Folding pathway of a multidomain protein depends on its topology of domain connectivity

The Biochemical Impact of Extracting an Embedded Adenylate Kinase Domain Using Circular Permutation

Adenylate kinases (AKs) have evolved AMP-binding and lid domains that are encoded as continuous polypeptides embedded at different locations within the discontinuous polypeptide encoding the core domain. A prior study showed that AK homologues of different stabilities consistently retain cellular activity following circular permutation that splits a region with high energetic frustration within the AMP-binding domain into discontinuous fragments. Herein, we show that mesophilic and thermophilic AKs having this topological restructuring retain activity and substrate-binding characteristics of the parental AK. While permutation decreased the activity of both AK homologues at physiological temperatures, the catalytic activity of the thermophilic AK increased upon permutation when assayed >30 °C below the melting temperature of the native AK. The thermostabilities of the permuted AKs were uniformly lower than those of native AKs, and they exhibited multiphasic unfolding transitions, unlike the native AKs, which presented cooperative thermal unfolding. In addition, proteolytic digestion revealed that permutation destabilized each AK in differing manners, and mass spectrometry suggested that the new termini within the AMP-binding domain were responsible for the increased proteolysis sensitivity. These findings illustrate how changes in contact order can be used to tune enzyme activity and alter folding dynamics in multidomain enzymes.

Folding pathway of a discontinuous two-domain protein

It is estimated that two-thirds of all proteins in higher organisms are composed of multiple domains, many of them containing discontinuous folds. However, to date, most in vitro protein folding studies have focused on small, single-domain proteins. As a model system for a two-domain discontinuous protein, we study the unfolding/refolding of a slow-folding double mutant of the maltose binding protein (DM-MBP) using single-molecule two- and three-color Förster Resonance Energy Transfer experiments. We observe a dynamic folding intermediate population in the N-terminal domain (NTD), C-terminal domain (CTD), and at the domain interface. The dynamic intermediate fluctuates rapidly between unfolded states and compact states, which have a similar FRET efficiency to the folded conformation. Our data reveals that the delayed folding of the NTD in DM-MBP is imposed by an entropic barrier with subsequent folding of the highly dynamic CTD. Notably, accelerated DM-MBP folding is routed through the same dynamic intermediate within the cavity of the GroEL/ES chaperone system, suggesting that the chaperonin limits the conformational space to overcome the entropic folding barrier. Our study highlights the subtle tuning and co-dependency in the folding of a discontinuous multi-domain protein.

Accurate prediction of protein folding mechanisms by simple structure-based statistical mechanical models

Recent breakthroughs in highly accurate protein structure prediction using deep neural networks have made considerable progress in solving the structure prediction component of the 'protein folding problem'. However, predicting detailed mechanisms of how proteins fold into specific native structures remains challenging, especially for multidomain proteins constituting most of the proteomes. Here, we develop a simple structure-based statistical mechanical model that introduces nonlocal interactions driving the folding of multidomain proteins. Our model successfully predicts protein folding processes consistent with experiments, without the limitations of protein size and shape. Furthermore, slight modifications of the model allow prediction of disulfide-oxidative and disulfide-intact protein folding. These predictions depict details of the folding processes beyond reproducing experimental results and provide a rationale for the folding mechanisms. Thus, our physics-based models enable accurate prediction of protein folding mechanisms with low computational complexity, paving the way for solving the folding process component of the 'protein folding problem'.

Different N-Glycosylation Sites Reduce the Activity of Recombinant DSPAα2

Bat plasminogen activators α2 (DSPAα2) has extremely high medicinal value as a powerful natural thrombolytic protein. However, wild-type DSPAα2 has two N-glycosylation sites (N185 and N398) and its non-human classes of high-mannose-type N-glycans may cause immune responses in vivo. By mutating the N-glycosylation sites, we aimed to study the effect of its N-glycan chain on plasminogen activation, fibrin sensitivity, and to observe the physicochemical properties of DSPAα2. A logical structure design was performed in this study. Four single mutants and one double mutant were constructed and expressed in Pichia pastoris. When the N398 site was eliminated, the plasminogen activator in the mutants had their activities reduced to ~40%. When the N185 site was inactivated, there was a weak decrease in the plasminogen activation of its mutant, while the fibrin sensitivity significantly decreased by ~10-fold. Neither N-glycosylation nor deglycosylation mutations changed the pH resistance or heat resistance of DSPAα2. This study confirms that N-glycosylation affects the biochemical function of DSPAα2, which provides a reference for subsequent applications of DSPAα2.

