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

Differential Effects of Sequence-Local versus Nonlocal Charge Patterns on Phase Separation and Conformational Dimensions of Polyampholytes as Model Intrinsically Disordered Proteins

Conformational properties of intrinsically disordered proteins (IDPs) are governed by a sequence-ensemble relationship. To differentiate the impact of sequence-local versus sequence-nonlocal features of an IDP's charge pattern on its conformational dimensions and its phase-separation propensity, the charge "blockiness" κ and the nonlocality-weighted sequence charge decoration (SCD) parameters are compared for their correlations with isolated-chain radii of gyration (Rgs) and upper critical solution temperatures (UCSTs) of polyampholytes modeled by random phase approximation, field-theoretic simulation, and coarse-grained molecular dynamics. SCD is superior to κ in predicting Rg because SCD accounts for effects of contact order, i.e., nonlocality, on dimensions of isolated chains. In contrast, κ and SCD are comparably good, though nonideal, predictors of UCST because frequencies of interchain contacts in the multiple-chain condensed phase are less sensitive to sequence positions than frequencies of intrachain contacts of an isolated chain, as reflected by κ correlating better with condensed-phase interaction energy than SCD.

Hallmarks and evolutionary drivers of cotranslational protein complex assembly

Recent discoveries have highlighted the prevalence of cotranslational assembly in proteomes, revealing a range of mechanisms that enables the assembly of protein complex subunits on the ribosome. Structural analyses have uncovered emergent properties that may inherently control whether a subunit undergoes cotranslational assembly. However, the evolutionary paths that have yielded such complexes over an extended timescale remain largely unclear. In this review, we reflect on historical experiments that contributed to the field, including breakthroughs that have made possible the proteome-wide detection of cotranslational assembly, and the technical challenges yet to be overcome. We introduce a simple framework that encapsulates the hallmarks of cotranslational assembly and discuss how results from new experiments are shaping our view of the mechanistic, structural and evolutionary factors driving the phenomenon.

Protein engineering using circular permutation - structure, function, stability, and applications

Protein engineering is important for creating novel variants from natural proteins, enabling a wide range of applications. Approaches such as rational design and directed evolution are routinely used to make new protein variants. Computational tools like de novo design can introduce new protein folds. Expanding the amino acid repertoire to include unnatural amino acids with non-canonical side chains in vitro by native chemical ligation and in vivo via codon expansion methods broadens sequence and structural possibilities. Circular permutation (CP) is an invaluable approach to redesigning a protein by rearranging the amino acid sequence, where the connectivity of the secondary structural elements is altered without changing the overall structure of the protein. Artificial CP proteins (CPs) are employed in various applications such as biocatalysis, sensing of small molecules by fluorescence, genome editing, ligand-binding protein switches, and optogenetic engineering. Many studies have shown that CP can lead to either reduced or enhanced stability or catalytic efficiency. The effects of CP on a protein's energy landscape cannot be predicted a priori. Thus, it is important to understand how CP can affect the thermodynamic and kinetic stability of a protein. In this review, we discuss the discovery and advancement of techniques to create protein CP, and existing reviews on CP. We delve into the plethora of biological applications for designed CP proteins. We subsequently discuss the experimental and computational reports on the effects of CP on the thermodynamic and kinetic stabilities of proteins of various topologies. An understanding of the various aspects of CP will allow the reader to design robust CP proteins for their specific purposes.

Binding and sensing diverse small molecules using shape-complementary pseudocycles

We describe an approach for designing high-affinity small molecule-binding proteins poised for downstream sensing. We use deep learning-generated pseudocycles with repeating structural units surrounding central binding pockets with widely varying shapes that depend on the geometry and number of the repeat units. We dock small molecules of interest into the most shape complementary of these pseudocycles, design the interaction surfaces for high binding affinity, and experimentally screen to identify designs with the highest affinity. We obtain binders to four diverse molecules, including the polar and flexible methotrexate and thyroxine. Taking advantage of the modular repeat structure and central binding pockets, we construct chemically induced dimerization systems and low-noise nanopore sensors by splitting designs into domains that reassemble upon ligand addition.

Deciphering Structural Traits for Thermal and Kinetic Stability across Protein Family Evolution through Ancestral Sequence Reconstruction

Natural proteins are frequently marginally stable, and an increase in environmental temperature can easily lead to unfolding. As a result, protein engineering to improve protein stability is an area of intensive research. Nonetheless, since there is usually a high degree of structural homology between proteins from thermophilic organisms and their mesophilic counterparts, the identification of structural determinants for thermoadaptation is challenging. Moreover, in many cases, it has become clear that the success of stabilization strategies is often dependent on the evolutionary history of a protein family. In the last few years, the use of ancestral sequence reconstruction (ASR) as a tool for elucidation of the evolutionary history of functional traits of a protein family has gained strength. Here, we used ASR to trace the evolutionary pathways between mesophilic and thermophilic kinases that participate in the biosynthetic pathway of vitamin B1 in bacteria. By combining biophysics approaches, X-ray crystallography, and molecular dynamics simulations, we found that the thermal stability of these enzymes correlates with their kinetic stability, where the highest thermal/kinetic stability is given by an increase in small hydrophobic amino acids that allow a higher number of interatomic hydrophobic contacts, making this type of interaction the main support for stability in this protein architecture. The results highlight the potential benefits of using ASR to explore the evolutionary history of protein sequence and structure to identify traits responsible for the kinetic and thermal stability of any protein architecture.

Targeting the protein folding transition state by mutation: Large scale (un)folding rate accelerations without altering native stability

Proteins are constantly undergoing folding and unfolding transitions, with rates that determine their homeostasis in vivo and modulate their biological function. The ability to optimize these rates without affecting overall native stability is hence highly desirable for protein engineering and design. The great challenge is, however, that mutations generally affect folding and unfolding rates with inversely complementary fractions of the net free energy change they inflict on the native state. Here we address this challenge by targeting the folding transition state (FTS) of chymotrypsin inhibitor 2 (CI2), a very slow and stable two-state folding protein with an FTS known to be refractory to change by mutation. We first discovered that the CI2's FTS is energetically taxed by the desolvation of several, highly conserved, charges that form a buried salt bridge network in the native structure. Based on these findings, we designed a CI2 variant that bears just four mutations and aims to selectively stabilize the FTS. This variant has >250-fold faster rates in both directions and hence identical native stability, demonstrating the success of our FTS-centric design strategy. With an optimized FTS, CI2 also becomes 250-fold more sensitive to proteolytic degradation by its natural substrate chymotrypsin, and completely loses its activity as inhibitor. These results indicate that CI2 has been selected through evolution to have a very unstable FTS in order to attain the kinetic stability needed to effectively function as protease inhibitor. Moreover, the CI2 case showcases that protein (un)folding rates can critically pivot around a few key residues-interactions, which can strongly modify the general effects of known structural factors such as domain size and fold topology. From a practical standpoint, our results suggest that future efforts should perhaps focus on identifying such critical residues-interactions in proteins as best strategy to significantly improve our ability to predict and engineer protein (un)folding rates.

