Subdomain competition, cooperativity, and topological frustration in the folding of CheY

Understanding the molecular basis of folding cooperativity through a comparative analysis of a multidomain protein and its isolated domains

Although cooperativity is a well-established and general property of folding, our current understanding of this feature in multidomain folding is still relatively limited. In fact, there are contrasting results indicating that the constituent domains of a multidomain protein may either fold independently on each other or exhibit interdependent supradomain phenomena. To address this issue, here we present the comparative analysis of the folding of a tandem repeat protein, comprising two contiguous PDZ domains, in comparison to that of its isolated constituent domains. By analyzing in detail the equilibrium and kinetics of folding at different experimental conditions, we demonstrate that despite each of the PDZ domains in isolation being capable of independent folding, at variance with previously characterized PDZ tandem repeats, the full-length construct folds and unfolds as a single cooperative unit. By exploiting quantitatively, the comparison of the folding of the tandem repeat to those observed for its constituent domains, as well as by characterizing a truncated variant lacking a short autoinhibitory segment, we successfully rationalize the molecular basis of the observed cooperativity and attempt to infer some general conclusions for multidomain systems.

Structures of permuted halves of a modern ribose-binding protein

Periplasmic binding proteins (PBPs) are a class of proteins that participate in the cellular transport of various ligands. They have been used as model systems to study mechanisms in protein evolution, such as duplication, recombination and domain swapping. It has been suggested that PBPs evolved from precursors half their size. Here, the crystal structures of two permuted halves of a modern ribose-binding protein (RBP) from Thermotoga maritima are reported. The overexpressed proteins are well folded and show a monomer-dimer equilibrium in solution. Their crystal structures show partially noncanonical PBP-like fold type I conformations with structural deviations from modern RBPs. One of the half variants forms a dimer via segment swapping, suggesting a high degree of malleability. The structural findings on these permuted halves support the evolutionary hypothesis that PBPs arose via a duplication event of a flavodoxin-like protein and further support a domain-swapping step that might have occurred during the evolution of the PBP-like fold, a process that is necessary to generate the characteristic motion of PBPs essential to perform their functions.

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.

Structure of the archaeal chemotaxis protein CheY in a domain-swapped dimeric conformation

Archaea are motile by the rotation of the archaellum. The archaellum switches between clockwise and counterclockwise rotation, and movement along a chemical gradient is possible by modulation of the switching frequency. This modulation involves the response regulator CheY and the archaellum adaptor protein CheF. In this study, two new crystal forms and protein structures of CheY are reported. In both crystal forms, CheY is arranged in a domain-swapped conformation. CheF, the protein bridging the chemotaxis signal transduction system and the motility apparatus, was recombinantly expressed, purified and subjected to X-ray data collection.

Frustration and folding of a TIM barrel protein

Triosephosphate isomerase (TIM) barrel proteins have not only a conserved architecture that supports a myriad of enzymatic functions, but also a conserved folding mechanism that involves on- and off-pathway intermediates. Although experiments have proven to be invaluable in defining the folding free-energy surface, they provide only a limited understanding of the structures of the partially folded states that appear during folding. Coarse-grained simulations employing native centric models are capable of sampling the entire energy landscape of TIM barrels and offer the possibility of a molecular-level understanding of the readout from sequence to structure. We have combined sequence-sensitive native centric simulations with small-angle X-ray scattering and time-resolved Förster resonance energy transfer to monitor the formation of structure in an intermediate in the Sulfolobus solfataricus indole-3-glycerol phosphate synthase TIM barrel that appears within 50 μs and must at least partially unfold to achieve productive folding. Simulations reveal the presence of a major and 2 minor folding channels not detected in experiments. Frustration in folding, i.e., backtracking in native contacts, is observed in the major channel at the initial stage of folding, as well as late in folding in a minor channel before the appearance of the native conformation. Similarities in global and pairwise dimensions of the early intermediate, the formation of structure in the central region that spreads progressively toward each terminus, and a similar rate-limiting step in the closing of the β-barrel underscore the value of combining simulation and experiment to unravel complex folding mechanisms at the molecular level.

The Role of Data in Model Building and Prediction: A Survey Through Examples

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of quantitative sciences, mean abstract mathematical or algorithmical representations. This short review discusses a few key examples from Physics, taken from dynamical systems theory, biophysics, and statistical mechanics, representing three paradigmatic procedures to build models and predictions from available data. In the case of dynamical systems we show how predictions can be obtained in a virtually model-free framework using the methods of analogues, and we briefly discuss other approaches based on machine learning methods. In cases where the complexity of systems is challenging, like in biophysics, we stress the necessity to include part of the empirical knowledge in the models to gain the minimal amount of realism. Finally, we consider many body systems where many (temporal or spatial) scales are at play—and show how to derive from data a dimensional reduction in terms of a Langevin dynamics for their slow components.

Folding a viral peptide in different membrane environments: pathway and sampling analyses

Flock House virus (FHV) is a well-characterized model system to study infection mechanisms in non-enveloped viruses. A key stage of the infection cycle is the disruption of the endosomal membrane by a component of the FHV capsid, the membrane active γ peptide. In this study, we perform all-atom molecular dynamics simulations of the 21 N-terminal residues of the γ peptide interacting with membranes of differing compositions. We carry out umbrella sampling calculations to study the folding of the peptide to a helical state in homogenous and heterogeneous membranes consisting of neutral and anionic lipids. From the trajectory data, we evaluate folding energetics and dissect the mechanism of folding in the different membrane environments. We conclude the study by analyzing the extent of configurational sampling by performing time-lagged independent component analysis.

