Theory, simulations, and experiments show that proteins fold by multiple pathways

Understanding the heterogeneity intrinsic to protein folding

Relating the native fold of a protein to its amino acid sequence remains a fundamental problem in biology. While computer algorithms have demonstrated recently their prowess in predicting what structure a particular amino acid sequence will fold to, an understanding of how and why a specific protein fold is achieved remains elusive. A major challenge is to define the role of conformational heterogeneity during protein folding. Recent experimental studies, utilizing time-resolved FRET, hydrogen-exchange coupled to mass spectrometry, and single-molecule force spectroscopy, often in conjunction with simulation, have begun to reveal how conformational heterogeneity evolves during folding, and whether an intermediate ensemble of defined free energy consists of different sub-populations of molecules that may differ significantly in conformation, energy and entropy.

Mutations of evolutionarily conserved aromatic residues suggest that misfolding of the mouse prion protein may commence in multiple ways

The misfolding of the mammalian prion protein from its α-helix rich cellular isoform to its β-sheet rich infectious isoform is associated with several neurodegenerative diseases. The determination of the structural mechanism by which misfolding commences, still remains an unsolved problem. In the current study, native-state hydrogen exchange coupled with mass spectrometry has revealed that the N state of the mouse prion protein (moPrP) at pH 4 is in dynamic equilibrium with multiple partially unfolded forms (PUFs) capable of initiating misfolding. Mutation of three evolutionarily conserved aromatic residues, Tyr168, Phe174, and Tyr217 present at the interface of the β2-α2 loop and the C-terminal end of α3 in the structured C-terminal domain of moPrP significantly destabilize the native state (N) of the protein. They also reduce the free energy differences between the N state and two PUFs identified as PUF1 and PUF2**. It is shown that PUF2** in which the β2-α2 loop and the C-terminal end of α3 are disordered, has the same stability as the previously identified PUF2*, but to have a very different structure. Misfolding can commence from both PUF1 and PUF2**, as it can from PUF2*. Hence, misfolding can commence and proceed in multiple ways from structurally distinct precursor conformations. The increased extents to which PUF1 and PUF2** are populated at equilibrium in the case of the mutant variants, greatly accelerate their misfolding. The results suggest that the three aromatic residues may have been evolutionarily selected to impede the misfolding of moPrP.

Replacement of the native cis prolines by alanine leads to simplification of the complex folding mechanism of a small globular protein

The folding mechanism of MNEI, a single-chain variant of naturally occurring double-chain monellin, is complex, with multiple parallel refolding channels. To determine whether its folding energy landscape could be simplified, the two native cis-prolines, Pro41 and Pro93, were mutated, singly and together, to Ala. The stability of P93A was the same as that of the wild-type protein, pWT; however, P41A and P41AP93A were destabilized by ∼0.9 kcal mol-1. The effects of the mutations on the very fast, fast, slow, and very slow phases of folding were studied. They showed that heterogeneity in the unfolded state arises due to cis to trans isomerization of the Gly92-Pro93 peptide bond. The Pro41 to Ala mutation abolished the very slow phase of folding, whereas surprisingly, the Pro93 to Ala mutation abolished the very fast phase of folding. Double-jump, interrupted folding experiments indicated that two sequential trans to cis proline isomerization steps, of the Gly92-Pro93 peptide bond followed by the Arg40-Pro41 peptide bond, lead to the formation of the native state. They also revealed the accumulation of a late native-like intermediate, N∗, which differs from the native state in the isomeric status of the Arg40-Pro41 bond, as well as in a few tertiary contacts as monitored by near-UV CD measurements. The Pro to Ala mutations not only eliminated the cis to trans Pro isomerization reaction in the unfolded state, but also the two trans to cis Pro isomerization reactions during folding. By doing so, and by differentially affecting the relative stabilities of folding intermediates, the mutations resulted in a simplification of the folding mechanism. The two Pro to Ala mutations together accelerate folding to such an extent that the native state forms more than 1000-fold faster than in the case of pWT.

The "Beacon" Structural Model of Protein Folding: Application for Trp-Cage in Water

Protein folding is a process in which a polypeptide must undergo folding process to obtain its three-dimensional structure. Thermodynamically, it is a process of enthalpy to overcome the loss of conformational entropy in folding. Folding is primarily related to hydrophobic interactions and intramolecular hydrogen bondings. During folding, hydrophobic interactions are regarded to be the driving forces, especially in the initial structural collapse of a protein. Additionally, folding is guided by the strong interactions within proteins, such as intramolecular hydrogen bondings related to the α-helices and β-sheets of proteins. Therefore, a protein is divided into the folding key (FK) regions related to intramolecular hydrogen bondings and the non-folding key (non-FK) regions. Various conformations are expected for FK and non-FK regions. Different from non-FK regions, it is necessary for FK regions to form the specific conformations in folding, which are regarded as the necessary folding pathways (or "beacons"). Additionally, sequential folding is expected for the FK regions, and the intermediate state is found during folding. They are reflected on the local basins in the free energy landscape (FEL) of folding. To demonstrate the structural model, molecular dynamics (MD) simulations are conducted on the folding pathway of the TRP-cage in water.

