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Machine learning models for predicting protein condensate formation from sequence determinants and embeddings

Intracellular phase separation of proteins into biomolecular condensates is increasingly recognised as an important phenomenon for cellular compartmentalisation and regulation of biological function. Different hypotheses about the parameters that determine the tendency of proteins to form condensates have been proposed with some of them probed experimentally through the use of constructs generated by sequence alterations. To broaden the scope of these observations, here, we established an in silico strategy for understanding on a global level the associations between protein sequence and condensate formation, and used this information to construct machine learning classifiers for predicting liquid-liquid phase separation (LLPS) from protein sequence. Our analysis highlighted that LLPS-prone sequences are more disordered, hydrophobic and of lower Shannon entropy than sequences in the Protein Data Bank or the Swiss-Prot database, and have their disordered regions enriched in polar, aromatic and charged residues. Using these determining features together with neural network based word2vec sequence embeddings, we developed machine learning classifiers for predicting protein condensate formation. Our model, trained to distinguish LLPS-prone sequences from structured proteins, achieved high accuracy (93%; 25-fold cross-validation) and identified condensate forming sequences from external independent test data at 97% sensitivity. Moreover, in combination with a classifier that had developed a nuanced insight into the features governing protein phase behaviour by learning to distinguish between sequences of varying LLPS propensity, the sensitivity was supplemented with high specificity (approximated ROC-AUC of 0.85). These results provide a platform rooted in molecular principles for understanding protein phase behaviour. The predictor is accessible from https://deephase.ch.cam.ac.uk/. Significance StatementThe tendency of many cellular proteins to form protein-rich biomolecular condensates underlies the formation of subcellular compartments and has been linked to various physiological functions. Understanding the molecular basis of this fundamental process and predicting protein phase behaviour have therefore become important objectives. To develop a global understanding of how protein sequence determines its phase behaviour, here, we constructed bespoke datasets of proteins of varying phase separation propensity and identified explicit biophysical and sequence-specific features common to phase separating proteins. Moreover, by combining this insight with neural network based sequence embeddings, we trained machine learning classifiers that identified phase separating sequences with high accuracy, including from independent external test data. The predictor is available from https://deephase.ch.cam.ac.uk/.

biophysics↗

Statistical Physics of DNA melting: Unveiling the artificial corrections for self-complementary sequences

DNA hybridization is at the heart of countless biological and biotechnological processes. Its theoretical modeling played a crucial role, since it has enabled extracting the relevant thermodynamic parameters from systematic measurements of DNA melting curves. However, in its current state, hybridization modelling requires introducing an extra entropic contribution in self-complementary sequences that lacks any biophysical meaning. In this article, we propose a framework based on statistical physics to describe DNA hybridization and melting in an arbitrary mixture of DNA strands. In particular, we are able to analytically derive closed expressions of the system partition functions for any number N of strings, and explicitly calculate them in two paradigmatic situations: (i) a system made of self-complementary sequences and (ii) a system comprising two mutually complementary sequences. We derive the melting curve in the thermodynamic limit (N [->] {infty}) of our description, which differs from the expression commonly used to evaluate the melting of self-complementary systems in that it does not require correcting terms. We provide a thorough study comprising limit cases and alternative approaches showing how our framework can give a comprehensive view of hybridization and melting phenomena. SIGNIFICANCEIn this study, we provide a transparent derivation of the melting curves of DNA duplexes using basic tools of statistical mechanics. We find that in the case of self-complementary sequences, our expression differs from the one used in literature, which is generally amended by the introduction of a phenomenological correction which in our approach becomes unnecessary. By offering a clean formal description of DNA hybridization, our approach sharpens our understanding of DNA interactions and opens the way to study the pairing of DNA oligomers away from any thermodynamic limit.

biophysics↗

What Markov state models can and cannot do: Correlation versus path-based observables in protein folding models

