Specific nucleus as the transition state for protein folding: evidence from the lattice model

The Mechanism of Folding of Human Frataxin in Comparison to the Yeast Homologue - Broad Energy Barriers and the General Properties of the Transition State

The funneled energy landscape theory suggests that the folding pathway of homologous proteins should converge at the late stages of folding. In this respect, proteins displaying a broad energy landscape for folding are particularly instructive, allowing inferring both the early, intermediate and late stages of folding. In this paper we explore the folding mechanisms of human frataxin, an essential mitochondrial protein linked to the neurodegenerative disorder Friedreich's ataxia. Building upon previous studies on the yeast homologue, the folding pathway of human frataxin is thoroughly examined, revealing a mechanism implying the presence of a broad energy barrier, reminiscent of the yeast counterpart. Through an extensive site-directed mutagenesis, we employed a Φ -value analysis to map native-like contacts in the folding transition state. The presence of a broad energy barrier facilitated the exploration of such contacts in both early and late folding events. We compared results from yeast and human frataxin providing insights into the impact of native topology on the folding mechanism and elucidating the properties of the underlying free energy landscape. The findings are discussed in the context of the funneled energy landscape theory of protein folding.

Function of the Conserved Non-Functional Residues in Apomyoglobin - to Determine and to Preserve Correct Topology of the Protein

In this paper the answer to O. B. Ptitsyn's question "What is the role of conserved non-functional residues in apomyoglobin" is presented, which is based on the research results of three laboratories. The role of conserved non-functional apomyoglobin residues in formation of native topology in the molten globule state of this protein is revealed. This fact allows suggesting that the conserved non-functional residues in this protein are indispensable for fixation and maintaining main elements of the correct topology of its secondary structure in the intermediate state. The correct topology is a native element in the intermediate state of the protein.

Protein-Inspired Control over Synthetic Polymer Folding for Structured Functional Nanoparticles in Water

The folding of proteins into functional nanoparticles with defined 3D structures has inspired chemists to create simple synthetic systems mimicking protein properties. The folding of polymers into nanoparticles in water proceeds via different strategies, resulting in the global compaction of the polymer chain. Herein, we review the different methods available to control the conformation of synthetic polymers and collapse/fold them into structured, functional nanoparticles, such as hydrophobic collapse, supramolecular self-assembly, and covalent cross-linking. A comparison is made between the design principles of protein folding to synthetic polymer folding and the formation of structured nanocompartments in water, highlighting similarities and differences in design and function. We also focus on the importance of structure for functional stability and diverse applications in complex media and cellular environments.

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.

An Introduction to the Stickers-and-Spacers Framework as Applied to Biomolecular Condensates

Cellular organization is determined by a combination of membrane-bound and membrane-less biomolecular assemblies that range from clusters of tens of molecules to micrometer-sized cellular bodies. Over the last decade, membrane-less assemblies have come to be referred to as biomolecular condensates, reflecting their ability to condense specific molecules with respect to the remainder of the cell. In many cases, the physics of phase transitions provides a conceptual framework and a mathematical toolkit to describe the assembly, maintenance, and dissolution of biomolecular condensates. Among the various quantitative and qualitative models applied to understand intracellular phase transitions, the stickers-and-spacers framework offers an intuitive yet rigorous means to map biomolecular sequences and structure to the driving forces needed for higher-order assembly. This chapter introduces the fundamental concepts behind the stickers-and-spacers model, considers its application to different biological systems, and discusses limitations and misconceptions around the model.

Protein folding problem: enigma, paradox, solution

The ability of protein chains to spontaneously form their three-dimensional structures is a long-standing mystery in molecular biology. The most conceptual aspect of this mystery is how the protein chain can find its native, "working" spatial structure (which, for not too big protein chains, corresponds to the global free energy minimum) in a biologically reasonable time, without exhaustive enumeration of all possible conformations, which would take billions of years. This is the so-called "Levinthal's paradox." In this review, we discuss the key ideas and discoveries leading to the current understanding of protein folding kinetics, including folding landscapes and funnels, free energy barriers at the folding/unfolding pathways, and the solution of Levinthal's paradox. A special role here is played by the "all-or-none" phase transition occurring at protein folding and unfolding and by the point of thermodynamic (and kinetic) equilibrium between the "native" and the "unfolded" phases of the protein chain (where the theory obtains the simplest form). The modern theory provides an understanding of key features of protein folding and, in good agreement with experiments, it (i) outlines the chain length-dependent range of protein folding times, (ii) predicts the observed maximal size of "foldable" proteins and domains. Besides, it predicts the maximal size of proteins and domains that fold under solely thermodynamic (rather than kinetic) control. Complementarily, a theoretical analysis of the number of possible protein folding patterns, performed at the level of formation and assembly of secondary structures, correctly outlines the upper limit of protein folding times.