Deep mining of the protein energy landscape

For over half a century, it has been known that protein molecules naturally undergo extensive structural fluctuations, and that these internal motions are intimately related to their functional properties. The energy landscape view has provided a powerful framework for describing the various physical states that proteins visit during their lifetimes. This Perspective focuses on the commonly neglected and often disparaged axis of the protein energy landscape: entropy. Initially seen largely as a barrier to functionally relevant states of protein molecules, it has recently become clear that proteins retain considerable conformational entropy in the "native" state, and that this entropy can and often does contribute significantly to the free energy of fundamental protein properties, processes, and functions. NMR spectroscopy, molecular dynamics simulations, and emerging crystallographic views have matured in parallel to illuminate dynamic disorder of the "ground state" of proteins and their importance in not only transiting between biologically interesting structures but also greatly influencing their stability, cooperativity, and contribution to critical properties such as allostery.

Heterogeneity in Protein Folding and Unfolding Reactions

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

Exploring the folding energy landscapes of heme proteins using a hybrid AWSEM-heme model

Heme is an active center in many proteins. Here we explore computationally the role of heme in protein folding and protein structure. We model heme proteins using a hybrid model employing the AWSEM Hamiltonian, a coarse-grained forcefield for the protein chain along with AMBER, an all-atom forcefield for the heme. We carefully designed transferable force fields that model the interactions between the protein and the heme. The types of protein-ligand interactions in the hybrid model include thioester covalent bonds, coordinated covalent bonds, hydrogen bonds, and electrostatics. We explore the influence of different types of hemes (heme b and heme c) on folding and structure prediction. Including both types of heme improves the quality of protein structure predictions. The free energy landscape shows that both types of heme can act as nucleation sites for protein folding and stabilize the protein folded state. In binding the heme, coordinated covalent bonds and thioester covalent bonds for heme c drive the heme toward the native pocket. The electrostatics also facilitates the search for the binding site.

A 200 nanoseconds all-atom simulation of the pH-dependent EF loop transition in bovine β-lactoglobulin. The role of the orientation of the E89 side chain

In silico molecular dynamics (MD) using crystallographic and NMR data was used to simulate the effects of the protonation state of E89 on the pH-dependent conformational rearrangement of the EF loop, also known as the Tanford transition, in a series of apo-β-lactoglobulin (BLG) structures. Compared to existing studies these simulations were carried out over a much longer time scale (200 ns where the stability of the transition can be evaluated) and used an explicit water model. We considered eight different entries from the Brookhaven Protein Data Bank (PDB) separated into two groups. We observed that fixing the protonation state of E89 prompts the transition of the EF loop only when its side chain is oriented under the loop and into the entrance of the interior cavity. The motion of the EF loop occurs mostly as a step-function and its timing varies greatly from ∼ 20 ns to ∼170 ns from the beginning of the simulation. Once the transition is completed, the protein appears to reach a stable conformation as in a true two-state transition. We also observed novel findings. When the transition occurs, the hydrogen bond between E89 and S116 is replaced with a salt bridge with Lys residues in the βC-CD loop-βD motif. This electrostatic interaction causes the distortion of this motif as well as the protrusion of the GH loop into the aperture of the cavity with the result of limiting the increase of its contour area despite the rotation of the EF loop.Communicated by Ramaswamy H. Sarma.

Rational Design of Protein-Specific Folding Modifiers

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

A conserved folding nucleus sculpts the free energy landscape of bacterial and archaeal orthologs from a divergent TIM barrel family

Orthologous proteins from the three superkingdoms have conserved their structures and functions over evolutionary time. We ask whether their folding mechanisms and the structures of their partially folded states are similarly conserved, using bacterial and archaeal representatives of the IGPS TIM barrel enzyme. Comparison of circular dichroism and fluorescence spectroscopic studies reveal a highly conserved mechanism, and hydrogen–deuterium exchange mass spectrometry analyses highlight similar cores of stability in regions dominated by clusters of branched aliphatic side chains. A bioinformatics analysis of hundreds of IGPS sequences from each superkingdom shows a very highly conserved sequence, V/ILLI, that nucleates the formation of a misfolded, microsecond intermediate and has existed since the last universal common ancestor of the IGPS family of proteins.

