Contact order, transition state placement and the refolding rates of single domain proteins

De novo design of a non-local β-sheet protein with high stability and accuracy

β-sheet proteins carry out critical functions in biology, and hence are attractive scaffolds for computational protein design. Despite this potential, de novo design of all-β-sheet proteins from first principles lags far behind the design of all-α or mixed-αβ domains owing to their non-local nature and the tendency of exposed β-strand edges to aggregate. Through study of loops connecting unpaired β-strands (β-arches), we have identified a series of structural relationships between loop geometry, side chain directionality and β-strand length that arise from hydrogen bonding and packing constraints on regular β-sheet structures. We use these rules to de novo design jellyroll structures with double-stranded β-helices formed by eight antiparallel β-strands. The nuclear magnetic resonance structure of a hyperthermostable design closely matched the computational model, demonstrating accurate control over the β-sheet structure and loop geometry. Our results open the door to the design of a broad range of non-local β-sheet protein structures.

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.

Size and topology modulate the effects of frustration in protein folding

The presence of conflicting interactions, or frustration, determines how fast biomolecules can explore their configurational landscapes. Recent experiments have provided cases of systems with slow reconfiguration dynamics, perhaps arising from frustration. While it is well known that protein folding speed and mechanism are strongly affected by the protein native structure, it is still unknown how the response to frustration is modulated by the protein topology. We explore the effects of nonnative interactions in the reconfigurational and folding dynamics of proteins with different sizes and topologies. We find that structural correlations related to the folded state size and topology play an important role in determining the folding kinetics of proteins that otherwise have the same amount of nonnative interactions. In particular, we find that the reconfiguration dynamics of α-helical proteins are more susceptible to frustration than β-sheet proteins of the same size. Our results may explain recent experimental findings and suggest that attempts to measure the degree of frustration due to nonnative interactions might be more successful with α-helical proteins.

Protein escape at the ribosomal exit tunnel: Effects of native interactions, tunnel length, and macromolecular crowding

How fast a post-translational nascent protein escapes from the ribosomal exit tunnel is relevant to its folding and protection against aggregation. Here, by using Langevin molecular dynamics, we show that non-local native interactions help decrease the escape time, and foldable proteins generally escape much faster than same-length, self-repulsive homopolymers at low temperatures. The escape process, however, is slowed down by the local interactions that stabilize the α-helices. The escape time is found to increase with both the tunnel length and the concentration of macromolecular crowders outside the tunnel. We show that a simple diffusion model described by the Smoluchowski equation with an effective linear potential can be used to map out the escape time distribution for various tunnel lengths and various crowder concentrations. The consistency between the simulation data and the diffusion model, however, is found only for the tunnel length smaller than a crossover length of 90 Å-110 Å, above which the escape time increases much faster with the tunnel length. It is suggested that the length of ribosomal exit tunnel has been selected by evolution to facilitate both the efficient folding and the efficient escape of single-domain proteins. We show that macromolecular crowders lead to an increase in the escape time, and attractive crowders are unfavorable for the folding of nascent polypeptide.

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

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

Rosetta Protein Structure Prediction from Hydroxyl Radical Protein Footprinting Mass Spectrometry Data

In recent years mass spectrometry-based covalent labeling techniques such as hydroxyl radical footprinting (HRF) have emerged as valuable structural biology techniques, yielding information on protein tertiary structure. These data, however, are not sufficient to predict protein structure unambiguously, as they provide information only on the relative solvent exposure of certain residues. Despite some recent advances, no software currently exists that can utilize covalent labeling mass spectrometry data to predict protein tertiary structure. We have developed the first such tool, which incorporates mass spectrometry derived protection factors from HRF labeling as a new centroid score term for the Rosetta scoring function to improve the prediction of protein tertiary structures. We tested our method on a set of four soluble benchmark proteins with known crystal structures and either published HRF experimental results or internally acquired data. Using the HRF labeling data, we rescored large decoy sets of structures predicted with Rosetta for each of the four benchmark proteins. As a result, the model quality improved for all benchmark proteins as compared to when scored with Rosetta alone. For two of the four proteins we were even able to identify atomic resolution models with the addition of HRF data.

Sixty-five years of the long march in protein secondary structure prediction: the final stretch?

