Cooperativity, connectivity, and folding pathways of multidomain proteins

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'.

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.

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.

Understanding the Folding Mediated Assembly of the Bacteriophage MS2 Coat Protein Dimers

The capsids of RNA viruses such as MS2 are great models for studying protein self-assembly because they are made almost entirely of multiple copies of a single coat protein (CP). Although CP is the minimal repeating unit of the capsid, previous studies have shown that CP exists as a homodimer (CP2) even in an acid-disassembled system, indicating that CP2 is an obligate dimer. Here, we investigate the molecular basis of this obligate dimerization using coarse-grained structure-based models and molecular dynamics simulations. We find that, unlike monomeric proteins of similar size, CP populates a single partially folded ensemble whose "foldedness" is sensitive to denaturing conditions. In contrast, CP2 folds similarly to single-domain proteins populating only the folded and the unfolded ensembles, separated by a prominent folding free energy barrier. Several intramonomer contacts form early, but the CP2 folding barrier is crossed only when the intermonomer contacts are made. A dissection of the structure of CP2 through mutant folding simulations shows that the folding barrier arises both from the topology of CP and the interface contacts of CP2. Together, our results show that CP2 is an obligate dimer because of kinetic stability, that is, dimerization induces a folding barrier and that makes it difficult for proteins in the dimer minimum to partially unfold and access the monomeric state without completely unfolding. We discuss the advantages of this obligate dimerization in the context of dimer design and virus stability.

Double Domain Swapping in Human γC and γD Crystallin Drives Early Stages of Aggregation

Human γD (HγD) and γC (HγC) are two-domain crystallin (Crys) proteins expressed in the nucleus of the eye lens. Structural perturbations in the protein often trigger aggregation, which eventually leads to cataract. To decipher the underlying molecular mechanism, it is important to characterize the partially unfolded conformations, which are aggregation-prone. Using a coarse grained protein model and molecular dynamics simulations, we studied the role of on-pathway folding intermediates in the early stages of aggregation. The multidimensional free energy surface revealed at least three different folding pathways with the population of partially structured intermediates. The two dominant pathways confirm sequential folding of the N-terminal [Ntd] and the C-terminal domains [Ctd], while the third, least favored, pathway involves intermediates where both the domains are partially folded. A native-like intermediate (I*), featuring the folded domains and disrupted interdomain contacts, gets populated in all three pathways. I* forms domain swapped dimers by swapping the entire Ntds and Ctds with other monomers. Population of such oligomers can explain the increased resistance to unfolding resulting in hysteresis observed in the folding experiments of HγD Crys. An ensemble of double domain swapped dimers are also formed during refolding, where intermediates consisting of partially folded Ntds and Ctds swap secondary structures with other monomers. The double domain swapping model presented in our study provides structural insights into the early events of aggregation in Crys proteins and identifies the key secondary structural swapping elements, where introducing mutations will aid in regulating the overall aggregation propensity.

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.

Gō model revisited

This review discusses Gō models broadly used in biomolecular simulations. I start with a brief description of the original lattice model study by Nobuhiro Gō. Then, the theory of protein folding behind Gō model, free energy approaches, and off-lattice Gō models are reviewed. I also mention a stringent test for the assumption in Gō models given from all-atom molecular dynamics simulations. Subsequently, I move to application of Gō models to protein dynamical functions. Various extension of Gō models is also reviewed. Finally, some publicly available tools to use Gō models are listed.

Directed evolution of the metalloproteinase inhibitor TIMP-1 reveals that its N- and C-terminal domains cooperate in matrix metalloproteinase recognition

Tissue inhibitors of metalloproteinases (TIMPs) are natural inhibitors of matrix metalloproteinases (MMPs), enzymes that contribute to cancer and many inflammatory and degenerative diseases. The TIMP N-terminal domain binds and inhibits an MMP catalytic domain, but the role of the TIMP C-terminal domain in MMP inhibition is poorly understood. Here, we employed yeast surface display for directed evolution of full-length human TIMP-1 to develop MMP-3-targeting ultrabinders. By simultaneously incorporating diversity into both domains, we identified TIMP-1 variants that were up to 10-fold improved in binding MMP-3 compared with WT TIMP-1, with inhibition constants (K_i ) in the low picomolar range. Analysis of individual and paired mutations from the selected TIMP-1 variants revealed cooperative effects between distant residues located on the N- and C-terminal TIMP domains, positioned on opposite sides of the interaction interface with MMP-3. Crystal structures of MMP-3 complexes with TIMP-1 variants revealed conformational changes in TIMP-1 near the cooperative mutation sites. Affinity was strengthened by cinching of a reciprocal "tyrosine clasp" formed between the N-terminal domain of TIMP-1 and proximal MMP-3 interface and by changes in secondary structure within the TIMP-1 C-terminal domain that stabilize interdomain interactions and improve complementarity to MMP-3. Our protein engineering and structural studies provide critical insight into the cooperative function of TIMP domains and the significance of peripheral TIMP epitopes in MMP recognition. Our findings suggest new strategies to engineer TIMP proteins for therapeutic applications, and our directed evolution approach may also enable exploration of functional domain interactions in other protein systems.