The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics

Despite the recent advances in the prediction of protein structures by deep neutral networks, the elucidation of protein-folding mechanisms remains challenging. A promising theory for describing protein folding is a coarse-grained statistical mechanical model called the Wako-Saitô-Muñoz-Eaton (WSME) model. The model can calculate the free-energy landscapes of proteins based on a three-dimensional structure with low computational complexity, thereby providing a comprehensive understanding of the folding pathways and the structure and stability of the intermediates and transition states involved in the folding reaction. In this review, we summarize previous and recent studies on protein folding and dynamics performed using the WSME model and discuss future challenges and prospects. The WSME model successfully predicted the folding mechanisms of small single-domain proteins and the effects of amino-acid substitutions on protein stability and folding in a manner that was consistent with experimental results. Furthermore, extended versions of the WSME model were applied to predict the folding mechanisms of multi-domain proteins and the conformational changes associated with protein function. Thus, the WSME model may contribute significantly to solving the protein-folding problem and is expected to be useful for predicting protein folding, stability, and dynamics in basic research and in industrial and medical applications.

Topological bio-scaling analysis as a universal measure of protein folding

Scaling relationships for polymeric molecules establish power law dependencies between the number of molecular segments and linear dimensions, such as the radius of gyration. They also establish spatial topological properties of the chains, such as their dimensionality. In the spatial domain, power exponents α = 1 (linear stretched molecule), α = 0.5 (the ideal chain) and α = 0.333 (compact globule) are significant. During folding, the molecule undergoes the transition from the one-dimensional linear to the three-dimensional globular state within a very short time. However, intermediate states with fractional dimensions can be stabilized by modifying the solubility (e.g. by changing the solution temperature). Topological properties, such as dimension, correlate with the interaction energy, and thus by tuning the solubility one can control molecular interaction. We investigate these correlations using the example of a well-studied short model of Trp-cage protein. The radius of gyration is used to estimate the fractal dimension of the chain at different stages of folding. It is expected that the same principle is applicable to much larger molecules and that topological (dimensional) characteristics can provide insights into molecular folding and interactions.

Cooperativity and Folding Kinetics in a Multidomain Protein with Interwoven Chain Topology

Although a large percentage of eukaryotic proteomes consist of proteins with multiple domains, not much is known about their assembly mechanism, especially those with intricate native state architectures. Some have a complex topology in which the structural elements along the sequence are interwoven in such a manner that the domains cannot be separated by cutting at any location along the sequence. Such proteins are multiply connected multidomain proteins (MMPs) with the three-domain (NMP, LID, and CORE) phosphotransferase enzyme adenylate kinase (ADK) being an example. We devised a coarse-grained model to simulate ADK folding initiated by changing either the temperature or guanidinium chloride (GdmCl) concentration. The simulations reproduce the experimentally measured melting temperatures (associated with two equilibrium transitions), FRET efficiency as a function of GdmCl concentration, and the folding times quantitatively. Although the NMP domain orders independently, cooperative interactions between the LID and the CORE domains are required for complete assembly of the enzyme. Kinetic simulations show that, on the collapse time scale, multiple interconnected metastable states are populated, attesting to the folding heterogeneity. The network of kinetically connected states reveals that the CORE domain folds only after the NMP and LID domains, reflecting the interwoven nature of the chain topology.

Structural and Kinetic Views of Molecular Chaperones in Multidomain Protein Folding

Despite recent developments in protein structure prediction, the process of the structure formation, folding, remains poorly understood. Notably, folding of multidomain proteins, which involves multiple steps of segmental folding, is one of the biggest questions in protein science. Multidomain protein folding often requires the assistance of molecular chaperones. Molecular chaperones promote or delay the folding of the client protein, but the detailed mechanisms are still unclear. This review summarizes the findings of biophysical and structural studies on the mechanism of multidomain protein folding mediated by molecular chaperones and explains how molecular chaperones recognize the client proteins and alter their folding properties. Furthermore, we introduce several recent studies that describe the concept of kinetics-activity relationships to explain the mechanism of functional diversity of molecular chaperones.