Protein secondary structure prediction began in 1951 when Pauling and Corey predicted helical and sheet conformations for protein polypeptide backbone even before the first protein structure was determined. Sixty-five years later, powerful new methods breathe new life into this field. The highest three-state accuracy without relying on structure templates is now at 82-84%, a number unthinkable just a few years ago. These improvements came from increasingly larger databases of protein sequences and structures for training, the use of template secondary structure information and more powerful deep learning techniques. As we are approaching to the theoretical limit of three-state prediction (88-90%), alternative to secondary structure prediction (prediction of backbone torsion angles and Cα-atom-based angles and torsion angles) not only has more room for further improvement but also allows direct prediction of three-dimensional fragment structures with constantly improved accuracy. About 20% of all 40-residue fragments in a database of 1199 non-redundant proteins have <6 Å root-mean-squared distance from the native conformations by SPIDER2. More powerful deep learning methods with improved capability of capturing long-range interactions begin to emerge as the next generation of techniques for secondary structure prediction. The time has come to finish off the final stretch of the long march towards protein secondary structure prediction.

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

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

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

Improved protein model quality assessments by changing the target function

Protein modeling quality is an important part of protein structure prediction. We have for more than a decade developed a set of methods for this problem. We have used various types of description of the protein and different machine learning methodologies. However, common to all these methods has been the target function used for training. The target function in ProQ describes the local quality of a residue in a protein model. In all versions of ProQ the target function has been the S-score. However, other quality estimation functions also exist, which can be divided into superposition- and contact-based methods. The superposition-based methods, such as S-score, are based on a rigid body superposition of a protein model and the native structure, while the contact-based methods compare the local environment of each residue. Here, we examine the effects of retraining our latest predictor, ProQ3D, using identical inputs but different target functions. We find that the contact-based methods are easier to predict and that predictors trained on these measures provide some advantages when it comes to identifying the best model. One possible reason for this is that contact based methods are better at estimating the quality of multi-domain targets. However, training on the S-score gives the best correlation with the GDT_TS score, which is commonly used in CASP to score the global model quality. To take the advantage of both of these features we provide an updated version of ProQ3D that predicts local and global model quality estimates based on different quality estimates.

Extracting the Hidden Distributions Underlying the Mean Transition State Structures in Protein Folding

The inherent conflict between noncovalent interactions and the large conformational entropy of the polypeptide chain forces folding reactions and their mechanisms to deviate significantly from chemical reactions. Accordingly, measures of structure in the transition state ensemble (TSE) are strongly influenced by the underlying distributions of microscopic folding pathways that are challenging to discern experimentally. Here, we present a detailed analysis of 150,000 folding transition paths of five proteins at three different thermodynamic conditions from an experimentally consistent statistical mechanical model. We find that the underlying TSE structural distributions are rarely unimodal, and the average experimental measures arise from complex underlying distributions. Unfolding pathways also exhibit subtle differences from folding counterparts due to a combination of Hammond behavior and native-state movements. Local interactions and topological complexity, to a lesser extent, are found to determine pathway heterogeneity, underscoring the importance of the balance between local and nonlocal energetics in protein folding.

Intrinsic Disorder in a Well-Folded Globular Protein

The folded structure of the heterodimeric sweet protein monellin mimics single-chain proteins with topology β1-α1-β2-β3-β4-β5 (chain A: β3-β4-β5; chain B: β1-α1-β2). Furthermore, like naturally occurring single-chain proteins of a similar size, monellin folds cooperatively with no detectable intermediates. However, the two monellin chains, A and B, are marginally structured in isolation and fold only upon binding to each other. Thus, monellin presents a unique opportunity to understand the design of intrinsically disordered proteins that fold upon binding. Here, we study the folding of a single-chain variant of monellin (scMn) using simulations of an all heavy-atom structure-based model. These simulations can explain mechanistic details derived from scMn experiments performed using several different structural probes. scMn folds cooperatively in our structure-based simulations, as is also seen in experiments. We find that structure formation near the transition-state ensemble of scMn is not uniformly distributed but is localized to a hairpin-like structure which contains one strand from each chain (β2, β3). Thus, the sequence and the underlying energetics of heterodimeric monellin promote the early formation of the interchain interface (β2-β3). By studying computational scMn mutants whose "interchain" interactions are deleted, we infer that this energy distribution allows the two protein chains to remain largely disordered when this interface is not folded. From these results, we suggest that cutting the protein backbone of a globular protein between residues which lie within its folding nucleus may be one way to construct two disordered fragments which fold upon binding.

