Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding

Pulling Forces Differentially Affect Refolding Pathways Due to Entangled Misfolded States in SARS-CoV-1 and SARS-CoV-2 Receptor Binding Domain

Single-molecule force spectroscopy (SMFS) experiments can monitor protein refolding by applying a small force of a few piconewtons (pN) and slowing down the folding process. Bell theory predicts that in the narrow force regime where refolding can occur, the folding time should increase exponentially with increased external force. In this work, using coarse-grained molecular dynamics simulations, we compared the refolding pathways of SARS-CoV-1 RBD and SARS-CoV-2 RBD (RBD refers to the receptor binding domain) starting from unfolded conformations with and without a force applied to the protein termini. For SARS-CoV-2 RBD, the number of trajectories that fold is significantly reduced with the application of a 5 pN force, indicating that, qualitatively consistent with Bell theory, refolding is slowed down when a pulling force is applied to the termini. In contrast, the refolding times of SARS-CoV-1 RBD do not change meaningfully when a force of 5 pN is applied. How this lack of a Bell response could arise at the molecular level is unknown. Analysis of the entanglement changes of the folded conformations revealed that in the case of SARS-CoV-1 RBD, an external force minimizes misfolding into kinetically trapped states, thereby promoting efficient folding and offsetting any potential slowdown due to the external force. These misfolded states contain non-native entanglements that do not exist in the native state of either SARS-CoV-1-RBD or SARS-CoV-2-RBD. These results indicate that non-Bell behavior can arise from this class of misfolding and, hence, may be a means of experimentally detecting these elusive, theoretically predicted states.

Rigid crosslinking of the CD3 complex leads to superior T cell stimulation

Functionally bivalent non-covalent Fab dimers (Bi-Fabs) specific for the TCR/CD3 complex promote CD3 signaling on T cells. While comparing functional responses to stimulation with Bi-Fab, F(ab')2 or mAb specific for the same CD3 epitope, we observed fratricide requiring anti-CD3 bridging of adjacent T cells. Surprisingly, anti-CD3 Bi-Fab ranked first in fratricide potency, followed by anti-CD3 F(ab')2 and anti-CD3 mAb. Low resolution structural studies revealed anti-CD3 Bi-Fabs and F(ab')2 adopt similar global shapes with CD3-binding sites oriented outward. However, under molecular dynamic simulations, anti-CD3 Bi-Fabs crosslinked CD3 more rigidly than F(ab')2. Furthermore, molecular modelling of Bi-Fab and F(ab')2 binding to CD3 predicted crosslinking of T cell antigen receptors located in opposing plasma membrane domains, a feature fitting with T cell fratricide observed. Thus, increasing rigidity of Fab-CD3 crosslinking between opposing effector-target pairs may result in stronger T cell effector function. These findings could guide improving clinical performance of bi-specific anti-CD3 drugs.

Knot or not? Identifying unknotted proteins in knotted families with sequence-based Machine Learning model

Knotted proteins, although scarce, are crucial structural components of certain protein families, and their roles continue to be a topic of intense research. Capitalizing on the vast collection of protein structure predictions offered by AlphaFold (AF), this study computationally examines the entire UniProt database to create a robust dataset of knotted and unknotted proteins. Utilizing this dataset, we develop a machine learning (ML) model capable of accurately predicting the presence of knots in protein structures solely from their amino acid sequences. We tested the model's capabilities on 100 proteins whose structures had not yet been predicted by AF and found agreement with our local prediction in 92% cases. From the point of view of structural biology, we found that all potentially knotted proteins predicted by AF can be classified only into 17 families. This allows us to discover the presence of unknotted proteins in families with a highly conserved knot. We found only three new protein families: UCH, DUF4253, and DUF2254, that contain both knotted and unknotted proteins, and demonstrate that deletions within the knot core could potentially account for the observed unknotted (trivial) topology. Finally, we have shown that in the majority of knotted families (11 out of 15), the knotted topology is strictly conserved in functional proteins with very low sequence similarity. We have conclusively demonstrated that proteins AF predicts as unknotted are structurally accurate in their unknotted configurations. However, these proteins often represent nonfunctional fragments, lacking significant portions of the knot core (amino acid sequence).