The amino acid sequences of proteins have evolved over billions of years, preserving their structures and functions while responding to evolutionary forces. Are there conserved sequence and structural elements that preserve the protein folding mechanisms? The functionally diverse and ancient (βα)_1–8 TIM barrel motif may answer this question. We mapped the complex six-state folding free energy surface of a ∼3.6 billion y old, bacterial indole-3-glycerol phosphate synthase (IGPS) TIM barrel enzyme by equilibrium and kinetic hydrogen–deuterium exchange mass spectrometry (HDX-MS). HDX-MS on the intact protein reported exchange in the native basin and the presence of two thermodynamically distinct on- and off-pathway intermediates in slow but dynamic equilibrium with each other. Proteolysis revealed protection in a small (α1β2) and a large cluster (β5α5β6α6β7) and that these clusters form cores of stability in I_a and I_bp. The strongest protection in both states resides in β4α4 with the highest density of branched aliphatic side chain contacts in the folded structure. Similar correlations were observed previously for an evolutionarily distinct archaeal IGPS, emphasizing a key role for hydrophobicity in stabilizing common high-energy folding intermediates. A bioinformatics analysis of IGPS sequences from the three superkingdoms revealed an exceedingly high hydrophobicity and surprising α-helix propensity for β4, preceded by a highly conserved βα-hairpin clamp that links β3 and β4. The conservation of the folding mechanisms for archaeal and bacterial IGPS proteins reflects the conservation of key elements of sequence and structure that first appeared in the last universal common ancestor of these ancient proteins.

Modern Kinetics and Mechanism of Protein Folding: A Retrospective

Modern experimental kinetics of protein folding began in the early 1990s with the introduction of nanosecond laser pulses to trigger the folding reaction, providing an almost 10⁶-fold improvement in time resolution over the stopped-flow method being employed at the time. These experiments marked the beginning of the "fast-folding" subfield that enabled investigation of the kinetics of formation of secondary structural elements and disordered loops for the first time, as well as the fastest folding proteins. When I started to work on this subject, a fast folding protein was one that folded in milliseconds. There were, moreover, no analytical theoretical models and no atomistic or coarse-grained molecular dynamics simulations to describe the mechanism. Two of the most important discoveries from my lab since then are a protein that folds in hundreds of nanoseconds, as determined from nanosecond laser temperature experiments, and the discovery that the theoretically predicted barrier crossing time is about the same for proteins that differ in folding rates by 10⁴-fold, as determined from single molecule fluorescence measurements. We also developed what has been called the "Hückel model" of protein folding, which quantitatively explains a wide range of equilibrium and kinetic measurements. This retrospective traces the history of contributions to the "fast folding" subfield from my lab until about 3 years ago, when I left protein folding to spend the rest of my research career trying to discover an inexpensive drug for treating sickle cell disease.

Fuzziness and Frustration in the Energy Landscape of Protein Folding, Function, and Assembly

Are all protein interactions fully optimized? Do suboptimal interactions compromise specificity? What is the functional impact of frustration? Why does evolution not optimize some contacts? Proteins and their complexes are best described as ensembles of states populating an energy landscape. These ensembles vary in breadth from narrow ensembles clustered around a single average X-ray structure to broader ensembles encompassing a few different functional "taxonomic" states on to near continua of rapidly interconverting conformations, which are called "fuzzy" or even "intrinsically disordered". Here we aim to provide a comprehensive framework for confronting the structural and dynamical continuum of protein assemblies by combining the concepts of energetic frustration and interaction fuzziness. The diversity of the protein structural ensemble arises from the frustrated conflicts between the interactions that create the energy landscape. When frustration is minimal after folding, it results in a narrow ensemble, but residual frustrated interactions result in fuzzy ensembles, and this fuzziness allows a versatile repertoire of biological interactions. Here we discuss how fuzziness and frustration play off each other as proteins fold and assemble, viewing their significance from energetic, functional, and evolutionary perspectives.We demonstrate, in particular, that the common physical origin of both concepts is related to the ruggedness of the energy landscapes, intramolecular in the case of frustration and intermolecular in the case of fuzziness. Within this framework, we show that alternative sets of suboptimal contacts may encode specificity without achieving a single structural optimum. Thus, we demonstrate that structured complexes may not be optimized, and energetic frustration is realized via different sets of contacts leading to multiplicity of specific complexes. Furthermore, we propose that these suboptimal, frustrated, or fuzzy interactions are under evolutionary selection and expand the biological repertoire by providing a multiplicity of biological activities. In accord, we show that non-native interactions in folding or interaction landscapes can cooperate to generate diverse functional states, which are essential to facilitate adaptation to different cellular conditions. Thus, we propose that not fully optimized structures may actually be beneficial for biological activities of proteins via an alternative set of suboptimal interactions. The importance of such variability has not been recognized across different areas of biology.This account provides a modern view on folding, function, and assembly across the protein universe. The physical framework presented here is applicable to the structure and dynamics continuum of proteins and opens up new perspectives for drug design involving not fully structured, highly dynamic protein assemblies.