Genetic heterogeneity and respiratory chain enzyme analysis in pediatric Indian patients with mitochondrial disorder: Report of novel variants in POLG1 gene and their functional implication using molecular dynamic simulation

Mitochondrial disorders are a heterogeneous group of disorders caused by mutations in the mitochondrial DNA or in nuclear genes encoding the mitochondrial proteins and subunits. Polymerase Gamma (POLG) is a nuclear gene and mutation in the POLG gene are one of the major causes of inherited mitochondrial disorders. In this study, 15 pediatric patients, with a wide spectrum of clinical phenotypes were screened using blood samples (n = 15) and muscle samples (n = 4). Respiratory chain enzyme analysis in the muscle samples revealed multi-complex deficiencies with Complex I deficiency present in (1/4) patients, Complex II (2/4), Complex III (3/4) and Complex IV (2/4) patients. Multiple large deletions were observed in 4/15 patients using LR-PCR. Whole exome sequencing (WES) revealed a compound heterozygous mutation consisting of a POLG1 novel variant (NP_002684.1:p.Trp261X) and a missense variant (NP_002684.1:p. Leu304Arg) in one patient and another patient harboring a novel homozygous POLG1 variant (NP_002684.1:p. Phe750Val). These variants (NP_002684.1:p. Leu304Arg) and (NP_002684.1:p. Phe750Val) and their interactions with DNA were modelled using molecular docking and molecular dynamics (MD) simulation studies. The protein conformation was analyzed as root mean square deviation (RMSD), root mean square fluctuation (RMSF) which showed local fluctuations in the mutants compared to the wildtype. However, Solvent Accessible Surface Area (SASA) significantly increased for NP_002684.1:p.Leu304Arg and decreased in NP_002684.1:p.Phe750Val mutants. Further, Contact Order analysis indicated that the Aromatic-sulfur interactions were destabilizing in the mutants. Overall, these in-silico analysis has revealed a destabilizing mutations suggesting pathogenic variants in POLG1 gene.

Biophysical characterization of the CXC chemokine receptor 2 ligands

The chemokines of the immune system act as first responders by operating as chemoattractants, directing immune cells to specific locations of inflamed tissues. This promiscuous network is comprised of 50 ligands and 18 receptors where the ligands may interact with the receptors in various oligomeric states i.e., monomers, homodimers, and heterodimers. Chemokine receptors are G-protein coupled receptors (GPCRs) present in the membrane of immune cells. The migration of immune cells occurs in response to a concentration gradient of the ligands. Chemotaxis of neutrophils is directed by CXC-ligand (CXCL) activation of the membrane bound CXC chemokine receptor 2 (CXCR2). CXCR2 plays an important role in human health and is linked to disorders such as autoimmune disorders, inflammation, and cancer. Yet, despite their important role, little is known about the biophysical characteristics controlling ligand:ligand and ligand:receptor interaction essential for biological activity. In this work, we study the homodimers of three of the CXCR2 cognate ligands, CXCL1, CXCL5, and CXCL8. The ligands share high structural integrity but a low sequence identity. We show that the sequence diversity has evolved different binding affinities and stabilities for the CXC-ligands resulting in diverse agonist/antagonist behavior. Furthermore, CXC-ligands fold through a three-state mechanism, populating a folded monomeric state before associating into an active dimer.

Importance of Inter-residue Contacts for Understanding Protein Folding and Unfolding Rates, Remote Homology, and Drug Design

Inter-residue interactions in protein structures provide valuable insights into protein folding and stability. Understanding these interactions can be helpful in many crucial applications, including rational design of therapeutic small molecules and biologics, locating functional protein sites, and predicting protein-protein and protein-ligand interactions. The process of developing machine learning models incorporating inter-residue interactions has been improved recently. This review highlights the theoretical models incorporating inter-residue interactions in predicting folding and unfolding rates of proteins. Utilizing contact maps to depict inter-residue interactions aids researchers in developing computer models for detecting remote homologs and interface residues within protein-protein complexes which, in turn, enhances our knowledge of the relationship between sequence and structure of proteins. Further, the application of contact maps derived from inter-residue interactions is highlighted in the field of drug discovery. Overall, this review presents an extensive assessment of the significant models that use inter-residue interactions to investigate folding rates, unfolding rates, remote homology, and drug development, providing potential future advancements in constructing efficient computational models in structural biology.

N-glycosylation as a eukaryotic protective mechanism against protein aggregation

The tendency for proteins to form aggregates is an inherent part of every proteome and arises from the self-assembly of short protein segments called aggregation-prone regions (APRs). While posttranslational modifications (PTMs) have been implicated in modulating protein aggregation, their direct role in APRs remains poorly understood. In this study, we used a combination of proteome-wide computational analyses and biophysical techniques to investigate the potential involvement of PTMs in aggregation regulation. Our findings reveal that while most PTM types are disfavored near APRs, N-glycosylation is enriched and evolutionarily selected, especially in proteins prone to misfolding. Experimentally, we show that N-glycosylation inhibits the aggregation of peptides in vitro through steric hindrance. Moreover, mining existing proteomics data, we find that the loss of N-glycans at the flanks of APRs leads to specific protein aggregation in Neuro2a cells. Our findings indicate that, among its many molecular functions, N-glycosylation directly prevents protein aggregation in higher eukaryotes.

Protein structuromics: A new method for protein structure-function crosstalk in glioma

Glioma is a type of tumor that starts in the glial cells of the brain or spine. Since the 1800s, when the disease was first named, its survival rates have always been unsatisfactory. Despite great advances in molecular biology and traditional treatment methods, many questions regarding cancer occurrence and the underlying mechanism remain to be answered. In this study, we assessed the protein structural features of 20 oncogenes and 20 anti-oncogenes via protein structure and dynamic analysis methods and 3D structural and systematic analyses of the structure-function relationships of proteins. All of these results directly indicate that unfavorable group proteins show more complex structures than favorable group proteins. As the tumor cell microenvironment changes, the balance of oncogene-related and anti-oncogene-related proteins is disrupted, and most of the structures of the two groups of proteins will be disrupted. However, more unfavorable group proteins will maintain and refold to achieve their correct shape faster and perform their functions more quickly than favorable group proteins, and the former thus support cancer development. We hope that these analyses will help promote mechanistic research and the development of new treatments for glioma.

Influence of the Sequence Motive Repeating Number on Protein Folding in Spider Silk Protein Films

Like multiblock copolymers, spider silk proteins are built of repetitive sequence motives. One prominent repetitive motif is based on the consensus sequence of spidroin 4 of the spider Araneus diadematus ADF4. The number x of the repeating sequence motives (C) determines the molecular weight of the recombinant ADF4-based, engineered spider silk protein denoted as eADF4(Cx). eADF4(Cx) can be used as a model for intrinsically disordered proteins (IDP) and to elucidate their folding. Herein, the influence of the variation of the sequence motive repeating number x (x = 1, 2, 4, 8, 16) on the protein folding within eADF4(Cx) films was investigated. eADF4(Cx) films were cast from 1,1,1,3,3,3-hexafluoropropan-2-ol (HFIP) solutions onto planar silicon model substrates, revealing mainly helical or random coil structure. Upon treatment with methanol vapor (ptm), the formation of crystalline β-sheets was triggered. Dichroic Fourier-transform infrared (FTIR) spectroscopy, circular dichroism, spectroscopic ellipsometry, atomic force microscopy, grazing-incidence small-angle X-ray scattering (GISAXS), grazing-incidence wide-angle X-ray scattering (GIWAXS), and electrokinetic and contact angle measurements were used to get information concerning the secondary structure and folding kinetics, orientation of β-sheets, the ratio of parallel/antiparallel β-sheets, domain sizes and distributions, surface topography, surface potential, hydrophobicity and the film integrity under water. Significant differences in the final β-sheet content, the share of antiparallel β-sheet structures, film integrity, surface potential, and isoelectric points between eADF4(Cx) with x = 1, 2 and eADF4(Cx) with x = 4, 8, 16 gave new insights in the molecular weight-dependent structure formation and film properties of IDP systems. GISAXS and kinetic measurements confirmed a relation between β-sheet crystal growth rate and final β-sheet crystal size. Further, competing effects of reduced diffusibility hindering accelerated crystal growth and enhanced backfolding promoting accelerated crystal growth with increasing molecular weight were discussed.