Key interaction patterns in proteins revealed by cluster expansion of the partition function

The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence design. To achieve this goal, we employed a cluster expansion of the partition function in the space of sequences and evaluated numerically the statistical importance of each cluster. An important feature of this procedure is that it is applied to a dense finite system. We found that patterns that contribute most to the partition function are cycles with even numbers of nodes, while cliques are typically detrimental. Each cluster also gives a contribute to the sequence entropy, which is a measure of the evolutionary designability of a fold. We compared the entropies associated with different interaction patterns to their abundances in the native structures of real proteins.

PSSNet-An Accurate Super-Secondary Structure for Protein Segmentation

A super-secondary structure (SSS) is a spatially unique ensemble of secondary structural elements that determine the three-dimensional shape of a protein and its function, rendering SSSs attractive as folding cores. Understanding known types of SSSs is important for developing a deeper understanding of the mechanisms of protein folding. Here, we propose a universal PSSNet machine-learning method for SSS recognition and segmentation. For various types of SSS segmentation, this method uses key characteristics of SSS geometry, including the lengths of secondary structural elements and the distances between them, torsion angles, spatial positions of Cα atoms, and primary sequences. Using four types of SSSs (βαβ-unit, α-hairpin, β-hairpin, αα-corner), we showed that extensive SSS sets could be reliably selected from the Protein Data Bank and AlphaFold 2.0 database of protein structures.

Atomic Simulation of the Binding of JAK1 and JAK2 with the Selective Inhibitor Ruxolitinib

Rheumatoid arthritis belongs to the group of chronic systemic autoimmune diseases characterized by the development of destructive synovitis and extra-articular manifestations. Cytokines regulate a wide range of inflammatory processes involved in the pathogenesis of rheumatoid arthritis and contribute to the induction of autoimmunity and chronic inflammation. Janus-associated kinase (JAK) and signal transducer and activator of transcription (STAT) proteins mediate cell signaling from cytokine receptors, and are involved in the pathogenesis of autoimmune and inflammatory diseases. Targeted small-molecule drugs that inhibit the functional activity of JAK proteins are used in clinical practice for the treatment of rheumatoid arthritis. In our study, we modeled the interactions of the small-molecule drug ruxolitinib with JAK1 and JAK2 isoforms and determined the binding selectivity using molecular docking. Molecular modeling data show that ruxolitinib selectively binds the JAK1 and JAK2 isoforms with a binding affinity of −8.3 and −8.0 kcal/mol, respectively. The stabilization of ligands in the cavity of kinases occurs primarily through hydrophobic interactions. The amino acid residues of the protein globules of kinases that are responsible for the correct positioning of the drug ruxolitinib and its retention have been determined.

Variable and Conserved Regions of Secondary Structure in the β-Trefoil Fold: Structure Versus Function

β-trefoil proteins exhibit an approximate C₃ rotational symmetry. An analysis of the secondary structure for members of this diverse superfamily of proteins indicates that it is comprised of remarkably conserved β-strands and highly-divergent turn regions. A fundamental “minimal” architecture can be identified that is devoid of heterogenous and extended turn regions, and is conserved among all family members. Conversely, the different functional families of β-trefoils can potentially be identified by their unique turn patterns (or turn “signature”). Such analyses provide clues as to the evolution of the β-trefoil family, suggesting a folding/stability role for the β-strands and a functional role for turn regions. This viewpoint can also guide de novo protein design of β-trefoil proteins having novel functionality.