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.

Fast H-DROP: A thirty times accelerated version of H-DROP for interactive SVM-based prediction of helical domain linkers

Efficient and rapid prediction of domain regions from amino acid sequence information alone is often required for swift structural and functional characterization of large multi-domain proteins. Here we introduce Fast H-DROP, a thirty times accelerated version of our previously reported H-DROP (Helical Domain linker pRediction using OPtimal features), which is unique in specifically predicting helical domain linkers (boundaries). Fast H-DROP, analogously to H-DROP, uses optimum features selected from a set of 3000 ones by combining a random forest and a stepwise feature selection protocol. We reduced the computational time from 8.5 min per sequence in H-DROP to 14 s per sequence in Fast H-DROP on an 8 Xeon processor Linux server by using SWISS-PROT instead of Genbank non-redundant (nr) database for generating the PSSMs. The sensitivity and precision of Fast H-DROP assessed by cross-validation were 33.7 and 36.2%, which were merely ~2% lower than that of H-DROP. The reduced computational time of Fast H-DROP, without affecting prediction performances, makes it more interactive and user-friendly. Fast H-DROP and H-DROP are freely available from http://domserv.lab.tuat.ac.jp/ .

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.

Single-molecule Force Spectroscopy Predicts a Misfolded, Domain-swapped Conformation in human γD-Crystallin Protein

Cataract is a protein misfolding disease where the size of the aggregate is directly related to the severity of the disorder. However, the molecular mechanisms that trigger the onset of aggregation remain unknown. Here we use a combination of protein engineering techniques and single-molecule force spectroscopy using atomic force microscopy to study the individual unfolding pathways of the human γD-crystallin, a multidomain protein that must remain correctly folded during the entire lifetime to guarantee lens transparency. When stretching individual polyproteins containing two neighboring HγD-crystallin monomers, we captured an anomalous misfolded conformation in which the β1 and β2 strands of the N terminus domain of two adjacent monomers swap. This experimentally elusive domain-swapped conformation is likely to be responsible for the increase in molecular aggregation that we measure in vitro. Our results demonstrate the power of force spectroscopy at capturing rare misfolded conformations with potential implications for the understanding of the molecular onset of protein aggregation.

Mapping the Topography of a Protein Energy Landscape

Protein energy landscapes are highly complex, yet the vast majority of states within them tend to be invisible to experimentalists. Here, using site-directed mutagenesis and exploiting the simplicity of tandem-repeat protein structures, we delineate a network of these states and the routes between them. We show that our target, gankyrin, a 226-residue 7-ankyrin-repeat protein, can access two alternative (un)folding pathways. We resolve intermediates as well as transition states, constituting a comprehensive series of snapshots that map early and late stages of the two pathways and show both to be polarized such that the repeat array progressively unravels from one end of the molecule or the other. Strikingly, we find that the protein folds via one pathway but unfolds via a different one. The origins of this behavior can be rationalized using the numerical results of a simple statistical mechanics model that allows us to visualize the equilibrium behavior as well as single-molecule folding/unfolding trajectories, thereby filling in the gaps that are not accessible to direct experimental observation. Our study highlights the complexity of repeat-protein folding arising from their symmetrical structures; at the same time, however, this structural simplicity enables us to dissect the complexity and thereby map the precise topography of the energy landscape in full breadth and remarkable detail. That we can recapitulate the key features of the folding mechanism by computational analysis of the native structure alone will help toward the ultimate goal of designed amino-acid sequences with made-to-measure folding mechanisms-the Holy Grail of protein folding.

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.