Markov state models (MSMs) have been widely applied to study the kinetics and pathways of protein conformational dynamics based on statistical analysis of molecular dynamics (MD) simulations. These MSMs coarse-grain both configuration space and time in ways that limit what kinds of observables they can reproduce with high fidelity over different spatial and temporal resolutions. Despite their popularity, there is still limited understanding of which biophysical observables can be computed from these MSMs in a robust and unbiased manner, and which suffer from the space-time coarse-graining intrinsic in the MSM model. Most theoretical arguments and practical validity tests for MSMs rely on long-time equilibrium kinetics, such as the slowest relaxation timescales and experimentally observable time-correlation functions. Here, we perform an extensive assessment of the ability of well-validated protein folding MSMs to accuractely reproduce path-based observable such as mean first-passage times (MFPTs) and transition path mechanisms compared to a direct trajectory analysis. We also assess a recently proposed class of history-augmented MSMs (haMSMs) that exploit additional information not accounted for in standard MSMs. We conclude with some practical guidance on the use of MSMs to study various problems in conformational dynamics of biomolecules. In brief, MSMs can accurately reproduce correlation functions slower than the lag time, but path-based observables can only be reliably reproduced if the lifetimes of states exceed the lag time, which is a much stricter requirement. Even in the presence of short-lived states, we find that haMSMs reproduce path-based observables more reliably.

biophysics↗

Dissecting the role of glutamine in seeding peptide aggregation.

Poly glutamine and glutamine-rich peptides play a central role in a plethora of pathological aggregation events. However, biophysical characterization of soluble oligomers --the most toxic species involved in these processes-- remains elusive due to their structural heterogeneity and dynamical nature. Here, we exploit the high spatio-temporal resolution of simulations as a computational microscope to characterize the aggregation propensity and morphology of a series of polyglutamine and glutamine-rich peptides. Comparative analysis of ab-initio aggregation pinpointed a double role for glutamines. In the first phase, glutamines mediate seeding by pairing monomeric peptides, which serve as primers for higher-order nucleation. According to the glutamine content, these low molecular-weight oligomers may then proceed to create larger aggregates. Once within the aggregates, buried glutamines continue to play a role in their maturation by optimizing solvent-protected hydrogen bonds networks. TOC / Abstract Figure O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=109 SRC="FIGDIR/small/381632v1_ufig1.gif" ALT="Figure 1"> View larger version (26K): org.highwire.dtl.DTLVardef@251f33org.highwire.dtl.DTLVardef@123506borg.highwire.dtl.DTLVardef@174d9cdorg.highwire.dtl.DTLVardef@875f00_HPS_FORMAT_FIGEXP M_FIG C_FIG

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A generalised mechano-kinetic model for use in multiscale simulation protocols.

Many biophysical systems and proteins undergo mesoscopic conformational changes in order to perform their biological function. However, these conformational changes often result from a cascade of atomistic interactions within a much larger overall object. For simulations of such systems, the computational cost of retaining high-resolution structural and dynamical information whilst at the same time observing large scale motions over long times is high. Furthermore, this cost is only going to increase as ever larger biological objects are observed experimentally at high resolution. We derive a generalised mechano-kinetic simulation framework which aims to compensate for these disparate time scales, capable of dynamically exploring a defined mechanical energy landscape whilst at the same time performing kinetic transitions between discretely defined states. With insight from the theory of Markov state models and transition state theory, the framework models continuous dynamical motion at coarse-grained length scales whilst simultaneously including fine-detail, chemical reactions or conformational changes implicitly using a kinetic model. The kinetic model is coupled to the dynamic model in a highly generalised manner, such that kinetic transition rates are continuously modulated by the dynamic simulation. Further, it can be applied to any defined continuous energy landscape, and hence, any existing dynamic simulation framework. We present a series of analytical examples to validate the framework, and showcase its capabilities for studying more complex systems by simulating protein unfolding via single-molecule force spectroscopy on an atomic force microscope. Author summaryOur intention with this work is to provide a generalised, highly coarse-grained model to allow kinetic processes (conformational changes, protein unfolding, chemical reactions etc) to occur within the context of a dynamic simulation. Performing computationally intensive dynamic simulations to obtain kinetic information can be unjustifiably costly and scientifically inefficient, and so we instead want to emphasise that experimentally available kinetic information can be used to infer the underlying dynamics they result from. We hope our work can begin a discussion on the topic of computationally efficient science, and continue the drive towards collaborative science between theory and experimentation.