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

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

Synthesis runs counter to directional folding of a nascent protein domain

Folding of individual domains in large proteins during translation helps to avoid otherwise prevalent inter-domain misfolding. How folding intermediates observed in vitro for the majority of proteins relate to co-translational folding remains unclear. Combining in vivo and single-molecule experiments, we followed the co-translational folding of the G-domain, encompassing the first 293 amino acids of elongation factor G. Surprisingly, the domain remains unfolded until it is fully synthesized, without collapsing into molten globule-like states or forming stable intermediates. Upon fully emerging from the ribosome, the G-domain transitions to its stable native structure via folding intermediates. Our results suggest a strictly sequential folding pathway initiating from the C-terminus. Folding and synthesis thus proceed in opposite directions. The folding mechanism is likely imposed by the final structure and might have evolved to ensure efficient, timely folding of a highly abundant and essential protein.

In vivo experiments and optical tweezers force-spectroscopy measurements assessing the co-translational folding of the G-domain from bacterial elongation factor G reveal a sequential folding pathway initiating from the C-terminus. These results suggest that protein folding and synthesis proceed in opposite directions.

Probing the conformational landscape and thermochemistry of DNA dinucleotide anions via helium nanodroplet infrared action spectroscopy

Isolation of biomolecules in vacuum facilitates characterization of the intramolecular interactions that determine three-dimensional structure, but experimental quantification of conformer thermochemistry remains challenging. Infrared spectroscopy of molecules trapped in helium nanodroplets is a promising methodology for the measurement of thermochemical parameters. When molecules are captured in a helium nanodroplet, the rate of cooling to an equilibrium temperature of ca. 0.4 K is generally faster than the rate of isomerization, resulting in "shock-freezing" that kinetically traps molecules in local conformational minima. This unique property enables the study of temperature-dependent conformational equilibria via infrared spectroscopy at 0.4 K, thereby avoiding the deleterious effects of spectral broadening at higher temperatures. Herein, we demonstrate the first application of this approach to ionic species by coupling electrospray ionization mass spectrometry (ESI-MS) with helium nanodroplet infrared action spectroscopy to probe the structure and thermochemistry of deprotonated DNA dinucleotides. Dinucleotide anions were generated by ESI, confined in an ion trap at temperatures between 90 and 350 K, and entrained in traversing helium nanodroplets. The infrared action spectra of the entrained ions show a strong dependence on pre-pickup ion temperature, consistent with the preservation of conformer population upon cooling to 0.4 K. Non-negative matrix factorization was utilized to identify component conformer infrared spectra and determine temperature-dependent conformer populations. Relative enthalpies and entropies of conformers were subsequently obtained from a van't Hoff analysis. IR spectra and conformer thermochemistry are compared to results from ion mobility spectrometry (IMS) and electronic structure methods. The implementation of ESI-MS as a source of dopant molecules expands the diversity of molecules accessible for thermochemical measurements, enabling the study of larger, non-volatile species.

Disordered proteins follow diverse transition paths as they fold and bind to a partner

Transition paths of macromolecular conformational changes such as protein folding are predicted to be heterogeneous. However, experimental characterization of the diversity of transition paths is extremely challenging because it requires measuring more than one distance during individual transitions. In this work, we used fast three-color single-molecule Förster resonance energy transfer spectroscopy to obtain the distribution of binding transition paths of a disordered protein. About half of the transitions follow a path involving strong non-native electrostatic interactions, resulting in a transition time of 300 to 800 microseconds. The remaining half follow more diverse paths characterized by weaker electrostatic interactions and more than 10 times shorter transition path times. The chain flexibility and non-native interactions make diverse binding pathways possible, allowing disordered proteins to bind faster than folded proteins.