Optimal allosteric stabilization sites using contact stabilization analysis

Proteins can be destabilized by a number of environmental factors such as temperature, pH, and mutation. The ability to subsequently restore function under these conditions by adding small molecule stabilizers, or by introducing disulfide bonds, would be a very powerful tool, but the physical principles that drive this stabilization are not well understood. The first problem lies is in choosing an appropriate binding site or disulfide bond location to best confer stability to the active site and restore function. Here, we present a general framework for predicting which allosteric binding sites correlate with stability in the active site. Using the Karanicolas-Brooks Gō-like model, we examine the dynamics of the enzyme β-glucuronidase using an Umbrella Sampling method to thoroughly sample the conformational landscape. Each intramolecular contact is assigned a score termed a "stabilization factor" that measures its correlation with structural changes in the active site. We have carried out this analysis for three different scaling strengths for the intramolecular contacts, and we examine how the calculated stabilization factors depend on the ensemble of destabilized conformations. We further examine a locally destabilized mutant of β-glucuronidase that has been characterized experimentally, and show that this brings about local changes in the stabilization factors. We find that the proximity to the active site is not sufficient to determine which contacts can confer active site stability. © 2016 Wiley Periodicals, Inc.

Folding of proteins with a flavodoxin-like architecture

The flavodoxin-like fold is a protein architecture that can be traced back to the universal ancestor of the three kingdoms of life. Many proteins share this α-β parallel topology and hence it is highly relevant to illuminate how they fold. Here, we review experiments and simulations concerning the folding of flavodoxins and CheY-like proteins, which share the flavodoxin-like fold. These polypeptides tend to temporarily misfold during unassisted folding to their functionally active forms. This susceptibility to frustration is caused by the more rapid formation of an α-helix compared to a β-sheet, particularly when a parallel β-sheet is involved. As a result, flavodoxin-like proteins form intermediates that are off-pathway to native protein and several of these species are molten globules (MGs). Experiments suggest that the off-pathway species are of helical nature and that flavodoxin-like proteins have a nonconserved transition state that determines the rate of productive folding. Folding of flavodoxin from Azotobacter vinelandii has been investigated extensively, enabling a schematic construction of its folding energy landscape. It is the only flavodoxin-like protein of which cotranslational folding has been probed. New insights that emphasize differences between in vivo and in vitro folding energy landscapes are emerging: the ribosome modulates MG formation in nascent apoflavodoxin and forces this polypeptide toward the native state.

Atomistic structural ensemble refinement reveals non-native structure stabilizes a sub-millisecond folding intermediate of CheY

The dynamics of globular proteins can be described in terms of transitions between a folded native state and less-populated intermediates, or excited states, which can play critical roles in both protein folding and function. Excited states are by definition transient species, and therefore are difficult to characterize using current experimental techniques. Here, we report an atomistic model of the excited state ensemble of a stabilized mutant of an extensively studied flavodoxin fold protein CheY. We employed a hybrid simulation and experimental approach in which an aggregate 42 milliseconds of all-atom molecular dynamics were used as an informative prior for the structure of the excited state ensemble. This prior was then refined against small-angle X-ray scattering (SAXS) data employing an established method (EROS). The most striking feature of the resulting excited state ensemble was an unstructured N-terminus stabilized by non-native contacts in a conformation that is topologically simpler than the native state. Using these results, we then predict incisive single molecule FRET experiments as a means of model validation. This study demonstrates the paradigm of uniting simulation and experiment in a statistical model to study the structure of protein excited states and rationally design validating experiments.

Evidence for the principle of minimal frustration in the evolution of protein folding landscapes

Theoretical and experimental studies have firmly established that protein folding can be described by a funneled energy landscape. This funneled energy landscape is the result of foldable protein sequences evolving following the principle of minimal frustration, which allows proteins to rapidly fold to their native biologically functional conformations. For a protein family with a given functional fold, the principle of minimal frustration suggests that, independent of sequence, all proteins within this family should fold with similar rates. However, depending on the optimal living temperature of the organism, proteins also need to modulate their thermodynamic stability. Consequently, the difference in thermodynamic stability should be primarily caused by differences in the unfolding rates. To test this hypothesis experimentally, we performed comprehensive thermodynamic and kinetic analyses of 15 different proteins from the thioredoxin family. Eight of these thioredoxins were extant proteins from psychrophilic, mesophilic, or thermophilic organisms. The other seven protein sequences were obtained using ancestral sequence reconstruction and can be dated back over 4 billion years. We found that all studied proteins fold with very similar rates but unfold with rates that differ up to three orders of magnitude. The unfolding rates correlate well with the thermodynamic stability of the proteins. Moreover, proteins that unfold slower are more resistant to proteolysis. These results provide direct experimental support to the principle of minimal frustration hypothesis.

