Determination of contact maps in proteins: A combination of structural and chemical approaches

Multiple-Basin Go̅-Martini for Investigating Conformational Transitions and Environmental Interactions of Proteins

Proteins are inherently dynamic molecules, and their conformational transitions among various states are essential for numerous biological processes, which are often modulated by their interactions with surrounding environments. Although molecular dynamics (MD) simulations are widely used to investigate these transitions, all-atom (AA) methods are often limited by short time scales and high computational costs, and coarse-grained (CG) implicit-solvent Go̅-like models are usually incapable of studying the interactions between proteins and their environments. Here, we present an approach called Multiple-basin Go̅-Martini, which combines the recent Go̅-Martini model with an exponential mixing scheme to facilitate the simulation of spontaneous protein conformational transitions in explicit environments. We demonstrate the versatility of our method through five diverse case studies: GlnBP, Arc, Hinge, SemiSWEET, and TRAAK, representing ligand-binding proteins, fold-switching proteins, de novo designed proteins, transporters, and mechanosensitive ion channels, respectively. Multiple-basin Go̅-Martini offers a new computational tool for investigating protein conformational transitions, identifying key intermediate states, and elucidating essential interactions between proteins and their environments, particularly protein-membrane interactions. In addition, this approach can efficiently generate thermodynamically meaningful data sets of protein conformational space, which may enhance deep learning-based models for predicting protein conformation distributions.

GōMartini 3: From large conformational changes in proteins to environmental bias corrections

Coarse-grained modeling has become an important tool to supplement experimental measurements, allowing access to spatio-temporal scales beyond all-atom based approaches. The GōMartini model combines structure- and physics-based coarse-grained approaches, balancing computational efficiency and accurate representation of protein dynamics with the capabilities of studying proteins in different biological environments. This paper introduces an enhanced GōMartini model, which combines a virtual-site implementation of Gō models with Martini 3. The implementation has been extensively tested by the community since the release of the reparametrized version of Martini. This work demonstrates the capabilities of the model in diverse case studies, ranging from protein-membrane binding to protein-ligand interactions and AFM force profile calculations. The model is also versatile, as it can address recent inaccuracies reported in the Martini protein model. Lastly, the paper discusses the advantages, limitations, and future perspectives of the Martini 3 protein model and its combination with Gō models.

Conformational and Stability Analysis of SARS-CoV-2 Spike Protein Variants by Molecular Simulation

We performed a comprehensive structural analysis of the conformational space of several spike (S) protein variants using molecular dynamics (MD) simulations. Specifically, we examined four well-known variants (Delta, BA.1, XBB.1.5, and JN.1) alongside the wild-type (WT) form of SARS-CoV-2. The conformational states of each variant were characterized by analyzing their distributions within a selected space of collective variables (CVs), such as inter-domain distances between the receptor-binding domain (RBD) and the N-terminal domain (NTD). Our primary focus was to identify conformational states relevant to potential structural transitions and to determine the set of native contacts (NCs) that stabilize these conformations. The results reveal that genetically more distant variants, such as XBB.1.5, BA.1, and JN.1, tend to adopt more compact conformational states compared to the WT. Additionally, these variants exhibit novel NC profiles, characterized by an increased number of specific contacts distributed among ionic, polar, and nonpolar residues. We further analyzed the impact of specific mutations, including T478K, N500Y, and Y504H. These mutations not only enhance interactions with the human host receptor but also alter inter-chain stability by introducing additional NCs compared to the WT. Consequently, these mutations may influence the accessibility of certain protein regions to neutralizing antibodies. Overall, these findings contribute to a deeper understanding of the structural and functional variations among S protein variants.

Nanomechanical footprint of SARS-CoV-2 variants in complex with a potent nanobody by molecular simulations

Rational design of novel antibody therapeutics against viral infections such as coronavirus relies on surface complementarity and high affinity for their effectiveness. Here, we explore an additional property of protein complexes, the intrinsic mechanical stability, in SARS-CoV-2 variants when complexed with a potent antibody. In this study, we utilized a recent implementation of the GōMartini 3 approach to investigate large conformational changes in protein complexes with a focus on the mechanostability of the receptor-binding domain (RBD) from WT, Alpha, Delta, and XBB.1.5 variants in complex with the H11-H4 nanobody. The analysis revealed moderate differences in mechanical stability among these variants. Also, we identified crucial residues in both the RBD and certain protein segments in the nanobody that contribute to this property. By performing pulling simulations and monitoring the presence of specific native and non-native contacts across the protein complex interface, we provided mechanistic insights into the dissociation process. Force-displacement profiles indicate a tensile force clamp mechanism associated with the type of protein complex. Our computational approach not only highlights the key mechanostable interactions that are necessary to maintain overall stability, but it also paves the way for the rational design of potent antibodies that are mechanostable and effective against emergent SARS-CoV-2 variants.

Martini 3 OliGo̅mers: A Scalable Approach for Multimers and Fibrils in GROMACS

Martini 3 is a widely used coarse-grained simulation method for large-scale biomolecular simulations. It can be combined with a Go̅ model to realistically describe higher-order protein structures while allowing the folding and unfolding events. However, as of today, this method has largely been used only for individual monomers. In this article, we describe how the Go̅ model can be implemented within the framework of Martini 3 for a multimer system, taking into account both intramolecular and intermolecular interactions in an oligomeric protein system. We demonstrate the method by showing how it can be applied to both structural stability maintenance and assembly/disassembly of protein oligomers, using aquaporin tetramer, insulin dimer, and amyloid-β fibril as examples. We find that addition of intermolecular Go̅ potentials stabilizes the quaternary structure of proteins. The strength of the Go̅ potentials can be tuned so that the internal fluctuations of proteins match the behavior of atomistic simulation models, however, the results also show that the use of too strong intermolecular Go̅ potentials weakens the chemical specificity of oligomerization. The Martini-Go̅ model presented here enables the use of Go̅ potentials in oligomeric molecular systems in a computationally efficient and parallelizable manner, especially in the case of homopolymers, where the number of identical protein monomers is high. This paves the way for coarse-grained simulations of large protein complexes, such as viral protein capsids and prion fibrils, in complex biological environments.