In the multi-domain protein adenylate kinase, domain insertion facilitates cooperative folding while accommodating function at domain interfaces

Having multiple domains in proteins can lead to partial folding and increased aggregation. Folding cooperativity, the all or nothing folding of a protein, can reduce this aggregation propensity. In agreement with bulk experiments, a coarse-grained structure-based model of the three-domain protein, E. coli Adenylate kinase (AKE), folds cooperatively. Domain interfaces have previously been implicated in the cooperative folding of multi-domain proteins. To understand their role in AKE folding, we computationally create mutants with deleted inter-domain interfaces and simulate their folding. We find that inter-domain interfaces play a minor role in the folding cooperativity of AKE. On further analysis, we find that unlike other multi-domain proteins whose folding has been studied, the domains of AKE are not singly-linked. Two of its domains have two linkers to the third one, i.e., they are inserted into the third one. We use circular permutation to modify AKE chain-connectivity and convert inserted-domains into singly-linked domains. We find that domain insertion in AKE achieves the following: (1) It facilitates folding cooperativity even when domains have different stabilities. Insertion constrains the N- and C-termini of inserted domains and stabilizes their folded states. Therefore, domains that perform conformational transitions can be smaller with fewer stabilizing interactions. (2) Inter-domain interactions are not needed to promote folding cooperativity and can be tuned for function. In AKE, these interactions help promote conformational dynamics limited catalysis. Finally, using structural bioinformatics, we suggest that domain insertion may also facilitate the cooperative folding of other multi-domain proteins.

Most individual protein domains fold in an all or nothing fashion. This cooperative folding is important because it reduces the existence of partially folded proteins which can stick to each other and create disease causing aggregates. However, numerous proteins have multiple domains, independent units of folding, stability and/or function. Several such proteins also fold cooperatively. It is thought that strong interactions between individual domains allow the folding to propagate from a nucleating domain to neighbouring ones and this enables cooperative folding in multi-domain proteins. Here, we computationally study the folding of the three-domain protein AKE and find instead that the topology of the protein, wherein the two less stable domains are inserted into the more stable one, promotes folding cooperativity. When the more stable domain is folded, the ends of the inserted domains are constrained and this allows them to fold easily. In such a protein topology, strong inter-domain interactions are not needed to promote folding cooperativity. Interface amino acids which would have been involved in ensuring that the domains fit together correctly can now be tuned for binding or catalysis or conformational transitions. Thus, inserted domains may be present in multi-domain proteins to promote both function and folding.

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

How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N- and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N- and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant.

Conserved prosegment residues stabilize a late-stage folding transition state of pepsin independently of ground states

The native folding of certain zymogen-derived enzymes is completely dependent upon a prosegment domain to stabilize the folding transition state, thereby catalyzing the folding reaction. Generally little is known about how the prosegment accomplishes this task. It was previously shown that the prosegment catalyzes a late-stage folding transition between a stable misfolded state and the native state of pepsin. In this study, the contributions of specific prosegment residues to catalyzing pepsin folding were investigated by introducing individual Ala substitutions and measuring the effects on the bimolecular folding reaction between the prosegment peptide and pepsin. The effects of mutations on the free energies of the individual misfolded and native ground states and the transition state were compared using measurements of prosegment-pepsin binding and folding kinetics. Five out of the seven prosegment residues examined yielded relatively large kinetic effects and minimal ground state perturbations upon mutation, findings which indicate that these residues form strengthened and/or non-native contacts in the transition state. These five residues are semi- to strictly conserved, while only a non-conserved residue had no kinetic effect. One conserved residue was shown to form native structure in the transition state. These results indicated that the prosegment, which is only 44 residues long, has evolved a high density of contacts that preferentially stabilize the folding transition state over the ground states. It is postulated that the prosegment forms extensive non-native contacts during the process of catalyzing correct inter- and intra-domain contacts during the final stages of folding. These results have implications for understanding the folding of multi-domain proteins and for the evolution of prosegment-catalyzed folding.