Linking computation and experiments to study the role of charge-charge interactions in protein folding and stability

Over the past two decades there has been an increase in appreciation for the role of surface charge-charge interactions in protein folding and stability. The perception shifted from the belief that charge-charge interactions are not important for protein folding and stability to the near quantitative understanding of how these interactions shape the folding energy landscape. This led to the ability of computational approaches to rationally redesign surface charge-charge interactions to modulate thermodynamic properties of proteins. Here we summarize our progress in understanding the role of charge-charge interactions for protein stability using examples drawn from my own laboratory and touch upon unanswered questions.

Sequence-, structure-, and dynamics-based comparisons of structurally homologous CheY-like proteins

We recently introduced a physically based approach to sequence comparison, the property factor method (PFM). In the present work, we apply the PFM approach to the study of a challenging set of sequences-the bacterial chemotaxis protein CheY, the N-terminal receiver domain of the nitrogen regulation protein NT-NtrC, and the sporulation response regulator Spo0F. These are all response regulators involved in signal transduction. Despite functional similarity and structural homology, they exhibit low sequence identity. PFM sequence comparison demonstrates a statistically significant qualitative difference between the sequence of CheY and those of the other two proteins that is not found using conventional alignment methods. This difference is shown to be consonant with structural characteristics, using distance matrix comparisons. We also demonstrate that residues participating strongly in native contacts during unfolding are distributed differently in CheY than in the other two proteins. The PFM result is also in accord with dynamic simulation results of several types. Molecular dynamics simulations of all three proteins were carried out at several temperatures, and it is shown that the dynamics of CheY are predicted to differ from those of NT-NtrC and Spo0F. The predicted dynamic properties of the three proteins are in good agreement with experimentally determined B factors and with fluctuations predicted by the Gaussian network model. We pinpoint the differences between the PFM and traditional sequence comparisons and discuss the informatic basis for the ability of the PFM approach to detect physical differences between these sequences that are not apparent from traditional alignment-based comparison.

Evolution of a protein folding nucleus

The folding nucleus (FN) is a cryptic element within protein primary structure that enables an efficient folding pathway and is the postulated heritable element in the evolution of protein architecture; however, almost nothing is known regarding how the FN structurally changes as complex protein architecture evolves from simpler peptide motifs. We report characterization of the FN of a designed purely symmetric β-trefoil protein by ϕ-value analysis. We compare the structure and folding properties of key foldable intermediates along the evolutionary trajectory of the β-trefoil. The results show structural acquisition of the FN during gene fusion events, incorporating novel turn structure created by gene fusion. Furthermore, the FN is adjusted by circular permutation in response to destabilizing functional mutation. FN plasticity by way of circular permutation is made possible by the intrinsic C3 cyclic symmetry of the β-trefoil architecture, identifying a possible selective advantage that helps explain the prevalence of cyclic structural symmetry in the proteome.

Geometrical Frustration in Interleukin-33 Decouples the Dynamics of the Functional Element from the Folding Transition State Ensemble

Interleukin-33 (IL-33) is currently the focus of multiple investigations into targeting pernicious inflammatory disorders. This mediator of inflammation plays a prevalent role in chronic disorders such as asthma, rheumatoid arthritis, and progressive heart disease. In order to better understand the possible link between the folding free energy landscape and functional regions in IL-33, a combined experimental and theoretical approach was applied. IL-33 is a pseudo- symmetrical protein composed of three distinct structural elements that complicate the folding mechanism due to competition for nucleation on the dominant folding route. Trefoil 1 constitutes the majority of the binding interface with the receptor whereas Trefoils 2 and 3 provide the stable scaffold to anchor Trefoil 1. We identified that IL-33 folds with a three-state mechanism, leading to a rollover in the refolding arm of its chevron plots in strongly native conditions. In addition, there is a second slower refolding phase that exhibits the same rollover suggesting similar limitations in folding along parallel routes. Characterization of the intermediate state and the rate limiting steps required for folding suggests that the rollover is attributable to a moving transition state, shifting from a post- to pre-intermediate transition state as you move from strongly native conditions to the midpoint of the transition. On a structural level, we found that initially, all independent Trefoil units fold equally well until a Q_CA of 0.35 when Trefoil 1 will backtrack in order to allow Trefoils 2 and 3 to fold in the intermediate state, creating a stable scaffold for Trefoil 1 to fold onto during the final folding transition. The formation of this intermediate state and subsequent moving transition state is a result of balancing the difficulty in folding the functionally important Trefoil 1 onto the remainder of the protein. Taken together our results indicate that the functional element of the protein is geometrically frustrated, requiring the more stable elements to fold first, acting as a scaffold for docking of the functional element to allow productive folding to the native state.

Multiscale enhanced sampling of intrinsically disordered protein conformations

In a recently developed multiscale enhanced sampling (MSES) technique, topology-based coarse-grained (CG) models are coupled to atomistic force fields to enhance the sampling of atomistic protein conformations. Here, the MSES protocol is refined by designing more sophisticated Hamiltonian/temperature replica exchange schemes that involve additional parameters in the MSES coupling restraint potential, to more carefully control how conformations are coupled between the atomistic and CG models. A specific focus is to derive an optimal MSES protocol for simulating conformational ensembles of intrinsically disordered proteins (IDPs). The efficacy of the refined protocols, referred to as MSES-soft asymptote (SA), was evaluated using two model peptides with various levels of residual helicities. The results show that MSES-SA generates more reversible helix-coil transitions and leads to improved convergence on various ensemble conformational properties. This study further suggests that more detailed CG models are likely necessary for more effective sampling of local conformational transition of IDPs. © 2015 Wiley Periodicals, Inc.