OLIVES: A Go̅-like Model for Stabilizing Protein Structure via Hydrogen Bonding Native Contacts in the Martini 3 Coarse-Grained Force Field

Coarse-grained molecular dynamics simulations enable the modeling of increasingly complex systems at millisecond timescales. The transferable coarse-grained force field Martini 3 has shown great promise in modeling a wide range of biochemical processes, yet folded proteins in Martini 3 are not stable without the application of external bias potentials, such as elastic networks or Go̅-like models. We herein develop an algorithm, called OLIVES, which identifies native contacts with hydrogen bond capabilities in coarse-grained proteins and use it to implement a novel Go̅-like model for Martini 3. We show that the protein structure instability originates in part from the lack of hydrogen bond energy in the coarse-grained force field representation. By using realistic hydrogen bond energies obtained from literature ab initio calculations, it is demonstrated that protein stability can be recovered by the reintroduction of a coarse-grained hydrogen bond network and that OLIVES removes the need for secondary structure restraints. OLIVES is validated against known protein complexes and at the same time addresses the open question of whether there is a need for protein quaternary structure bias in Martini 3 simulations. It is shown that OLIVES can reduce the number of bias terms, hereby speeding up Martini 3 simulations of proteins by up to ≈30% on a GPU architecture compared to the established Go̅MARTINI Go̅-like model.

Exploring the Ligand Binding and Conformational Dynamics of the Substrate-Binding Domain 1 of the ABC Transporter GlnPQ

The adenosine triphosphate (ATP)-binding cassette (ABC) importer GlnPQ from Lactococcus lactis has two sequential covalently linked substrate-binding domains (SBDs), which capture the substrates and deliver them to the translocon. The two SBDs differ in their ligand specificities, binding affinities and the distance to the transmembrane domain; interestingly, both SBDs can bind their ligands simultaneously without affecting each other. In this work, we studied the binding of ligands to both SBDs using X-ray crystallography and molecular dynamics simulations. We report three high-resolution structures of SBD1, namely, the wild-type SBD1 with bound asparagine or arginine, and E184D SBD1 with glutamine bound. Molecular dynamics (MD) simulations provide a detailed insight into the dynamics associated with open-closed transitions of the SBDs.

Effect of the Lys62Ala Mutation on the Thermal Stability of BstHPr Protein by Molecular Dynamics

We analyzed the thermal stability of the BstHPr protein through the site-directed point mutation Lys62 replaced by Ala residue using molecular dynamics simulations at five different temperatures: 298, 333, 362, 400, and 450 K, for periods of 1 μs and in triplicate. The results from the mutant thermophilic BstHPrm protein were compared with those of the wild-type thermophilic BstHPr protein and the mesophilic BsHPr protein. Structural and molecular interaction analyses show that proteins lose stability as temperature increases. Mutant and wild-type proteins behave similarly up to 362 K. However, at 400 K the mutant protein shows greater structural instability, losing more buried hydrogen bonds and exposing more of its non-polar residues to the solvent. Therefore, in this study, we confirmed that the salt bridge network of the Glu3-Lys62-Glu36 triad, made up of the Glu3-Lys62 and Glu36-Lys62 ion pairs, provides thermal stability to the thermophilic BstHPr protein.

Structural Rearrangements of Pigeon Cryptochrome 4 Undergoing a Complete Redox Cycle

Cryptochrome is currently the major contender of a protein to underpin magnetoreception, the ability to sense the Earth's magnetic field. Among various types of cryptochromes, cryptochrome 4 has been identified as the likely magnetoreceptor in migratory birds. All-atom molecular dynamics (MD) studies have offered first insights into the structural dynamics of cryptochrome but are limited to a short time scale due to large computational demands. Here, we employ coarse-grained MD simulations to investigate the emergence of long-lived states and conformational changes in pigeon cryptochrome 4. Our coarse-grained simulations complete the picture by permitting observation on a significantly longer time scale. We observe conformational transitions in the phosphate-binding loop of pigeon cryptochrome 4 upon activation and identify prominent motions in residues 440-460, suggesting a possible role as a signaling state of the protein or as a gated interaction site for forming protein complexes that might facilitate downstream processes. The findings highlight the importance of considering longer time scales in studying cryptochrome dynamics and magnetoreception. Coarse-grained MD simulations offer a valuable tool to unravel the complex behavior of cryptochrome proteins and shed new light on the mechanisms underlying their role in magnetoreception. Further exploration of these conformational changes and their functional implications may contribute to a deeper understanding of the molecular mechanisms of magnetoreception in birds.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Computational Peptide Design Cotargeting Glucagon and Glucagon-like Peptide-1 Receptors

Peptides are sustainable alternatives to conventional therapeutics for G protein-coupled receptor (GPCR) linked disorders, promising biocompatible and tailorable next-generation therapeutics for metabolic disorders including type-2 diabetes, as agonists of the glucagon receptor (GCGR) and the glucagon-like peptide-1 receptor (GLP-1R). However, single agonist peptides activating GLP-1R to stimulate insulin secretion also suppress obesity-linked glucagon release. Hence, bioactive peptides cotargeting GCGR and GLP-1R may remediate the blood glucose and fatty acid metabolism imbalance, tackling both diabetes and obesity to supersede current monoagonist therapy. Here, we design and model optimized peptide sequences starting from peptide sequences derived from earlier phage-displayed library screening, identifying those with predicted molecular binding profiles for dual agonism of GCGR and GLP-1R. We derive design rules from extensive molecular dynamics simulations based on peptide-receptor binding. Our newly designed coagonist peptide exhibits improved predicted coupled binding affinity for GCGR and GLP-1R relative to endogenous ligands and could in the future be tested experimentally, which may provide superior glycemic and weight loss control.