De novo protein folding on computers. Benefits and challenges

There has been recent success in prediction of the three-dimensional folded native structures of proteins, most famously by the AlphaFold Algorithm running on Google's/Alphabet's DeepMind computer. However, this largely involves machine learning of protein structures and is not a de novo protein structure prediction method for predicting three-dimensional structures from amino acid residue sequences. A de novo approach would be based almost entirely on general principles of energy and entropy that govern protein folding energetics, and importantly do so without the use of the amino acid sequences and structural features of other proteins. Most consider that problem as still unsolved even though it has occupied leading scientists for decades. Many consider that it remains one of the major outstanding issues in modern science. There is crucial continuing help from experimental findings on protein unfolding and refolding in the laboratory, but only to a limited extent because many researchers consider that the speed by which real proteins folds themselves, often from milliseconds to minutes, is itself still not fully understood. This is unfortunate, because a practical solution to the problem would probably have a major effect on personalized medicine, the pharmaceutical industry, biotechnology, and nanotechnology, including for example "smaller" tasks such as better modeling of flexible "unfolded" regions of the SARS-COV-2 spike glycoprotein when interacting with its cell receptor, antibodies, and therapeutic agents. Some important ideas from earlier studies are given before moving on to lessons from periodic and aperiodic crystals, and a possible role for quantum phenomena. The conclusion is that better computation of entropy should be the priority, though that is presented guardedly.

Hydrogen Bonding Sequence Directed Coil-Globule Transition in Water Soluble Thermoresponsive Polymers

The origin of the coil-globule transition for water-soluble thermoresponsive polymers frequently used in nanomaterials remains elusive. Using polypropylene oxide as an example we demonstrate by means of atomistic molecular dynamics simulations that temperature-induced increase in the sequence length of monomers that are not hydrogen bonded to water drives the coil-globule transition. Longer chains statistically exhibit longer sequences which serve as nucleation sites for hydrophobic cluster formation, facilitating chain collapse at lower temperature in agreement with experimental data.

Protein folding - seeing is deceiving

This Perspective is intended to raise questions about the conventional interpretation of protein folding. According to the conventional interpretation, developed over many decades, a protein population can visit a vast number of conformations under unfolding conditions, but a single dominant native population emerges under folding conditions. Accordingly, folding comes with a substantial loss of conformational entropy. How is this price paid? The conventional answer is that favorable interactions between and among the side chains can compensate for entropy loss, and moreover, these interactions are responsible for the structural particulars of the native conformation. Challenging this interpretation, the Perspective introduces a proposal that high energy (i.e., unfavorable) excluding interactions winnow the accessible population substantially under physical-chemical conditions that favor folding. Both steric clash and unsatisfied hydrogen bond donors and acceptors are classified as excluding interactions, so called because conformers with such disfavored interactions will be largely excluded from the thermodynamic population. Both excluding interactions and solvent factors that induce compactness are somewhat nonspecific, yet together they promote substantial chain organization. Moreover, proteins are built on a backbone scaffold consisting of α-helices and strands of β-sheet, where the number of hydrogen bond donors and acceptors is exactly balanced. These repetitive secondary structural elements are the only two conformers that can be both completely hydrogen-bond satisfied and extended indefinitely without encountering a steric clash. Consequently, the number of fundamental folds is limited to no more than ~10,000 for a protein domain. Once excluding interactions are taken into account, the issue of "frustration" is largely eliminated and the Levinthal paradox is resolved. Putting the "bottom line" at the top: it is likely that hydrogen-bond satisfaction represents a largely under-appreciated parameter in protein folding models.

A Specific Set of Heterogeneous Native Interactions Yields Efficient Knotting in Protein Folding

Native interactions are crucial for folding, and non-native interactions appear to be critical for efficiently knotting proteins. Therefore, it is important to understand both their roles in the folding of knotted proteins. It has been proposed that non-native interactions drive the correct order of contact formation, which is essential to avoid backtracking and efficiently self-tie. In this study, we ask if non-native interactions are strictly necessary to tangle a protein or if the correct order of contact formation can be assured by a specific set of native, but otherwise heterogeneous (i.e., having distinct energies), interactions. In order to address this problem, we conducted extensive Monte Carlo simulations of lattice models of protein-like sequences designed to fold into a preselected knotted conformation embedding a trefoil knot. We were able to identify a specific set of heterogeneous native interactions that drives efficient knotting and is able to fold the protein when combined with the remaining native interactions modeled as homogeneous. This specific set of heterogeneous native interactions is strictly enough to efficiently self-tie. A distinctive feature of these native interactions is that they do not backtrack because their energies ensure the correct order of contact formation. Furthermore, they stabilize a knotted intermediate state, which is en route to the native structure. Our results thus show that-at least in the context of the adopted model-non-native interactions are not necessary to knot a protein. However, when they are taken into account in protein energetics, it is possible to find specific, nonlocal non-native interactions that operate as a scaffold that assists the knotting step.