biophysics↗

ATP hydrolysis coordinates the activities of two motors in a dimeric chromatin remodeling enzyme

ATP-dependent chromatin remodelers are essential enzymes that restructure eukaryotic genomes to enable all DNA-based processes. The diversity and complexity of these processes are matched by the complexity of the enzymes that carry them out, making remodelers a challenging class of molecular motors to study by conventional methods. Here we use a single molecule biophysical assay to overcome some of these challenges, enabling a detailed mechanistic dissection of a paradigmatic remodeler reaction, that of sliding a nucleosome towards the longer DNA linker. We focus on how two motors of a dimeric remodeler coordinate to accomplish such directional sliding. We find that ATP hydrolysis by both motors promotes coordination, suggesting a role for ATP in resolving the competition for directional commitment. Furthermore, we show an artificially constitutive dimer is no more or less coordinated, but is more processive, suggesting a cell could modulate a remodelers oligomeric state to modulate local chromatin dynamics.

biophysics↗

Ultrafast Brownian-ratchet mechanism for protein translocation by a AAA+ machine

AAA+ ring-shaped machines, such as ClpB and Hsp104, mediate substrate translocation through their central channel by a set of pore loops. Recent structural studies suggested a universal hand-over-hand translocation mechanism, in which pore loops are moving rigidly in tandem with their corresponding subunits. However, functional and biophysical studies are in discord with this model. Here, we directly measure the real-time dynamics of the pore loops of ClpB and their response to substrate binding, using single-molecule FRET spectroscopy. All pore loops undergo large-amplitude fluctuations on the microsecond timescale, and change their conformation upon interaction with substrate proteins. Pore-loop conformational dynamics are modulated by nucleotides and strongly correlate with disaggregation activity. The differential behavior of the pore loops along the axial channel points to a fast Brownian-ratchet translocation mechanism, which likely acts in parallel to the much slower hand-over-hand process.

biophysics↗

Nucleosome plasticity is a critical element of chromatin liquid-liquid phase separation and multivalent nucleosome interactions

Liquid-liquid phase separation (LLPS) of chromatin is an important mechanism that helps explain the membrane-less compartmentalization of the nucleus. Because chromatin compaction and LLPS are collective phenomena, linking their modulation to biophysical features of individual nucleosomes is challenging. Here, we develop a novel multiscale chromatin model that integrates atomistic representations, a chemically-specific coarse-grained model, and a minimal model. In tandem, we devise a transferable Debye-length exchange molecular dynamics approach to achieve enhanced sampling of high-resolution chromatin. We find that nucleosome thermal fluctuations become significant at physiological salt concentrations and destabilize the 30-nm fiber. Nucleosome breathing favors stochastic folding of chromatin and promotes LLPS by simultaneously boosting the transient nature and heterogeneity of nucleosome-nucleosome contacts, and the effective nucleosome valency. Our results put forward the intrinsic plasticity of nucleosomes as a key element in the liquid-like behavior of chromatin, and help reconcile longstanding differences between fiber-based and in vivo chromatin models.

biophysics↗

N-terminal VP1 truncations favor T=1 norovirus-like particles

Noroviruses cause immense sporadic gastroenteritis outbreaks worldwide. Emerging genotypes, which are divided based on VP1 sequence, further enhance this public threat. Self-assembling properties of the human norovirus major capsid protein VP1 are crucial for using virus-like particles (VLPs) for vaccine development. However, there is no vaccine available yet. Here, VLPs from different variants produced in insect cells are characterized in detail using a set of biophysical and structural tools. We are using native mass spectrometry, gas-phase electrophoretic mobility molecular analysis and proteomics to get clear insights into particle size, structure, composition as well as stability. Generally, noroviruses have been known to form mainly T=3 particles. Importantly, we identify a major truncation in the capsid proteins as a likely cause for the formation of merely T=1 particles. For vaccine development, particle production needs to be a reproducible, reliable process. Understanding the underlying processes in capsid size variation will help to produce particles of a defined capsid size presenting antigens consistent with intact virions. Next to vaccine production itself, this would be immensely beneficial for bio-/nano-technological approaches using viral particles as carriers or triggers for immunological reactions.