Folding and functions of knotted proteins

Topologically knotted proteins have entangled structural elements within their native structures that cannot be disentangled simply by pulling from the N- and C-termini. Systematic surveys have identified different types of knotted protein structures, constituting as much as 1% of the total entries within the Protein Data Bank. Many knotted proteins rely on their knotted structural elements to carry out evolutionarily conserved biological functions. Being knotted may also provide mechanical stability to withstand unfolding-coupled proteolysis. Reconfiguring a knotted protein topology by circular permutation or cyclization provides insights into the importance of being knotted in the context of folding and functions. With the explosion of predicted protein structures by artificial intelligence, we are now entering a new era of exploring the entangled protein universe.

Circular permutation at azurin's active site slows down its folding

Circular permutation (CP) is a technique by which the primary sequence of a protein is rearranged to create new termini. The connectivity of the protein is altered but the overall protein structure generally remains unperturbed. Understanding the effect of CP can help design robust proteins for numerous applications such as in genetic engineering, optoelectronics, and improving catalytic activity. Studies on different protein topologies showed that CP usually affects protein stability as well as unfolding rates. Though a significant number of proteins contain metals or other cofactors, reports of metalloprotein CPs are rare. Thus, we chose a bacterial metalloprotein, azurin, and its CP within the metal-binding site (cpF114). We studied the stabilities, folding, and unfolding rates of apo- and Zn2+-bound CP azurin using fluorescence and circular dichroism. The introduced CP had destabilizing effects on the protein. Also, the folding of the Zn2+-CP protein was much slower than that of the Zn2+-WT or apo-protein. We compared this study to our previously reported azurin-cpN42, where we had observed an equilibrium and kinetic intermediate. cpF114 exhibits an apparent two-state equilibrium unfolding but has an off-pathway kinetic intermediate. Our study hinted at CP as a method to modify the energy landscape of proteins to alter their folding pathways. WT azurin, being a faster folder, may have evolved to optimize the folding rate of metal-bound protein compared to its CPs, albeit all of them have the same structure and function. Our study underscores that protein sequence and protein termini positions are crucial for metalloproteins. TOC Figure. (Top) Zn2+-azurin WT structure (PDB code: 1E67) and 2-D topology diagram of Zn2+-cpF114 azurin. (Bottom) Cartoon diagram representing folding (red arrows) and unfolding (blue arrows) of apo- and Zn2+- WT and cpF114 azurins. The width of the arrows represents the rate of the corresponding processes.

Assessing protein model quality based on deep graph coupled networks using protein language model

Model quality evaluation is a crucial part of protein structural biology. How to distinguish high-quality models from low-quality models, and to assess which high-quality models have relatively incorrect regions for improvement, are remain a challenge. More importantly, the quality assessment of multimer models is a hot topic for structure prediction. In this study, we propose GraphCPLMQA, a novel approach for evaluating residue-level model quality that combines graph coupled networks and embeddings from protein language models. The GraphCPLMQA consists of a graph encoding module and a transform-based convolutional decoding module. In encoding module, the underlying relational representations of sequence and high-dimensional geometry structure are extracted by protein language models with Evolutionary Scale Modeling. In decoding module, the mapping connection between structure and quality is inferred by the representations and low-dimensional features. Specifically, the triangular location and residue level contact order features are designed to enhance the association between the local structure and the overall topology. Experimental results demonstrate that GraphCPLMQA using single-sequence embedding achieves the best performance compared with the CASP15 residue-level interface evaluation methods among 9108 models in the local residue interface test set of CASP15 multimers. In CAMEO blind test (20 May 2022 to 13 August 2022), GraphCPLMQA ranked first compared with other servers (https://www.cameo3d.org/quality-estimation). GraphCPLMQA also outperforms state-of-the-art methods on 19, 035 models in CASP13 and CASP14 monomer test set.

Domain swap facilitates structural transitions of spider silk protein C-terminal domains

Domain swap is a mechanism of protein dimerization where the two interacting domains exchange parts of their structure. Web spiders make use of the process in the connection of C-terminal domains (CTDs) of spidroins, the soluble protein building blocks that form tough silk fibers. Besides providing connectivity and solubility, spidroin CTDs are responsible for inducing structural transitions during passage through an acidified assembly zone within spinning ducts. The underlying molecular mechanisms are elusive. Here, we studied the folding of five homologous spidroin CTDs from different spider species or glands. Four of these are domain-swapped dimers formed by five-helix bundles from spidroins of major and minor ampullate glands. The fifth is a dimer that lacks domain swap, formed by four-helix bundles from a spidroin of a flagelliform gland. Spidroins from this gland do not undergo structural transitions whereas the others do. We found a three-state mechanism of folding and dimerization that was conserved across homologues. In chemical denaturation experiments the native CTD dimer unfolded to a dimeric, partially structured intermediate, followed by full unfolding to denatured monomers. The energetics of the individual folding steps varied between homologues. Contrary to the common belief that domain swap stabilizes protein assemblies, the non-swapped homologue was most stable and folded four orders of magnitude faster than a swapped variant. Domain swap of spidroin CTDs induces an entropic penalty to the folding of peripheral helices, thus unfastening them for acid-induced unfolding within a spinning duct, which primes them for refolding into alternative structures during silk formation.

Folding kinetics of an entangled protein

The possibility of the protein backbone adopting lasso-like entangled motifs has attracted increasing attention. After discovering the surprising abundance of natively entangled protein domain structures, it was shown that misfolded entangled subpopulations might become thermosensitive or escape the homeostasis network just after translation. To investigate the role of entanglement in shaping folding kinetics, we introduce a novel indicator and analyze simulations of a coarse-grained, structure-based model for two small single-domain proteins. The model recapitulates the well-known two-state folding mechanism of a non-entangled SH3 domain. However, despite its small size, a natively entangled antifreeze RD1 protein displays a rich refolding behavior, populating two distinct kinetic intermediates: a short-lived, entangled, near-unfolded state and a longer-lived, non-entangled, near-native state. The former directs refolding along a fast pathway, whereas the latter is a kinetic trap, consistently with known experimental evidence of two different characteristic times. Upon trapping, the natively entangled loop folds without being threaded by the N-terminal residues. After trapping, the native entangled structure emerges by either backtracking to the unfolded state or threading through the already formed but not yet entangled loop. Along the fast pathway, trapping does not occur because the native contacts at the closure of the lasso-like loop fold after those involved in the N-terminal thread, confirming previous predictions. Despite this, entanglement may appear already in unfolded configurations. Remarkably, a longer-lived, near-native intermediate, with non-native entanglement properties, recalls what was observed in cotranslational folding.