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

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

Evolution of frustrated and stabilising contacts in reconstructed ancient proteins

Energetic properties of a protein are a major determinant of its evolutionary fitness. Using a reconstruction algorithm, dating the reconstructed proteins and calculating the interaction network between their amino acids through a coevolutionary approach, we studied how the interactions that stabilise 890 proteins, belonging to five families, evolved for billions of years. In particular, we focused our attention on the network of most strongly attractive contacts and on that of poorly optimised, frustrated contacts. Our results support the idea that the cluster of most attractive interactions extends its size along evolutionary time, but from the data, we cannot conclude that protein stability or that the degree of frustration tends always to decrease.

Oligomerization of a symmetric β-trefoil protein in response to folding nucleus perturbation

Gene duplication and fusion events in protein evolution are postulated to be responsible for the common protein folds exhibiting internal rotational symmetry. Such evolutionary processes can also potentially yield regions of repetitive primary structure. Repetitive primary structure offers the potential for alternative definitions of critical regions, such as the folding nucleus (FN). In principle, more than one instance of the FN potentially enables an alternative folding pathway in the face of a subsequent deleterious mutation. We describe the targeted mutation of the carboxyl-terminal region of the (internally located) FN of the de novo designed purely-symmetric β-trefoil protein Symfoil-4P. This mutation involves wholesale replacement of a repeating trefoil-fold motif with a "blade" motif from a β-propeller protein, and postulated to trap that region of the Symfoil-4P FN in a nonproductive folding intermediate. The resulting protein (termed "Bladefoil") is shown to be cooperatively folding, but as a trimeric oligomer. The results illustrate how symmetric protein architectures have potentially diverse folding alternatives available to them, including oligomerization, when preferred pathways are perturbed.

Templated folding of intrinsically disordered proteins

Much of our current knowledge of biological chemistry is founded in the structure-function relationship, whereby sequence determines structure that determines function. Thus, the discovery that a large fraction of the proteome is intrinsically disordered, while being functional, has revolutionized our understanding of proteins and raised new and interesting questions. Many intrinsically disordered proteins (IDPs) have been determined to undergo a disorder-to-order transition when recognizing their physiological partners, suggesting that their mechanisms of folding are intrinsically different from those observed in globular proteins. However, IDPs also follow some of the classic paradigms established for globular proteins, pointing to important similarities in their behavior. In this review, we compare and contrast the folding mechanisms of globular proteins with the emerging features of binding-induced folding of intrinsically disordered proteins. Specifically, whereas disorder-to-order transitions of intrinsically disordered proteins appear to follow rules of globular protein folding, such as the cooperative nature of the reaction, their folding pathways are remarkably more malleable, due to the heterogeneous nature of their folding nuclei, as probed by analysis of linear free-energy relationship plots. These insights have led to a new model for the disorder-to-order transition in IDPs termed "templated folding," whereby the binding partner dictates distinct structural transitions en route to product, while ensuring a cooperative folding.

Solution of Levinthal's Paradox and a Physical Theory of Protein Folding Times

“How do proteins fold?” Researchers have been studying different aspects of this question for more than 50 years. The most conceptual aspect of the problem is how protein can find the global free energy minimum in a biologically reasonable time, without exhaustive enumeration of all possible conformations, the so-called “Levinthal’s paradox.” Less conceptual but still critical are aspects about factors defining folding times of particular proteins and about perspectives of machine learning for their prediction. We will discuss in this review the key ideas and discoveries leading to the current understanding of folding kinetics, including the solution of Levinthal’s paradox, as well as the current state of the art in the prediction of protein folding times.

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or "width" of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.

The Effect of Proline cis-trans Isomerization on the Folding of the C-Terminal SH2 Domain from p85

SH2 domains are protein domains that modulate protein-protein interactions through a specific interaction with sequences containing phosphorylated tyrosines. In this work, we analyze the folding pathway of the C-terminal SH2 domain of the p85 regulatory subunit of the protein PI3K, which presents a proline residue in a cis configuration in the loop between the βE and βF strands. By employing single and double jump folding and unfolding experiments, we demonstrate the presence of an on-pathway intermediate that transiently accumulates during (un)folding. By comparing the kinetics of folding of the wild-type protein to that of a site-directed variant of C-SH2 in which the proline was replaced with an alanine, we demonstrate that this intermediate is dictated by the peptidyl prolyl cis-trans isomerization. The results are discussed in the light of previous work on the effect of peptidyl prolyl cis-trans isomerization on folding events.