An implementation of the Martini coarse-grained force field in OpenMM

We describe a complete implementation of Martini 2 and Martini 3 in the OpenMM molecular dynamics software package. Martini is a widely used coarse-grained force field with applications in biomolecular simulation, materials, and broader areas of chemistry. It is implemented as a force field but makes extensive use of facilities unique to the GROMACS software, including virtual sites and bonded terms that are not commonly used in standard atomistic force fields. OpenMM is a flexible molecular dynamics package widely used for methods development and is competitive in speed on GPUs with other commonly used packages. OpenMM has facilities to easily implement new force field terms, external forces and fields, and other nonstandard features, which we use to implement all force field terms used in Martini 2 and Martini 3. This allows Martini simulations, starting with GROMACS topology files that are processed by custom scripts, with all the added flexibility of OpenMM. We provide a GitHub repository with test cases, compare accuracy and performance between GROMACS and OpenMM, and discuss the limitations of our implementation in terms of direct comparison with GROMACS. We describe a use case that implements the Modeling Employing Limited Data method to apply experimental constraints in a Martini simulation to efficiently determine the structure of a protein complex. We also discuss issues and a potential solution with the Martini 2 topology for cholesterol.

Facilitating CG Simulations with MAD: The MArtini Database Server

The MArtini Database (MAD - https://mad.ibcp.fr) is a web server designed for the sharing of structures and topologies of molecules parametrized with the Martini coarse-grained (CG) force field. MAD can also convert atomistic structures into CG structures and prepare complex systems (including proteins, lipids, etc.) for molecular dynamics (MD) simulations at the CG level. It is dedicated to the generation of input files for Martini 3, the most recent version of this popular CG force field. Specifically, the MAD server currently includes tools to submit or retrieve CG models of a wide range of molecules (lipids, carbohydrates, nanoparticles, etc.), transform atomistic protein structures into CG structures and topologies, with fine control on the process and assemble biomolecules into large systems, and deliver all files necessary to start simulations in the GROMACS MD engine.

May the force be with you: The role of hyper-mechanostability of the bone sialoprotein binding protein during early stages of Staphylococci infections

The bone sialoprotein-binding protein (Bbp) is a mechanoactive MSCRAMM protein expressed on the surface of Staphylococcus aureus that mediates adherence of the bacterium to fibrinogen-α (Fgα), a component of the bone and dentine extracellular matrix of the host cell. Mechanoactive proteins like Bbp have key roles in several physiological and pathological processes. Particularly, the Bbp: Fgα interaction is important in the formation of biofilms, an important virulence factor of pathogenic bacteria. Here, we investigated the mechanostability of the Bbp: Fgα complex using in silico single-molecule force spectroscopy (SMFS), in an approach that combines results from all-atom and coarse-grained steered molecular dynamics (SMD) simulations. Our results show that Bbp is the most mechanostable MSCRAMM investigated thus far, reaching rupture forces beyond the 2 nN range in typical experimental SMFS pulling rates. Our results show that high force-loads, which are common during initial stages of bacterial infection, stabilize the interconnection between the protein's amino acids, making the protein more "rigid". Our data offer new insights that are crucial on the development of novel anti-adhesion strategies.

Can Polymer Helicity Affect Topological Chirality of Polymer Knots?

We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbors along the chain contour. The sign and magnitude of the coupling coefficient u determine the sense and strength of helicity. The corrugation of the helix is adjusted via the radius R of a spherical, hard excluded volume around each WLC segment. Open and compact helices are, respectively, obtained for R that is either zero or smaller than the length of the WLC bond, and R that is a few times larger than the bond length. We use a Monte Carlo algorithm to sample polymer conformations for different values of u, spanning the range from achiral polymers to chains with well-developed helices. Monitoring the average helix torsion and fluctuations of chiral order as a function of u, for two very different chain lengths, demonstrates that the coil-helix transition in this model is not a phase transition but a crossover. Statistical analysis of conformations forming the simplest chiral knots, 3₁, 5₁, and 5₂, demonstrates that topological mirror symmetry is broken─knots formed by helices with a given sense prefer one handedness over the other. For the 3₁ and 5₁ knots, positive helical sense favors positive handedness. Intriguingly, an opposite trend is observed for 5₂ knots, where positive helical sense promotes negative handedness. We argue that this special coupling between helicity and topological chirality stems from a generic mechanism: conformations where some of the knot crossings are found in "braids" formed by two tightly interwoven sections of the polymer.

A scoring function for the prediction of protein complex interfaces based on the neighborhood preferences of amino acids

Proteins often assemble into functional complexes, the structures of which are more difficult to obtain than those of the individual protein molecules. Given the structures of the subunits, it is possible to predict plausible complex models via computational methods such as molecular docking. Assessing the quality of the predicted models is crucial to obtain correct complex structures. Here, an energy-scoring function was developed based on the interfacial residues of structures in the Protein Data Bank. The statistically derived energy function (Nepre) imitates the neighborhood preferences of amino acids, including the types and relative positions of neighboring residues. Based on the preference statistics, a program iNepre was implemented and its performance was evaluated with several benchmarking decoy data sets. The results show that iNepre scores are powerful in model ranking to select the best protein complex structures.