Illuminating protein space with a programmable generative model

Three billion years of evolution has produced a tremendous diversity of protein molecules1, but the full potential of proteins is likely to be much greater. Accessing this potential has been challenging for both computation and experiments because the space of possible protein molecules is much larger than the space of those likely to have functions. Here we introduce Chroma, a generative model for proteins and protein complexes that can directly sample novel protein structures and sequences, and that can be conditioned to steer the generative process towards desired properties and functions. To enable this, we introduce a diffusion process that respects the conformational statistics of polymer ensembles, an efficient neural architecture for molecular systems that enables long-range reasoning with sub-quadratic scaling, layers for efficiently synthesizing three-dimensional structures of proteins from predicted inter-residue geometries and a general low-temperature sampling algorithm for diffusion models. Chroma achieves protein design as Bayesian inference under external constraints, which can involve symmetries, substructure, shape, semantics and even natural-language prompts. The experimental characterization of 310 proteins shows that sampling from Chroma results in proteins that are highly expressed, fold and have favourable biophysical properties. The crystal structures of two designed proteins exhibit atomistic agreement with Chroma samples (a backbone root-mean-square deviation of around 1.0 Å). With this unified approach to protein design, we hope to accelerate the programming of protein matter to benefit human health, materials science and synthetic biology.

Unveiling Metastable Ensembles of GRB2 and the Relevance of Interdomain Communication during Folding

The folding process of multidomain proteins is a highly intricate phenomenon involving the assembly of distinct domains into a functional three-dimensional structure. During this process, each domain may fold independently while interacting with others. The folding of multidomain proteins can be influenced by various factors, including their composition, the structure of each domain, or the presence of disordered regions, as well as the surrounding environment. Misfolding of multidomain proteins can lead to the formation of nonfunctional structures associated with a range of diseases, including cancers or neurodegenerative disorders. Understanding this process is an important step for many biophysical analyses such as stability, interaction, malfunctioning, and rational drug design. One such multidomain protein is growth factor receptor-bound protein 2 (GRB2), an adaptor protein that is essential in regulating cell survival. GRB2 consists of one central Src homology 2 (SH2) domain flanked by two Src homology 3 (SH3) domains. The SH2 domain interacts with phosphotyrosine regions in other proteins, while the SH3 domains recognize proline-rich regions on protein partners during cell signaling. Here, we combined computational and experimental techniques to investigate the folding process of GRB2. Through computational simulations, we sampled the conformational space and mapped the mechanisms involved by the free energy profiles, which may indicate possible intermediate states. From the molecular dynamics trajectories, we used the energy landscape visualization method (ELViM), which allowed us to visualize a three-dimensional (3D) representation of the overall energy surface. We identified two possible parallel folding routes that cannot be seen in a one-dimensional analysis, with one occurring more frequently during folding. Supporting these results, we used differential scanning calorimetry (DSC) and fluorescence spectroscopy techniques to confirm these intermediate states in vitro. Finally, we analyzed the deletion of domains to compare our model outputs to previously published results, supporting the presence of interdomain modulation. Overall, our study highlights the significance of interdomain communication within the GRB2 protein and its impact on the formation, stability, and structural plasticity of the protein, which are crucial for its interaction with other proteins in key signaling pathways.

Appraisal of blob-Based Approaches in the Prediction of Protein Folding Times

A series of reports published in the last 3 years has illustrated that a blob-based model (BBM) can predict the folding time of proteins from their primary amino acid (aa) sequence based on three simple rules established to characterize the long-range backbone dynamics (LRBD) of racemic polypeptides. The sole use of LRBD to predict protein folding times with the BBM represents a radical departure from all other prediction methods currently applied to determine protein folding times, which rely instead on parameters such as the structure content, folding kinetics, chain length, amino acid properties, or contact topography of proteins. Furthermore, the built-in modularity of the BBM enables the parametrization and inclusion of new phenomena affecting the LRBD of polypeptides, while its conceptual simplicity makes it an interesting new mathematical tool for studying protein folding. However, its novelty implies that its relationship with many other methods used to predict protein folding times has not been well researched. Consequently, the purpose of this report is to uncover the physical phenomena encountered during protein folding that are best described by the BBM through the identification of parameters that have been recognized over the years as being strong predictors for protein folding, such as protein size, topology, structural class, and folding kinetics. This was accomplished by determining the parameters most strongly correlated with the folding times predicted by the BBM. While the BBM in its present form appears to be a good indicator of the folding times of the vast majority of the 195 proteins considered so far, this report finds that it excels for moderately large proteins that are primarily composed of locally formed structural motifs such as α-helices or for proteins that fold in multiple steps. Altogether, these observations based on the use of the BBM support the notion that proteins fold the way they do because the LRBD of polypeptides is mostly driven by the local interactions experienced between aa's within reach of one another.

K-Pro: Kinetics Data on Proteins and Mutants

The study of protein folding plays a crucial role in improving our understanding of protein function and of the relationship between genetics and phenotypes. In particular, understanding the thermodynamics and kinetics of the folding process is important for uncovering the mechanisms behind human disorders caused by protein misfolding. To address this issue, it is essential to collect and curate experimental kinetic and thermodynamic data on protein folding. K-Pro is a new database designed for collecting and storing experimental kinetic data on monomeric proteins, with a two-state folding mechanism. With 1,529 records from 62 proteins corresponding to 65 structures, K-Pro contains various kinetic parameters such as the logarithm of the folding and unfolding rates, Tanford's β and the ϕ values. When available, the database also includes thermodynamic parameters associated with the kinetic data. K-Pro features a user-friendly interface that allows browsing and downloading kinetic data of interest. The graphical interface provides a visual representation of the protein and mutants, and it is cross-linked to key databases such as PDB, UniProt, and PubMed. K-Pro is open and freely accessible through https://folding.biofold.org/k-pro and supports the latest versions of popular browsers.

TMH Stab-pred: Predicting the stability of α-helical membrane proteins using sequence and structural features

The folding and stability of transmembrane proteins (TMPs) are governed by the insertion of secondary structural elements into the cell membrane followed by their assembly. Understanding the important features that dictate the stability of TMPs is important for elucidating their functions. In this work, we related sequence and structure-based parameters with free energy (ΔG0) of α-helical membrane proteins. Our results showed that the free energy transfer of hydrophobic peptides, relative contact order, total interaction energy, number of hydrogen bonds and lipid accessibility of transmembrane regions are important for stability. Further, we have developed multiple-regression models to predict the stability of α-helical membrane proteins using these features and our method can predict the stability with a correlation and mean absolute error (MAE) of 0.89 and 1.21 kcal/mol, respectively, on jack-knife test. The method was validated with a blind test set of three recently reported experimental ΔG0, which could predict the stability within an average MAE of 0.51 kcal/mol. Further, we developed a webserver for predicting the stability and it is freely available at (https://web.iitm.ac.in/bioinfo2/TMHS/). The importance of selected parameters and limitations are discussed.

Structure and mechanism of a neuropeptide-activated channel in the ENaC/DEG superfamily

Phe-Met-Arg-Phe-amide (FMRFamide)-activated sodium channels (FaNaCs) are a family of channels activated by the neuropeptide FMRFamide, and, to date, the underlying ligand gating mechanism remains unknown. Here we present the high-resolution cryo-electron microscopy structures of Aplysia californica FaNaC in both apo and FMRFamide-bound states. AcFaNaC forms a chalice-shaped trimer and possesses several notable features, including two FaNaC-specific insertion regions, a distinct finger domain and non-domain-swapped transmembrane helix 2 in the transmembrane domain (TMD). One FMRFamide binds to each subunit in a cleft located in the top-most region of the extracellular domain, with participation of residues from the neighboring subunit. Bound FMRFamide adopts an extended conformation. FMRFamide binds tightly to A. californica FaNaC in an N terminus-in manner, which causes collapse of the binding cleft and induces large local conformational rearrangements. Such conformational changes are propagated downward toward the TMD via the palm domain, possibly resulting in outward movement of the TMD and dilation of the ion conduction pore.