Life in Phases: Intra- and Inter- Molecular Phase Transitions in Protein Solutions

Proteins, these evolutionarily-edited biological polymers, are able to undergo intramolecular and intermolecular phase transitions. Spontaneous intramolecular phase transitions define the folding of globular proteins, whereas binding-induced, intra- and inter- molecular phase transitions play a crucial role in the functionality of many intrinsically-disordered proteins. On the other hand, intermolecular phase transitions are the behind-the-scenes players in a diverse set of macrosystemic phenomena taking place in protein solutions, such as new phase nucleation in bulk, on the interface, and on the impurities, protein crystallization, protein aggregation, the formation of amyloid fibrils, and intermolecular liquid-liquid or liquid-gel phase transitions associated with the biogenesis of membraneless organelles in the cells. This review is dedicated to the systematic analysis of the phase behavior of protein molecules and their ensembles, and provides a description of the major physical principles governing intramolecular and intermolecular phase transitions in protein solutions.

Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps

The diffusion map is a dimensionality reduction method. The reduction coordinates are associated with the leading eigenfunctions of the backward Fokker-Planck operator, providing a dynamic meaning for these coordinates. One of the key factors that affect the accuracy of diffusion map embedding is the dynamic measure implemented in the Gaussian kernel. A common practice in diffusion map study of molecular systems is to approximate dynamic proximity with RMSD (root-mean-square deviation). In this paper, we present a hybrid geometry-energy based kernel. Since high energy-barriers may exist between geometrically similar conformations, taking both RMSD and energy difference into account in the kernel can better describe conformational transitions between neighboring conformations and lead to accurate embedding. We applied our diffusion map method to the β-hairpin of the B1 domain of streptococcal protein G and to Trp-cage. Our results in β-hairpin show that the diffusion map embedding achieves better results with the hybrid kernel than that with the RMSD-based kernel in terms of free energy landscape characterization and a new correlation measure between the cluster center Euclidean distances in the reduced-dimension space and the reciprocals of the total net flow between these clusters. In addition, our diffusion map analysis of the ultralong molecular dynamics trajectory of Trp-cage has provided a unified view of its folding mechanism. These promising results demonstrate the effectiveness of our diffusion map approach in the analysis of the dynamics and thermodynamics of molecular systems. The hybrid geometry-energy criterion could be also useful as a general dynamic measure for other purposes.

Binding induced folding: Lessons from the kinetics of interaction between NTAIL and XD

Intrinsically Disordered Proteins (IDPs) are a class of protein that exert their function despite lacking a well-defined three-dimensional structure, which is sometimes achieved only upon binding to their natural ligands. This feature implies the folding of IDPs to be generally coupled with a binding event, representing an interesting challenge for kinetic studies. In this review, we recapitulate some of the most important findings of IDPs binding-induced folding mechanisms obtained by analyzing their binding kinetics. Furthermore, by focusing on the interaction between the Measles virus N_TAIL protein, a prototypical IDP, and its physiological partner, the X domain, we recapitulate the major theoretical and experimental approaches that were used to describe binding induced folding.

Structural characterization of an on-pathway intermediate and transition state in the folding of the N-terminal SH2 domain from SHP2

Src Homology 2 (SH2) domains are a class of protein domains that present a conserved three-dimensional structure and possess a crucial role in mediating protein-protein interactions. Despite their importance and abundance in the proteome, knowledge about the folding properties of SH2 domain is limited. Here we present an extensive mutational analysis (Φ value analysis) of the folding pathway of the N-SH2 domain of the Src homology region 2 domain-containing phosphatase-2 (SHP2) protein, a 104 residues domain that presents the classical SH2 domain fold (two α-helices flanking a central β-sheet composed of 3-5 antiparallel β-strands), with a fundamental role in mediating the interaction of SHP2 with its substrates and triggering key metabolic pathways in the cell. By analysing folding kinetic data we demonstrated that the folding pathway of N-SH2 presents an obligatory on-pathway intermediate that accumulates during the folding reaction. The production of 24 conservative site-directed variants allowed us to perform a Φ value analysis, by which we could fully characterize the intermediate and the transition state native-like interactions, providing a detailed quantitative analysis of the folding pathway of N-SH2. Results highlight the presence of a hydrophobic nucleus that stabilizes the intermediate, leading to a higher degree of native-like interactions in the transition state. Data are discussed and compared with previous works on SH2 domains.