A hierarchy of coupling free energies underlie the thermodynamic and functional architecture of protein structures

Protein sequences and structures evolve by satisfying varied physical and biochemical constraints. This multi-level selection is enabled not just by the patterning of amino acids on the sequence, but also via coupling between residues in the native structure. Here, we employ an energetically detailed statistical mechanical model with millions of microstates to extract such long-range structural correlations, i.e. thermodynamic coupling free energies, from a diverse family of protein structures. We find that despite the intricate and anisotropic distribution of coupling patterns, the majority of residues (>70%) are only marginally coupled contributing to functional motions and catalysis. Physical origins of ‘sectors’, determinants of native ensemble heterogeneity in extant, ancient and designed proteins, and the basis for allostery emerge naturally from coupling free energies. The statistical framework highlights how evolutionary selection and optimization occur at the level of global interaction network for a given protein fold impacting folding, function, and allosteric outputs.

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Evolution of protein structures occurs at the level of global interaction network.

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More than 70% of the protein residues are weakly or marginally coupled.

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Functional ‘sector’ regions are a manifestation of marginal coupling.

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Coupling indices vary across the entire proteins in extant-ancient and natural-designed pairs.

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The proposed methodology can be used to understand allostery and epistasis.

Effects of electrostatic interactions on global folding and local conformational dynamics of a multidomain Y-family DNA polymerase

The Y-family DNA polymerases specialize in translesion DNA synthesis, which is essential for replicating damaged DNA. The Y-family polymerases, which are made up of four stable domains, exhibit extensive distributions of charged residues, and are responsible for the tight formation of the protein-DNA complex. However, it is still unclear how the electrostatic interactions influence the conformational dynamics of the polymerases. Here, we focus on the case of a prototype Y-family DNA polymerase, Dpo4. Using coarse-grained models including a salt-dependent electrostatic potential, we investigate the effects of the electrostatic interactions on the folding process of Dpo4. Our simulations show that strong electrostatic interactions result in a three-state folding of Dpo4, consistent with the experimental observations. This folding process exhibits low cooperativity led by low salt concentration, where the individual domains fold one by one through one single pathway. Since the refined folding order of domains in multidomain proteins can shrink the configurational space, we suggest that the electrostatic interactions facilitate the Dpo4 folding. In addition, we study the local conformational dynamics of Dpo4 in terms of fluctuation and frustration analyses. We show that the electrostatic interactions can exaggerate the local conformational properties, which are in favor of the large-scale conformational transition of Dpo4 during the functional DNA binding. Our results underline the importance of electrostatic interactions in the conformational dynamics of Dpo4 at both the global and local scale, providing useful guidance in protein engineering at the multidomain level.

Investigating the trade-off between folding and function in a multidomain Y-family DNA polymerase

The way in which multidomain proteins fold has been a puzzling question for decades. Until now, the mechanisms and functions of domain interactions involved in multidomain protein folding have been obscure. Here, we develop structure-based models to investigate the folding and DNA-binding processes of the multidomain Y-family DNA polymerase IV (DPO4). We uncover shifts in the folding mechanism among ordered domain-wise folding, backtracking folding, and cooperative folding, modulated by interdomain interactions. These lead to ‘U-shaped’ DPO4 folding kinetics. We characterize the effects of interdomain flexibility on the promotion of DPO4–DNA (un)binding, which probably contributes to the ability of DPO4 to bypass DNA lesions, which is a known biological role of Y-family polymerases. We suggest that the native topology of DPO4 leads to a trade-off between fast, stable folding and tight functional DNA binding. Our approach provides an effective way to quantitatively correlate the roles of protein interactions in conformational dynamics at the multidomain level.