Finding the needle in the haystack: towards solving the protein-folding problem computationally

Prediction of protein tertiary structures from amino acid sequence and understanding the mechanisms of how proteins fold, collectively known as "the protein folding problem," has been a grand challenge in molecular biology for over half a century. Theories have been developed that provide us with an unprecedented understanding of protein folding mechanisms. However, computational simulation of protein folding is still difficult, and prediction of protein tertiary structure from amino acid sequence is an unsolved problem. Progress toward a satisfying solution has been slow due to challenges in sampling the vast conformational space and deriving sufficiently accurate energy functions. Nevertheless, several techniques and algorithms have been adopted to overcome these challenges, and the last two decades have seen exciting advances in enhanced sampling algorithms, computational power and tertiary structure prediction methodologies. This review aims at summarizing these computational techniques, specifically conformational sampling algorithms and energy approximations that have been frequently used to study protein-folding mechanisms or to de novo predict protein tertiary structures. We hope that this review can serve as an overview on how the protein-folding problem can be studied computationally and, in cases where experimental approaches are prohibitive, help the researcher choose the most relevant computational approach for the problem at hand. We conclude with a summary of current challenges faced and an outlook on potential future directions.

Helical Propensity Affects the Conformational Properties of the Denatured State of Cytochrome c'

Changing the helical propensity of a polypeptide sequence might be expected to affect the conformational properties of the denatured state of a protein. To test this hypothesis, alanines at positions 83 and 87 near the center of helix 3 of cytochrome c' from Rhodopseudomonas palustris were mutated to serine to decrease the stability of this helix. A set of 13 single histidine variants in the A83S/A87S background were prepared to permit assessment of the conformational properties of the denatured state using histidine-loop formation in 3 M guanidine hydrochloride. The data are compared with previous histidine-heme loop formation data for wild-type cytochrome c'. As expected, destabilization of helix 3 decreases the global stabilities of the histidine variants in the A83S/A87S background relative to the wild-type background. Loop stability versus loop size data yields a scaling exponent of 2.1 ± 0.2, similar to the value of 2.3 ± 0.2 obtained for wild-type cytochrome c'. However, the stabilities of all histidine-heme loops, which contain the helix 3 sequence segment, are increased in the A83S/A87S background compared to the wild-type background. Rate constants for histidine-heme loop breakage are similar for the wild-type and A83S/A87S variants. However, for histidine-heme loops that contain the helix 3 sequence segment, the rate constants for loop formation increase in the A83S/A87S background compared to the wild-type background. Thus, residual helical structure appears to stiffen the polypeptide chain slowing loop formation in the denatured state. The implications of these results for protein folding mechanisms are discussed.

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.

Characterization of the structural ensembles of p53 TAD2 by molecular dynamics simulations with different force fields

The conformations of p53 TAD2 in complexes and sampled in simulations with five force fields.

Coiled coil protein origami: from modular design principles towards biotechnological applications

This review illustrates the current state in designing coiled-coil-based proteins with an emphasis on coiled coil protein origami structures and their potential.

Designed Protein Origami

Proteins are highly perfected natural molecular machines, owing their properties to the complex tertiary structures with precise spatial positioning of different functional groups that have been honed through millennia of evolutionary selection. The prospects of designing new molecular machines and structural scaffolds beyond the limits of natural proteins make design of new protein folds a very attractive prospect. However, de novo design of new protein folds based on optimization of multiple cooperative interactions is very demanding. As a new alternative approach to design new protein folds unseen in nature, folds can be designed as a mathematical graph, by the self-assembly of interacting polypeptide modules within the single chain. Orthogonal coiled-coil dimers seem like an ideal building module due to their shape, adjustable length, and above all their designability. Similar to the approach of DNA nanotechnology, where complex tertiary structures are designed from complementary nucleotide segments, a polypeptide chain composed of a precisely specified sequence of coiled-coil forming segments can be designed to self-assemble into polyhedral scaffolds. This modular approach encompasses long-range interactions that define complex tertiary structures. We envision that by expansion of the toolkit of building blocks and design strategies of the folding pathways protein origami technology will be able to construct diverse molecular machines.

Density discriminates between thermophilic and mesophilic proteins

Despite an intense interest and a remarkable number of studies on the subject, the relationships between thermostability and (primary, secondary and tertiary) structure of proteins are still not fully understood. Here, comparing the protein density - defined by the ratio between the residue number and protein excluded volume - for a set of thermophilic/mesophilic pairs, we provide evidence that this property is connected to the optimal growth temperature. In particular, our results indicate that thermophilic proteins have - in general - a lower density with respect to the mesophilic counterparts, being such a correlation more pronounced for optimal growth temperature differences greater than 40°C. The effect of the protein thermostability changes on the molecular shape is also presented.