The ribosome stabilizes partially folded intermediates of a nascent multi-domain protein

Co-translational folding is crucial to ensure the production of biologically active proteins. The ribosome can alter the folding pathways of nascent polypeptide chains, yet a structural understanding remains largely inaccessible experimentally. We have developed site-specific labelling of nascent chains to detect and measure, using ¹⁹F nuclear magnetic resonance (NMR) spectroscopy, multiple states accessed by an immunoglobulin-like domain within a tandem repeat protein during biosynthesis. By examining ribosomes arrested at different stages during translation of this common structural motif, we observe highly broadened NMR resonances attributable to two previously unidentified intermediates, which are stably populated across a wide folding transition. Using molecular dynamics simulations and corroborated by cryo-electron microscopy, we obtain models of these partially folded states, enabling experimental verification of a ribosome-binding site that contributes to their high stabilities. We thus demonstrate a mechanism by which the ribosome could thermodynamically regulate folding and other co-translational processes.

Most proteins must fold co-translationally on the ribosome to adopt biologically active conformations, yet structural, mechanistic descriptions are lacking. Using ¹⁹F NMR spectroscopy to study a nascent multi-domain protein has now enabled the identification of two co-translational folding intermediates that are significantly more stable than intermediates formed off the ribosome, suggesting that the ribosome may thermodynamically regulate folding.

Contact-Based Analysis of Aggregation of Intrinsically Disordered Proteins

We review the contact-based description of aggregation of intrinsically disordered proteins in coarse-grained and all-atom models. We consider polyglutamines and polyalanines at various concentrations of the peptides. We also study associations of two chains of α-synuclein and up to 20 chains of a 12-residue-long segment of protein tau. We demonstrate that the total number of two-chain association events (in an aggregate that comprises at least two chains) provides a useful measure of the propensity to aggregate. This measure is consistent, for instance, with the previously reported mass spectroscopy data. The distribution of the number of association events is given essentially by a power law as a function of the duration of these events. The corresponding exponent depends on the protein and the temperature but not on the concentration of the proteins.

Assessing the Stability of Biological Fibrils by Molecular-Scale Simulations

The nanomechanical characterization of several biological fibrils that are the result of protein aggregation via molecular dynamics simulation is nowadays feasible, and together with atomic force microscopy experiments has widened our understanding of the forces in the regime of pN-nN and system sizes of about hundreds of nanometers. Several methodologies have been developed to achieve this target, and they range from the atomistic representation via molecular force fields to coarse-grained strategies that provide comparable results with experiments in a systematic way. In this chapter, we discuss several methodologies for the calculation of mechanical parameters, such as the elastic constants of relevant biological systems. They are presented together with details about parameterization and current limitations. Then, we discuss some of the applications of such methodologies for the description of bacterial filament and β-amyloid systems. Finally, the latest lines of development are discussed.

ProteinTools: a toolkit to analyze protein structures

The experimental characterization and computational prediction of protein structures has become increasingly rapid and precise. However, the analysis of protein structures often requires researchers to use several software packages or web servers, which complicates matters. To provide long-established structural analyses in a modern, easy-to-use interface, we implemented ProteinTools, a web server toolkit for protein structure analysis. ProteinTools gathers four applications so far, namely the identification of hydrophobic clusters, hydrogen bond networks, salt bridges, and contact maps. In all cases, the input data is a PDB identifier or an uploaded structure, whereas the output is an interactive dynamic web interface. Thanks to the modular nature of ProteinTools, the addition of new applications will become an easy task. Given the current need to have these tools in a single, fast, and interpretable interface, we believe that ProteinTools will become an essential toolkit for the wider protein research community. The web server is available at https://proteintools.uni-bayreuth.de.

Nascent Folding of Proteins Across the Three Domains of Life

We study the nascent behavior of three model coarse-grained proteins in six rigid all-atom structures representing ribosomes that come from three domains of life. The synthesis of the proteins is implemented as a growth process. The geometry of the exit tunnel is quantified and shown to differ between the domains of life: both in volume and the size of constriction sites. This results in different characteristic times of capture within the tunnel and various probabilities of the escape. One of the proteins studied is the bacterial YibK which is knotted in its native state. A fraction of the trajectories results in knotting and the probability of doing so is largest for the bacterial ribosomes. Relaxing the condition of the rigidness of the ribosomes should result in a better avoidance of trapping and better proper folding.

Optimizing Gō-MARTINI Coarse-Grained Model for F-BAR Protein on Lipid Membrane

Coarse-grained (CG) molecular dynamics (MD) simulations allow us to access much larger length and time scales than atomistic MD simulations, providing an attractive alternative to the conventional simulations. Based on the well-known MARTINI CG force field, the recently developed Gō-MARTINI model for proteins describes large-amplitude structural dynamics, which has not been possible with the commonly used elastic network model. Using the Gō-MARTINI model, we conduct MD simulations of the F-BAR Pacsin1 protein on lipid membrane. We observe that structural changes of the non-globular protein are largely dependent on the definition of the native contacts in the Gō model. To address this issue, we introduced a simple cutoff scheme and tuned the cutoff distance of the native contacts and the interaction strength of the Lennard-Jones potentials in the Gō-MARTINI model. With the optimized Gō-MARTINI model, we show that it reproduces structural fluctuations of the Pacsin1 dimer from atomistic simulations. We also show that two Pacsin1 dimers properly assemble through lateral interaction on the lipid membrane. Our work presents a first step towards describing membrane remodeling processes in the Gō-MARTINI CG framework by simulating a crucial step of protein assembly on the membrane.