Hidden kinetic traps in multidomain folding highlight the presence of a misfolded but functionally competent intermediate

Much of our current knowledge on protein folding is based on work focused on isolated domains. In this study, using a combination of NMR and kinetic experiments, we depict the folding pathway of a multidomain construct comprising two PDZ domains in tandem, belonging to the protein Whirlin. We demonstrate the presence of a misfolded intermediate that competes with productive folding. Interestingly, we show that, unexpectedly, this misfolded state retains the native-like functional ability to bind its physiological ligand, representing a clear example of a functionally competent misfolded state. On the basis of these results and a comparative analysis of the amino acidic sequences of Whirlin from different species, we propose a possible physiological role of the misfolded intermediate.

Although more than 75% of the proteome is composed of multidomain proteins, current knowledge of protein folding is based primarily on studies of isolated domains. In this work, we describe the folding mechanism of a multidomain tandem construct comprising two distinct covalently bound PDZ domains belonging to a protein called Whirlin, a scaffolding protein of the hearing apparatus. In particular, via a synergy between NMR and kinetic experiments, we demonstrate the presence of a misfolded intermediate that competes with productive folding. In agreement with the view that tandem domain swapping is a potential source of transient misfolding, we demonstrate that such a kinetic trap retains native-like functional activity, as shown by the preserved ability to bind its physiological ligand. Thus, despite the general knowledge that protein misfolding is intimately associated with dysfunction and diseases, we provide a direct example of a functionally competent misfolded state. Remarkably, a bioinformatics analysis of the amino acidic sequence of Whirlin from different species suggests that the tendency to perform tandem domain swapping between PDZ1 and PDZ2 is highly conserved, as demonstrated by their unexpectedly high sequence identity. On the basis of these observations, we discuss on a possible physiological role of such misfolded intermediate.

Confinement and Crowding Effects on Folding of a Multidomain Y-Family DNA Polymerase

Proteins in vivo endure highly various interactions from the luxuriant surrounding macromolecular cosolutes. Confinement and macromolecular crowding are the two major effects that should be considered while comparing the results of protein dynamics from in vitro to in vivo. However, efforts have been largely focused on single domain protein folding up to now, and the quantifications of the in vivo effects in terms of confinements and crowders on modulating the structure and dynamics as well as the physical understanding of the underlying mechanisms on multidomain protein folding are still challenging. Here we developed a topology-based model to investigate folding of a multidomain Y-family DNA polymerase (DPO4) within spherical confined space and in the presence of repulsive and attractive crowders. We uncovered that the entropic component of the thermodynamic driving force led by confinements and repulsive crowders increases the stability of folded states relative to the folding intermediates and unfolded states, while the enthalpic component of the thermodynamic driving force led by attractive crowders gives rise to the opposite effects with less stability. We found that the shapes of DPO4 conformations influenced by the confinements and the crowders are quite different even when only the entropic component of the thermodynamic driving force is considered. We uncovered that under all in vivo conditions, the folding cooperativity of DPO4 decreases compared to that in bulk. We showed that the loss of folding cooperativity can promote the sequential domain-wise folding, which was widely found in cotranslational multidomain protein folding, and effectively prohibit the backtracking led by topological frustrations during multidomain protein folding processes.

Cotranslational folding allows misfolding-prone proteins to circumvent deep kinetic traps

Many large proteins suffer from slow or inefficient folding in vitro. It has long been known that this problem can be alleviated in vivo if proteins start folding cotranslationally. However, the molecular mechanisms underlying this improvement have not been well established. To address this question, we use an all-atom simulation-based algorithm to compute the folding properties of various large protein domains as a function of nascent chain length. We find that for certain proteins, there exists a narrow window of lengths that confers both thermodynamic stability and fast folding kinetics. Beyond these lengths, folding is drastically slowed by nonnative interactions involving C-terminal residues. Thus, cotranslational folding is predicted to be beneficial because it allows proteins to take advantage of this optimal window of lengths and thus avoid kinetic traps. Interestingly, many of these proteins' sequences contain conserved rare codons that may slow down synthesis at this optimal window, suggesting that synthesis rates may be evolutionarily tuned to optimize folding. Using kinetic modeling, we show that under certain conditions, such a slowdown indeed improves cotranslational folding efficiency by giving these nascent chains more time to fold. In contrast, other proteins are predicted not to benefit from cotranslational folding due to a lack of significant nonnative interactions, and indeed these proteins' sequences lack conserved C-terminal rare codons. Together, these results shed light on the factors that promote proper protein folding in the cell and how biomolecular self-assembly may be optimized evolutionarily.