Single-chain dimers from de novo immunoglobulins as robust scaffolds for multiple binding loops

Antibody derivatives have sought to recapitulate the antigen binding properties of antibodies, but with improved biophysical attributes convenient for therapeutic, diagnostic and research applications. However, their success has been limited by the naturally occurring structure of the immunoglobulin dimer displaying hypervariable binding loops, which is hard to modify by traditional engineering approaches. Here, we devise geometrical principles for de novo designing single-chain immunoglobulin dimers, as a tunable two-domain architecture that optimizes biophysical properties through more favorable dimer interfaces. Guided by these principles, we computationally designed protein scaffolds that were hyperstable, structurally accurate and robust for accommodating multiple functional loops, both individually and in combination, as confirmed through biochemical assays and X-ray crystallography. We showcase the modularity of this architecture by deep-learning-based diversification, opening up the possibility for tailoring the number, positioning, and relative orientation of ligand-binding loops targeting one or two distal epitopes. Our results provide a route to custom-design robust protein scaffolds for harboring multiple functional loops.

Pathfinder: Protein folding pathway prediction based on conformational sampling

The study of protein folding mechanism is a challenge in molecular biology, which is of great significance for revealing the movement rules of biological macromolecules, understanding the pathogenic mechanism of folding diseases, and designing protein engineering materials. Based on the hypothesis that the conformational sampling trajectory contain the information of folding pathway, we propose a protein folding pathway prediction algorithm named Pathfinder. Firstly, Pathfinder performs large-scale sampling of the conformational space and clusters the decoys obtained in the sampling. The heterogeneous conformations obtained by clustering are named seed states. Then, a resampling algorithm that is not constrained by the local energy basin is designed to obtain the transition probabilities of seed states. Finally, protein folding pathways are inferred from the maximum transition probabilities of seed states. The proposed Pathfinder is tested on our developed test set (34 proteins). For 11 widely studied proteins, we correctly predicted their folding pathways and specifically analyzed 5 of them. For 13 proteins, we predicted their folding pathways to be further verified by biological experiments. For 6 proteins, we analyzed the reasons for the low prediction accuracy. For the other 4 proteins without biological experiment results, potential folding pathways were predicted to provide new insights into protein folding mechanism. The results reveal that structural analogs may have different folding pathways to express different biological functions, homologous proteins may contain common folding pathways, and α-helices may be more prone to early protein folding than β-strands.

Three-helix bundle and SH3-type barrels: autonomously stable structural motifs in small and large proteins

In this study, we investigated two variants of a three-helix bundle and SH3-type barrel, compact in space, present in small and large proteins of various living organisms. Using a neural graph network, proteins with three-helix bundle (n = 1377) and SH3-type barrels (n = 1914) spatial folds were selected. Molecular experiments were performed for small proteins with these folds, and motifs were studied autonomously outside the protein environment at 300, 340, and 370 K. A comparative analysis of the main parameters of the structures in the course of the experiment was performed, including gyration radius, area accessible to the solvent, number of hydrophobic and hydrogen bonds, and root-mean-square deviation of atomic positions (RMSD). We exhibited an autonomous stability of the studied folds outside the protein environment in an aquatic medium. We aimed to demonstrate the possibility of analyzing three-helix bundle and SH3-type barrels autonomously outside the protein globule, thereby reducing the computational time and increasing performance without significant loss of information.Communicated by Ramaswamy H. Sarma.

De Novo Design of a β-Helix Tau Protein Scaffold: An Oligomer-Selective Vaccine Immunogen Candidate for Alzheimer's Disease

Tau pathology is associated with many neurodegenerative disorders, including Alzheimer's disease (AD), where the spatio-temporal pattern of tau neurofibrillary tangles strongly correlates with disease progression, which motivates therapeutics selective for misfolded tau. Here, we introduce a new avidity-enhanced, multi-epitope approach for protein-misfolding immunogen design, which is predicted to mimic the conformational state of an exposed epitope in toxic tau oligomers. A predicted oligomer-selective tau epitope 343KLDFK347 was scaffolded by designing a β-helix structure that incorporated multiple instances of the 16-residue tau fragment 339VKSEKLDFKDRVQSKI354. Large-scale conformational ensemble analyses involving Jensen-Shannon Divergence and the embedding depth D showed that the multi-epitope scaffolding approach, employed in designing the β-helix scaffold, was predicted to better discriminate toxic tau oligomers than other "monovalent" strategies utilizing a single instance of an epitope for vaccine immunogen design. Using Rosetta, 10,000 sequences were designed and screened for the linker portions of the β-helix scaffold, along with a C-terminal stabilizing α-helix that interacts with the linkers, to optimize the folded structure and stability of the scaffold. Structures were ranked by energy, and the lowest 1% (82 unique sequences) were verified using AlphaFold. Several selection criteria involving AlphaFold are implemented to obtain a lead-designed sequence. The structure was further predicted to have free energetic stability by using Hamiltonian replica exchange molecular dynamics (MD) simulations. The synthesized β-helix scaffold showed direct binding in surface plasmon resonance (SPR) experiments to several antibodies that were raised to the structured epitope using a designed cyclic peptide. Moreover, the strength of binding of these antibodies to in vitro tau oligomers correlated with the strength of binding to the β-helix construct, suggesting that the construct presents an oligomer-like conformation and may thus constitute an effective oligomer-selective immunogen.

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.

An in-silico study to understand the effect of lineage diversity on cold shock response: unveiling protein-RNA interactions among paralogous CSPs of E. coli

Cold shock proteins (CSPs) are small, cytoplasmic, ubiquitous and acidic proteins. They have a single nucleic acid-binding domain and pose as "RNA chaperones" by binding to ssRNA in a low sequence specificity and cooperative manner. They are found in a family of nine homologous CSPs in E. coli. CspA, CspB, CspG and CspI are immensely cold inducible, CspE and CspC are consistently released at usual physiological temperatures and CspD is also induced under nutrient stress. The paralogous protein pairs CSPA/CSPB, CSPC/CSPE, CSPG/CSPI and CSPF/CSPH were first identified. The eight proteins were subjected to molecular modelling and simulation to obtain the most stable conformation in correspondence to their equilibrated RMSD and RMSF graph. The results were compared and it was observed that CSPB, CSPE, CSPF and CSPI were more stable than their paralogous partner conforming to their near equilibrated RMSD curve and low fluctuating RMSF graph. The paralogous proteins were docked with ssRNA and simultaneously binding affinity, interaction types, electrostatic surface potential, hydrophobicity, conformational analysis and SASA were calculated to minutely study and understand the molecular mechanism initiated by these proteins. It was found that CSPB, CSPC, CSPH and CSPI displayed higher affinity towards ssRNA than their paralogous partner. The results further corroborated with ΔGmmgbsa and ΔGfold energy. Between the paralogous pairs CSPC, CSPH and CSPI exhibited higher binding free energy than their partner. Further, CSPB, CSPC and CSPI exhibited higher folding free energy than their paralogous pair. CSPH exhibited highest ΔGmmgbsa of - 522.2 kcal/mol and lowest was displayed by CSPG of around - 309.3 kcal/mol. Highest number of mutations were recognised in CSPF/CSPH and CSPG/CSPI pair. Difference in interaction pattern was maximum in CSPF/CSPH owing to their high number of non-synonymous substitutions. Maximum difference in surface electrostatic potential was observed in case of CSPA, CSPG and CSPF. This research work emphasizes on discerning the molecular mechanism initiated by these proteins with a structural, mutational and functional approach.

Supplementary Information

The online version contains supplementary material available at 10.1007/s13205-023-03656-2.