A structurally heterogeneous transition state underlies coupled binding and folding of disordered proteins

Many intrinsically disordered proteins (IDPs) attain a well-defined structure in a coupled folding and binding reaction with another protein. Such reactions may involve early to late formation of different native structural regions along the reaction pathway. To obtain insights into the transition state for a coupled binding and folding reaction, we performed restrained molecular dynamics simulations using previously determined experimental binding Φ_b values of the interaction between two IDP domains: the activation domain from the p160 transcriptional co-activator for thyroid hormone and retinoid receptors (ACTR) and the nuclear co-activator binding domain (NCBD) of CREB-binding protein, each forming three well-defined α-helices upon binding. These simulations revealed that both proteins are largely disordered in the transition state for complex formation, except for two helices, one from each domain, that display a native-like structure. The overall transition state structure was extended and largely dynamic with many weakly populated contacts. To test the transition state model, we combined site-directed mutagenesis with kinetic experiments, yielding results consistent with overall diffuse interactions and formation of native intramolecular interactions in the third NCBD helix during the binding reaction. Our findings support the view that the transition state and, by inference, any encounter complex in coupled binding and folding reactions are structurally heterogeneous and largely independent of specific interactions. Furthermore, experimental Φ_b values and Brønsted plots suggested that the transition state is globally robust with respect to most mutations but can display more native-like features for some highly destabilizing mutations, possibly because of Hammond behavior or ground-state effects.

Correlating topology and thermodynamics to predict protein structure sensitivity to point mutations

The relation between distribution of hydrophobic amino acids along with protein chains and their structure is far from being completely understood. No reliable method allowsab initioprediction of the folded structure from this distribution of physicochemical properties, even when they are highly degenerated by considering only two classes: hydrophobic and polar. Establishment of long-range hydrophobic three dimension (3D) contacts is essential for the formation of the nucleus, a key process in the early steps of protein folding. Thus, a large number of 3D simulation studies were developed to challenge this issue. They are nowadays evaluated in a specific chapter of the molecular modeling competition, Critical Assessment of Protein Structure Prediction. We present here a simulation of the early steps of the folding process for 850 proteins, performed in a discrete 3D space, which results in peaks in the predicted distribution of intra-chain noncovalent contacts. The residues located at these peak positions tend to be buried in the core of the protein and are expected to correspond to critical positions in the sequence, important both for folding and structural (or similarly, energetic in the thermodynamic hypothesis) stability. The degree of stabilization or destabilization due to a point mutation at the critical positions involved in numerous contacts is estimated from the calculated folding free energy difference between mutated and native structures. The results show that these critical positions are not tolerant towards mutation. This simulation of the noncovalent contacts only needs a sequence as input, and this paper proposes a validation of the method by comparison with the prediction of stability by well-established programs.

Accurate Protein-Folding Transition-Path Statistics from a Simple Free-Energy Landscape

A central goal of protein-folding theory is to predict the stochastic dynamics of transition paths-the rare trajectories that transit between the folded and unfolded ensembles-using only thermodynamic information, such as a low-dimensional equilibrium free-energy landscape. However, commonly used one-dimensional landscapes typically fall short of this aim, because an empirical coordinate-dependent diffusion coefficient has to be fit to transition-path trajectory data in order to reproduce the transition-path dynamics. We show that an alternative, first-principles free-energy landscape predicts transition-path statistics that agree well with simulations and single-molecule experiments without requiring dynamical data as an input. This "topological configuration" model assumes that distinct, native-like substructures assemble on a time scale that is slower than native-contact formation but faster than the folding of the entire protein. Using only equilibrium simulation data to determine the free energies of these coarse-grained intermediate states, we predict a broad distribution of transition-path transit times that agrees well with the transition-path durations observed in simulations. We further show that both the distribution of finite-time displacements on a one-dimensional order parameter and the ensemble of transition-path trajectories generated by the model are consistent with the simulated transition paths. These results indicate that a landscape based on transient folding intermediates, which are often hidden by one-dimensional projections, can form the basis of a predictive model of protein-folding transition-path dynamics.