biophysics↗

Multi-parameter formulation development for an HIV-vaccine protein with direct validation of epitope binding integrity and stoichiometry

Vaccines are on the front line-of-defense against infectious diseases, ranging from threats we are familiar with, including polio, tuberculosis, or HIV, to novel and emerging threats such as SARS-CoV-2. Successful development of new protein-based vaccines requires sophisticated and efficient development of storage and formulation conditions. Here we demonstrate the combined power of 2binds sophisticated buffer matrix FORMOscreen(R) and NanoTemper Technologies novel Prometheus Panta high-throughput Dynamic Light Scattering/Nano Differential Scanning Fluorimetry instrument. We show that this combination can comprehensively improve critical biophysical parameters for the HIV-1 vaccine BG505-SOSIP and find the optimal formulation condition with unmatched efficiency.

biophysics↗

Mechanistic basis for ubiquitin modulation of a protein energy landscape

Ubiquitin is a common posttranslational modification canonically associated with targeting proteins to the 26S proteasome for degradation and also plays a role in numerous other non-degradative cellular processes. Ubiquitination at certain sites destabilizes the substrate protein, with consequences for proteasomal processing, while ubiquitination at other sites has little energetic effect. How this site specificity--and, by extension, the myriad effects of ubiquitination on substrate proteins--arises remains unknown. Here, we systematically characterize the atomic-level effects of ubiquitination at various sites on a model protein, barstar, using a combination of NMR, hydrogen-deuterium exchange mass spectrometry, and molecular dynamics simulation. We find that, regardless of the site of modification, ubiquitination does not induce large structural rearrangements in the substrate. Destabilizing modifications, however, increase fluctuations from the native state resulting in exposure of the substrates C terminus. Both of the sites occur in regions of barstar with relatively high conformational flexibility. Destabilization, however, appears to occur through different thermodynamic mechanisms, involving a reduction in entropy in one case and a loss in enthalpy in another. By contrast, ubiquitination at a non-destabilizing site protects the substrate C terminus through intermittent formation of a structural motif with the last three residues of ubiquitin. Thus, the biophysical effects of ubiquitination at a given site depend greatly on local context. Taken together, our results reveal how a single post-translational modification can generate a broad array of distinct effects, providing a framework to guide the design of proteins and therapeutics with desired degradation and quality-control properties. (248 words) Significance StatementFluctuations on a protein energy landscapes encode the mechanistic basis for vital biological processes not always evident from static structures alone. Ubiquitination, a key posttranslational modification, can affect a proteins energy landscape with consequences for proteasomal degradation, but the molecular mechanisms driving ubiquitin-induced energetic changes remain elusive. Here, we systematically characterize the energetic effects of ubiquitination at three sites on a model protein. We find that distinct thermodynamic mechanisms can produce the same outcome of ubiquitin-induced destabilization at sensitive sites. At a non-sensitive site, we observe formation of a substrate-ubiquitin interaction that may serve to protect against destabilization. This work will enable development of predictive models of the effect of ubiquitin at any given site on a protein with implications for understanding and engineering regulated ubiquitin signaling and protein quality control in vivo.

biophysics↗

Construction of a liquid-liquid phase separation system from the gel-sol transition of elongated protein microgels in a crowding agent