Conformational frustration in calmodulin-target recognition

Calmodulin (CaM) is a primary calcium (Ca(2+) )-signaling protein that specifically recognizes and activates highly diverse target proteins. We explored the molecular basis of target recognition of CaM with peptides representing the CaM-binding domains from two Ca(2+) -CaM-dependent kinases, CaMKI and CaMKII, by employing experimentally constrained molecular simulations. Detailed binding route analysis revealed that the two CaM target peptides, although similar in length and net charge, follow distinct routes that lead to a higher binding frustration in the CaM-CaMKII complex than in the CaM-CaMKI complex. We discovered that the molecular origin of the binding frustration is caused by intermolecular contacts formed with the C-domain of CaM that need to be broken before the formation of intermolecular contacts with the N-domain of CaM. We argue that the binding frustration is important for determining the kinetics of the recognition process of proteins involving large structural fluctuations.

Modulation of frustration in folding by sequence permutation

Folding of globular proteins can be envisioned as the contraction of a random coil unfolded state toward the native state on an energy surface rough with local minima trapping frustrated species. These substructures impede productive folding and can serve as nucleation sites for aggregation reactions. However, little is known about the relationship between frustration and its underlying sequence determinants. Chemotaxis response regulator Y (CheY), a 129-amino acid bacterial protein, has been shown previously to populate an off-pathway kinetic trap in the microsecond time range. The frustration has been ascribed to premature docking of the N- and C-terminal subdomains or, alternatively, to the formation of an unproductive local-in-sequence cluster of branched aliphatic side chains, isoleucine, leucine, and valine (ILV). The roles of the subdomains and ILV clusters in frustration were tested by altering the sequence connectivity using circular permutations. Surprisingly, the stability and buried surface area of the intermediate could be increased or decreased depending on the location of the termini. Comparison with the results of small-angle X-ray-scattering experiments and simulations points to the accelerated formation of a more compact, on-pathway species for the more stable intermediate. The effect of chain connectivity in modulating the structures and stabilities of the early kinetic traps in CheY is better understood in terms of the ILV cluster model. However, the subdomain model captures the requirement for an intact N-terminal domain to access the native conformation. Chain entropy and aliphatic-rich sequences play crucial roles in biasing the early events leading to frustration in the folding of CheY.

Sequence analysis on the information of folding initiation segments in ferredoxin-like fold proteins

BACKGROUND

While some studies have shown that the 3D protein structures are more conservative than their amino acid sequences, other experimental studies have shown that even if two proteins share the same topology, they may have different folding pathways. There are many studies investigating this issue with molecular dynamics or Go-like model simulations, however, one should be able to obtain the same information by analyzing the proteins' amino acid sequences, if the sequences contain all the information about the 3D structures. In this study, we use information about protein sequences to predict the location of their folding segments. We focus on proteins with a ferredoxin-like fold, which has a characteristic topology. Some of these proteins have different folding segments.

RESULTS

Despite the simplicity of our methods, we are able to correctly determine the experimentally identified folding segments by predicting the location of the compact regions considered to play an important role in structural formation. We also apply our sequence analyses to some homologues of each protein and confirm that there are highly conserved folding segments despite the homologues' sequence diversity. These homologues have similar folding segments even though the homology of two proteins' sequences is not so high.

CONCLUSION

Our analyses have proven useful for investigating the common or different folding features of the proteins studied.

Balancing bond, nonbond, and gō-like terms in coarse grain simulations of conformational dynamics

Characterization of the protein conformational landscape remains a challenging problem, whether it concerns elucidating folding mechanisms, predicting native structures or modeling functional transitions. Coarse-grained molecular dynamics simulation methods enable exhaustive sampling of the energetic landscape at resolutions of biological interest. The general utility of structure-based models is reviewed along with their differing levels of approximation. Simple Gō models incorporate attractive native interactions and repulsive nonnative contacts, resulting in an ideal smooth landscape. Non-Gō coarse-grained models reduce the parameter set as needed but do not include bias to any desired native structure. While non-Gō models have achieved limited success in protein coarse-graining, they can be combined with native structured-based potentials to create a balanced and powerful force field. Recent applications of such Gō-like models have yielded insight into complex folding mechanisms and conformational transitions in large macromolecules. The accuracy and usefulness of reduced representations are also revealed to be a function of the mathematical treatment of the intrinsic bonded topology.

Sequence-dependent base-stacking stabilities guide tRNA folding energy landscapes

The folding of bacterial tRNAs with disparate sequences has been observed to proceed in distinct folding mechanisms despite their structural similarity. To explore the folding landscapes of tRNA, we performed ion concentration-dependent coarse-grained TIS model MD simulations of several E. coli tRNAs to compare their thermodynamic melting profiles to the classical absorbance spectra of Crothers and co-workers. To independently validate our findings, we also performed atomistic empirical force field MD simulations of tRNAs, and we compared the base-to-base distances from coarse-grained and atomistic MD simulations to empirical base-stacking free energies. We then projected the free energies to the secondary structural elements of tRNA, and we observe distinct, parallel folding mechanisms whose differences can be inferred on the basis of their sequence-dependent base-stacking stabilities. In some cases, a premature, nonproductive folding intermediate corresponding to the Ψ hairpin loop must backtrack to the unfolded state before proceeding to the folded state. This observation suggests a possible explanation for the fast and slow phases observed in tRNA folding kinetics.