Characterization of Structural and Energetic Differences between Conformations of the SARS-CoV-2 Spike Protein

The novel coronavirus disease 2019 (COVID-19) pandemic has disrupted modern societies and their economies. The resurgence in COVID-19 cases as part of the second wave is observed across Europe and the Americas. The scientific response has enabled a complete structural characterization of the Severe Acute Respiratory Syndrome-novel Coronavirus 2 (SARS-CoV-2). Among the most relevant proteins required by the novel coronavirus to facilitate the cell entry mechanism is the spike protein. This protein possesses a receptor-binding domain (RBD) that binds the cellular angiotensin-converting enzyme 2 (ACE2) and then triggers the fusion of viral and host cell membranes. In this regard, a comprehensive characterization of the structural stability of the spike protein is a crucial step to find new therapeutics to interrupt the process of recognition. On the other hand, it has been suggested that the participation of more than one RBD is a possible mechanism to enhance cell entry. Here, we discuss the protein structural stability based on the computational determination of the dynamic contact map and the energetic difference of the spike protein conformations via the mapping of the hydration free energy by the Poisson-Boltzmann method. We expect our result to foster the discussion of the number of RBD involved during recognition and the repurposing of new drugs to disable the recognition by discovering new hotspots for drug targets apart from the flexible loop in the RBD that binds the ACE2.

Quantitative determination of mechanical stability in the novel coronavirus spike protein

We report on the novel observation about the gain in nanomechanical stability of the SARS-CoV-2 (CoV2) spike (S) protein in comparison with SARS-CoV from 2002 (CoV1). Our findings have several biological implications in the subfamily of coronaviruses, as they suggest that the receptor binding domain (RBD) (∼200 amino acids) plays a fundamental role as a damping element of the massive viral particle's motion prior to cell-recognition, while also facilitating viral attachment, fusion and entry. The mechanical stability via pulling of the RBD is 250 pN and 200 pN for CoV2 and CoV1 respectively, and the additional stability observed for CoV2 (∼50 pN) might play a role in the increasing spread of COVID-19.

Mechanical Unfolding of Proteins-A Comparative Nonequilibrium Molecular Dynamics Study

Mechanical signals regulate functions of mechanosensitive proteins by inducing structural changes that are determinant for force-dependent interactions. Talin is a focal adhesion protein that is known to extend under mechanical load, and it has been shown to unfold via intermediate states. Here, we compared different nonequilibrium molecular dynamics (MD) simulations to study unfolding of the talin rod. We combined boxed MD (BXD), steered MD, and umbrella sampling (US) techniques and provide free energy profiles for unfolding of talin rod subdomains. We conducted BXD, steered MD, and US simulations at different detail levels and demonstrate how these different techniques can be used to study protein unfolding under tension. Unfolding free energy profiles determined by BXD suggest that the intermediate states in talin rod subdomains are stabilized by force during unfolding, and US confirmed these results.

Effect of Protein Flexibility from Coarse-Grained Elastic Network Parameterizations on the Calculation of Free Energy Profiles of Ligand Binding

The characterization of the affinity and binding mechanism of specific molecules to a protein active site is scientifically and industrially relevant for many applications. In principle, this information can be obtained using molecular dynamics (MD) simulations by calculating the free energy profile of the process. However, this is a computationally demanding calculation. Currently, coarse-grained (CG) force fields are very well implemented for MD simulations of biomolecular systems. These computationally efficient force fields are a major advantage to the study of large model systems and/or those requiring long simulation times. The Martini model is currently one of the most popular CG force fields for these systems. For the specific case of protein simulations, to correctly maintain the macromolecular three-dimensional structure, the Martini model needs to include an elastic network (EN). In this work, the effect of protein flexibility, as induced by three EN models compatible with the Martini force field, was tested on the calculation of free energy profiles for protein-ligand binding. The EN models used were ElNeDyn, GoMartini, and GEN. The binding of triolein (TOG) and triacetin (TAG) to a lipase protein (thermomyces lanuginosa lipase-TLL) was used as a case study. The results show that inclusion of greater flexibility in the CG parameterization of proteins is of high importance in the calculation of the free energy profiles of protein-ligand systems. However, care must be taken in order to avoid unjustified large protein deformations. In addition, due to molecular flexibility there may be no absolute need for the center of the ligand to reach the center of the protein-binding site. The calculation of the energy profile to a distance of about 0.5 nm from the active site center can be sufficient to differentiate the affinity of different ligands to a protein.

Proteins at curved fluid-fluid interfaces in a coarse-grained model

We employ an empirical coarse-grained model with a proposed Gaussian-like interfacial potential to describe proteins at curved fluid-fluid interfaces such as occurring in bubbles and droplets. We consider the air-water and oil-water interfaces. We study the mass distributions and the geometry of the aqueous proteins as a function of the radius of curvature for protein G and two lipid transfer proteins. At curved interfaces the distortion of the proteins is different than at flat interfaces. We find that the proteins come closer to the surface of a bubble than to the surface of similarly curved droplet. In addition, the bubbles adsorb more proteins. We identify the pinning residues. We demonstrate the existence of the second layer in the density profile for sufficiently dense solutions.

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins

We present a new coarse-grained C_α-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Transient knots in intrinsically disordered proteins and neurodegeneration

We provide a brief overview of the topological features found in structured proteins and of the dynamical processes that involve knots. We then discuss the knotted states that arise in the intrinsically disordered polyglutamine and α-synuclein. We argue that the existence of the knotted conformations stalls degradation by proteases and thus enhances aggregation. This mechanism works if the length of a peptide chain exceeds a threshold, as in the Huntington disease. We also study the cavities that form within the conformations of the disordered proteins. The volume of the cavities varies in time in a way that is different than that of the radius of gyration or the end-to-end distance. In addition, we study the traffic between the conformational basins and identify patterns associated with the deep and shallow knots. The results are obtained by molecular dynamics simulations that use coarse-grained and all-atom models (with and without the explicit solvent).