Are there double knots in proteins? Prediction and in vitro verification based on TrmD-Tm1570 fusion from C. nitroreducens

We have been aware of the existence of knotted proteins for over 30 years-but it is hard to predict what is the most complicated knot that can be formed in proteins. Here, we show new and the most complex knotted topologies recorded to date-double trefoil knots (31 #31). We found five domain arrangements (architectures) that result in a doubly knotted structure in almost a thousand proteins. The double knot topology is found in knotted membrane proteins from the CaCA family, that function as ion transporters, in the group of carbonic anhydrases that catalyze the hydration of carbon dioxide, and in the proteins from the SPOUT superfamily that gathers 31 knotted methyltransferases with the active site-forming knot. For each family, we predict the presence of a double knot using AlphaFold and RoseTTaFold structure prediction. In the case of the TrmD-Tm1570 protein, which is a member of SPOUT superfamily, we show that it folds in vitro and is biologically active. Our results show that this protein forms a homodimeric structure and retains the ability to modify tRNA, which is the function of the single-domain TrmD protein. However, how the protein folds and is degraded remains unknown.

Mathematical topology and geometry-based classification of tauopathies

Neurodegenerative diseases, like Alzheimer's, are associated with the presence of neurofibrillary lesions formed by tau protein filaments in the cerebral cortex. While it is known that different morphologies of tau filaments characterize different neurodegenerative diseases, there are few metrics of global and local structure complexity that enable to quantify their structural diversity rigorously. In this manuscript, we employ for the first time mathematical topology and geometry to classify neurodegenerative diseases by using cryo-electron microscopy structures of tau filaments that are available in the Protein Data Bank. By employing mathematical topology metrics (Gauss linking integral, writhe and second Vassiliev measure) we achieve a consistent, but more refined classification of tauopathies, than what was previously observed through visual inspection. Our results reveal a hierarchy of classification from global to local topology and geometry characteristics. In particular, we find that tauopathies can be classified with respect to the handedness of their global conformations and the handedness of the relative orientations of their repeats. Progressive supranuclear palsy is identified as an outlier, with a more complex structure than the rest, reflected by a small, but observable knotoid structure (a diagrammatic structure representing non-trivial topology). This topological characteristic can be attributed to a pattern in the beginning of the R3 repeat that is present in all tauopathies but at different extent. Moreover, by comparing single filament to paired filament structures within tauopathies we find a consistent change in the side-chain orientations with respect to the alpha carbon atoms at the area of interaction.

Non-covalent Lasso Entanglements in Folded Proteins: Prevalence, Functional Implications, and Evolutionary Significance

One-third of protein domains in the CATH database contain a recently discovered tertiary topological motif: non-covalent lasso entanglements, in which a segment of the protein backbone forms a loop closed by non-covalent interactions between residues and is threaded one or more times by the N- or C-terminal backbone segment. Unknown is how frequently this structural motif appears across the proteomes of organisms. And the correlation of these motifs with various classes of protein function and biological processes have not been quantified. Here, using a combination of protein crystal structures, AlphaFold2 predictions, and Gene Ontology terms we show that in E. coli, S. cerevisiae and H. sapiens that 71%, 52% and 49% of globular proteins contain one-or-more non-covalent lasso entanglements in their native fold, and that some of these are highly complex with multiple threading events. Further, proteins containing these tertiary motifs are consistently enriched in certain functions and biological processes across these organisms and depleted in others, strongly indicating an influence of evolutionary selection pressures acting positively and negatively on the distribution of these motifs. Together, these results demonstrate that non-covalent lasso entanglements are widespread and indicate they may be extensively utilized for protein function and subcellular processes, thus impacting phenotype.

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.