Structure-function crosstalk in liver cancer research: Protein structuromics

Liver cancer can be primary (starting in the liver) or secondary (cancer that has spread from elsewhere to the liver, known as liver metastasis). Liver metastasis is more common than primary liver cancer. Despite great advances in molecular biology methods and treatments, liver cancer is still associated with a poor survival rate and a high death rate, and there is no cure. Many questions remain regarding the mechanisms of liver cancer occurrence and development as well as tumor reoccurrence after treatment. In this study, we assessed the protein structural features of 20 oncogenes and 20 anti-oncogenes via protein structure and dynamic analysis methods and 3D structural and systematic analyses of the structure-function relationships of proteins. Our aim was to provide new insights that may inform research on the development and treatment of liver cancer.

Metal-binding and circular permutation-dependent thermodynamic and kinetic stability of azurin

Native topology is known to determine the folding kinetics and the energy landscape of proteins. Furthermore, the circular permutation (CP) of proteins alters the order of the secondary structure connectivity while retaining the three-dimensional structure, making it an elegant and powerful approach to altering native topology. Previous studies elucidated the influence of CP in proteins with different folds such as Greek key β-barrel, β-sandwich, β-α-β, and all α-Greek key. CP mainly affects the protein stability and unfolding kinetics, while folding kinetics remains mostly unaltered. However, the effect of CP on metalloproteins is yet to be elaborately studied. The active site of metalloproteins poses an additional complexity in studying protein folding. Here, we investigate a CP variant (cpN42) of azurin-in both metal-free and metal-bound (holo) forms. As observed earlier in other proteins, apo-forms of wild-type (WT) and cpN42 fold with similar rates. In contrast, zinc-binding accelerates the folding of WT but decelerates the folding of cpN42. On zinc-binding, the spontaneous folding rate of WT increases by >250 times that of cpN42, which is unprecedented and the highest for any CP to date. On the other hand, zinc-binding reduces the spontaneous unfolding rate of cpN42 by ~100 times, making the WT and CP azurins unfold at similar rates. Our study demonstrates metal binding as a novel way to modulate the unfolding and folding rates of CPs compared to their WT counterparts. We hope our study increases the understanding of the effect of CP on the folding mechanism and energy landscape of metalloproteins.

Functional advantages of building nanosystems using multiple molecular components

Over half of all the natural nanomachines in living organisms are multimeric and likely exploit the self-assembly of their components to provide functional benefits. However, the advantages and disadvantages of building nanosystems using multiple molecular components remain relatively unexplored at the thermodynamic, kinetic and functional levels. In this study we used theory and a simple DNA-based model that forms the same nanostructures with different numbers of components to advance our knowledge in this area. Despite its lower assembly rate, we found that a system built with three components may undergo a more cooperative assembly transition from less preorganized components, which facilitates the emergence of functionalities. Using simple variations of its components, we also found that trimeric nanosystems display a much higher level of programmability than their dimeric counterparts because they can assemble with various levels of cooperativity, self-inhibition and time-dependent properties. We show here how two simple strategies (for example, cutting and adding components) can be employed to efficiently programme the regulatory function of a more complex, artificially selected, RNA-cleaving catalytic nanosystem.

Computational prediction of protein folding rate using structural parameters and network centrality measures

Protein folding is a complex physicochemical process whereby a polymer of amino acids samples numerous conformations in its unfolded state before settling on an essentially unique native three-dimensional (3D) structure. To understand this process, several theoretical studies have used a set of 3D structures, identified different structural parameters, and analyzed their relationships using the natural logarithmic protein folding rate (ln(k_f)). Unfortunately, these structural parameters are specific to a small set of proteins that are not capable of accurately predicting ln(k_f) for both two-state (TS) and non-two-state (NTS) proteins. To overcome the limitations of the statistical approach, a few machine learning (ML)-based models have been proposed using limited training data. However, none of these methods can explain plausible folding mechanisms. In this study, we evaluated the predictive capabilities of ten different ML algorithms using eight different structural parameters and five different network centrality measures based on newly constructed datasets. In comparison to the other nine regressors, support vector machine was found to be the most appropriate for predicting ln(k_f) with mean absolute differences of 1.856, 1.55, and 1.745 for the TS, NTS, and combined datasets, respectively. Furthermore, combining structural parameters and network centrality measures improves the prediction performance compared to individual parameters, indicating that multiple factors are involved in the folding process.

Deep mining of the protein energy landscape

For over half a century, it has been known that protein molecules naturally undergo extensive structural fluctuations, and that these internal motions are intimately related to their functional properties. The energy landscape view has provided a powerful framework for describing the various physical states that proteins visit during their lifetimes. This Perspective focuses on the commonly neglected and often disparaged axis of the protein energy landscape: entropy. Initially seen largely as a barrier to functionally relevant states of protein molecules, it has recently become clear that proteins retain considerable conformational entropy in the "native" state, and that this entropy can and often does contribute significantly to the free energy of fundamental protein properties, processes, and functions. NMR spectroscopy, molecular dynamics simulations, and emerging crystallographic views have matured in parallel to illuminate dynamic disorder of the "ground state" of proteins and their importance in not only transiting between biologically interesting structures but also greatly influencing their stability, cooperativity, and contribution to critical properties such as allostery.

Synergetic Effects of Alanine and Glycine in Blob-Based Methods for Predicting Protein Folding Times

The polypeptide PGlyAlaGlu was prepared with 20 mol % glycine (Gly), 36 mol % d,l-alanine (Ala), and 44 mol % d,l-glutamic acid (Glu) and labeled with the dye 1-pyrenemethylamine to yield a series of Py-PGlyAlaGlu samples. The fluorescence decays of the Py-PGlyAlaGlu samples were analyzed according to the fluorescence blob model (FBM) to obtain the number N_blob^exp of amino acids (aa's) encompassed inside the subvolume V_blob of the polypeptide probed by an excited pyrene. An N_blob^exp value of 29 (±2) was retrieved for Py-PGlyAlaGlu, which was much larger than for any of the copolypeptide PGlyGlu or PAlaGlu prepared with either Gly and Glu or Ala and Glu, respectively. The continuous increase in N_blob^exp with decreasing side chain size (SCS) from 10 aa's for PGlu to 16 aa's for PAlaGlu and 22 aa's for PGlyGlu was used earlier to define the reach of an aa and determine the groups of aa's that could interact with each other along a polypeptide backbone according to their SCS. These groups of aa's, referred to as blobs, led to the implementation of blob-based models (BBM) to predict the folding time τ_F^theo,BBM of 145 proteins, which was found to match their experimental folding time τ_F^exp with a relatively high 0.71 correlation coefficient. Nevertheless, the much higher N_blob^exp value found for Py-PGlyAlaGlu compared to all other pyrene-labeled polypeptides studied to date indicates that the reach of aa's along a polypeptide sequence is affected not only by SCS but also by synergetic effects between different aa's. Following this new insight, a revised BBM was implemented to predict τ_F^theo,BBM for 195 proteins assuming the existence or absence of synergies to control the interactions between aa's along a polypeptide sequence. Similarly good correlation coefficients of 0.71 and 0.74 were obtained for a direct 1:1 comparison of τ_F^exp and τ_F^theo,BBM for the 195 proteins without and with synergies, respectively. This result suggests that synergetic effects between different aa's have little effect on τ_F^theo,BBM predicted from BBM underlying the robustness of this methodology.