Computational methods in the study of self-entangled proteins: a critical appraisal

The existence of self-entangled proteins, the native structure of which features a complex topology, unveils puzzling, and thus fascinating, aspects of protein biology and evolution. The discovery that a polypeptide chain can encode the capability to self-entangle in an efficient and reproducible way during folding, has raised many questions, regarding the possible function of these knots, their conservation along evolution, and their role in the folding paradigm. Understanding the function and origin of these entanglements would lead to deep implications in protein science, and this has stimulated the scientific community to investigate self-entangled proteins for decades by now. In this endeavour, advanced experimental techniques are more and more supported by computational approaches, that can provide theoretical guidelines for the interpretation of experimental results, and for the effective design of new experiments. In this review we provide an introduction to the computational study of self-entangled proteins, focusing in particular on the methodological developments related to this research field. A comprehensive collection of techniques is gathered, ranging from knot theory algorithms, that allow detection and classification of protein topology, to Monte Carlo or molecular dynamics strategies, that constitute crucial instruments for investigating thermodynamics and kinetics of this class of proteins.

Differentiating between Inactive and Active States of Rhodopsin by Atomic Force Microscopy in Native Membranes

Membrane proteins, including G protein-coupled receptors (GPCRs), present a challenge in studying their structural properties under physiological conditions. Moreover, to better understand the activity of proteins requires examination of single molecule behaviors rather than ensemble averaged behaviors. Force-distance curve-based AFM (FD-AFM) was utilized to directly probe and localize the conformational states of a GPCR within the membrane at nanoscale resolution based on the mechanical properties of the receptor. FD-AFM was applied to rhodopsin, the light receptor and a prototypical GPCR, embedded in native rod outer segment disc membranes from photoreceptor cells of the retina in mice. Both FD-AFM and computational studies on coarse-grained models of rhodopsin revealed that the active state of the receptor has a higher Young's modulus compared to the inactive state of the receptor. Thus, the inactive and active states of rhodopsin could be differentiated based on the stiffness of the receptor. Differentiating the states based on the Young's modulus allowed for the mapping of the different states within the membrane. Quantifying the active states present in the membrane containing the constitutively active G90D rhodopsin mutant or apoprotein opsin revealed that most receptors adopt an active state. Traditionally, constitutive activity of GPCRs has been described in terms of two-state models where the receptor can achieve only a single active state. FD-AFM data are inconsistent with a two-state model but instead require models that incorporate multiple active states.

Mechanical and thermodynamic properties of Aβ42, Aβ40, and α-synuclein fibrils: a coarse-grained method to complement experimental studies

We perform molecular dynamics simulation on several relevant biological fibrils associated with neurodegenerative diseases such as Aβ₄₀, Aβ₄₂, and α-synuclein systems to obtain a molecular understanding and interpretation of nanomechanical characterization experiments. The computational method is versatile and addresses a new subarea within the mechanical characterization of heterogeneous soft materials. We investigate both the elastic and thermodynamic properties of the biological fibrils in order to substantiate experimental nanomechanical characterization techniques that are quickly developing and reaching dynamic imaging with video rate capabilities. The computational method qualitatively reproduces results of experiments with biological fibrils, validating its use in extrapolation to macroscopic material properties. Our computational techniques can be used for the co-design of new experiments aiming to unveil nanomechanical properties of biological fibrils from a point of view of molecular understanding. Our approach allows a comparison of diverse elastic properties based on different deformations , i.e., tensile (Y _L), shear (S), and indentation (Y _T) deformation. From our analysis, we find a significant elastic anisotropy between axial and transverse directions (i.e., Y _T > Y _L) for all systems. Interestingly, our results indicate a higher mechanostability of Aβ₄₂ fibrils compared to Aβ₄₀, suggesting a significant correlation between mechanical stability and aggregation propensity (rate) in amyloid systems. That is, the higher the mechanical stability the faster the fibril formation. Finally, we find that α-synuclein fibrils are thermally less stable than β-amyloid fibrils. We anticipate that our molecular-level analysis of the mechanical response under different deformation conditions for the range of fibrils considered here will provide significant insights for the experimental observations.

RIP-MD: a tool to study residue interaction networks in protein molecular dynamics

Protein structure is not static; residues undergo conformational rearrangements and, in doing so, create, stabilize or break non-covalent interactions. Molecular dynamics (MD) is a technique used to simulate these movements with atomic resolution. However, given the data-intensive nature of the technique, gathering relevant information from MD simulations is a complex and time consuming process requiring several computational tools to perform these analyses. Among different approaches, the study of residue interaction networks (RINs) has proven to facilitate the study of protein structures. In a RIN, nodes represent amino-acid residues and the connections between them depict non-covalent interactions. Here, we describe residue interaction networks in protein molecular dynamics (RIP-MD), a visual molecular dynamics (VMD) plugin to facilitate the study of RINs using trajectories obtained from MD simulations of proteins. Our software generates RINs from MD trajectory files. The non-covalent interactions defined by RIP-MD include H-bonds, salt bridges, VdWs, cation-π, π–π, Arginine–Arginine, and Coulomb interactions. In addition, RIP-MD also computes interactions based on distances between C_αs and disulfide bridges. The results of the analysis are shown in an user friendly interface. Moreover, the user can take advantage of the VMD visualization capacities, whereby through some effortless steps, it is possible to select and visualize interactions described for a single, several or all residues in a MD trajectory. Network and descriptive table files are also generated, allowing their further study in other specialized platforms. Our method was written in python in a parallelized fashion. This characteristic allows the analysis of large systems impossible to handle otherwise. RIP-MD is available at http://www.dlab.cl/ripmd.