How soluble misfolded proteins bypass chaperones at the molecular level

Subpopulations of soluble, misfolded proteins can bypass chaperones within cells. The extent of this phenomenon and how it happens at the molecular level are unknown. Through a meta-analysis of the experimental literature we find that in all quantitative protein refolding studies there is always a subpopulation of soluble but misfolded protein that does not fold in the presence of one or more chaperones, and can take days or longer to do so. Thus, some misfolded subpopulations commonly bypass chaperones. Using multi-scale simulation models we observe that the misfolded structures that bypass various chaperones can do so because their structures are highly native like, leading to a situation where chaperones do not distinguish between the folded and near-native-misfolded states. More broadly, these results provide a mechanism by which long-time scale changes in protein structure and function can persist in cells because some misfolded states can bypass components of the proteostasis machinery.

Is Posttranslational Folding More Efficient Than Refolding from a Denatured State: A Computational Study

The folding of proteins into their native conformation is a complex process that has been extensively studied over the past half-century. The ribosome, the molecular machine responsible for protein synthesis, is known to interact with nascent proteins, adding further complexity to the protein folding landscape. Consequently, it is unclear whether the folding pathways of proteins are conserved on and off the ribosome. The main question remains: to what extent does the ribosome help proteins fold? To address this question, we used coarse-grained molecular dynamics simulations to compare the mechanisms by which the proteins dihydrofolate reductase, type III chloramphenicol acetyltransferase, and d-alanine-d-alanine ligase B fold during and after vectorial synthesis on the ribosome to folding from the full-length unfolded state in bulk solution. Our results reveal that the influence of the ribosome on protein folding mechanisms varies depending on the size and complexity of the protein. Specifically, for a small protein with a simple fold, the ribosome facilitates efficient folding by helping the nascent protein avoid misfolded conformations. However, for larger and more complex proteins, the ribosome does not promote folding and may contribute to the formation of intermediate misfolded states cotranslationally. These misfolded states persist posttranslationally and do not convert to the native state during the 6 μs runtime of our coarse-grain simulations. Overall, our study highlights the complex interplay between the ribosome and protein folding and provides insight into the mechanisms of protein folding on and off the ribosome.

Entangled Motifs in Membrane Protein Structures

Entangled motifs are found in one-third of protein domain structures, a reference set that contains mostly globular proteins. Their properties suggest a connection with co-translational folding. Here, we wish to investigate the presence and properties of entangled motifs in membrane protein structures. From existing databases, we build a non-redundant data set of membrane protein domains, annotated with the monotopic/transmembrane and peripheral/integral labels. We evaluate the presence of entangled motifs using the Gaussian entanglement indicator. We find that entangled motifs appear in one-fifth of transmembrane and one-fourth of monotopic proteins. Surprisingly, the main features of the distribution of the values of the entanglement indicator are similar to the reference case of general proteins. The distribution is conserved across different organisms. Differences with respect to the reference set emerge when considering the chirality of entangled motifs. Although the same chirality bias is found for single-winding motifs in both membrane and reference proteins, the bias is reversed, strikingly, for double-winding motifs only in the reference set. We speculate that these observations can be rationalized in terms of the constraints exerted on the nascent chain by the co-translational bio-genesis machinery, which is different for membrane and globular proteins.

Evolutionary conservation of amino acids contributing to the protein folding transition state

The question of whether amino acids critical to protein folding kinetics are evolutionarily conserved has been investigated intensively in the past, but no consensus has yet been reached. Recently, we have demonstrated that the transition state, dictating folding kinetics, is characterized as the state of maximum dynamic cooperativity, i.e., the state of maximum correlations between amino acid contact formations. Here, we investigate the evolutionary conservation of those amino acids contributing significantly to the dynamic cooperativity. We find a strong indication of a new kind of relationship-necessary but not sufficient causality-between the evolutionary conservation and the dynamic cooperativity: larger contributions to the dynamic cooperativity arise from more conserved residues, but not vice versa. This holds for all the protein systems for which long folding simulation trajectories are available. To our knowledge, this is the first systematic demonstration of any kind of evolutionary conservation of amino acids relevant to folding kinetics.