Factors That Control the Force Needed to Unfold a Membrane Protein in Silico Depend on the Mode of Denaturation

Single-molecule force spectroscopy methods, such as AFM and magnetic tweezers, have proved extremely beneficial in elucidating folding pathways for soluble and membrane proteins. To identify factors that determine the force rupture levels in force-induced membrane protein unfolding, we applied our near-atomic-level Upside molecular dynamics package to study the vertical and lateral pulling of bacteriorhodopsin (bR) and GlpG, respectively. With our algorithm, we were able to selectively alter the magnitudes of individual interaction terms and identify that, for vertical pulling, hydrogen bond strength had the strongest effect, whereas other non-bonded protein and membrane-protein interactions had only moderate influences, except for the extraction of the last helix where the membrane-protein interactions had a stronger influence. The up-down topology of the transmembrane helices caused helices to be pulled out as pairs. The rate-limiting rupture event often was the loss of H-bonds and the ejection of the first helix, which then propagated tension to the second helix, which rapidly exited the bilayer. The pulling of the charged linkers across the membrane had minimal influence, as did changing the bilayer thickness. For the lateral pulling of GlpG, the rate-limiting rupture corresponded to the separation of the helices within the membrane, with the H-bonds generally being broken only afterward. Beyond providing a detailed picture of the rupture events, our study emphasizes that the pulling mode greatly affects the factors that determine the forces needed to unfold a membrane protein.

How do salt and lipids affect conformational dynamics of Aβ42 monomers in water?

It is well established that amyloid β-protein (Aβ) self-assembly is involved in triggering of Alzheimer's disease. On the other hand, evidence of physiological function of Aβ interacting with lipids has only begun to emerge. Details of Aβ-lipid interactions, which may underlie physiological and pathological activities of Aβ, are not well understood. Here, the effects of salt and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) lipids on conformational dynamics of Aβ42 monomer in water are examined by all-atom molecular dynamics (MD). We acquired six sets of 250 ns long MD trajectories for each of the three lipid concentrations (0, 27, and 109 mM) in the absence and presence of 150 mM salt. Ten replica trajectories per set are used to enhance sampling of Aβ42 conformational space. We show that salt facilitates long-range tertiary contacts in Aβ42, resulting in more compact Aβ42 conformations. By contrast, addition of lipids results in lipid-concentration dependent Aβ42 unfolding concomitant with enhanced stability of the turn in the A21-A30 region. At the high lipid concentration, salt enables the N-terminal region of Aβ42 to form long-range tertiary contacts and interact with lipids, which results in formation of a parallel β-strand. Aβ42 forms stable lipid-protein complexes whereby the protein is adhered to the lipid cluster rather than embedded into it. We propose that the inability of Aβ42 monomer to get embedded into the lipid cluster may be important for facilitating repair of leaks in the blood-brain barrier without penetrating and damaging cellular membranes.

DALI shines a light on remote homologs: One hundred discoveries

Structural comparison reveals remote homology that often fails to be detected by sequence comparison. The DALI web server (http://ekhidna2.biocenter.helsinki.fi/dali) is a platform for structural analysis that provides database searches and interactive visualization, including structural alignments annotated with secondary structure, protein families and sequence logos, and 3D structure superimposition supported by color-coded sequence and structure conservation. Here, we are using DALI to mine the AlphaFold Database version 1, which increased the structural coverage of protein families by 20%. We found 100 remote homologous relationships hitherto unreported in the current reference database for protein domains, Pfam 35.0. In particular, we linked 35 domains of unknown function (DUFs) to the previously characterized families, generating a functional hypothesis that can be explored downstream in structural biology studies. Other findings include gene fusions, tandem duplications, and adjustments to domain boundaries. The evidence for homology can be browsed interactively through live examples on DALI's website.

Protein dynamics: The future is bright and complicated!

Biological life depends on motion, and this manifests itself in proteins that display motion over a formidable range of time scales spanning from femtoseconds vibrations of atoms at enzymatic transition states, all the way to slow domain motions occurring on micro to milliseconds. An outstanding challenge in contemporary biophysics and structural biology is a quantitative understanding of the linkages among protein structure, dynamics, and function. These linkages are becoming increasingly explorable due to conceptual and methodological advances. In this Perspective article, we will point toward future directions of the field of protein dynamics with an emphasis on enzymes. Research questions in the field are becoming increasingly complex such as the mechanistic understanding of high-order interaction networks in allosteric signal propagation through a protein matrix, or the connection between local and collective motions. In analogy to the solution to the "protein folding problem," we argue that the way forward to understanding these and other important questions lies in the successful integration of experiment and computation, while utilizing the present rapid expansion of sequence and structure space. Looking forward, the future is bright, and we are in a period where we are on the doorstep to, at least in part, comprehend the importance of dynamics for biological function.

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.

Friends in need: How chaperonins recognize and remodel proteins that require folding assistance

Chaperonins are biological nanomachines that help newly translated proteins to fold by rescuing them from kinetically trapped misfolded states. Protein folding assistance by the chaperonin machinery is obligatory in vivo for a subset of proteins in the bacterial proteome. Chaperonins are large oligomeric complexes, with unusual seven fold symmetry (group I) or eight/nine fold symmetry (group II), that form double-ring constructs, enclosing a central cavity that serves as the folding chamber. Dramatic large-scale conformational changes, that take place during ATP-driven cycles, allow chaperonins to bind misfolded proteins, encapsulate them into the expanded cavity and release them back into the cellular environment, regardless of whether they are folded or not. The theory associated with the iterative annealing mechanism, which incorporated the conformational free energy landscape description of protein folding, quantitatively explains most, if not all, the available data. Misfolded conformations are associated with low energy minima in a rugged energy landscape. Random disruptions of these low energy conformations result in higher free energy, less folded, conformations that can stochastically partition into the native state. Two distinct mechanisms of annealing action have been described. Group I chaperonins (GroEL homologues in eubacteria and endosymbiotic organelles), recognize a large number of misfolded proteins non-specifically and operate through highly coordinated cooperative motions. By contrast, the less well understood group II chaperonins (CCT in Eukarya and thermosome/TF55 in Archaea), assist a selected set of substrate proteins. Sequential conformational changes within a CCT ring are observed, perhaps promoting domain-by-domain substrate folding. Chaperonins are implicated in bacterial infection, autoimmune disease, as well as protein aggregation and degradation diseases. Understanding the chaperonin mechanism and the specific proteins they rescue during the cell cycle is important not only for the fundamental aspect of protein folding in the cellular environment, but also for effective therapeutic strategies.

Effects of Residual Composition and Distribution on the Structural Characteristics of the Protein

The effect of ratio and consecutive number of hydrophobic residues in the repeating unit of protein chains was investigated by MD simulation. The modified off-lattice HNP model was applied in this study. The protein chains constituted by different HNP ratios or different numbers of consecutively hydrophobic residues with the same chain length were simulated under a broad temperature range. We concluded that the proteins with higher ratio or larger number of sequentially hydrophobic residues present more orientated and compact structure under a certain low temperature. It is attributed to the lower non-bonded potential energy between H-H residual pairs, especially more hydrophobic residues in a procession among the protein chain. Considering the microscopic structure of the protein, more residue contacts are achieved with the proteins with higher ratios and sequential H residues under the low temperature. Meanwhile, with the ratio and consecutive number of H residues increasing, the distribution of stem length showed a transition from exponential decline to unimodal and even multiple peaks, indicating the specific ordered structure formed. These results provide an insight into 3D structural properties of proteins from their residue sequences, which has a primary structure at molecular level and, ultimately, a practical possibility of applying in biotechnological applications.

