employing Limited Data (MELD) were developed to tackle this issue; human intelligence involvement (e.g, “Foldit” Game) is another interesting effort. During the past two decades, the ability of protein folding simulation was continuously rising. For now, the folding simulation for the proteins with dozens of amino acids can reach a time scale of millisecond, while the protein size able to do effective folding simulation is around 100 amino acids. The targets of protein folding simulation have been largely expanded and now include both the in vitro and the in vivo folding such as co-translational folding, chaperone-assistant folding, small-molecule- induced folding and metal-coupled folding. Folding rate and folding type are two important parameters related with the protein folding process and now they can be predicted by statistical and machine-learning approaches based on different levels of structural features such as the topological properties of tertiary structure, the contents of secondary structure and the amino acid frequencies of primary structure. The result of a protein folding process is the formation of a protein structure. According to the hierarchy of structural organization, the protein structure prediction problem includes secondary structure prediction, tertiary structure prediction and quaternary structure prediction. By now, the secondary structure prediction algorithm has experienced five generations and the current accuracy is about 80% for 3-classes prediction. The tertiary structure prediction approaches mainly include two categories: template-based modeling and free modeling, with the former having higher accuracy and the latter having larger application scope. The quaternary structure prediction includes the prediction of complex structure and the prediction of the possibility of protein-protein interaction, and these predictions can be performed based on protein 3D structure or merely amino acid sequence. Structure related parameter prediction also attracted research interests, including the predictions of protein structural classes, secondary structure contents, disordered regions, solvent accessible surface region and the amino acid contacting pairs in the interface of protein-protein interaction. In the end, some possible development directions worth noticing in the future of protein folding research were suggested and they are: the coupling between protein folding and binding, the fusion of protein folding research with systems biology and the application of deep-learning techniques in the field of protein folding prediction.

This paper proposes a generalization of the well-known folding funnel concept of proteins. In the funnel model the polypeptide chain is treated as an individual object not interacting with other proteins. Since biological systems are considerably crowded, protein-protein interaction is a fundamental feature during the life cycle of proteins. The folding superfunnel proposed here describes the folding process of interacting proteins in various situations. The first example discussed is the folding of the freshly synthesized protein with the aid of chaperones. Another important aspect of protein-protein interactions is the folding of the recently characterized intrinsically disordered proteins, where binding to target proteins plays a crucial role in the completion of the folding process. The third scenario where the folding superfunnel is used is the formation of aggregates from destabilized proteins, which is an important factor in case of several conformational diseases. The folding superfunnel constructed here with the minimal assumption about the interaction potential explains all three cases mentioned above. Proteins 2016; 84:1009-1016. © 2016 Wiley Periodicals, Inc.

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

This chapter (The Amino Acid Sequences of Proteins Determine Folding and Non-folding) continues where Chap. 1 left off. Amino acid sequences determine the folded structure of proteins. The manner in which the protein folds is visualized by an energy landscape called a protein folding funnel. This chapter describes the funnel and how it relates to three-dimensional protein structure. This chapter describes the spin glass theory which also visualizes protein folding. Regions of amino acids called foldons are described. The 20 amino acid building blocks of proteins are enumerated in this chapter. The ice-like blanket that surrounds a protein and its effects on folding are described in this chapter. Other forces that stabilize the folded structure are described. This chapter defines and describes intrinsically disordered proteins (IDP) and intrinsically disordered protein regions (IDPR) and their functions. Effects of hypoxia on protein structure are discussed. Scaffolding and hubs are described.

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps., Comment: 9 pages, 5 figures

While the theory of protein folding is well developed, including concepts such as rugged energy landscape, folding funnel, etc., the same degree of understanding has not been reached for the description of the dynamics of allosteric transitions in proteins. This is not only due to the small size of the structural change upon ligand binding to an allosteric site, but also due to challenges in designing experiments that directly observe such an allosteric transition. On the basis of recent pump-probe-type experiments (Buchli et al. 2013 Proc. Natl Acad. Sci. USA 110 , 11 725–11 730. ( doi:10.1073/pnas.1306323110 )) and non-equilibrium molecular dynamics simulations (Buchenberg et al. 2017 Proc. Natl Acad. Sci. USA 114 , E6804–E6811. ( doi:10.1073/pnas.1707694114 )) studying an photoswitchable PDZ2 domain as model for an allosteric transition, we outline in this perspective how such a description of allosteric communication might look. That is, calculating the dynamical content of both experiment and simulation (which agree remarkably well with each other), we find that allosteric communication shares some properties with downhill folding, except that it is an ‘order–order’ transition. Discussing the multiscale and hierarchical features of the dynamics, the validity of linear response theory as well as the meaning of ‘allosteric pathways’, we conclude that non-equilibrium experiments and simulations are a promising way to study dynamical aspects of allostery. This article is part of a discussion meeting issue ‘Allostery and molecular machines’.