A method for partitioning the information contained in a protein sequence between its structure and function

Proteins employ the information stored in the genetic code and translated into their sequences to carry out well-defined functions in the cellular environment. The possibility to encode for such functions is controlled by the balance between the amount of information supplied by the sequence and that left after that the protein has folded into its structure. We study the amount of information necessary to specify the protein structure, providing an estimate that keeps into account the thermodynamic properties of protein folding. We thus show that the information remaining in the protein sequence after encoding for its structure (the 'information gap') is very close to what needed to encode for its function and interactions. Then, by predicting the information gap directly from the protein sequence, we show that it may be possible to use these insights from information theory to discriminate between ordered and disordered proteins, to identify unknown functions, and to optimize artificially-designed protein sequences.

The Role of Evolutionary Selection in the Dynamics of Protein Structure Evolution

Homology modeling is a powerful tool for predicting a protein's structure. This approach is successful because proteins whose sequences are only 30% identical still adopt the same structure, while structure similarity rapidly deteriorates beyond the 30% threshold. By studying the divergence of protein structure as sequence evolves in real proteins and in evolutionary simulations, we show that this nonlinear sequence-structure relationship emerges as a result of selection for protein folding stability in divergent evolution. Fitness constraints prevent the emergence of unstable protein evolutionary intermediates, thereby enforcing evolutionary paths that preserve protein structure despite broad sequence divergence. However, on longer timescales, evolution is punctuated by rare events where the fitness barriers obstructing structure evolution are overcome and discovery of new structures occurs. We outline biophysical and evolutionary rationale for broad variation in protein family sizes, prevalence of compact structures among ancient proteins, and more rapid structure evolution of proteins with lower packing density.

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.

Fold and flexibility: what can proteins' mechanical properties tell us about their folding nucleus?

The determination of a protein's folding nucleus, i.e. a set of native contacts playing an important role during its folding process, remains an elusive yet essential problem in biochemistry. In this work, we investigate the mechanical properties of 70 protein structures belonging to 14 protein families presenting various folds using coarse-grain Brownian dynamics simulations. The resulting rigidity profiles combined with multiple sequence alignments show that a limited set of rigid residues, which we call the consensus nucleus, occupy conserved positions along the protein sequence. These residues' side chains form a tight interaction network within the protein's core, thus making our consensus nuclei potential folding nuclei. A review of experimental and theoretical literature shows that most (above 80%) of these residues were indeed identified as folding nucleus member in earlier studies.

Controlling Allosteric Networks in Proteins

Allosteric transition, defined as conformational changes induced by ligand binding, is one of the fundamental properties of proteins. Allostery has been observed and characterized in many proteins, and has been recently utilized to control protein function via regulation of protein activity. Here, we review the physical and evolutionary origin of protein allostery, as well as its importance to protein regulation, drug discovery, and biological processes in living systems. We describe recently developed approaches to identify allosteric pathways, connected sets of pairwise interactions that are responsible for propagation of conformational change from the ligand-binding site to a distal functional site. We then present experimental and computational protein engineering approaches for control of protein function by modulation of allosteric sites. As an example of application of these approaches, we describe a synergistic computational and experimental approach to rescue the cystic-fibrosis-associated protein cystic fibrosis transmembrane conductance regulator, which upon deletion of a single residue misfolds and causes disease. This example demonstrates the power of allosteric manipulation in proteins to both elucidate mechanisms of molecular function and to develop therapeutic strategies that rescue those functions. Allosteric control of proteins provides a tool to shine a light on the complex cascades of cellular processes and facilitate unprecedented interrogation of biological systems.

Effects of heme binding on myoglobin folding: Coarse grained molecular simulations

Many proteins contain cofactors, such as heme, ATP and metal ions. Binding of cofactors is not only essential for their biological functions, but also can reshape the intrinsic energy landscape of protein molecules and modulate the folding and stability. However, the molecular mechanism of cofactor coupled protein folding is not well understood. In this work, we study the cofactor coupled folding of myoglobin, which is a typical cofactor (heme) containing protein, by performing molecular dynamics simulations with a structure-based protein model developed based on the energy landscape theory. We showed that the heme binding increases the stability of the myoglobin. More importantly, the heme binding tends to increase the protein folding cooperativity, and switch the folding process from a “three-state” mechanism to a “two-state” mechanism. We also showed that the folding pathways of the myoglobin can be modulated by the heme binding. By performing comparative simulations, we revealed that the above effects of heme binding are resulted from the heme induced folding of F-helix, which is otherwise unstructured at apo state, and the heme mediated contacting interactions around the heme binding site. The simulation results are consistent with available experimental data, and provide insights into the molecular mechanism of the effects of cofactor binding on the protein folding and stability.