Disordered peptide chains in an α-C-based coarse-grained model

We construct a one-bead-per-residue coarse-grained dynamical model to describe intrinsically disordered proteins at significantly longer timescales than in the all-atom models. In this model, inter-residue contacts form and disappear during the course of the time evolution. The contacts may arise between the sidechains, the backbones or the sidechains and backbones of the interacting residues. The model yields results that are consistent with many all-atom and experimental data on these systems. We demonstrate that the geometrical properties of various homopeptides differ substantially in this model. In particular, the average radius of gyration scales with the sequence length in a residue-dependent manner.

Nonnative Energetic Frustrations in Protein Folding at Residual Level: A Simulation Study of Homologous Immunoglobulin-like β-Sandwich Proteins

Nonnative interactions cause energetic frustrations in protein folding and were found to dominate key events in folding intermediates. However, systematically characterizing energetic frustrations that are caused by nonnative intra-residue interactions at residual resolution is still lacking. Recently, we studied the folding of a set of homologous all-α proteins and found that nonnative-contact-based energetic frustrations are highly correlated to topology of the protein native-contact network. Here, we studied the folding of nine homologous immunoglobulin-like (Ig-like) β-sandwich proteins, and examined nonnative-contact-based energetic frustrations Gō-like model. Our calculations showed that nonnative-interaction-based energetic frustrations in β-sandwich proteins are much more complicated than those in all-α proteins, and they exhibit highly heterogeneous effects on the folding of secondary structures. Further, the nonnative interactions introduced distinct correlations in the folding of different folding-patches of β-sandwich proteins. Taken together, a strong interplay might exist between nonnative-interaction energetic frustrations and the protein native-contact networks, which ensures that β-sandwich domains adopt a common folding mechanism.

Dual binding in cohesin-dockerin complexes: the energy landscape and the role of short, terminal segments of the dockerin module

The assembly of the polysaccharide degradating cellulosome machinery is mediated by tight binding between cohesin and dockerin domains. We have used an empirical model known as FoldX as well as molecular mechanics methods to determine the free energy of binding between a cohesin and a dockerin from Clostridium thermocellum in two possible modes that differ by an approximately 180° rotation. Our studies suggest that the full-length wild-type complex exhibits dual binding at room temperature, i.e., the two modes of binding have comparable probabilities at equilibrium. The ability to bind in the two modes persists at elevated temperatures. However, single-point mutations or truncations of terminal segments in the dockerin result in shifting the equilibrium towards one of the binding modes. Our molecular dynamics simulations of mechanical stretching of the full-length wild-type cohesin-dockerin complex indicate that each mode of binding leads to two kinds of stretching pathways, which may be mistakenly taken as evidence of dual binding.

The length but not the sequence of peptide linker modules exerts the primary influence on the conformations of protein domains in cellulosome multi-enzyme complexes

Cellulosomes are large multi-protein catalysts produced by various anaerobic microorganisms to efficiently degrade plant cell-wall polysaccharides down into simple sugars. X-ray and physicochemical structural characterisations show that cellulosomes are composed of numerous protein domains that are connected by unstructured polypeptide segments, yet the properties and possible roles of these 'linker' peptides are largely unknown. We have performed coarse-grained and all-atom molecular dynamics computer simulations of a number of cellulosomal linkers of different lengths and compositions. Our data demonstrates that the effective stiffness of the linker peptides, as quantified by the equilibrium fluctuations in the end-to-end distances, depends primarily on the length of the linker and less so on the specific amino acid sequence. The presence of excluded volume - provided by the domains that are connected - dampens the motion of the linker residues and reduces the effective stiffness of the linkers. Simultaneously, the presence of the linkers alters the conformations of the protein domains that are connected. We demonstrate that short, stiff linkers induce significant rearrangements in the folded domains of the mini-cellulosome composed of endoglucanase Cel8A in complex with scaffoldin ScafT (Cel8A-ScafT) of Clostridium thermocellum as well as in a two-cohesin system derived from the scaffoldin ScaB of Acetivibrio cellulolyticus. We give experimentally testable predictions on structural changes in protein domains that depend on the length of linkers.

Elastic moduli of biological fibers in a coarse-grained model: crystalline cellulose and β-amyloids

We study the mechanical response of cellulose and β-amyloid microfibrils to three types of deformation: tensile, indentational, and shear. The cellulose microfibrils correspond to the allomorphs Iα or Iβ whereas the β-amyloid microfibrils correspond to the polymorphs of either two- or three-fold symmetry. This response can be characterized by three elastic moduli, namely, Y_L, Y_T, and S. We use a structure-based coarse-grained model to analyze the deformations in a unified manner. We find that each of the moduli is almost the same for the two allomorphs of cellulose but Y_L is about 20 times larger than Y_T (140 GPa vs. 7 GPa), indicating the existence of significant anisotropy. For cellulose we note that the anisotropy results from the involvement of covalent bonds in stretching. For β-amyloid, the sense of anisotropy is opposite to that of cellulose. In the three-fold symmetry case, Y_L is about half of Y_T (3 vs. 7) whereas for two-fold symmetry the anisotropy is much larger (1.6 vs. 21 GPa). The S modulus is derived to be 1.2 GPa for three-fold symmetry and one half of it for the other symmetry and 3.0 GPa for cellulose. The values of the moduli reflect deformations in the hydrogen-bond network. Unlike in our theoretical approach, no experiment can measure all three elastic moduli with the same apparatus. However, our theoretical results are consistent with various measured values: typical Y_L for cellulose Iβ ranges from 133 to 155 GPa, Y_T from 2 to 25 GPa, and S from 1.8 to 3.8 GPa. For β-amyloid, the experimental values of S and Y_T are about 0.3 GPa and 3.3 GPa respectively, while the value of Y_L has not been reported.