Successes and challenges in simulating the folding of large proteins

Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments, and to test the effects of mutations and small molecules on folding. However, whereas major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multidomain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization, and interactions with cellular chaperones remain poorly understood. Molecular dynamics based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates, and pathways. Further, increases in computational power and methodological advances have made folding simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Gō and related structure-based models that can predict the effects of the native structure on folding to all-atom-based methods that include side-chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold, expanding our ability to predict and manipulate protein folding.

Thermodynamics and folding landscapes of large proteins from a statistical mechanical model

Statistical mechanical models that afford an intermediate resolution between macroscopic chemical models and all-atom simulations have been successful in capturing folding behaviors of many small single-domain proteins. However, the applicability of one such successful approach, the Wako-Saitô-Muñoz-Eaton (WSME) model, is limited by the size of the protein as the number of conformations grows exponentially with protein length. In this work, we surmount this size limitation by introducing a novel approximation that treats stretches of 3 or 4 residues as blocks, thus reducing the phase space by nearly three orders of magnitude. The performance of the 'bWSME' model is validated by comparing the predictions for a globular enzyme (RNase H) and a repeat protein (IκBα), against experimental observables and the model without block approximation. Finally, as a proof of concept, we predict the free-energy surface of the 370-residue, multi-domain maltose binding protein and identify an intermediate in good agreement with single-molecule force-spectroscopy measurements. The bWSME model can thus be employed as a quantitative predictive tool to explore the conformational landscapes of large proteins, extract the structural features of putative intermediates, identify parallel folding paths, and thus aid in the interpretation of both ensemble and single-molecule experiments.

Folding with a protein's native shortcut network

A complex network approach to protein folding is proposed, wherein a protein's contact map is reconceptualized as a network of shortcut edges, and folding is steered by a structural characteristic of this network. Shortcut networks are generated by a known message passing algorithm operating on protein residue networks. It is found that the shortcut networks of native structures (SCN0s) are relevant graph objects with which to study protein folding at a formal level. The logarithm form of their contact order (SCN0_lnCO) correlates significantly with folding rate of two-state and nontwo-state proteins. The clustering coefficient of SCN0s (C_SCN0 ) correlates significantly with folding rate, transition-state placement and stability of two-state folders. Reasonable folding pathways for several model proteins are produced when C_SCN0 is used to combine protein segments incrementally to form the native structure. The folding bias captured by C_SCN0 is detectable in non-native structures, as evidenced by Molecular Dynamics simulation generated configurations for the fast folding Villin-headpiece peptide. These results support the use of shortcut networks to investigate the role protein geometry plays in the folding of both small and large globular proteins, and have implications for the design of multibody interaction schemes in folding models. One facet of this geometry is the set of native shortcut triangles, whose attributes are found to be well-suited to identify dehydrated intraprotein areas in tight turns, or at the interface of different secondary structure elements.

Switching Protein Conformational Substates by Protonation and Mutation

Protein modules that regulate the availability and conformational status of transcription factors determine the rapidity, duration, and magnitude of cellular response to changing conditions. One such system is the single-gene product Cnu, a four-helix bundle transcription co-repressor, which acts as a molecular thermosensor regulating the expression of virulence genes in enterobacteriaceae through modulation of its native conformational ensemble. Cnu and related genes have also been implicated in pH-dependent expression of virulence genes. We hypothesize that protonation of a conserved buried histidine (H45) in Cnu promotes large electrostatic frustration, thus disturbing the H-NS, a transcription factor, binding face. Spectroscopic and calorimetric methods reveal that H45 exhibits a suppressed p K_a of ∼5.1, the protonation of which switches the conformation to an alternate native ensemble in which the fourth helix is disordered. The population redistribution can also be achieved through a mutation H45V, which does not display any switching behavior at pH values greater than 4. The Wako-Saitô-Muñoz-Eaton (WSME) statistical mechanical model predicts specific differences in the conformations and fluctuations of the fourth and first helices of Cnu determining the observed pH response. We validate these predictions through fluorescence lifetime measurements of a sole tryptophan, highlighting the presence of both native and non-native interactions in the regions adjoining the binding face of Cnu. Our combined experimental-computational study thus shows that Cnu acts both as a thermo- and pH-sensor orchestrated via a subtle but quantifiable balance between the weak packing of a structural element and protonation of a buried histidine that promotes electrostatic frustration.