Conservation of inter-residue interactions and prediction of folding rates of domain repeats

Domains are the main structural and functional units of larger proteins. They tend to be contiguous in primary structure and can fold and function independently. It has been observed that 10-20% of all encoded proteins contain duplicated domains and the average pairwise sequence identity between them is usually low. In the present study, we have analyzed the structural similarity between domain repeats of proteins with known structures available in the Protein Data Bank using structure-based inter-residue interaction measures such as the number of long-range contacts, surrounding hydrophobicity, and pairwise interaction energy. We used RADAR program for detecting the repeats in a protein sequence which were further validated using Pfam domain assignments. The sequence identity between the repeats in domains ranges from 20 to 40% and their secondary structural elements are well conserved. The number of long-range contacts, surrounding hydrophobicity calculations and pairwise interaction energy of the domain repeats clearly reveal the conservation of 3-D structure environment in the repeats of domains. The proportions of mainchain-mainchain hydrogen bonds and hydrophobic interactions are also highly conserved between the repeats. The present study has suggested that the computation of these structure-based parameters will give better clues about the tertiary environment of the repeats in domains. The folding rates of individual domains in the repeats predicted using the long-range order parameter indicate that the predicted folding rates correlate well with most of the experimentally observed folding rates for the analyzed independently folded domains.

Modulation of a protein free-energy landscape by circular permutation

Circular permutations usually retain the native structure and function of a protein while inevitably perturbing its folding dynamics. By using simulations with a structure-based model and a rigorous methodology to determine free-energy surfaces from trajectories, we evaluate the effect of a circular permutation on the free-energy landscape of the protein T4 lysozyme. We observe changes which, although subtle, largely affect the cooperativity between the two subdomains. Such a change in cooperativity has been previously experimentally observed and recently also characterized using single molecule optical tweezers and the Crooks relation. The free-energy landscapes show that both the wild type and circular permutant have an on-pathway intermediate, previously experimentally characterized, in which one of the subdomains is completely formed. The landscapes, however, differ in the position of the rate-limiting step for folding, which occurs before the intermediate in the wild type and after in the circular permutant. This shift of transition state explains the observed change in the cooperativity. The underlying free-energy landscape thus provides a microscopic description of the folding dynamics and the connection between circular permutation and the loss of cooperativity experimentally observed.

Identification of cancer fusion drivers using network fusion centrality

SUMMARY

Gene fusions are being discovered at an increasing rate using massively parallel sequencing technologies. Prioritization of cancer fusion drivers for validation cannot be performed using traditional single-gene based methods because fusions involve portions of two partner genes. To address this problem, we propose a novel network analysis method called fusion centrality that is specifically tailored for prioritizing gene fusions. We first propose a domain-based fusion model built on the theory of exon/domain shuffling. The model leads to a hypothesis that a fusion is more likely to be an oncogenic driver if its partner genes act like hubs in a network because the fusion mutation can deregulate normal functions of many other genes and their pathways. The hypothesis is supported by the observation that for most known cancer fusion genes, at least one of the fusion partners appears to be a hub in a network, and even for many fusions both partners appear to be hubs. Based on this model, we construct fusion centrality, a multi-gene-based network metric, and use it to score fusion drivers. We show that the fusion centrality outperforms other single gene-based methods. Specifically, the method successfully predicts most of 38 newly discovered fusions that had validated oncogenic importance. To our best knowledge, this is the first network-based approach for identifying fusion drivers.

AVAILABILITY

Matlab code implementing the fusion centrality method is available upon request from the corresponding authors.

Multidomain protein solves the folding problem by multifunnel combined landscape: theoretical investigation of a Y-family DNA polymerase

Approximately three-fourths of eukaryotic proteins are composed of multiple independently folded domains. However, much of our understanding is based on single domain proteins or isolated domains whose studies directly lead to well-known energy landscape theory in which proteins fold by navigating through a funneled energy landscape toward native structure ensembles. The degrees of freedom for proteins with multiple domains are many orders of magnitude larger than that for single domain proteins. Now, the question arises: How do the multidomain proteins solve the "protein folding problem"? Here, we specifically address this issue by exploring the structure folding relationship of Sulfolobus solfataricus DNA polymerase IV (DPO4), a prototype Y-family DNA polymerase which contains a polymerase core consisting of a palm (P domain), a finger (F domain), and a thumb domain (T domain) in addition to a little finger domain (LF domain). The theoretical results are in good agreement with the experimental data and lead to several theoretical predictions. Finally, we propose that for rapid folding into well-defined conformations which carry out the biological functions, four-domain DPO4 employs a divide-and-conquer strategy, that is, combining multiple individual folding funnels into a single funnel (domains fold independently and then coalesce). In this way, the degrees of freedom for multidomain proteins are polynomial rather than exponential, and the conformational search process can be reduced effectively from a large to a smaller time scale.