Proteini su makromolekule koje se sastoje od 20 različitih aminokiselina te imaju mnogobrojne biološke uloge. Nativno stanje predstavlja jedinstveno, stabilno i kinetički dostupno stanje minimalne slobodne energije u koje se protein treba smotati kako bi mogao obavljati svoju biološku funkciju. Proces u kojem se nesmotani polipeptidni lanac smata u nativno stanje naziva se mehanizam smatanja proteina. Razumijevanje mehanizma smatanja proteina nam pomaže u predviđanju trodimenzionalne strukture proteina na osnovi njegove primarne strukture te ima značajnu medicinsku važnost jer pogrešno smotani proteini uzrokuju neizlječive neurodegenerativne bolesti. Napretci u razumijevanju mehanizma smatanja proteina otvaraju jako mnogo mogućnosti u analiziranju uzroka neurodegenerativnih bolesti te predstavljaju prvi korak prema pronalasku lijekova. Zbog biološkog značaja postoji jako mnogo knjiga i znanstvenih radova na temu proteina i njihovog smatanja. Za sada postoji nekoliko modela smatanja proteina, ali općeniti model koji bi bio primjenjiv na širok raspon proteina još uvijek ne postoji., Proteins are macromolecules consisting of 20 different amino acids and have many biological functions. Native state represents a unique, stable and kinetically available state of minimal free energy in which protein should be folded so that it can perform its biological function. The process in which polypeptide chain is taken into its native state is called the mechanism of protein folding. Understanding the mechanism of protein folding helps us to predict the three-dimensional protein structure on the basis of its primary structure and also have a significant role in medicine because misfolded proteins cause incurable neurodegenerative diseases. Advances in understanding the mechanism of protein folding open up many opportunities to analyse the cause of neurodegenerative diseases and represent the first step towards finding drugs. Because of its biological importance there are a lot of books and scientific papers on proteins and their folding. For now, there are several models of protein folding, but general model that would be applicable to wide range of proteins still does not exist.

α-Helical hairpin (two-helix bundle) is a structure motif composed of two interacting helices connected by a turn or a short loop. It is an important model for protein folding studies, filling the gap between isolated α-helix and larger all-α domains. Here, we present, for the first time, successful folding simulations of an α-helical hairpin. Our RSFF1 and RSFF2 force fields give very similar predicted structures of this αtα peptide, which is in good agreement with its NMR structure. Our simulations also give site-specific stability of α-helix formation in good agreement with amide hydrogen exchange experiments. Combining the folding free energy landscapes and analyses of structures sampled in five different ranges of the fraction of native contacts (Q), a folding mechanism of αtα is proposed. The most stable sites of Q9-E15 in helix-1 and E24-A30 in helix-2 close to the loop region act as the folding initiation sites. The formation of interhelix side-chain contacts also initiates near the loop region, but some residues in the central parts of the two helices also form contacts quite early. The two termini fold at a final stage, and the loop region remains flexible during the whole folding process. This mechanism is similar to the "zipping out" pathway of β-hairpin folding.

Integrated-tempering-sampling molecular dynamics simulation is utilized to investigate the folding of a 67-residue three-α-helix bundle, α3W. Reversible folding and unfolding can be observed in individual trajectories and a total of 28 folding events are achieved within 7 μs simulation, giving sufficient sampling on the configuration space of protein folding. The native-like state with a left-handed topology constitutes the largest fraction of the conformational ensemble sampled by the simulation. In addition, a misfolded state with mirror-image (right-handed) topology is observed with smaller population. The free energy landscape analysis demonstrates that the folding of α3W is initiated by the formation of α-helical secondary structures and is followed by the assembling of folded α-helices to construct tertiary structure. The “correct” α-helix assembling which leads to the native structure is mainly dominated by inter-helical hydrophobic interactions whereas the “incorrect” assembling which leads to a misfolded mirror-image structure is highly affected by not only hydrophobic but also charge interactions. It is speculated on the basis of the present study on α3W and other studies on the B domain of protein A and α3D that the misfolding probability of α-helix bundle proteins is dependent on the strength of intra-protein hydrophobic and charge interactions: proteins containing stronger hydrophobic interactions but weaker charge interactions should have smaller misfolding probability. The importance of intra-protein hydrophobic interactions in preventing protein misfolding has been also seen in our previous studies on β-hairpins. Therefore, the present study along with our previous studies provide comprehensive, atomic-level picture of the folding/misfolding of α-helix bundle and β-hairpin proteins.