Delineating the conformational dynamics of intermediate structures on the unfolding pathway of β-lactoglobulin in aqueous urea and dimethyl sulfoxide

The funnel shaped energy landscape model of the protein folding suggests that progression of folding proceeds through multiple pathways, having the multiple intermediates which leads to multidimensional free-energy surface. Herein, we applied all-atom MD simulation to conduct a comparative study on the structure of β-lactoglobulin (β-LgA) in aqueous mixture of 8 M urea and 8 M dimethyl sulfoxide (DMSO), at different temperatures. The cumulative results of multiple simulations suggest a common unfolding pathway of β-LgA, occurred through the stable and meta-stable intermediates (I), in both urea and DMSO. However, the free-energy landscape (FEL) analyses show that the structural transitions of I-states are energetically different. In urea, FEL shows distinct ensemble of intermediates, I1 and I2, separated by the energy barrier of ∼3.0 kcal mol^-1. Similarly, we find the population of two distinct I1 and I2 states in DMSO, however, the I1 appeared transiently around ∼30-35 ns and is short-lived. But, the I2 ensemble is observed structurally compact and long-lived (∼50-150 ns) as compared to unfolding in urea. Furthermore, the I1 and I2 are separated through a high energy barrier of ∼6.0 kcal mol^-1. Thus, our results provide the structural insights of intermediates which essentially bear the signature of a different unfolding pathway of β-LgA in urea and DMSO.Abbreviationsβ-LgAβ-lactoglobulinDMSOdimethyl sulfoxideFELfree-energy landscapeGdmClguanidinium chlorideIintermediate stateMGmolten globule statePMEparticle mesh EwaldQfraction of native contactsRMSDroot mean square deviationRMSFroot mean square fluctuationR_gradius of gyrationSASAsolvent Accessible Surface AreascSASAthe side chain SASATrptryptophanCommunicated by Ramaswamy H. Sarma.

Diverse Folding Pathways of HIV-1 Protease Monomer on a Rugged Energy Landscape

The modern energy landscape theory of protein folding predicts multiple folding pathways connecting a myriad of unfolded conformations and a well-defined folded state. However, direct experimental observation of heterogeneous folding pathways is difficult. Naturally evolved proteins typically exhibit a smooth folding energy landscape for fast and efficient folding by avoiding unfavorable kinetic traps. In this case, rapid fluctuations between unfolded conformations result in apparent two-state behavior and make different pathways indistinguishable. However, the landscape roughness can be different, depending on the selection pressures during evolution. Here, we characterize the unusually rugged folding energy landscape of human immunodeficiency virus-1 protease monomer using single-molecule Förster resonance energy transfer spectroscopy. Our data show that fluctuations between unfolded conformations are slow, which enables the experimental observation of heterogeneous folding pathways as predicted by the landscape theory. Although the landscape ruggedness is sensitive to the mutations and fluorophore locations, the folding rate is similar for various protease constructs. The natural evolution of the protease to have a rugged energy landscape likely results from intrinsic pressures to maintain robust folding when human immunodeficiency virus-1 mutates frequently, which is essential for its survival.

Variational consistent histories as a hybrid algorithm for quantum foundations

Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers’ utility for the Consistent Histories formalism, which has previously been employed to study quantum cosmology, quantum paradoxes, and the quantum-to-classical transition. We present a variational hybrid quantum-classical algorithm for finding consistent histories, which should revitalize interest in this formalism by allowing classically impossible calculations to be performed. In our algorithm, the quantum computer evaluates the decoherence functional (with exponential speedup in both the number of qubits and the number of times in the history) and a classical optimizer adjusts the history parameters to improve consistency. We implement our algorithm on a cloud quantum computer to find consistent histories for a spin in a magnetic field and on a simulator to observe the emergence of classicality for a chiral molecule.

The Consistent Histories formalism can solve paradoxes in quantum mechanics, but finding such consistent sets of histories requires a computational overhead which is exponential in the problem’s size. Here, the authors report a variational hybrid algorithm solving this problem using polynomial resources.

Searching the Optimal Folding Routes of a Complex Lasso Protein

Understanding how polypeptides can efficiently and reproducibly attain a self-entangled conformation is a compelling biophysical challenge that might shed new light on our general knowledge of protein folding. Complex lassos, namely self-entangled protein structures characterized by a covalent loop sealed by a cysteine bridge, represent an ideal test system in the framework of entangled folding. Indeed, because cysteine bridges form in oxidizing conditions, they can be used as on/off switches of the structure topology to investigate the role played by the backbone entanglement in the process. In this work, we have used molecular dynamics to simulate the folding of a complex lasso glycoprotein, granulocyte-macrophage colony-stimulating factor, modeling both reducing and oxidizing conditions. Together with a well-established Gō-like description, we have employed the elastic folder model, a coarse-grained, minimalistic representation of the polypeptide chain driven by a structure-based angular potential. The purpose of this study is to assess the kinetically optimal pathways in relation to the formation of the native topology. To this end, we have implemented an evolutionary strategy that tunes the elastic folder model potentials to maximize the folding probability within the early stages of the dynamics. The resulting protein model is capable of folding with high success rate, avoiding the kinetic traps that hamper the efficient folding in the other tested models. Employing specifically designed topological descriptors, we could observe that the selected folding routes avoid the topological bottleneck by locking the cysteine bridge after the topology is formed. These results provide valuable insights on the selection of mechanisms in self-entangled protein folding while, at the same time, the proposed methodology can complement the usage of established minimalistic models and draw useful guidelines for more detailed simulations.