Spontaneous refolding of the large multidomain protein malate synthase G proceeds through misfolding traps

Most protein folding studies until now focus on single domain or truncated proteins. Although great insights in the folding of such systems has been accumulated, very little is known regarding the proteins containing multiple domains. It has been shown that the high stability of domains, in conjunction with inter-domain interactions, manifests as a frustrated energy landscape, causing complexity in the global folding pathway. However, multidomain proteins despite containing independently foldable, loosely cooperative sections can fold into native states with amazing speed and accuracy. To understand the complexity in mechanism, studies were conducted previously on the multidomain protein malate synthase G (MSG), an enzyme of the glyoxylate pathway with four distinct and adjacent domains. It was shown that the protein refolds to a functionally active intermediate state at a fast rate, which slowly produces the native state. Although experiments decoded the nature of the intermediate, a full description of the folding pathway was not elucidated. In this study, we use a battery of biophysical techniques to examine the protein's folding pathway. By using multiprobe kinetics studies and comparison with the equilibrium behavior of protein against urea, we demonstrate that the unfolded polypeptide undergoes conformational compaction to a misfolded intermediate within milliseconds of refolding. The misfolded product appears to be stabilized under moderate denaturant concentrations. Further folding of the protein produces a stable intermediate, which undergoes partial unfolding-assisted large segmental rearrangements to achieve the native state. This study reveals an evolved folding pathway of the multidomain protein MSG, which involves surpassing the multiple misfolding traps during refolding.

Unified understanding of folding and binding mechanisms of globular and intrinsically disordered proteins

Extensive experimental and theoretical studies have advanced our understanding of the mechanisms of folding and binding of globular proteins, and coupled folding and binding of intrinsically disordered proteins (IDPs). The forces responsible for conformational changes and binding are common in both proteins; however, these mechanisms have been separately discussed. Here, we attempt to integrate the mechanisms of coupled folding and binding of IDPs, folding of small and multi-subdomain proteins, folding of multimeric proteins, and ligand binding of globular proteins in terms of conformational selection and induced-fit mechanisms as well as the nucleation–condensation mechanism that is intermediate between them. Accumulating evidence has shown that both the rate of conformational change and apparent rate of binding between interacting elements can determine reaction mechanisms. Coupled folding and binding of IDPs occurs mainly by induced-fit because of the slow folding in the free form, while ligand binding of globular proteins occurs mainly by conformational selection because of rapid conformational change. Protein folding can be regarded as the binding of intramolecular segments accompanied by secondary structure formation. Multi-subdomain proteins fold mainly by the induced-fit (hydrophobic collapse) mechanism, as the connection of interacting segments enhances the binding (compaction) rate. Fewer hydrophobic residues in small proteins reduce the intramolecular binding rate, resulting in the nucleation–condensation mechanism. Thus, the folding and binding of globular proteins and IDPs obey the same general principle, suggesting that the coarse-grained, statistical mechanical model of protein folding is promising for a unified theoretical description of all mechanisms.

Probing the Acid-Induced Packing Structure Changes of the Molten Globule Domains of a Protein near Equilibrium Unfolding

Using simultaneously scanning small-angle X-ray scattering (SAXS) and UV-vis absorption with integrated online size exclusion chromatography, supplemental with molecular dynamics simulations, we unveil the long-postulated global structure evolution of a model multidomain protein bovine serum albumin (BSA) during acid-induced unfolding. Our results differentiate three global packing structures of the three molten globule domains of BSA, forming three intermediates I₁, I₂, and E along the unfolding pathway. The I₁-I₂ transition, overlooked in all previous studies, involves mainly coordinated reorientations across interconnected molten globule subdomains, and the transition activates a critical pivot domain opening of the protein for entering into the E form, with an unexpectedly large unfolding free energy change of -9.5 kcal mol^-1, extracted based on the observed packing structural changes. The revealed local packing flexibility and rigidity of the molten globule domains in the E form elucidate how collective motions of the molten globule domains profoundly influence the folding-unfolding pathway of a multidomain protein.