Binding and folding of the small bacterial chaperone HdeA

The small pH stress-sensing chaperone HdeA helps pathogenic enteric E. coli survive passage through the severely acidic environment of the mammalian stomach. Under stress conditions, HdeA transitions from an inactive folded dimer to a chaperone-active unfolded monomer to prevent the acid-induced aggregation of periplasmic proteins. Here we use a topology-based Gō-like model to delineate the relationship between dimer interface formation and monomer folding and to better understand the structural details of the chaperone activation mechanism. Free energy surfaces show that dimer interface formation and monomer folding proceed concurrently through an on-pathway dimeric intermediate in which one monomer is partially unfolded. The absence of a preexisting fully folded monomer in the proposed binding mechanism is in agreement with HdeA's rapid chaperone response. Binding between unfolded monomers exhibits an enhancement of molecular recognition reminiscent of the fly-casting mechanism. Overall, our simulations further highlight the efficient nature of HdeA's chaperone response and we anticipate that knowledge of a dimeric intermediate will facilitate the interpretation of experimental studies.

Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9

Markov State Models (MSMs) provide an automated framework to investigate the dynamical properties of high-dimensional molecular simulations. These models can provide a human-comprehensible picture of the underlying process, and have been successfully used to study protein folding, protein aggregation, protein ligand binding, and other biophysical systems. The MSM requires the construction of a discrete state-space such that two points are in the same state if they can interconvert rapidly. In the following, we suggest an improved method, which utilizes second order Independent Components Analysis (also known as time-structure based Independent Components Analysis, or tICA), to construct the state-space. We apply this method to simulations of NTL9 (provided by Lindorff-Larsen et al. Science2011), and show that the MSM is an improvement over previously built models using conventional distance metrics. Additionally, the resulting model provides insight into the role of non-native contacts by revealing many slow timescales associated with compact, non-native states.

Backtracking due to residual structure in the unfolded state changes the folding of the third fibronectin type III domain from tenascin-C

Residual structure in the unfolded state of a protein may play a crucial role in folding and stability. In the present study, using an all (heavy)-atom structure based model and replica exchange molecular dynamics simulations, we explored the folding landscape of the third fibronectin type III domain from tenascin-C (TNfn3). Specifically, both the wild type (WT) and a variant with two additional amino acids, Gly-Leu (GL), at the C-terminus (WT(+GL)) were studied. We found that, although both domains of TNfn3 are topologically frustrated, the early formation of the native contacts from the C-terminal end of WT(+GL) causes more "backtracking" than in the WT. As a result, the WT exhibits a two-state folding behavior with a broad transition-state ensemble, whereas the WT(+GL) folds through a metastable intermediate state. Furthermore, our study confirmed that the core of both proteins is conformationally heterogeneous and noncompact, and folds late mainly due to backtracking of the part of the core. Finally, in agreement with the previous experimental studies, our results clearly demonstrated distinct thermodynamic behavior of the two proteins with WT(+GL) being more stable.

The dominant folding route minimizes backbone distortion in SH3

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

De novo prediction of protein folding pathways and structure using the principle of sequential stabilization

Motivated by the relationship between the folding mechanism and the native structure, we develop a unified approach for predicting folding pathways and tertiary structure using only the primary sequence as input. Simulations begin from a realistic unfolded state devoid of secondary structure and use a chain representation lacking explicit side chains, rendering the simulations many orders of magnitude faster than molecular dynamics simulations. The multiple round nature of the algorithm mimics the authentic folding process and tests the effectiveness of sequential stabilization (SS) as a search strategy wherein 2° structural elements add onto existing structures in a process of progressive learning and stabilization of structure found in prior rounds of folding. Because no a priori knowledge is used, we can identify kinetically significant non-native interactions and intermediates, sometimes generated by only two mutations, while the evolution of contact matrices is often consistent with experiments. Moreover, structure prediction improves substantially by incorporating information from prior rounds. The success of our simple, homology-free approach affirms the validity of our description of the primary determinants of folding pathways and structure, and the effectiveness of SS as a search strategy.

Protein stability and dynamics modulation: the case of human frataxin

Frataxin (FXN) is an α/β protein that plays an essential role in iron homeostasis. Apparently, the function of human FXN (hFXN) depends on the cooperative formation of crucial interactions between helix α1, helix α2, and the C-terminal region (CTR) of the protein. In this work we quantitatively explore these relationships using a purified recombinant fragment hFXN90-195. This variant shows the hydrodynamic behavior expected for a monomeric globular domain. Circular dichroism, fluorescence, and NMR spectroscopies show that hFXN90-195 presents native-like secondary and tertiary structure. However, chemical and temperature induced denaturation show that CTR truncation significantly destabilizes the overall hFXN fold. Accordingly, limited proteolysis experiments suggest that the native-state dynamics of hFXN90-195 and hFXN90-210 are indeed different, being the former form much more sensitive to the protease at specific sites. The overall folding dynamics of hFXN fold was further explored with structure-based protein folding simulations. These suggest that the native ensemble of hFXN can be decomposed in at least two substates, one with consolidation of the CTR and the other without consolidation of the CTR. Explicit-solvent all atom simulations identify some of the proteolytic target sites as flexible regions of the protein. We propose that the local unfolding of CTR may be a critical step for the global unfolding of hFXN, and that modulation of the CTR interactions may strongly affect hFXN physiological function.