Measuring the average shape of transition paths during the folding of a single biological molecule

Transition paths represent the parts of a reaction where the energy barrier separating products and reactants is crossed. They are essential to understanding reaction mechanisms, yet many of their properties remain unstudied. Here, we report measurements of the average shape of transition paths, studying the folding of DNA hairpins as a model system for folding reactions. Individual transition paths were detected in the folding trajectories of hairpins with different sequences held under tension in optical tweezers, and path shapes were computed by averaging all transitions in the time domain, 〈t(x)〉, or by averaging transitions of a given duration in the extension domain, 〈x(t|τ)〉 _τ Whereas 〈t(x)〉 was close to straight, with only a subtle curvature, 〈x(t|τ)〉 _τ had more pronounced curvature that fit well to theoretical expectations for the dominant transition path, returning diffusion coefficients similar to values obtained previously from independent methods. Simulations suggested that 〈t(x)〉 provided a less reliable representation of the path shape than 〈x(t|τ)〉 _τ , because it was far more sensitive to the effects of coupling the molecule to the experimental force probe. Intriguingly, the path shape variance was larger for some hairpins than others, indicating sequence-dependent changes in the diversity of transition paths reflective of differences in the character of the energy barriers, such as the width of the barrier saddle-point or the presence of parallel paths through multiple barriers between the folded and unfolded states. These studies of average path shapes point the way forward for probing the rich information contained in path shape fluctuations.

The combined force field-sampling problem in simulations of disordered amyloid-β peptides

Molecular dynamics simulations of intrinsically disordered proteins (IDPs) can provide high resolution structural ensembles if the force field is accurate enough and if the simulation sufficiently samples the conformational space of the IDP with the correct weighting of sub-populations. Here, we investigate the combined force field-sampling problem by testing a standard force field as well as newer fixed charge force fields, the latter specifically motivated for better description of unfolded states and IDPs, and comparing them with a standard temperature replica exchange (TREx) protocol and a non-equilibrium Temperature Cool Walking (TCW) sampling algorithm. The force field and sampling combinations are used to characterize the structural ensembles of the amyloid-beta peptides Aβ42 and Aβ43, which both should be random coils as shown recently by experimental nuclear magnetic resonance (NMR) and 2D Förster resonance energy transfer (FRET) experiments. The results illustrate the key importance of the sampling algorithm: while the standard force field using TREx is in poor agreement with the NMR J-coupling and nuclear Overhauser effect and 2D FRET data, when using the TCW method, the standard and optimized protein-water force field combinations are in very good agreement with the same experimental data since the TCW sampling method produces qualitatively different ensembles than TREx. We also discuss the relative merit of the 2D FRET data when validating structural ensembles using the different force fields and sampling protocols investigated in this work for small IDPs such as the Aβ42 and Aβ43 peptides.

Nature's Shortcut to Protein Folding

This Feature Article presents a view of the protein folding transition based on the hypothesis that Nature has built features within the sequences that enable a Shortcut to efficient folding. Nature's Shortcut is proposed to be the early establishment of a set of nonlocal weak contacts, constituting protein loops that significantly constrain regions of the collapsed disordered protein into a native-like low-resolution fluctuating topology of major sections of the backbone. Nature's establishment of this scaffold of nonlocal contacts is claimed to bypass what would otherwise be a nearly hopeless unaided search for the final three-dimensional structure in proteins longer than ∼100 amino acids. To support this main contention of the Feature Article, the loop hypothesis (LH) description of early folding events is experimentally tested with time-resolved Förster resonance energy transfer techniques for adenylate kinase, and the data are shown to be consistent with theoretical predictions from the sequential collapse model (SCM). The experimentally based LH and the theoretically founded SCM are argued to provide a unified picture of the role of nonlocal contacts as constituting Nature's Shortcut to protein folding. Importantly, the SCM is shown to reliably predict key nonlocal contacts utilizing only primary sequence information. This view on Nature's Shortcut is open to the protein community for further detailed assessment, including its practical consequences, by suitable application of advanced experimental and computational techniques.