Self-assembly of model proteins into virus capsids

We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions. Previous studies of the capsid self-assembly involved solid objects of a supramolecular scale, e.g. corresponding to capsomeres, with engineered couplings and stochastic movements. In our approach, a single capsid is dissociated by an application of a high temperature for a variable period and then the system is cooled down to allow for self-assembly. The restoration of the capsid proceeds to various extent, depending on the nature of the dissociated state, but is rarely complete because some proteins depart too far unless the process takes place in a confined space.

Stiffness of the C-terminal disordered linker affects the geometry of the active site in endoglucanase Cel8A

Cellulosomes are complex multi-enzyme machineries which efficiently degrade plant cell-wall polysaccharides. The multiple domains of the cellulosome proteins are often tethered together by intrinsically disordered regions. The properties and functions of these disordered linkers are not well understood. In this work, we study endoglucanase Cel8A, which is a relevant enzymatic component of the cellulosomes of Clostridium thermocellum. We use both all-atom and coarse-grained simulations to investigate how the conformations of the catalytic domain of Cel8A are affected by the disordered linker at its C terminus. We find that when the endoglucanase is bound to its substrate, the effective stiffness of the linker can influence the distances between groups of amino-acid residues throughout the entire enzymatic domain. In particular, variations in the linker stiffness can lead to small changes in the geometry of the active-site cleft. We suggest that such geometrical changes may have an effect on the catalytic activity of the enzyme.

Structural Changes in Barley Protein LTP1 Isoforms at Air-Water Interfaces

We use a coarse-grained model to study the conformational changes in two barley proteins, LTP1 and its ligand adduct isoform LTP1b, that result from their adsorption to the air-water interface. The model introduces the interface through hydropathy indices. We justify the model by all-atom simulations. The choice of the proteins is motivated by making attempts to understand formation and stability of foam in beer. We demonstrate that both proteins flatten out at the interface and can make a continuous stabilizing and denser film. We show that the degree of the flattening depends on the protein (the layers of LTP1b should be denser than those of LTP1) and on the presence of glycation. It also depends on the number (≤4) of the disulfide bonds in the proteins. The geometry of the proteins is sensitive to the specificity of the absent bonds. We provide estimates of the volume of cavities of the proteins when away from the interface.

Combining the MARTINI and Structure-Based Coarse-Grained Approaches for the Molecular Dynamics Studies of Conformational Transitions in Proteins

The application of coarse-grained (CG) models in biology is essential to access large length and time scales required for the description of many biological processes. The ELNEDIN protein model is based on the well-known MARTINI CG force-field and incorporates additionally harmonic bonds of a certain spring constant within a defined cutoff distance between pairs of residues, in order to preserve the native structure of the protein. In this case, the use of unbreakable harmonic bonds hinders the study of unfolding and folding processes. To overcome this barrier we have replaced the harmonic bonds with Lennard-Jones interactions based on the contact map of the native protein structure as is done in Go̅-like models. This model exhibits very good agreement with all-atom simulations and the ELNEDIN. Moreover, it can capture the structural motion linked to particular catalytic activity in the Man5B protein, in agreement with all-atom simulations. In addition, our model is based on the van der Waals radii, instead of a cutoff distance, which results in a smaller contact map. In conclusion, we anticipate that our model will provide further possibilities for studying biological systems based on the MARTINI CG force-field by using advanced-sampling methods, such as parallel tempering and metadynamics.

Topological transformations in proteins: effects of heating and proximity of an interface

Using a structure-based coarse-grained model of proteins, we study the mechanism of unfolding of knotted proteins through heating. We find that the dominant mechanisms of unfolding depend on the temperature applied and are generally distinct from those identified for folding at its optimal temperature. In particular, for shallowly knotted proteins, folding usually involves formation of two loops whereas unfolding through high-temperature heating is dominated by untying of single loops. Untying the knots is found to generally precede unfolding unless the protein is deeply knotted and the heating temperature exceeds a threshold value. We then use a phenomenological model of the air-water interface to show that such an interface can untie shallow knots, but it can also make knots in proteins that are natively unknotted.

Structural fluctuations and thermal stability of proteins in crowded environments: effects of the excluded volume

We perform molecular dynamics simulations for a simple coarse-grained model of a protein placed inside of a softly repulsive sphere of radius R. The protein is surrounded either by a number of same molecules or a number of spherical crowding particles that immitate other biomolecules such as the osmolytes. The two descriptions are shown to lead to distinct results when testing thermal stability as assessed by studying the unfolding times as a function of temperature. We consider three examples of proteins and show that crowding increases the thermal stability provided the inter-protein or protein-crowder interactions are repulsive. On the other hand, an introduction of attraction between the proteins is found to destabilize the proteins. Crowding by repulsive crowder particles is seen to enhance the RMSF in certain exposed regions. The effect grows on decreasing the size of the crowding particles. In the absence of crowding the RMSF anticorrelates with the coordination number related to the residue-residue interaction.

Dual binding mode in cohesin-dockerin complexes as assessed through stretching studies

A recent experimental study by Jobst et al. of stretching of a wild-type (WT) cohesin-dockerin complex has identified two kinds of the force-displacement patterns, with a single or double-peaked final rupture, which are termed "short" and "long" here. This duality has been interpreted as arising from the existence of two kinds of binding. Here, we analyze the separation of two cohesin-dockerin complexes of C. thermocellum theoretically. We use a coarse-grained structure-based model and the values of the pulling speeds are nearly experimental. In their native states, the two systems differ in the mutual binding orientations of the molecules in the complex. We demonstrate that the WT complex (PDB:1OHZ) unravels along two possible pathways that are qualitatively consistent with the presence of the short and long patterns observed experimentally. On the other hand, the mutated complex (PDB:2CCL) leads only to short trajectories. The short and long stretching pathways also appear in the cohesin-dockerin-Xmodule complex (PDB:4IU3, WT) of R. flavefaciens. Thus the duality in the stretching patterns need not be necessarily due to the duality in binding.