Liquid proteinaceous materials have been frequently found in cells or tissues and are crucial for various biological processes. Unlike their solid-state counterparts, liquid-state protein compartments are challenging to engineer and control at the microscale. Conventionally, gelation (sol-gel transition) of biological molecules has been thought to be the intermediate step between liquid-liquid phase separation (LLPS) states and insoluble aggregates that are related to protein functions, malfunctions and even diseases. However, the opposite process, i.e., the gel-sol transition of materials, has not been broadly explored. Here we describe a thermoresponsive gel-sol transition of a protein in a crowded environment that results in a demixed LLPS state, contradicting the common consequence of a one-phase protein solution by the end of such transition at elevated temperature without crowding agents. We also demonstrate a simple method to monitor the gel-sol transition by showing that elongated gelatin microgels can evolve towards a spherical morphology in the crowding agents because of interfacial tension. The LLPS system was explored for the diffusion of small particles for drug-release application scenarios. Our results demonstrate a route for the rapid construction of LLPS models, where the gel-sol transition of the protein-rich phase is monitorable. The models are featured with tunable size and dimensional monodispersity of dispersed condensates. The present study can be employed in biophysics and bioengineering with practices such as 3D printing and temperature sensing.

biophysics↗

Capacity to multitask limits cellular chemotaxis

Chemotaxis is ubiquitous in many biological processes, but it still remains elusive how cells sense and decipher multiple chemical cues. In this study, we postulate a hypothesis that the chemotactic performance of cells under complex cues is regulated by the signal processing capacity of the cellular sensory machinery. The underlying rationale is that cells in vivo should be able to sense and process multiple chemical cues, whose magnitude and compositions are entangled, to determine their migration direction. We experimentally show that the combination of TGF-{beta} and EGF suppresses the chemotactic performance of cancer cells using independent receptors to sense the two cues. Based on this observation, we develop a biophysical framework suggesting that the antagonism is caused by the saturation of the signal processing capacity, but not by the mutual repression. Our framework suggests the significance of the signal processing capacity in the cellular sensory machinery.

biophysics↗

Allosteric conformational ensembles have unlimited capacity for integrating information

Integration of binding information by macromolecular entities is fundamental to cellular functionality. Recent work has shown that such integration cannot be explained by pairwise cooperativities, in which binding is modulated by binding at another site. Higher-order cooperativities (HOCs), in which binding is collectively modulated by multiple other binding events, appears to be necessary but an appropriate mechanism has been lacking. We show here that HOCs arise through allostery, in which effective cooperativity emerges indirectly from an ensemble of dynamically-interchanging conformations. Conformational ensembles play important roles in many cellular processes but their integrative capabilities remain poorly understood. We show that sufficiently complex ensembles can implement any form of information integration achievable without energy expenditure, including all HOCs. Our results provide a rigorous biophysical foundation for analysing the integration of binding information through allostery. We discuss the implications for eukaryotic gene regulation, where complex conformational dynamics accompanies widespread information integration.

biophysics↗

Computational Analysis of Dynamic Allostery and Control in the three SARS-CoV-2 non-structural proteins

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which caused the COVID-19 pandemic, has no vaccine or antiviral drugs available to the public, at the time of writing. The virus non-structural proteins are promising drug targets because of their vital role in the viral cycle. A significant body of work has been focused on finding inhibitors which covalently and competitively bind the active site of the non-structural proteins, but little has been done to address regions other than the active site, i.e. for non-competitive inhibition. Here we extend previous work on the SARS-CoV-2 Mpro (nsp5) to three other SARS-CoV-2 proteins: host shutoff factor (nsp1), papain-like protease (nsp3, also known as PLpro) and RNA-dependent RNA-polymerase (nsp12, also known as RdRp) in complex with nsp7 and nsp8 cofactors. Using open-source software (DDPT) to construct Elastic Network Models (ENM) of the chosen proteins we analyse their fluctuation dynamics and thermodynamics, as well as using this protein family to study convergence and robustness of the ENM. Exhaustive 2-point mutational scans of the ENM and their effect on fluctuation free energies suggest several new candidate regions, distant from the active site, for control of the proteins function, which may assist the drug development based on the current small molecule binding screens. The results also provide new insights, including non-additive effects of double-mutation or inhibition, into the active biophysical research field of protein fluctuation allostery and its underpinning dynamical structure.