Characterization of heterogeneous intermediate ensembles on the guanidinium chloride-induced unfolding pathway of β-lactoglobulin

Folding pathway of β-LgA (β-lactoglobulin) evolves through the conformational α→β transition. The α→β transition is a molecular hallmark of various neurodegenerative diseases. Thus, β-LgA may serve as a good model for understanding molecular mechanism of protein aggregation involved in neurodegenerative diseases. Here, we studied the conformational dynamics of β-LgA in 6 M GdmCl at different temperatures using MD simulations. Structural order parameters such as RMSD, R_g, SASA, native contacts (Q), hydrophobic distal-matrix and free-energy landscape (FEL) were used to investigate the conformational transitions. Our results show that GdmCl destabilizes secondary and tertiary structure of β-LgA by weakening the hydrophobic interactions and hydrogen bond network. Multidimensional FEL shows the presence of different unfolding intermediates at 400 K. I1 is long-lived intermediate which has mostly intact native secondary structure, but loose tertiary structure. I2 is structurally compact intermediate formed after the partial loss of secondary structure. The transiently and infrequently buried evolution of W19 shows that intermediate conformational ensembles are structurally heterogeneous. We observed that the intermediate conformations are largely stabilized by non-native H-bonds. The outcome of this work provides the molecular details of intermediates trapped due to non-native interactions that may be regarded as pathogenic conformations involved in neurodegenerative diseases.Communicated by Ramaswamy H. Sarma.

Experimental evidence of symmetry breaking of transition-path times

While thermal rates of state transitions in classical systems have been studied for almost a century, associated transition-path times have only recently received attention. Uphill and downhill transition paths between states at different free energies should be statistically indistinguishable. Here, we systematically investigate transition-path-time symmetry and report evidence of its breakdown on the molecular- and meso-scale out of equilibrium. In automated Brownian dynamics experiments, we establish first-passage-time symmetries of colloids driven by femtoNewton forces in holographically-created optical landscapes confined within microchannels. Conversely, we show that transitions which couple in a path-dependent manner to fluctuating forces exhibit asymmetry. We reproduce this asymmetry in folding transitions of DNA-hairpins driven out of equilibrium and suggest a topological mechanism of symmetry breakdown. Our results are relevant to measurements that capture a single coordinate in a multidimensional free energy landscape, as encountered in electrophysiology and single-molecule fluorescence experiments.

From Levinthal's Paradox to the Effects of Cell Environmental Perturbation on Protein Folding

BACKGROUND

The rapidly increasing number of known protein sequences calls for more efficient methods to predict the Three-Dimensional (3D) structures of proteins, thus providing basic knowledge for rational drug design. Understanding the folding mechanism of proteins is valuable for predicting their 3D structures and for designing proteins with new functions and medicinal applications. Levinthal's paradox is that although the astronomical number of conformations possible even for proteins as small as 100 residues cannot be fully sampled, proteins in nature normally fold into the native state within timescales ranging from microseconds to hours. These conflicting results reveal that there are factors in organisms that can assist in protein folding.

METHODS

In this paper, we selected a crowded cell-like environment and temperature, and the top three Posttranslational Modifications (PTMs) as examples to show that Levinthal's paradox does not reflect the folding mechanism of proteins. We then revealed the effects of these factors on protein folding.

RESULTS

The results summarized in this review indicate that a crowded cell-like environment, temperature, and the top three PTMs reshape the Free Energy Landscapes (FELs) of proteins, thereby regulating the folding process. The balance between entropy and enthalpy is the key to understanding the effect of the crowded cell-like environment and PTMs on protein folding. In addition, the stability/flexibility of proteins is regulated by temperature.

CONCLUSION

This paper concludes that the cellular environment could directly intervene in protein folding. The long-term interactions of the cellular environment and sequence evolution may enable proteins to fold efficiently. Therefore, to correctly understand the folding mechanism of proteins, the effect of the cellular environment on protein folding should be considered.

On the Natural Structure of Amino Acid Patterns in Families of Protein Sequences

All known terrestrial proteins are coded as continuous strings of ≈20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method to search for patterns and groupings of patterns in protein sequences using a mathematically precise definition for "repetition", an efficient algorithmic implementation and a robust scoring system with no adjustable parameters. We show that the sequence patterns can be well-separated into disjoint classes according to their recurrence in nested structures. The statistics of the occurrences of patterns indicate that short repetitions are sufficient to account for the differences between natural families and randomized groups of sequences by more than 10 standard deviations, while contiguous sequence patterns shorter than 5 residues are effectively random in their occurrences. A small subset of patterns is sufficient to account for a robust "familiarity" definition between arbitrary sets of sequences.