Evolution of intrinsic disorder in eukaryotic proteins

Conformational flexibility conferred though regions of intrinsic structural disorder allows proteins to behave as dynamic molecules. While it is well-known that intrinsically disordered regions can undergo disorder-to-order transitions in real-time as part of their function, we also are beginning to learn more about the dynamics of disorder-to-order transitions along evolutionary time-scales. Intrinsically disordered regions endow proteins with functional promiscuity, which is further enhanced by the ability of some of these regions to undergo real-time disorder-to-order transitions. Disorder content affects gene retention after whole genome duplication, but it is not necessarily conserved. Altered patterns of disorder resulting from evolutionary disorder-to-order transitions indicate that disorder evolves to modify function through refining stability, regulation, and interactions. Here, we review the evolution of intrinsically disordered regions in eukaryotic proteins. We discuss the interplay between secondary structure and disorder on evolutionary time-scales, the importance of disorder for eukaryotic proteome expansion and functional divergence, and the evolutionary dynamics of disorder.

Rules for connectivity of secondary structure elements in protein: Two-layer αβ sandwiches

In protein structures, the fold is described according to the spatial arrangement of secondary structure elements (SSEs: α-helices and β-strands) and their connectivity. The connectivity or the pattern of links among SSEs is one of the most important factors for understanding the variety of protein folds. In this study, we introduced the connectivity strings that encode the connectivities by using the types, positions, and connections of SSEs, and computationally enumerated all the connectivities of two-layer αβ sandwiches. The calculated connectivities were compared with those in natural proteins determined using MICAN, a nonsequential structure comparison method. For 2α-4β, among 23,000 of all connectivities, only 48 were free from irregular connectivities such as loop crossing. Of these, only 20 were found in natural proteins and the superfamilies were biased toward certain types of connectivities. A similar disproportional distribution was confirmed for most of other spatial arrangements of SSEs in the two-layer αβ sandwiches. We found two connectivity rules that explain the bias well: the abundances of interlayer connecting loops that bridge SSEs in the distinct layers; and nonlocal β-strand pairs, two spatially adjacent β-strands located at discontinuous positions in the amino acid sequence. A two-dimensional plot of these two properties indicated that the two connectivity rules are not independent, which may be interpreted as a rule for the cooperativity of proteins.

Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔG_align, the probability of aligning tertiary contact partners, and ΔG_tert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔG_HJH) or from changes in the electrostatic environment (ΔG_+/-) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔG_tert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔG_tert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

Topology of polymer chains under nanoscale confinement

Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l_p under a spherical confinement of radius R_c. At low values of l_p/R_c, the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l_p/R_c, the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l_p/R_c, at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross topologies have nearly the same contact orders. Such degeneracy implies that the kinetics and transition rates between the topological states cannot be solely explained by contact order. We expect these findings to be of general importance in understanding chaperone assisted protein folding, chromosome architecture, and the evolution of molecular folds.

Exploring the Sequence-based Prediction of Folding Initiation Sites in Proteins

Protein folding is a complex process that can lead to disease when it fails. Especially poorly understood are the very early stages of protein folding, which are likely defined by intrinsic local interactions between amino acids close to each other in the protein sequence. We here present EFoldMine, a method that predicts, from the primary amino acid sequence of a protein, which amino acids are likely involved in early folding events. The method is based on early folding data from hydrogen deuterium exchange (HDX) data from NMR pulsed labelling experiments, and uses backbone and sidechain dynamics as well as secondary structure propensities as features. The EFoldMine predictions give insights into the folding process, as illustrated by a qualitative comparison with independent experimental observations. Furthermore, on a quantitative proteome scale, the predicted early folding residues tend to become the residues that interact the most in the folded structure, and they are often residues that display evolutionary covariation. The connection of the EFoldMine predictions with both folding pathway data and the folded protein structure suggests that the initial statistical behavior of the protein chain with respect to local structure formation has a lasting effect on its subsequent states.