Force-induced unfolding simulations of the human Notch1 negative regulatory region: possible roles of the heterodimerization domain in mechanosensing

Notch receptors are core components of the Notch signaling pathway and play a central role in cell fate decisions during development as well as tissue homeostasis. Upon ligand binding, Notch is sequentially cleaved at the S2 site by an ADAM protease and at the S3 site by the γ-secretase complex. Recent X-ray structures of the negative regulatory region (NRR) of the Notch receptor reveal an auto-inhibited fold where three protective Lin12/Notch repeats (LNR) of the NRR shield the S2 cleavage site housed in the heterodimerization (HD) domain. One of the models explaining how ligand binding drives the NRR conformation from a protease-resistant state to a protease-sensitive one invokes a mechanical force exerted on the NRR upon ligand endocytosis. Here, we combined physics-based atomistic simulations and topology-based coarse-grained modeling to investigate the intrinsic and force-induced folding and unfolding mechanisms of the human Notch1 NRR. The simulations support that external force applied to the termini of the NRR disengages the LNR modules from the heterodimerization (HD) domain in a well-defined, largely sequential manner. Importantly, the mechanical force can further drive local unfolding of the HD domain in a functionally relevant fashion that would provide full proteolytic access to the S2 site prior to heterodimer disassociation. We further analyzed local structural features, intrinsic folding free energy surfaces, and correlated motions of the HD domain. The results are consistent with a model in which the HD domain possesses inherent mechanosensing characteristics that could be utilized during Notch activation. This potential role of the HD domain in ligand-dependent Notch activation may have implications for understanding normal and aberrant Notch signaling.

Synergistic folding of two intrinsically disordered proteins: searching for conformational selection

Intrinsically disordered proteins (IDPs) lack stable structures under physiological conditions but often fold into stable structures upon specific binding. These coupled binding and folding processes underlie the organization of cellular regulatory networks, and a mechanistic understanding is thus of fundamental importance. Here, we investigated the synergistic folding of two IDPs, namely, the NCBD domain of transcription coactivator CBP and the p160 steroid receptor coactivator ACTR, using a topology-based model that was carefully calibrated to balance intrinsic folding propensities and intermolecular interactions. As one of the most structured IDPs, NCBD is a plausible candidate that interacts through conformational selection-like mechanisms, where binding is mainly initiated by pre-existing folded-like conformations. Indeed, the simulations demonstrate that, even though binding and folding of both NCBD and ACTR is highly cooperative on the baseline level, the tertiary folding of NCBD is best described by the "extended conformational selection" model that involves multiple stages of selection and induced folding. The simulations further predict that the NCBD/ACTR recognition is mainly initiated by forming a mini folded core that includes the second and third helices of NCBD and ACTR. These predictions are fully consistent with independent physics-based atomistic simulations as well as a recent experimental mapping of the H/D exchange protection factors. The current work thus adds to the limited number of existing mechanistic studies of coupled binding and folding of IDPs, and provides a first direct demonstration of how conformational selection might contribute to efficient recognition of IDPs. Interestingly, even for highly structured IDPs like NCBD, the recognition is initiated by the more disordered C-terminal segment and with substantial contribution from induced folding. Together with existing studies of IDP interaction mechanisms, this argues that induced folding is likely prevalent in IDP-protein interaction, and emphasizes the importance of understanding how IDPs manage to fold efficiently upon (nonspecific) binding. Success of the current study also further supports the notion that, with careful calibration, topology-based models can be effective tools for mechanistic study of IDP interaction and regulation, especially when combined with physics-based atomistic simulations and experiments.

Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.

Topological constraints: using RNA secondary structure to model 3D conformation, folding pathways, and dynamic adaptation

Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles in steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure.

Multi-scaled explorations of binding-induced folding of intrinsically disordered protein inhibitor IA3 to its target enzyme

Biomolecular function is realized by recognition, and increasing evidence shows that recognition is determined not only by structure but also by flexibility and dynamics. We explored a biomolecular recognition process that involves a major conformational change – protein folding. In particular, we explore the binding-induced folding of IA3, an intrinsically disordered protein that blocks the active site cleft of the yeast aspartic proteinase saccharopepsin (YPrA) by folding its own N-terminal residues into an amphipathic alpha helix. We developed a multi-scaled approach that explores the underlying mechanism by combining structure-based molecular dynamics simulations at the residue level with a stochastic path method at the atomic level. Both the free energy profile and the associated kinetic paths reveal a common scheme whereby IA3 binds to its target enzyme prior to folding itself into a helix. This theoretical result is consistent with recent time-resolved experiments. Furthermore, exploration of the detailed trajectories reveals the important roles of non-native interactions in the initial binding that occurs prior to IA3 folding. In contrast to the common view that non-native interactions contribute only to the roughness of landscapes and impede binding, the non-native interactions here facilitate binding by reducing significantly the entropic search space in the landscape. The information gained from multi-scaled simulations of the folding of this intrinsically disordered protein in the presence of its binding target may prove useful in the design of novel inhibitors of aspartic proteinases.