DomainMapper: Accurate domain structure annotation including those with non-contiguous topologies

Automated domain annotation is an important tool for structural informatics. These pipelines typically involve searching query sequences against hidden Markov model (HMM) profiles, yielding matches to profiles for various domains. However, domain annotation can be ambiguous or inaccurate when proteins contain domains with non-contiguous residue ranges, and especially when insertional domains are hosted within them. Here, we present DomainMapper, an algorithm that accurately assigns a unique domain structure annotation to a query sequence, including those with complex topologies. We validate our domain assignments using the AlphaFold database and confirm that non-contiguity is pervasive (10.74% of all domains in yeast and 4.52% in human). Using this resource, we find that certain folds have strong propensities to be non-contiguous or insertional across the Tree of Life. DomainMapper is freely available and can be ran as a single command-line function.

Fuzzy spherical truncation-based multi-linear protein descriptors: From their definition to application in structural-related predictions

This study introduces a set of fuzzy spherically truncated three-dimensional (3D) multi-linear descriptors for proteins. These indices codify geometric structural information from kth spherically truncated spatial-(dis)similarity two-tuple and three-tuple tensors. The coefficients of these truncated tensors are calculated by applying a smoothing value to the 3D structural encoding based on the relationships between two and three amino acids of a protein embedded into a sphere. At considering, the geometrical center of the protein matches with center of the sphere, the distance between each amino acid involved in any specific interaction and the geometrical center of the protein can be computed. Then, the fuzzy membership degree of each amino acid from an spherical region of interest is computed by fuzzy membership functions (FMFs). The truncation value is finally a combination of the membership degrees from interacting amino acids, by applying the arithmetic mean as fusion rule. Several fuzzy membership functions with diverse biases on the calculation of amino acids memberships (e.g., Z-shaped (close to the center), PI-shaped (middle region), and A-Gaussian (far from the center)) were considered as well as traditional truncation functions (e.g., Switching). Such truncation functions were comparatively evaluated by exploring: 1) the frequency of membership degrees, 2) the variability and orthogonality analyses among them based on the Shannon Entropy’s and Principal Component’s methods, respectively, and 3) the prediction performance of alignment-free prediction of protein folding rates and structural classes. These analyses unraveled the singularity of the proposed fuzzy spherically truncated MDs with respect to the classical (non-truncated) ones and respect to the MDs truncated with traditional functions. They also showed an improved prediction power by attaining an external correlation coefficient of 95.82% in the folding rate modelling and an accuracy of 100% in distinguishing structural protein classes. These outcomes are better than the ones attained by existing approaches, justifying the theoretical contribution of this report. Thus, the fuzzy spherically truncated-based protein descriptors from MuLiMs-MCoMPAs (http://tomocomd.com/mulims-mcompas) are promising alignment-free predictors for modeling protein functions and properties.

De novo design of immunoglobulin-like domains

Antibodies, and antibody derivatives such as nanobodies, contain immunoglobulin-like (Ig) β-sandwich scaffolds which anchor the hypervariable antigen-binding loops and constitute the largest growing class of drugs. Current engineering strategies for this class of compounds rely on naturally existing Ig frameworks, which can be hard to modify and have limitations in manufacturability, designability and range of action. Here, we develop design rules for the central feature of the Ig fold architecture—the non-local cross-β structure connecting the two β-sheets—and use these to design highly stable Ig domains de novo, confirm their structures through X-ray crystallography, and show they can correctly scaffold functional loops. Our approach opens the door to the design of antibody-like scaffolds with tailored structures and superior biophysical properties.

The immunoglobulin domain framework of antibodies has been a long standing design challenge. Here, the authors describe design rules for tailoring these domains and show they can be accurately designed, de novo, with high stability and the ability to scaffold functional loops.

Configurational entropy, transition rates, and optimal interactions for rapid folding in coarse-grained model proteins

Under certain conditions, the dynamics of coarse-grained models of solvated proteins can be described using a Markov state model, which tracks the evolution of populations of configurations. The transition rates among states that appear in the Markov model can be determined by computing the relative entropy of states and their mean first passage times. In this paper, we present an adaptive method to evaluate the configurational entropy and the mean first passage times for linear chain models with discontinuous potentials. The approach is based on event-driven dynamical sampling in a massively parallel architecture. Using the fact that the transition rate matrix can be calculated for any choice of interaction energies at any temperature, it is demonstrated how each state's energy can be chosen such that the average time to transition between any two states is minimized. The methods are used to analyze the optimization of the folding process of two protein systems: the crambin protein and a model with frustration and misfolding. It is shown that the folding pathways for both systems are comprised of two regimes: first, the rapid establishment of local bonds, followed by the subsequent formation of more distant contacts. The state energies that lead to the most rapid folding encourage multiple pathways, and they either penalize folding pathways through kinetic traps by raising the energies of trapping states or establish an escape route from the trapping states by lowering free energy barriers to other states that rapidly reach the native state.

Circuit topology predicts pathogenicity of missense mutations

The contact topology of a protein determines important aspects of the folding process. The topological measure of contact order has been shown to be predictive of the rate of folding. Circuit topology is emerging as another fundamental descriptor of biomolecular structure, with predicted effects on the folding rate. We analyze the residue‐based circuit topological environments of 21 K mutations labeled as pathogenic or benign. Multiple statistical lines of reasoning support the conclusion that the number of contacts in two specific circuit topological arrangements, namely inverse parallel and cross relations, with contacts involving the mutated residue have discriminatory value in determining the pathogenicity of human variants. We investigate how results vary with residue type and according to whether the gene is essential. We further explore the relationship to a number of structural features and find that circuit topology provides nonredundant information on protein structures and pathogenicity of mutations. Results may have implications for the polymer physics of protein folding and suggest that “local” topological information, including residue‐based circuit topology and residue contact order, could be useful in improving state‐of‐the‐art machine learning algorithms for pathogenicity prediction.

Free-energy landscape of two-state protein acylphosphatase with large contact order revealed by force-dependent folding and unfolding dynamics

Acylphosphatase (AcP) is a small protein with 98 amino acid residues that catalyzes the hydrolysis of carboxyl-phosphate bonds. AcP is a typical two-state protein with slow folding rate due to its relatively large contact order in the native structure. The mechanical properties and unfolding behavior of AcP has been studied by atomic force microscope. Here using stable magnetic tweezers, we measured the force-dependent folding rates within a force range 1-3 pN, and unfolding rates 15-40 pN. The obtained unfolding rates show different force sensitivities at forces below and above ∼27 pN, which determines a free-energy landscape with two energy barriers. Our results indicate that the free-energy landscape of small globule proteins have general Bactrian camel shape, and large contact order of the native state produces a high barrier dominate at low forces.

The Local Topological Free Energy of the SARS-CoV-2 Spike Protein

The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its Spike protein. Understanding protein rearrangement and identifying specific amino acids where mutations affect protein rearrangement has attracted much attention for drug development. In this manuscript, we use a mathematical method to characterize the local topology/geometry of the SARS-CoV-2 Spike protein backbone. Our results show that local conformational changes in the FP, HR1, and CH domains are associated with global conformational changes in the RBD domain. The SARS-CoV-2 variants analyzed in this manuscript (alpha, beta, gamma, delta Mink, G614, N501) show differences in the local conformations of the FP, HR1, and CH domains as well. Finally, most mutations of concern are either in or in the vicinity of high local topological free energy conformations, suggesting that high local topological free energy conformations could be targets for mutations with significant impact of protein function. Namely, the residues 484, 570, 614, 796, and 969, which are present in variants of concern and are targeted as important in protein function, are predicted as such from our model.