The N-Terminal Domain of Ribosomal Protein L9 Folds via a Diffuse and Delocalized Transition State

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

Transiently disordered tails accelerate folding of globular proteins

Numerous biological proteins exhibit intrinsic disorder at their termini, which are associated with multifarious functional roles. Here, we show the surprising result that an increased percentage of terminal short transiently disordered regions with enhanced flexibility (TstDREF) is associated with accelerated folding rates of globular proteins. Evolutionary conservation of predicted disorder at TstDREFs and drastic alteration of folding rates upon point-mutations suggest critical regulatory role(s) of TstDREFs in shaping the folding kinetics. TstDREFs are associated with long-range intramolecular interactions and the percentage of native secondary structural elements physically contacted by TstDREFs exhibit another surprising positive correlation with folding kinetics. These results allow us to infer probable molecular mechanisms behind the TstDREF-mediated regulation of folding kinetics that challenge protein biochemists to assess by direct experimental testing.

When fast is better: protein folding fundamentals and mechanisms from ultrafast approaches

Protein folding research stalled for decades because conventional experiments indicated that proteins fold slowly and in single strokes, whereas theory predicted a complex interplay between dynamics and energetics resulting in myriad microscopic pathways. Ultrafast kinetic methods turned the field upside down by providing the means to probe fundamental aspects of folding, test theoretical predictions and benchmark simulations. Accordingly, experimentalists could measure the timescales for all relevant folding motions, determine the folding speed limit and confirm that folding barriers are entropic bottlenecks. Moreover, a catalogue of proteins that fold extremely fast (microseconds) could be identified. Such fast-folding proteins cross shallow free energy barriers or fold downhill, and thus unfold with minimal co-operativity (gradually). A new generation of thermodynamic methods has exploited this property to map folding landscapes, interaction networks and mechanisms at nearly atomic resolution. In parallel, modern molecular dynamics simulations have finally reached the timescales required to watch fast-folding proteins fold and unfold in silico. All of these findings have buttressed the fundamentals of protein folding predicted by theory, and are now offering the first glimpses at the underlying mechanisms. Fast folding appears to also have functional implications as recent results connect downhill folding with intrinsically disordered proteins, their complex binding modes and ability to moonlight. These connections suggest that the coupling between downhill (un)folding and binding enables such protein domains to operate analogically as conformational rheostats.

Quantifying Nonnative Interactions in the Protein-Folding Free-Energy Landscape

Protein folding is a central problem in biological physics. Energetic roughness is an important aspect that controls protein-folding stability and kinetics. The roughness is associated with conflicting interactions in the protein and is also known as frustration. Recent studies indicate that an addition of a small amount of energetic frustration may enhance folding speed for certain proteins. In this study, we have investigated the conditions under which frustration increases the folding rate. We used a Cα structure-based model to simulate a group of proteins. We found that the free-energy barrier at the transition state (ΔF) correlates with nonnative-contact variation (ΔA), and the simulated proteins are clustered according to their fold motifs. These findings are corroborated by the Clementi-Plotkin analytical model. As a consequence, the optimum frustration regime for protein folding can be predicted analytically.

EPSILON-CP: using deep learning to combine information from multiple sources for protein contact prediction

BACKGROUND

Accurately predicted contacts allow to compute the 3D structure of a protein. Since the solution space of native residue-residue contact pairs is very large, it is necessary to leverage information to identify relevant regions of the solution space, i.e. correct contacts. Every additional source of information can contribute to narrowing down candidate regions. Therefore, recent methods combined evolutionary and sequence-based information as well as evolutionary and physicochemical information. We develop a new contact predictor (EPSILON-CP) that goes beyond current methods by combining evolutionary, physicochemical, and sequence-based information. The problems resulting from the increased dimensionality and complexity of the learning problem are combated with a careful feature analysis, which results in a drastically reduced feature set. The different information sources are combined using deep neural networks.

RESULTS

On 21 hard CASP11 FM targets, EPSILON-CP achieves a mean precision of 35.7% for top- L/10 predicted long-range contacts, which is 11% better than the CASP11 winning version of MetaPSICOV. The improvement on 1.5L is 17%. Furthermore, in this study we find that the amino acid composition, a commonly used feature, is rendered ineffective in the context of meta approaches. The size of the refined feature set decreased by 75%, enabling a significant increase in training data for machine learning, contributing significantly to the observed improvements.

CONCLUSIONS

Exploiting as much and diverse information as possible is key to accurate contact prediction. Simply merging the information introduces new challenges. Our study suggests that critical feature analysis can improve the performance of contact prediction methods that combine multiple information sources. EPSILON-CP is available as a webservice: http://compbio.robotics.tu-berlin.de/epsilon/.