The intrinsically disordered peptide IA3 is the endogenous inhibitor for the enzyme named yeast aspartic proteinase saccharopepsin (YPrA). In the presence of YPrA, IA3 folds itself into an amphipathic helix that blocks the active site cleft of the enzyme. We developed a multi-scaled approach to explore the underlying mechanism of this binding-induced ordering transition. Our approach combines a structure-based molecular dynamics model at the residue level with a stochastic path method at the atomic level. Our simulations suggest that IA3 inhibits YPrA through an induced-fit mechanism where the enzyme (YPrA) induces conformational change of its inhibitor (IA3). This expands the definition of an induced-fit model from its original meaning that the binding of substrate (IA3) drives conformational change in the protein (YPrA). Our result is consistent with recent kinetic experiments and provides a microscopic explanation for the underlying mechanism. We also discuss the important roles of non-native interactions and backtracking. These results enrich our understanding of the enzyme-inhibition mechanism and may have value in the design of drugs.

The folding of single domain proteins--have we reached a consensus?

Rather than stressing the most recent advances in the field, this review highlights the fundamental topics where disagreement remains and where adequate experimental data are lacking. These topics include properties of the denatured state and the role of residual structure, the nature of the fundamental steps and barriers, the extent of pathway heterogeneity and non-native interactions, recent comparisons between theory and experiment, and finally, dynamical properties of the folding reaction.

Topological frustration in beta alpha-repeat proteins: sequence diversity modulates the conserved folding mechanisms of alpha/beta/alpha sandwich proteins

The thermodynamic hypothesis of Anfinsen postulates that structures and stabilities of globular proteins are determined by their amino acid sequences. Chain topology, however, is known to influence the folding reaction, in that motifs with a preponderance of local interactions typically fold more rapidly than those with a larger fraction of nonlocal interactions. Together, the topology and sequence can modulate the energy landscape and influence the rate at which the protein folds to the native conformation. To explore the relationship of sequence and topology in the folding of beta alpha-repeat proteins, which are dominated by local interactions, we performed a combined experimental and simulation analysis on two members of the flavodoxin-like, alpha/beta/alpha sandwich fold. Spo0F and the N-terminal receiver domain of NtrC (NT-NtrC) have similar topologies but low sequence identity, enabling a test of the effects of sequence on folding. Experimental results demonstrated that both response-regulator proteins fold via parallel channels through highly structured submillisecond intermediates before accessing their cis prolyl peptide bond-containing native conformations. Global analysis of the experimental results preferentially places these intermediates off the productive folding pathway. Sequence-sensitive Gō-model simulations conclude that frustration in the folding in Spo0F, corresponding to the appearance of the off-pathway intermediate, reflects competition for intra-subdomain van der Waals contacts between its N- and C-terminal subdomains. The extent of transient, premature structure appears to correlate with the number of isoleucine, leucine, and valine (ILV) side chains that form a large sequence-local cluster involving the central beta-sheet and helices alpha2, alpha 3, and alpha 4. The failure to detect the off-pathway species in the simulations of NT-NtrC may reflect the reduced number of ILV side chains in its corresponding hydrophobic cluster. The location of the hydrophobic clusters in the structure may also be related to the differing functional properties of these response regulators. Comparison with the results of previous experimental and simulation analyses on the homologous CheY argues that prematurely folded unproductive intermediates are a common property of the beta alpha-repeat motif.

Unfolding simulations reveal the mechanism of extreme unfolding cooperativity in the kinetically stable alpha-lytic protease

Kinetically stable proteins, those whose stability is derived from their slow unfolding kinetics and not thermodynamics, are examples of evolution's best attempts at suppressing unfolding. Especially in highly proteolytic environments, both partially and fully unfolded proteins face potential inactivation through degradation and/or aggregation, hence, slowing unfolding can greatly extend a protein's functional lifetime. The prokaryotic serine protease α-lytic protease (αLP) has done just that, as its unfolding is both very slow (t_1/2 ∼1 year) and so cooperative that partial unfolding is negligible, providing a functional advantage over its thermodynamically stable homologs, such as trypsin. Previous studies have identified regions of the domain interface as critical to αLP unfolding, though a complete description of the unfolding pathway is missing. In order to identify the αLP unfolding pathway and the mechanism for its extreme cooperativity, we performed high temperature molecular dynamics unfolding simulations of both αLP and trypsin. The simulated αLP unfolding pathway produces a robust transition state ensemble consistent with prior biochemical experiments and clearly shows that unfolding proceeds through a preferential disruption of the domain interface. Through a novel method of calculating unfolding cooperativity, we show that αLP unfolds extremely cooperatively while trypsin unfolds gradually. Finally, by examining the behavior of both domain interfaces, we propose a model for the differential unfolding cooperativity of αLP and trypsin involving three key regions that differ between the kinetically stable and thermodynamically stable classes of serine proteases.