Cooperativity and modularity in protein folding

A simple statistical mechanical model proposed by Wako and Saitô has explained the aspects of protein folding surprisingly well. This model was systematically applied to multiple proteins by Muñoz and Eaton and has since been referred to as the Wako-Saitô-Muñoz-Eaton (WSME) model. The success of the WSME model in explaining the folding of many proteins has verified the hypothesis that the folding is dominated by native interactions, which makes the energy landscape globally biased toward native conformation. Using the WSME and other related models, Saitô emphasized the importance of the hierarchical pathway in protein folding; folding starts with the creation of contiguous segments having a native-like configuration and proceeds as growth and coalescence of these segments. The Φ-values calculated for barnase with the WSME model suggested that segments contributing to the folding nucleus are similar to the structural modules defined by the pattern of native atomic contacts. The WSME model was extended to explain folding of multi-domain proteins having a complex topology, which opened the way to comprehensively understanding the folding process of multi-domain proteins. The WSME model was also extended to describe allosteric transitions, indicating that the allosteric structural movement does not occur as a deterministic sequential change between two conformations but as a stochastic diffusive motion over the dynamically changing energy landscape. Statistical mechanical viewpoint on folding, as highlighted by the WSME model, has been renovated in the context of modern methods and ideas, and will continue to provide insights on equilibrium and dynamical features of proteins.

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

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

Where the complex things are: single molecule and ensemble spectroscopic investigations of protein folding dynamics

Progress in our understanding of the simple folding dynamics of small proteins and the complex dynamics of large proteins is reviewed. Recent characterizations of the folding transition path of small proteins revealed a simple dynamics explainable by the native centric model. In contrast, the accumulated data showed the substates containing residual structures in the unfolded state and partially populated intermediates, causing complexity in the early folding dynamics of small proteins. The size of the unfolded proteins in the absence of denaturants is likely expanded but still controversial. The steady progress in the observation of folding of large proteins has clarified the rapid formation of long-range contacts that seem inconsistent with the native centric model, suggesting that the folding strategy of large proteins is distinct from that of small proteins.

Nonspecific yet decisive: Ubiquitination can affect the native-state dynamics of the modified protein

Ubiquitination is one of the most common post-translational modifications of proteins, and mediates regulated protein degradation among other cellular processes. A fundamental question regarding the mechanism of protein ubiquitination is whether and how ubiquitin affects the biophysical nature of the modified protein. For some systems, it was shown that the position of ubiquitin within the attachment site is quite flexible and ubiquitin does not specifically interact with its substrate. Nevertheless, it was revealed that polyubiquitination can decrease the thermal stability of the modified protein in a site-specific manner because of alterations of the thermodynamic properties of the folded and unfolded states. In this study, we used detailed atomistic simulations to focus on the molecular effects of ubiquitination on the native structure of the modified protein. As a model, we used Ubc7, which is an E2 enzyme whose in vivo ubiquitination process is well characterized and known to lead to degradation. We found that, despite the lack of specific direct interactions between the ubiquitin moiety and Ubc7, ubiquitination decreases the conformational flexibility of certain regions of the substrate Ubc7 protein, which reduces its entropy and thus destabilizes it. The strongest destabilizing effect was observed for systems in which Lys48-linked tetra-ubiquitin was attached to sites used for in vivo degradation. These results reveal how changes in the configurational entropy of the folded state may modulate the stability of the protein's native state. Overall, our results imply that ubiquitination can modify the biophysical properties of the attached protein in the folded state and that, in some proteins, different ubiquitination sites will lead to different biophysical outcomes. We propose that this destabilizing effect of polyubiquitin on the substrate is linked to the functions carried out by the modification, and in particular, regulatory control of protein half-life through proteasomal degradation.