How synonymous mutations alter enzyme structure and function over long timescales

The specific activity of enzymes can be altered over long timescales in cells by synonymous mutations that alter a messenger RNA molecule's sequence but not the encoded protein's primary structure. How this happens at the molecular level is unknown. Here, we use multiscale modelling of three Escherichia coli enzymes (type III chloramphenicol acetyltransferase, D-alanine-D-alanine ligase B and dihydrofolate reductase) to understand experimentally measured changes in specific activity due to synonymous mutations. The modelling involves coarse-grained simulations of protein synthesis and post-translational behaviour, all-atom simulations to test robustness and quantum mechanics/molecular mechanics calculations to characterize enzymatic function. We show that changes in codon translation rates induced by synonymous mutations cause shifts in co-translational and post-translational folding pathways that kinetically partition molecules into subpopulations that very slowly interconvert to the native, functional state. Structurally, these states resemble the native state, with localized misfolding near the active sites of the enzymes. These long-lived states exhibit reduced catalytic activity, as shown by their increased activation energies for the reactions they catalyse.

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.

Pulse labeling reveals the tail end of protein folding by proteome profiling

Accurate and efficient folding of nascent protein sequences into their native states requires support from the protein homeostasis network. Herein we probe which newly translated proteins are thermo-sensitive, making them susceptible to misfolding and aggregation under heat stress using pulse-SILAC mass spectrometry. We find a distinct group of proteins that is highly sensitive to this perturbation when newly synthesized but not once matured. These proteins are abundant and highly structured. Notably, they display a tendency to form β sheet secondary structures, have more complex folding topology, and are enriched for chaperone-binding motifs, suggesting a higher demand for chaperone-assisted folding. These polypeptides are also more often components of stable protein complexes in comparison with other proteins. Combining these findings suggests the existence of a specific subset of proteins in the cell that is particularly vulnerable to misfolding and aggregation following synthesis before reaching the native state.

Mechanical regulation of talin through binding and history-dependent unfolding

Talin is a force-sensing multidomain protein and a major player in cellular mechanotransduction. Here, we use single-molecule magnetic tweezers to investigate the mechanical response of the R8 rod domain of talin. We find that under various force cycles, the R8 domain of talin can display a memory-dependent behavior: At the same low force (<10 pN), the same protein molecule shows vastly different unfolding kinetics. This history-dependent behavior indicates the evolution of a unique force-induced native state. We measure through mechanical unfolding that talin R8 domain binds one of its ligands, DLC1, with much higher affinity than previously reported. This strong interaction can explain the antitumor response of DLC1 by regulating inside-out activation of integrins. Together, our results paint a complex picture for the mechanical unfolding of talin in the physiological range and a new mechanism of function of DLC1 to regulate inside-out activation of integrins.

Universal protein misfolding intermediates can bypass the proteostasis network and remain soluble and less functional

Some misfolded protein conformations can bypass proteostasis machinery and remain soluble in vivo. This is an unexpected observation, as cellular quality control mechanisms should remove misfolded proteins. Three questions, then, are: how do long-lived, soluble, misfolded proteins bypass proteostasis? How widespread are such misfolded states? And how long do they persist? We address these questions using coarse-grain molecular dynamics simulations of the synthesis, termination, and post-translational dynamics of a representative set of cytosolic E. coli proteins. We predict that half of proteins exhibit misfolded subpopulations that bypass molecular chaperones, avoid aggregation, and will not be rapidly degraded, with some misfolded states persisting for months or longer. The surface properties of these misfolded states are native-like, suggesting they will remain soluble, while self-entanglements make them long-lived kinetic traps. In terms of function, we predict that one-third of proteins can misfold into soluble less-functional states. For the heavily entangled protein glycerol-3-phosphate dehydrogenase, limited-proteolysis mass spectrometry experiments interrogating misfolded conformations of the protein are consistent with the structural changes predicted by our simulations. These results therefore provide an explanation for how proteins can misfold into soluble conformations with reduced functionality that can bypass proteostasis, and indicate, unexpectedly, this may be a wide-spread phenomenon.