Understanding the molecular basis of stability in Kunitz (STI) family of inhibitors in terms of a conserved core tryptophan residue: A theoretical investigation

β-trefoil is one of the superfolds among proteins. Important classes of proteins like Interleukins (ILs), FibroblastGrowth Factors (FGFs), Kunitz (STI) family of inhibitors etc. belong to this fold. Kunitz (STI) family of inhibitors of proteins possess a highly conserved and structurally important Trytophan 91 (W91) residue, which stitches the top layer of the barrel with the lid. In this article we have investigated the molecular insights of the involvement of this W91 residue in the stability and folding pathway of Kunitz (STI) family. Winged bean Chymotrypsin inhibitor (WCI), a member of Kunitz (STI) family was chosen as a model system for carrying out the work. Molecular dynamics (MD) simulations were run with a set of total six proteins, including wild type WCI (WT) & five mutants namely W91F, W91M, W91A, W91H and W91I. Among all of them the coordinates of four proteins were taken from their crystal structures deposited in the Protein Data Bank (PDB), where as the coordinates for the rest two was generated using in-silico modelling. Our results suggest that truly this W91 residue plays a determining role in stability and folding pathway of Kunitz (STI) family. The mutants are less stable and more susceptible to quicker unfolding at higher temperatures compared to the wild type WCI. These effects are most pronounced for the smallest mutants namely W91H and W91A, indicating more is the cavity created by mutation at W91 position more the proteins becomes unstable.

Lessons from making the Structural Classification of Proteins (SCOP) and their implications for protein structure modelling

The Structural Classification of Proteins (SCOP) database has facilitated the development of many tools and algorithms and it has been successfully used in protein structure prediction and large-scale genome annotations. During the development of SCOP, numerous exceptions were found to topological rules, along with complex evolutionary scenarios and peculiarities in proteins including the ability to fold into alternative structures. This article reviews cases of structural variations observed for individual proteins and among groups of homologues, knowledge of which is essential for protein structure modelling.

Widespread position-specific conservation of synonymous rare codons within coding sequences

Synonymous rare codons are considered to be sub-optimal for gene expression because they are translated more slowly than common codons. Yet surprisingly, many protein coding sequences include large clusters of synonymous rare codons. Rare codons at the 5’ terminus of coding sequences have been shown to increase translational efficiency. Although a general functional role for synonymous rare codons farther within coding sequences has not yet been established, several recent reports have identified rare-to-common synonymous codon substitutions that impair folding of the encoded protein. Here we test the hypothesis that although the usage frequencies of synonymous codons change from organism to organism, codon rarity will be conserved at specific positions in a set of homologous coding sequences, for example to tune translation rate without altering a protein sequence. Such conservation of rarity–rather than specific codon identity–could coordinate co-translational folding of the encoded protein. We demonstrate that many rare codon cluster positions are indeed conserved within homologous coding sequences across diverse eukaryotic, bacterial, and archaeal species, suggesting they result from positive selection and have a functional role. Most conserved rare codon clusters occur within rather than between conserved protein domains, challenging the view that their primary function is to facilitate co-translational folding after synthesis of an autonomous structural unit. Instead, many conserved rare codon clusters separate smaller protein structural motifs within structural domains. These smaller motifs typically fold faster than an entire domain, on a time scale more consistent with translation rate modulation by synonymous codon usage. While proteins with conserved rare codon clusters are structurally and functionally diverse, they are enriched in functions associated with organism growth and development, suggesting an important role for synonymous codon usage in organism physiology. The identification of conserved rare codon clusters advances our understanding of distinct, functional roles for otherwise synonymous codons and enables experimental testing of the impact of synonymous codon usage on the production of functional proteins.

Proteins are long linear polymers that must fold into complex three-dimensional shapes in order to carry out their cellular functions. Every protein is synthesized by the ribosome, which decodes each trinucleotide codon in an mRNA coding sequence in order to select the amino acid residue that will occupy each position in the protein sequence. Most amino acids can be encoded by more than one codon, but these synonymous codons are not used with equal frequency. Rare codons are associated with generally slower rates for protein synthesis, and for this reason have traditionally been considered mildly deleterious for efficient protein production. However, because synonymous codon substitutions do not change the sequence of the encoded protein, the majority view is that they merely reflect genomic ‘background noise’. To the contrary, here we show that the positions of many synonymous rare codons are conserved in mRNA sequences that encode structurally similar proteins from a diverse range of organisms. These results suggest that rare codons have a functional role related to the production of functional proteins, potentially to regulate the rate of protein synthesis and the earliest steps of protein folding, while synthesis is still underway.