Statistical mechanics of protein allostery: roles of backbone and side-chain structural fluctuations

A statistical mechanical model of allosteric transition of proteins is developed by extending the structure-based model of protein folding to cases that a protein has two different native conformations. Partition function is calculated exactly within the model and free-energy surfaces associated with allostery are derived. In this paper, the model of allosteric transition proposed in a previous paper [Proc. Natl. Acad. Sci. U.S.A 134, 7775 (2010)] is reformulated to describe both fluctuation in side-chain configurations and that in backbone structures in a balanced way. The model is applied to example proteins, Ras, calmodulin, and CheY: Ras undergoes the allosteric transition between guanosine diphosphate (GDP)-bound and guanosine triphosphate (GTP)-bound forms, and the model results show that the GDP-bound form is stabilized enough to prevent unnecessary signal transmission, but the conformation in the GTP-bound state bears large fluctuation in side-chain configurations, which may help to bind multiple target proteins for multiple pathways of signaling. The calculated results of calmodulin show the scenario of sequential ordering in Ca(2+) binding and the associated allosteric conformational change, which are realized though the sequential appearing of pre-existing structural fluctuations, i.e., fluctuations to show structures suitable to bind Ca(2+) before its binding. Here, the pre-existing fluctuations to accept the second and third Ca(2+) ions are dominated by the side-chain fluctuation. In CheY, the calculated side-chain fluctuation of Tyr106 is coordinated with the backbone structural change in the β4-α4 loop, which explains the pre-existing Y-T coupling process in this protein. Ability of the model to explain allosteric transitions of example proteins supports the view that the large entropic effects lower the free-energy barrier of allosteric transition.

Contributions of aromatic pairs to the folding and stability of long-lived human γD-crystallin

Human γD-crystallin (HγD-Crys) is a highly stable protein that remains folded in the eye lens for the majority of an individual's lifetime. HγD-Crys exhibits two homologous crystallin domains, each containing two Greek key motifs with eight β-strands. Six aromatic pairs (four Tyr/Tyr, one Tyr/Phe and one Phe/Phe) are present in the β-hairpin sequences of the Greek keys. Ultraviolet damage to the aromatic residues in lens crystallins may contribute to the genesis of cataract. Mutant proteins with these aromatic residues substituted with alanines were constructed and expressed in E. coli. All mutant proteins except F115A and F117A had lower thermal stability than the WT protein. In equilibrium experiments in guanidine hydrochloride (GuHCl), all mutant proteins had lower thermodynamic stability than the WT protein. N-terminal domain (N-td) substitutions shifted the N-td transition to lower GuHCl concentration, but the C-terminal domain (C-td) transition remained unaffected. C-td substitutions led to a more cooperative unfolding/refolding process, with both the N-td and C-td transitions shifted to lower GuHCl concentration. The aromatic pairs conserved for each Greek key motif (Greek key pairs) had larger contributions to both thermal stability and thermodynamic stability than the other pairs. Aromatic-aromatic interaction was estimated as 1.5-2.0 kcal/mol. In kinetic experiments, N-td substitutions accelerated the early phase of unfolding, while C-td substitutions accelerated the late phase, suggesting independent domain unfolding. Only substitutions of the second Greek key pair of each crystallin domain slowed refolding. The second Greek keys may provide nucleation sites during the folding of the double-Greek-key crystallin domains.

Analysis of the equilibrium and kinetics of the ankyrin repeat protein myotrophin

We apply the Wako-Saito-Muñoz-Eaton model to the study of myotrophin, a small ankyrin repeat protein, whose folding equilibrium and kinetics have been recently characterized experimentally. The model, which is a native-centric with binary variables, provides a finer microscopic detail than the Ising model that has been recently applied to some different repeat proteins, while being still amenable for an exact solution. In partial agreement with the experiments, our results reveal a weakly three-state equilibrium and a two-state-like kinetics of the wild-type protein despite the presence of a nontrivial free-energy profile. These features appear to be related to a careful "design" of the free-energy landscape, so that mutations can alter this picture, stabilizing some intermediates and changing the position of the rate-limiting step. Also, the experimental findings of two alternative pathways, an N-terminal and a C-terminal one, are qualitatively confirmed, even if the variations in the rates upon the experimental mutations cannot be quantitatively reproduced. Interestingly, the folding and unfolding pathways appear to be different, even if closely related: a property that is not generally considered in the phenomenological interpretation of the experimental data.