Topological dynamics of an intrinsically disordered N‐terminal domain of the human androgen receptor

Human androgen receptor contains a large N‐terminal domain (AR‐NTD) that is highly dynamic and this poses a major challenge for experimental and computational analysis to decipher its conformation. Misfolding of the AR‐NTD is implicated in prostate cancer and Kennedy's disease, yet our knowledge of its structure is limited to primary sequence information of the chain and a few functionally important secondary structure motifs. Here, we employed an innovative combination of molecular dynamics simulations and circuit topology (CT) analysis to identify the tertiary structure of AR‐NTD. We found that the AR‐NTD adopts highly dynamic loopy conformations with two identifiable regions with distinct topological make‐up and dynamics. This consists of a N‐terminal region (NR, residues 1–224) and a C‐terminal region (CR, residues 225–538), which carries a dense core. Topological mapping of the dynamics reveals a traceable time‐scale dependent topological evolution. NR adopts different positioning with respect to the CR and forms a cleft that can partly enclose the hormone‐bound ligand‐binding domain (LBD) of the androgen receptor. Furthermore, our data suggest a model in which dynamic NR and CR compete for binding to the DNA‐binding domain of the receptor, thereby regulating the accessibility of its DNA‐binding site. Our approach allowed for the identification of a previously unknown regulatory binding site within the CR core, revealing the structural mechanisms of action of AR inhibitor EPI‐001, and paving the way for other drug discovery applications.

The protein folding rate and the geometry and topology of the native state

Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or not). By analyzing a small set of two-state and multi-state proteins with no knots or slipknots, our results show that 95.4% of the analyzed proteins have non-trivial topological characteristics, as reflected by the second Vassiliev measure, and that the logarithm of the experimental protein folding rate depends on both the local geometry and the topology of the protein’s native state.

Computational investigation reveals that the mutant strains of SARS-CoV2 have differential structural and binding properties

BACKGROUND AND OBJECTIVES

Remarkable infectivity of severe acute respiratory syndrome-coronavirus 2 (SARS-CoV2) is due to the rapid emergence of various strains which enable the virus to ruling the world. Over the course of SARS-CoV2 pandemic, the scientific communities worldwide are responding to newly emerging genetic variants. However, mechanism behind the persistent infection of these variants is still not known due to the paucity of study of these variants at molecular level. In this scenario, computational methods have immense utility in understanding the molecular and functional properties of different variants.

METHODS

The various mutants (MTs) of SpikeS1 receptor binding domain (RBD) of highly infectious SARS-CoV2 strains were manifested and elucidated the protein structure and binding strength using molecular dynamics (MD) simulation and protein-protein docking approaches.

RESULTS

MD simulation study showed that all MTs exhibited stable structures with altered functional properties. Furthermore, the binding strength of different MTs along with WT (wildtype) was revealed that MTs showed differential binding affinities to host protein with high binding strength exhibited by V367F and V483A MTs.

CONCLUSION

Hence, this study shed light on the molecular basis of infection caused by different variants of SARS-CoV2, which might play an important role in to cease the transmission and pathogenesis of virus and also implicate in rational designing of a specific drug.

Role of cotranslational folding for β-sheet-enriched proteins: A perspective from molecular dynamics simulations

The formations of correct three-dimensional structures of proteins are essential to their functions. Cotranslational folding is vital for proteins to form correct structures in vivo. Although some experiments have shown that cotranslational folding can improve the efficiency of folding, its microscopic mechanism is not yet clear. Previously, we built a model of the ribosomal exit tunnel and investigated the cotranslational folding of a three-helix protein by using all-atom molecular dynamics simulations. Here we study the cotranslational folding of three β-sheet-enriched proteins using the same method. The results show that cotranslational folding can enhance the helical population in most cases and reduce non-native long-range contacts before emerging from the ribosomal exit tunnel. After exiting the tunnel, all proteins fall into local minimal states and the structural ensembles of cotranslational folding show more helical conformations than those of free folding. In particular, for one of the three proteins, the GTT WW domain, we find that one local minimum state of the cotranslational folding is the known folding intermediate, which is not found in free folding. This result suggests that the cotranslational folding may increase the folding efficiency by accelerating the sampling more than by avoiding the misfolded state, which is presently a mainstream viewpoint.