Proteins, synthesized as linear polymers of amino acids, fold up into compact native states, burying their hydrophobic amino acids into their interiors. Protein folding minimizes the non-specific interactions that unfolded protein chains can make, which include aggregation with other proteins and degradation by proteases. Unfortunately, even in the native state, proteins can partially unfold, opening up regions of their structure and making these adverse events possible. Some proteins, particularly those in harsh environments full of proteases, have evolved to virtually eliminate partial unfolding, significantly reducing their rate of degradation. This elimination of partial unfolding is termed “cooperative,” because unfolding is an all-or-none process. One class of proteins has diverged into two families, one bacterial and highly cooperative and the other animal and non-cooperative. We have used detailed simulations of unfolding for members of each family, α-lytic protease (bacterial) and trypsin (animal) to understand the unfolding pathways of each and the mechanism for the differential unfolding cooperativity. Our results explain prior biochemical experiments, reproduce the large difference in unfolding cooperativity between the families, and point to the interface between α-lytic protease's two domains as essential to establishing unfolding cooperativity. As seen in an unrelated protein family, generation of a cooperative domain interface may be a common evolutionary response for ensuring the highest protein stability.

Residue-specific analysis of frustration in the folding landscape of repeat beta/alpha protein apoflavodoxin

Flavodoxin adopts the common repeat beta/alpha topology and folds in a complex kinetic reaction with intermediates. To better understand this reaction, we analyzed a set of Desulfovibrio desulfuricans apoflavodoxin variants with point mutations in most secondary structure elements by in vitro and in silico methods. By equilibrium unfolding experiments, we first revealed how different secondary structure elements contribute to overall protein resistance to heat and urea. Next, using stopped-flow mixing coupled with far-UV circular dichroism, we probed how individual residues affect the amount of structure formed in the experimentally detected burst-phase intermediate. Together with in silico folding route analysis of the same point-mutated variants and computation of growth in nucleation size during early folding, computer simulations suggested the presence of two competing folding nuclei at opposite sides of the central beta-strand 3 (i.e., at beta-strands 1 and 4), which cause early topological frustration (i.e., misfolding) in the folding landscape. Particularly, the extent of heterogeneity in folding nuclei growth correlates with the in vitro burst-phase circular dichroism amplitude. In addition, phi-value analysis (in vitro and in silico) of the overall folding barrier to apoflavodoxin's native state revealed that native-like interactions in most of the beta-strands must form in transition state. Our study reveals that an imbalanced competition between the two sides of apoflavodoxin's central beta-sheet directs initial misfolding, while proper alignment on both sides of beta-strand 3 is necessary for productive folding.

Insights from coarse-grained Gō models for protein folding and dynamics

Exploring the landscape of large scale conformational changes such as protein folding at atomistic detail poses a considerable computational challenge. Coarse-grained representations of the peptide chain have therefore been developed and over the last decade have proved extremely valuable. These include topology-based Gō models, which constitute a smooth and funnel-like approximation to the folding landscape. We review the many variations of the Gō model that have been employed to yield insight into folding mechanisms. Their success has been interpreted as a consequence of the dominant role of the native topology in folding. The role of local contact density in determining protein dynamics is also discussed and is used to explain the ability of Gō-like models to capture sequence effects in folding and elucidate conformational transitions.

Coevolution of function and the folding landscape: correlation with density of native contacts

The relationship between the folding landscape and function of evolved proteins is explored by comparison of the folding mechanisms for members of the flavodoxin fold. CheY, Spo0F, and NtrC have unrelated functions and low sequence homology but share an identical topology. Recent coarse-grained simulations show that their folding landscapes are uniquely tuned to properly suit their respective biological functions. Enhanced packing in Spo0F and its limited conformational dynamics compared to CheY or NtrC lead to frustration in its folding landscape. Simulation as well as experimental results correlate with the local density of native contacts for these and a sample of other proteins. In particular, protein regions of low contact density are observed to become structured late in folding; concomitantly, these dynamic regions are often involved in binding or conformational rearrangements of functional importance. These observations help to explain the widespread success of Gō-like coarse-grained models in reproducing protein dynamics.

Kinetic traps in the folding of beta alpha-repeat proteins: CheY initially misfolds before accessing the native conformation

The beta alpha-repeat class of proteins, represented by the (beta alpha)(8) barrel and the alpha/beta/alpha sandwich, are among the most common structural platforms in biology. Previous studies on the folding mechanisms of these motifs have revealed or suggested that the initial event involves the submillisecond formation of a kinetically trapped species that must at least partially unfold before productive folding to the respective native conformation can occur. To test the generality of these observations, CheY, a bacterial response regulator, was subjected to an extensive analysis of its folding reactions. Although earlier studies had proposed the formation of an off-pathway intermediate, the data available were not sufficient to rule out an alternative on-pathway mechanism. A global analysis of single- and double-jump kinetic data, combined with equilibrium unfolding data, was used to show that CheY folds and unfolds through two parallel channels defined by the state of isomerization of a prolyl peptide bond in the active site. Each channel involves a stable, highly structured folding intermediate whose kinetic properties are better described as the properties of an off-pathway species. Both intermediates subsequently flow through the unfolded state ensemble and adopt the native cis-prolyl isomer prior to forming the native state. Initial collapse to off-pathway folding intermediates is a common feature of the folding mechanisms of beta alpha-repeat proteins, perhaps reflecting the favored partitioning to locally determined substructures that cannot directly access the native conformation. Productive folding requires the dissipation of these prematurely folded substructures as a prelude to forming the larger-scale transition state that leads to the native conformation. Results from Gō-modeling studies in the accompanying paper elaborate on the topological frustration in the folding free-energy landscape of CheY.