Quantitative prediction of protein folding behaviors from a simple statistical model

The statistical nature of the protein folding process requires the use of equally detailed yet simple models that lend themselves to characterize experiments. One such model is the Wako-Saitô-Muñoz-Eaton model, that we extend here to include solvation effects (WSME-S), introduced via empirical terms. We employ the novel version to analyze the folding of two proteins, gpW and SH3, that have similar size and thermodynamic stability but with the former folding 3 orders of magnitude faster than SH3. A quantitative analysis reveals that gpW presents at most marginal barriers, in contrast to SH3 that folds following a simple two-state approximation. We reproduce the observed experimental differences in melting temperature in gpW as seen by different experimental spectroscopic probes and the shape of the rate-temperature plot. In parallel, we predict the folding complexity expected in gpW from the analysis of both the residue-level thermodynamics and kinetics. SH3 serves as a stringent control with neither folding complexity nor dispersion in melting temperatures being observed. The extended model presented here serves as an ideal tool not only to characterize folding data but also to make experimentally testable predictions.

Entropic mechanism of large fluctuation in allosteric transition

A statistical mechanical model of allosteric transitions in proteins is developed by extending the structure-based model of protein folding to cases of multiple native conformations. The partition function is calculated exactly within the model and the free-energy surface reflecting allostery is derived. This approach is applied to an example protein, the receiver domain of the bacterial enhancer-binding protein NtrC. The model predicts the large entropy associated with a combinatorial number of preexisting transition routes. This large entropy lowers the free-energy barrier of the allosteric transition, which explains the large structural fluctuation observed in the NMR data of NtrC. The global allosteric transformation of NtrC is explained by the shift of preexisting distribution of conformations upon phosphorylation, but the local structural adjustment around the phosphorylation site is explained by the complementary induced-fit mechanism. Structural disordering accompanied by fluctuating interactions specific to two allosteric conformations underlies a large number of routes of allosteric transition.

Interdomain Ca(2+) effects in Escherichia coli alpha-haemolysin: Ca(2+) binding to the C-terminal domain stabilizes both C- and N-terminal domains

alpha-Haemolysin (HlyA) is a toxin secreted by pathogenic Escherichia coli, whose lytic activity requires submillimolar Ca(2+) concentrations. Previous studies have shown that Ca(2+) binds within the Asp and Gly rich C-terminal nonapeptide repeat domain (NRD) in HlyA. The presence of the NRD puts HlyA in the RTX (Repeats in Toxin) family of proteins. We tested the stability of the whole protein, the amphipathic helix domain and the NRD, in both the presence and absence of Ca(2+) using native HlyA, a truncated form of HlyADeltaN601 representing the C-terminal domain, and a novel mutant HlyA W914A whose intrinsic fluorescence indicates changes in the N-terminal domain. Fluorescence and infrared spectroscopy, tryptic digestion, and urea denaturation techniques concur in showing that calcium binding to the repeat domain of alpha-haemolysin stabilizes and compacts both the NRD and the N-terminal domains of HlyA. The stabilization of the N-terminus through Ca(2+) binding to the C-terminus reveals long-range inter-domain structural effects. Considering that RTX proteins consist, in general, of a Ca(2+)-binding NRD and separate function-specific domains, the long-range stabilizing effects of Ca(2+) in HlyA may well be common to other members of this family.

Ubiquitin not only serves as a tag but also assists degradation by inducing protein unfolding

Protein ubiquitination controls the cellular fate of numerous eukaryotic proteins. Despite its importance, many fundamental questions remain regarding its mechanism. One such question is how ubiquitination alters the biophysical properties of the modified protein and whether these alterations are significant in the cellular context. In this study, we investigate the effects of ubiquitination on the folding thermodynamics and mechanism of various substrates using computational tools and find that ubiquitination changes the thermal stability of modified proteins in a manner relevant to cellular processes. These changes depend on the substrate modification site and on the type of ubiquitination. Ubiquitination of the substrate Ubc7 at the residues that are modified in vivo prior to proteasomal degradation uniquely results in significant thermal destabilization and a local unwinding near the modification site, which indicates that ubiquitination possibly facilitates the unfolding process and improves substrate degradation efficiency. With respect to the substrate p19(4inkd), our results support a synergetic effect of ubiquitination and phosphorylation on the degradation process via enhanced thermal destabilization. Our study implies that, in addition to its known role as a recognition signal, the ubiquitin attachment may be directly involved in the cellular process it regulates by changing the biophysical properties of the substrate.