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Molecular recognition of sugar binding in a melibiose transporter MelB by X-ray crystallography

The symporter melibiose permease MelB is the best-studied representative from MFS_2 family and the only protein in this large family with crystal structure determined. Previous thermodynamic studies show that MelB utilizes a cooperative binding as the core mechanism for its obligatory symport. Here we present two sugar-bound X-ray crystal structures of a Salmonella typhimurium MelB D59C uniport mutant that binds and catalyzes melibiose transport uncoupled to either cation, as determined by biochemical and biophysical characterizations. The two structures with bound nitrophenyl--D-galactoside or dodecyl-{beta}-D-melibioside, which were refined to a resolution of 3.05 or 3.15 [A], respectively, are virtually identical at an outward-facing conformation; each one contains a -galactoside molecule in the middle of protein. In the substrate-binding site, the galactosyl moiety on both ligands are at an essentially same configuration, so a galactoside specificity determinant pocket can be recognized, and hence the molecular recognition mechanism for the binding of sugar in MelB is deciphered. The data also allow to assign the conserved cation-binding pocket, which is directly connected to the sugar specificity determinant pocket. The intimate connection between the two selection sites lays the structural basis for the cooperative binding and coupled transport. This key structural finding answered the long-standing question on the substrate binding for the Na+-coupled MFS family of transporters. SignificanceMajor facilitator superfamily_2 transporters contain >10,000 members that are widely expressed from bacteria to mammalian cells, and catalyze uptake of varied nutrients from sugars to phospholipids. While several crystal structures with bound sugar for other MFS permeases have been determined, they are either uniporters or symporters coupled solely to H+. MelB catalyzes melibiose symport with either Na+, Li+, or H+, a prototype for Na+-coupled MFS transporters, but its sugar recognition has been a long-unsolved puzzle. Two high-resolution crystal structures presented here clearly reveal the molecular recognition mechanism for the binding of sugar in MelB. The substrate-binding site is characterized with a small specificity groove adjoining a large nonspecific cavity, which could offer a potential for future exploration of active transporters for drug delivery.

biophysics↗

Solubility product constant directs the formation of biomolecular condensates

Biomolecular condensates, formed by liquid-liquid phase separation (LLPS), are important cellular structures. Using stochastic network-free kinetic models, we establish a physical-chemical basis for the concentration threshold of heterotypic multivalent molecules required for LLPS. We associate phase separation with a bimodal partitioning of the cluster distribution into small oligomers vs. huge polymers. The simulations reveal that LLPS obeys the solubility product constant (Ksp): the product of monomer concentrations, accounting for ideal stoichiometries, does not exceed a threshold no matter how much additional monomer is added to the system - additional monomer is funneled into large clusters. The Ksp applies over a range of valencies and stoichiometries. However, consistent with the importance of disordered domains for LLPS, removing flexible linker domains funnels valency-matched monomers into a "dimer trap", and Ksp no longer defines a threshold for large cluster formation. We propose Ksp as a new tool for elucidating biomolecular condensate biophysics.

biophysics↗

Stable Polymer Bilayers for Protein Channel Recordings at High Guanidinium Chloride Concentrations

Use of chaotropic reagents is common in biophysical characterization of biomolecules. When the study involves transmembrane protein channels, the stability of the protein channel and supporting bilayer membrane must be considered. In this letter we show that planar bilayers composed of poly(1,2-butadiene)-b-poly(ethylene oxide) diblock copolymer are stable and leak-free at high guanidinium chloride concentrations, in contrast to diphytanoyl phosphatidylcholine bilayers which exhibit deleterious leakage under similar conditions. Further, insertion and functional analysis of channels such as -hemolysin and MspA are straightforward in these polymer membranes. Finally, we demonstrate that -hemolysin channels maintain their structural integrity at 2M guanidinium chloride concentrations using blunt DNA hairpins as molecular reporters.

biophysics↗