To characterize experimentally the ruggedness of the free energy landscape of protein folding is challenging, because the distributed small free energy barriers are usually dominated by one, or a few, large activation free energy barriers. This study delineates changes in the roughness of the free energy landscape by making use of the observation that a decrease in ruggedness is accompanied invariably by an increase in folding cooperativity. Hydrogen exchange (HX) coupled to mass spectrometry was used to detect transient sampling of local energy minima and the global unfolded state on the free energy landscape of the small protein single-chain monellin. Under native conditions, local noncooperative openings result in interconversions between Boltzmann-distributed intermediate states, populated on an extremely rugged "uphill" energy landscape. The cooperativity of these interconversions was increased by selectively destabilizing the native state via mutations, and further by the addition of a chemical denaturant. The perturbation of stability alone resulted in seven backbone amide sites exchanging cooperatively. The size of the cooperatively exchanging and/or unfolding unit did not depend on the extent of protein destabilization. Only upon the addition of a denaturant to a destabilized mutant variant did seven additional backbone amide sites exchange cooperatively. Segmentwise analysis of the HX kinetics of the mutant variants further confirmed that the observed increase in cooperativity was due to the smoothing of the ruggedness of the free energy landscape of folding of the protein by the chemical denaturant.

Water is known to play a critical role in protein folding and stability. Here we develop and employ a coarse-grained (CG) model to directly explore the role of water in shaping the conformational landscape explored during protein folding. For this purpose, we simulate a designed sequence with binary patterning of neutral and hydrophobic residues, which is capable of folding to a three-helix bundle in explicit water. We find two folded states of this sequence, with rotation of the helices occurring to trade between hydrophobic packing and water expulsion from the core. This work provides insight into the role of water and hydrophobicity in generating competing folded states for a protein.

According to the thermodynamic hypothesis, the native state of proteins is that in which the free energy of the system is at its lowest, so that at normal temperature and pressure, proteins evolve to that state. We selected four proteins representative of each of the four classes, and for each protein make four simulations, one starting from the native structure and the other three starting from the structure obtained by threading the sequence of one protein onto the native backbone fold of the other three proteins. Because of their large conformational distances with respect to the native structure, the three alternative initial structures cannot be considered as local minima within the native ensemble of the corresponding protein. As expected, the initial native states are preserved in the .5 μs simulations performed here and validate the simulations. On the other hand, when the initial state is not native, an analysis of the trajectories does not reveal any evolution towards the native state, during that time. These results indicate that the distribution of protein conformations is multipeak shaped, so that apart from the peak corresponding to the native state, there are other peaks associated with average structures that are very different from the native and that can last as long as the native state.

The protein folding (Levinthal’s) paradox states that it would not be possible in a physically meaningful time to a protein to reach the native (functional) conformation by a random search of the enormously large number of possible structures. This paradox has been solved: it was shown that small biases toward the native conformation result in realistic folding times of realistic-length sequences. This solution of the paradox is, however, not amenable to most chemistry or biology students due to the demanding mathematics. Here, a simplification of the study of the paradox and its solution is provided so that it is accessible to chemists and biologists at an undergraduate or graduate level. Despite its simplicity, the model captures some fundamental aspects of the protein folding mechanism and allows students to grasp the actual significance of the popular folding funnel representation of the protein energy landscape. The analysis of the folding model provides a rich basis for a discussion of the relations...

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., Graphical Abstract, Highlights • Homologous spectrin domains have very different folding kinetics and mechanisms. • R15 has been engineered to fold and unfold slowly similar to R16 and R17. • The folding pathway is entirely unchanged. • R15 is a rare example of a protein with an inflexible transition state.