Slowest-first protein translation scheme: Structural asymmetry and co-translational folding

Proteins are translated from the N to the C terminus, raising the basic question of how this innate directionality affects their evolution. To explore this question, we analyze 16,200 structures from the Protein Data Bank (PDB). We find remarkable enrichment of α helices at the C terminus and β strands at the N terminus. Furthermore, this α-β asymmetry correlates with sequence length and contact order, both determinants of folding rate, hinting at possible links to co-translational folding (CTF). Hence, we propose the "slowest-first" scheme, whereby protein sequences evolved structural asymmetry to accelerate CTF: the slowest of the cooperatively folding segments are positioned near the N terminus so they have more time to fold during translation. A phenomenological model predicts that CTF can be accelerated by asymmetry in folding rate, up to double the rate, when folding time is commensurate with translation time; analysis of the PDB predicts that structural asymmetry is indeed maximal in this regime. This correspondence is greater in prokaryotes, which generally require faster protein production. Altogether, this indicates that accelerating CTF is a substantial evolutionary force whose interplay with stability and functionality is encoded in secondary structure asymmetry.

Vassiliev measures of complexity of open and closed curves in 3-space

In this article, we define Vassiliev measures of complexity for open curves in 3-space. These are related to the coefficients of the enhanced Jones polynomial of open curves in 3-space. These Vassiliev measures are continuous functions of the curve coordinates; as the ends of the curve tend to coincide, they converge to the corresponding Vassiliev invariants of the resulting knot. We focus on the second Vassiliev measure from the enhanced Jones polynomial for closed and open curves in 3-space. For closed curves, this second Vassiliev measure can be computed by a Gauss code diagram and it has an integral formulation, the double alternating self-linking integral. The double alternating self-linking integral is a topological invariant of closed curves and a continuous function of the curve coordinates for open curves in 3-space. For polygonal curves, the double alternating self-linking integral obtains a simpler expression in terms of geometric probabilities.

Topological principles of protein folding

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.

Topoly: Python package to analyze topology of polymers

The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.

Structural characterization of calcium-binding sunflower seed and peanut peptides and enhanced calcium transport by calcium complexes in Caco-2 cells

BACKGROUND

Peptide-Ca complexes can promote Ca absorption. The present study aimed to determine the transport mechanism and structural characteristics of sunflower seed and peanut peptides with high Ca binding capacity with respect to developing third-generation Ca supplements and functional food ingredients.

RESULTS

High Ca-binding fractions of 1-3 kDa sunflower seed peptide (SSP₄ ) and ≥ 10 kDa peanut peptide (PP₁ ) had higher amount of Ca transported than CaCl₂ and two hydrolyzed proteins in Caco-2 cells. SSP₄ and PP₁ were separated by Ca ion metal chelate affinity chromatography, and high Ca-binding fractions were observed for SSP₄ -P₂ and PP₁ -P₂ . The amino acid sequences of SSP₄ -P₂ and PP₁ -P₂ were characterized by high-performance liquid chromatography-electrospray ionization-time of flight mass spectrometry. Seven and eight peptides were identified from SSP₄ -P₂ and PP₁ -P₂ , respectively. These peptides had molecular weights ranging from 1500 Da to 2500 Da and a large number of characteristic amino acid sequences, such as EEEQQQ, EQ-QQQ-QQ, QQ-QQQQQ, E-EEE, EE-EEQ, RR, Q-QQ-QQQ, EE-EQ-EE-Q, QQ-QQQQ, and Q-QQQQ, where 'E' is glutamic acid and 'Q' is glutamine.

CONCLUSION

SSP₄ and PP₁ can promote Ca transport in Caco-2 cells without affecting cell permeability. The amino acid sequences of SSP₄ -P₂ and PP₁ -P₂ with high Ca-binding abilities contain characteristic sequences, such as continuous glutamic acid and glutamine, and have low molecular weights. © 2020 Society of Chemical Industry.