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.

Analysis of core-periphery organization in protein contact networks reveals groups of structurally and functionally critical residues

The representation of proteins as networks of interacting amino acids, referred to as protein contact networks (PCN), and their subsequent analyses using graph theoretic tools, can provide novel insights into the key functional roles of specific groups of residues. We have characterized the networks corresponding to the native states of 66 proteins (belonging to different families) in terms of their core-periphery organization. The resulting hierarchical classification of the amino acid constituents of a protein arranges the residues into successive layers - having higher core order - with increasing connection density, ranging from a sparsely linked periphery to a densely intra-connected core (distinct from the earlier concept of protein core defined in terms of the three-dimensional geometry of the native state, which has least solvent accessibility). Our results show that residues in the inner cores are more conserved than those at the periphery. Underlining the functional importance of the network core, we see that the receptor sites for known ligand molecules of most proteins occur in the innermost core. Furthermore, the association of residues with structural pockets and cavities in binding or active sites increases with the core order. From mutation sensitivity analysis, we show that the probability of deleterious or intolerant mutations also increases with the core order. We also show that stabilization centre residues are in the innermost cores, suggesting that the network core is critically important in maintaining the structural stability of the protein. A publicly available Web resource for performing core-periphery analysis of any protein whose native state is known has been made available by us at http://www.imsc.res.in/ ~sitabhra/proteinKcore/index.html.

Layers: A molecular surface peeling algorithm and its applications to analyze protein structures

We present an algorithm 'Layers' to peel the atoms of proteins as layers. Using Layers we show an efficient way to transform protein structures into 2D pattern, named residue transition pattern (RTP), which is independent of molecular orientations. RTP explains the folding patterns of proteins and hence identification of similarity between proteins is simple and reliable using RTP than with the standard sequence or structure based methods. Moreover, Layers generates a fine-tunable coarse model for the molecular surface by using non-random sampling. The coarse model can be used for shape comparison, protein recognition and ligand design. Additionally, Layers can be used to develop biased initial configuration of molecules for protein folding simulations. We have developed a random forest classifier to predict the RTP of a given polypeptide sequence. Layers is a standalone application; however, it can be merged with other applications to reduce the computational load when working with large datasets of protein structures. Layers is available freely at http://www.csb.iitkgp.ernet.in/applications/mol_layers/main.

Reduction of the Search Space for the Folding of Proteins at the Level of Formation and Assembly of Secondary Structures: A New View on the Solution of Levinthal's Paradox

The complete volume of the protein conformation space is, by many orders of magnitude, smaller at the level of secondary structure elements than that at the level of amino acid residues; the latter, according to Levinthal's estimate, scales approximately as 10(2 L), with L being the number of residues in the chain, whereas the former, as demonstrated in this paper, scales no faster than ∼L(N), with N being the number of the secondary structure elements, which is approximately equal to L/15. This drastic decrease in the exponent (L/15 instead of 2 L) explains why sampling of the conformation space does not contradict the ability of the protein chain to find its most stable fold.

Knotted proteins: A tangled tale of Structural Biology

Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.

Biophysics of protein evolution and evolutionary protein biophysics

The study of molecular evolution at the level of protein-coding genes often entails comparing large datasets of sequences to infer their evolutionary relationships. Despite the importance of a protein's structure and conformational dynamics to its function and thus its fitness, common phylogenetic methods embody minimal biophysical knowledge of proteins. To underscore the biophysical constraints on natural selection, we survey effects of protein mutations, highlighting the physical basis for marginal stability of natural globular proteins and how requirement for kinetic stability and avoidance of misfolding and misinteractions might have affected protein evolution. The biophysical underpinnings of these effects have been addressed by models with an explicit coarse-grained spatial representation of the polypeptide chain. Sequence-structure mappings based on such models are powerful conceptual tools that rationalize mutational robustness, evolvability, epistasis, promiscuous function performed by 'hidden' conformational states, resolution of adaptive conflicts and conformational switches in the evolution from one protein fold to another. Recently, protein biophysics has been applied to derive more accurate evolutionary accounts of sequence data. Methods have also been developed to exploit sequence-based evolutionary information to predict biophysical behaviours of proteins. The success of these approaches demonstrates a deep synergy between the fields of protein biophysics and protein evolution.