Thermodynamics of Protein Folding Studied by Umbrella Sampling along a Reaction Coordinate of Native Contacts

Spontaneous transitions between the native and non-native protein conformations are normally rare events that hardly take place in typical unbiased molecular dynamics simulations. It was recently demonstrated that such transitions can be well described by a reaction coordinate, Q, that represents the collective fraction of the native contacts between the protein atoms. Here we attempt to use this reaction coordinate to enhance the conformational sampling. We perform umbrella sampling simulations with biasing potentials on Q for two model proteins, Trp-Cage and BBA, using the CHARMM force field. Hamiltonian replica exchange is implemented in these simulations to further facilitate the sampling. The simulations appear to have reached satisfactory convergence, resulting in unbiased free energies as a function of Q. In addition to the native structure, multiple folded conformations are identified in the reconstructed equilibrium ensemble. Some conformations without any native contacts nonetheless have rather compact geometries and are stabilized by hydrogen bonds not present in the native structure. Whereas the enhanced sampling along Q reasonably reproduces the equilibrium conformational space, we also find that the folding of an α-helix in Trp-Cage is a slow degree of freedom orthogonal to Q and therefore cannot be accelerated by biasing the reaction coordinate. Overall, we conclude that whereas Q is an excellent parameter to analyze the simulations, it is not necessarily a perfect reaction coordinate for enhanced sampling, and better incorporation of other slow degrees of freedom may further improve this reaction coordinate.

Long-Range Interactions in Riboswitch Control of Gene Expression

Riboswitches are widespread RNA motifs that regulate gene expression in response to fluctuating metabolite concentrations. Known primarily from bacteria, riboswitches couple specific ligand binding and changes in RNA structure to mRNA expression in cis. Crystal structures of the ligand binding domains of most of the phylogenetically widespread classes of riboswitches, each specific to a particular metabolite or ion, are now available. Thus, the bound states-one end point-have been thoroughly characterized, but the unbound states have been more elusive. Consequently, it is less clear how the unbound, sensing riboswitch refolds into the ligand binding-induced output state. The ligand recognition mechanisms of riboswitches are diverse, but we find that they share a common structural strategy in positioning their binding sites at the point of the RNA three-dimensional fold where the residues farthest from one another in sequence meet. We review how riboswitch folds adhere to this fundamental strategy and propose future research directions for understanding and harnessing their ability to specifically control gene expression.

Entropic stabilization of a deubiquitinase provides conformational plasticity and slow unfolding kinetics beneficial for functioning on the proteasome

Human ubiquitin C-terminal hydrolyase UCH-L5 is a topologically knotted deubiquitinase that is activated upon binding to the proteasome subunit Rpn13. The length of its intrinsically disordered cross-over loop is essential for substrate recognition. Here, we showed that the catalytic domain of UCH-L5 exhibits higher equilibrium folding stability with an unfolding rate on the scale of 10⁻⁸ s⁻¹, over four orders of magnitudes slower than its paralogs, namely UCH-L1 and -L3, which have shorter cross-over loops. NMR relaxation dynamics analysis confirmed the intrinsic disorder of the cross-over loop. Hydrogen deuterium exchange analysis further revealed a positive correlation between the length of the cross-over loop and the degree of local fluctuations, despite UCH-L5 being thermodynamically and kinetically more stable than the shorter UCHs. Considering the role of UCH-L5 in removing K48-linked ubiquitin to prevent proteasomal degradation of ubiquitinated substrates, our findings offered mechanistic insights into the evolution of UCH-L5. Compared to its paralogs, it is entropically stabilized to withstand mechanical unfolding by the proteasome while maintaining structural plasticity. It can therefore accommodate a broad range of substrate geometries at the cost of unfavourable entropic loss.

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.

Perplexing cooperative folding and stability of a low-sequence complexity, polyproline 2 protein lacking a hydrophobic core

The burial of hydrophobic side chains in a protein core generally is thought to be the major ingredient for stable, cooperative folding. Here, we show that, for the snow flea antifreeze protein (sfAFP), stability and cooperativity can occur without a hydrophobic core, and without α-helices or β-sheets. sfAFP has low sequence complexity with 46% glycine and an interior filled only with backbone H-bonds between six polyproline 2 (PP2) helices. However, the protein folds in a kinetically two-state manner and is moderately stable at room temperature. We believe that a major part of the stability arises from the unusual match between residue-level PP2 dihedral angle bias in the unfolded state and PP2 helical structure in the native state. Additional stabilizing factors that compensate for the dearth of hydrophobic burial include shorter and stronger H-bonds, and increased entropy in the folded state. These results extend our understanding of the origins of cooperativity and stability in protein folding, including the balance between solvent and polypeptide chain entropies.