GISA: using Gauss Integrals to identify rare conformations in protein structures

The native structure of a protein is important for its function, and therefore methods for exploring protein structures have attracted much research. However, rather few methods are sensitive to topologic-geometric features, the examples being knots, slipknots, lassos, links, and pokes, and with each method aimed only for a specific set of such configurations. We here propose a general method which transforms a structure into a ”fingerprint of topological-geometric values” consisting in a series of real-valued descriptors from mathematical Knot Theory. The extent to which a structure contains unusual configurations can then be judged from this fingerprint. The method is not confined to a particular pre-defined topology or geometry (like a knot or a poke), and so, unlike existing methods, it is general. To achieve this our new algorithm, GISA, as a key novelty produces the descriptors, so called Gauss integrals, not only for the full chains of a protein but for all its sub-chains. This allows fingerprinting on any scale from local to global. The Gauss integrals are known to be effective descriptors of global protein folds. Applying GISA to sets of several thousand high resolution structures, we first show how the most basic Gauss integral, the writhe, enables swift identification of pre-defined geometries such as pokes and links. We then apply GISA with no restrictions on geometry, to show how it allows identifying rare conformations by finding rare invariant values only. In this unrestricted search, pokes and links are still found, but also knotted conformations, as well as more highly entangled configurations not previously described. Thus, an application of the basic scan method in GISA’s tool-box revealed 10 known cases of knots as the top positive writhe cases, while placing at the top of the negative writhe 14 cases in cis-trans isomerases sharing a spatial motif of little secondary structure content, which possibly has gone unnoticed. Possible general applications of GISA are fold classification and structural alignment based on local Gauss integrals. Others include finding errors in protein models and identifying unusual conformations that might be important for protein folding and function. By its broad potential, we believe that GISA will be of general benefit to the structural bioinformatics community. GISA is coded in C and comes as a command line tool. Source and compiled code for GISA plus read-me and examples are publicly available at GitHub (https://github.com).

On folding of entangled proteins: knots, lassos, links and θ-curves

Around 6% of protein structures deposited in the PDB are entangled, forming knots, slipknots, lassos, links, and θ-curves. In each of these cases, the protein backbone weaves through itself in a complex way, and at some point passes through a closed loop, formed by other regions of the protein structure. Such a passing can be interpreted as crossing a topological barrier. How proteins overcome such barriers, and therefore different degrees of frustration, challenged scientists and has shed new light on the field of protein folding. In this review, we summarize the current knowledge about the free energy landscape of proteins with non-trivial topology. We describe identified mechanisms which lead proteins to self-tying. We discuss the influence of excluded volume, such as crowding and chaperones, on tying, based on available data. We briefly discuss the diversity of topological complexity of proteins and their evolution. We also list available tools to investigate non-trivial topology. Finally, we formulate intriguing and challenging questions at the boundary of biophysics, bioinformatics, biology, and mathematics, which arise from the discovery of entangled proteins.

Cotranslational Folding of Proteins on the Ribosome

Many proteins in the cell fold cotranslationally within the restricted space of the polypeptide exit tunnel or at the surface of the ribosome. A growing body of evidence suggests that the ribosome can alter the folding trajectory in many different ways. In this review, we summarize the recent examples of how translation affects folding of single-domain, multiple-domain and oligomeric proteins. The vectorial nature of translation, the spatial constraints of the exit tunnel, and the electrostatic properties of the ribosome-nascent peptide complex define the onset of early folding events. The ribosome can facilitate protein compaction, induce the formation of intermediates that are not observed in solution, or delay the onset of folding. Examples of single-domain proteins suggest that early compaction events can define the folding pathway for some types of domain structures. Folding of multi-domain proteins proceeds in a domain-wise fashion, with each domain having its role in stabilizing or destabilizing neighboring domains. Finally, the assembly of protein complexes can also begin cotranslationally. In all these cases, the ribosome helps the nascent protein to attain a native fold and avoid the kinetic traps of misfolding.

Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.