Evolved Minimal Frustration in Multifunctional Biomolecules

Protein folding is often viewed in terms of a funneled potential or free energy landscape. A variety of experiments now indicate the existence of multifunnel landscapes, associated with multifunctional biomolecules. Here, we present evidence that these systems have evolved to exhibit the minimal number of funnels required to fulfill their cellular functions, suggesting an extension to the principle of minimum frustration. We find that minimal disruptive mutations result in additional funnels, and the associated structural ensembles become more diverse. The same trends are observed in an atomic cluster. These observations suggest guidelines for rational design of engineered multifunctional biomolecules.

A folding nucleus and minimal ATP binding domain of Hsp70 identified by single-molecule force spectroscopy

The folding pathways of large proteins are complex, with many of them requiring the aid of chaperones and others folding spontaneously. Along the folding pathways, partially folded intermediates are frequently populated; their role in the driving of the folding process is unclear. The structures of these intermediates are generally not amenable to high-resolution structural techniques because of their transient nature. Here we employed single-molecule force measurements to scrutinize the hierarchy of intermediate structures along the folding pathway of the nucleotide binding domain (NBD) of Escherichia coli Hsp70 DnaK. DnaK-NBD is a member of the sugar kinase superfamily that includes Hsp70s and the cytoskeletal protein actin. Using optical tweezers, a stable nucleotide-binding competent en route folding intermediate comprising lobe II residues (183-383) was identified as a critical checkpoint for productive folding. We obtained a structural snapshot of this folding intermediate that shows native-like conformation. To assess the fundamental role of folded lobe II for efficient folding, we turned our attention to yeast mitochondrial NBD, which does not fold without a dedicated chaperone. After replacing the yeast lobe II residues with stable E. coli lobe II, the obtained chimeric protein showed native-like ATPase activity and robust folding into the native state, even in the absence of chaperone. In summary, lobe II is a stable nucleotide-binding competent folding nucleus that is the key to time-efficient folding and possibly resembles a common ancestor domain. Our findings provide a conceptual framework for the folding pathways of other members of this protein superfamily.

Study of protein folding under native conditions by rapidly switching the hydrostatic pressure inside an NMR sample cell

Development of specialized instrumentation enables rapid switching of the hydrostatic pressure inside an operating NMR spectrometer. This technology allows observation of protein signals during the repeated folding process. Applied to ubiquitin, a previously extensively studied model of protein folding, the methodology reveals an initially highly dynamic state that deviates relatively little from random coil behavior but also provides evidence for numerous repeatedly failed folding events, previously only observed in computer simulations. Above room temperature, direct NMR evidence shows a ∼50% fraction of proteins folding through an on-pathway kinetic intermediate, thereby revealing two equally efficient parallel folding pathways.

In general, small proteins rapidly fold on the timescale of milliseconds or less. For proteins with a substantial volume difference between the folded and unfolded states, their thermodynamic equilibrium can be altered by varying the hydrostatic pressure. Using a pressure-sensitized mutant of ubiquitin, we demonstrate that rapidly switching the pressure within an NMR sample cell enables study of the unfolded protein under native conditions and, vice versa, study of the native protein under denaturing conditions. This approach makes it possible to record 2D and 3D NMR spectra of the unfolded protein at atmospheric pressure, providing residue-specific information on the folding process. ¹⁵N and ¹³C chemical shifts measured immediately after dropping the pressure from 2.5 kbar (favoring unfolding) to 1 bar (native) are close to the random-coil chemical shifts observed for a large, disordered peptide fragment of the protein. However, ¹⁵N relaxation data show evidence for rapid exchange, on a ∼100-μs timescale, between the unfolded state and unstable, structured states that can be considered as failed folding events. The NMR data also provide direct evidence for parallel folding pathways, with approximately one-half of the protein molecules efficiently folding through an on-pathway kinetic intermediate, whereas the other half fold in a single step. At protein concentrations above ∼300 μM, oligomeric off-pathway intermediates compete with folding of the native state.

Protein folding transition path times from single molecule FRET

The transition path is the tiny segment of a single molecule trajectory when the free energy barrier between states is crossed and for protein folding contains all of the information about the self-assembly mechanism. As a first step toward obtaining structural information during the transition path from experiments, single molecule FRET spectroscopy has been used to determine average transition path times from a photon-by-photon analysis of fluorescence trajectories. These results, obtained for several different proteins, have already provided new and demanding tests that support both the accuracy of all-atom molecular dynamics simulations and the basic postulates of energy landscape theory of protein folding.