There and back again: Two views on the protein folding puzzle

The ability of protein chains to spontaneously form their spatial structures is a long-standing puzzle in molecular biology. Experimentally measured folding times of single-domain globular proteins range from microseconds to hours: the difference (10-11 orders of magnitude) is the same as that between the life span of a mosquito and the age of the universe. This review describes physical theories of rates of overcoming the free-energy barrier separating the natively folded (N) and unfolded (U) states of protein chains in both directions: "U-to-N" and "N-to-U". In the theory of protein folding rates a special role is played by the point of thermodynamic (and kinetic) equilibrium between the native and unfolded state of the chain; here, the theory obtains the simplest form. Paradoxically, a theoretical estimate of the folding time is easier to get from consideration of protein unfolding (the "N-to-U" transition) rather than folding, because it is easier to outline a good unfolding pathway of any structure than a good folding pathway that leads to the stable fold, which is yet unknown to the folding protein chain. And since the rates of direct and reverse reactions are equal at the equilibrium point (as follows from the physical "detailed balance" principle), the estimated folding time can be derived from the estimated unfolding time. Theoretical analysis of the "N-to-U" transition outlines the range of protein folding rates in a good agreement with experiment. Theoretical analysis of folding (the "U-to-N" transition), performed at the level of formation and assembly of protein secondary structures, outlines the upper limit of protein folding times (i.e., of the time of search for the most stable fold). Both theories come to essentially the same results; this is not a surprise, because they describe overcoming one and the same free-energy barrier, although the way to the top of this barrier from the side of the unfolded state is very different from the way from the side of the native state; and both theories agree with experiment. In addition, they predict the maximal size of protein domains that fold under solely thermodynamic (rather than kinetic) control and explain the observed maximal size of the "foldable" protein domains.

Prediction of Local Quality of Protein Structure Models Considering Spatial Neighbors in Graphical Models

Protein tertiary structure prediction methods have matured in recent years. However, some proteins defy accurate prediction due to factors such as inadequate template structures. While existing model quality assessment methods predict global model quality relatively well, there is substantial room for improvement in local quality assessment, i.e. assessment of the error at each residue position in a model. Local quality is a very important information for practical applications of structure models such as interpreting/designing site-directed mutagenesis of proteins. We have developed a novel local quality assessment method for protein tertiary structure models. The method, named Graph-based Model Quality assessment method (GMQ), explicitly considers the predicted quality of spatially neighboring residues using a graph representation of a query protein structure model. GMQ uses conditional random field as its core of the algorithm, and performs a binary prediction of the quality of each residue in a model, indicating if a residue position is likely to be within an error cutoff or not. The accuracy of GMQ was improved by considering larger graphs to include quality information of more surrounding residues. Moreover, we found that using different edge weights in graphs reflecting different secondary structures further improves the accuracy. GMQ showed competitive performance on a benchmark for quality assessment of structure models from the Critical Assessment of Techniques for Protein Structure Prediction (CASP).

Early Folding Events, Local Interactions, and Conservation of Protein Backbone Rigidity

Protein folding is in its early stages largely determined by the protein sequence and complex local interactions between amino acids, resulting in lower energy conformations that provide the context for further folding into the native state. We compiled a comprehensive data set of early folding residues based on pulsed labeling hydrogen deuterium exchange experiments. These early folding residues have corresponding higher backbone rigidity as predicted by DynaMine from sequence, an effect also present when accounting for the secondary structures in the folded protein. We then show that the amino acids involved in early folding events are not more conserved than others, but rather, early folding fragments and the secondary structure elements they are part of show a clear trend toward conserving a rigid backbone. We therefore propose that backbone rigidity is a fundamental physical feature conserved by proteins that can provide important insights into their folding mechanisms and stability.

The low populated folding intermediate of a mutant of the Fyn SH3 domain identified by a simple model

The low populated on-pathway folding intermediate of the A39V/N53P/V55L Fyn SH3 domain is captured by a native-centric model augmented by sequence-dependent nonnative hydrophobic interactions.