Assessment of Two Restraint Potentials for Coarse-Grained Chemical-Cross-Link-Assisted Modeling of Protein Structures.

The influence of distance restraints from chemical cross-link mass spectroscopy (XL-MS) on the quality of protein structures modeled with the coarse-grained UNRES force field was assessed by using a protocol based on multiplexed replica exchange molecular dynamics, in which both simulated and experimental cross-link restraints were employed, for 23 small proteins. Six cross-links with upper distance boundaries from 4 Å to 12 Å (azido benzoic acid succinimide (ABAS), triazidotriazine (TATA), succinimidyldiazirine (SDA), disuccinimidyl adipate (DSA), disuccinimidyl glutarate (DSG), and disuccinimidyl suberate (BS3)) and two types of restraining potentials ((i) simple flat-bottom Lorentz-like potentials dependent on side chain distance (all cross-links) and (ii) distance- and orientation-dependent potentials determined based on molecular dynamics simulations of model systems (DSA, DSG, BS3, and SDA)) were considered. The Lorentz-like potentials with properly set parameters were found to produce a greater number of higher-quality models compared to unrestrained simulations than the MD-based potentials, because the latter can force too long distances between side chains. Therefore, the flat-bottom Lorentz-like potentials are recommended to represent cross-link restraints. It was also found that significant improvement of model quality upon the introduction of cross-link restraints is obtained when the sum of differences of indices of cross-linked residues exceeds 150.

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.

Toward Consistent Physics-Based Modeling of Local Backbone Structures and Chirality Change of Proteins in Coarse-Grained Approaches.

A reliable representation of local interactions is critical for the accuracy of modeling protein structure and dynamics at both the all-atom and coarse-grained levels. The development of local (mainly torsional) potentials was focused on careful parametrization of the predetermined (usually Fourier) formulas rather than on their physics-based derivation. In this Perspective we discuss the state-of-the-art methods for modeling local interactions, including the scale-consistent theory developed in our laboratory, which implies that the coarse-grained torsional potentials inseparably depend on the virtual-bond angles adjacent to a given dihedral and that multitorsional terms should be considered. We extend the treatment to split the residue-based torsional potentials into the site-based regular and improper torsional potentials. These considerations are illustrated with the revised torsional potentials and improper-torsional potentials involving the l-alanine residue and the improper-torsional potential corresponding to serine-residue enantiomerization. Applications of the new approach in coarse-grained modeling and revising all-atom force fields are discussed.

Ligand binding of interleukin-8: a comparison of glycosaminoglycans and acidic peptides.

Recognition and binding of regulatory proteins to glycosaminoglycans (GAGs) from the extracellular matrix is a process of high biological importance. The interaction between negatively charged sulfate or carboxyl groups of the GAGs and clusters of basic amino acids on the protein is crucial in this binding process and it is believed that electrostatics represent the key factor for this interaction. However, given the rather undirected nature of electrostatics, it is important to achieve a clear understanding of its role in protein-GAG interactions and how specificity and selectivity in these systems can be achieved, when the classical key-lock binding motif is not applicable. Here, we compare protein binding of a highly charged heparin (HP) hexasaccharide with four de novo designed decapeptides of varying negative net charge. The charge density of these peptides was comparable to typical GAGs of the extracellular matrix. We used the regulatory protein interleukin-8 (IL-8) because its interactions with GAGs are well described. All four peptide ligands bind to the same epitope of IL-8 but show much weaker binding affinity as revealed in 1H-15N HSQC NMR titration experiments. Complementary molecular docking and molecular dynamics simulations revealed further atomistic details of the interaction mode of GAG versus peptide ligands. Overall, similar contributions to the binding energy and hydrogen bond formation are determined for HP and the highly charged peptides, suggesting that the entropic loss of the peptides upon binding likely account for the remarkably different affinity of GAG versus peptide ligands to IL-8.

Extension of the SUGRES-1P Coarse-Grained Model of Polysaccharides to Heparin.

Heparin is an unbranched periodic polysaccharide composed of negatively charged monomers and involved in key biological processes, including anticoagulation, angiogenesis, and inflammation. Its structure and dynamics have been studied extensively using experimental as well as theoretical approaches. The conventional approach of computational chemistry applied to the analysis of biomolecules is all-atom molecular dynamics, which captures the interactions of individual atoms by solving Newton's equation of motion. An alternative is molecular dynamics simulations using coarse-grained models of biomacromolecules, which offer a reduction of the representation and consequently enable us to extend the time and size scale of simulations by orders of magnitude. In this work, we extend the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules developed in our laboratory to heparin. We carried out extensive tests to estimate the optimal weights of energy terms of the effective energy function as well as the optimal Debye-Hückel screening factor for electrostatic interactions. We applied the model to study unbound heparin molecules of polymerization degree ranging from 6 to 68 residues. We compare the obtained coarse-grained heparin conformations with models obtained from X-ray diffraction studies of heparin. The SUGRES-1P force field was able to accurately predict the general shape and global characteristics of heparin molecules.

Long-Time Dynamics of Selected Molecular-Motor Components Using a Physics-Based Coarse-Grained Approach.

Molecular motors are essential for the movement and transportation of macromolecules in living organisms. Among them, rotatory motors are particularly efficient. In this study, we investigated the long-term dynamics of the designed left-handed alpha/alpha toroid (PDB: 4YY2), the RBM2 flagellum protein ring from Salmonella (PDB: 6SD5), and the V-type Na+-ATPase rotor in Enterococcus hirae (PDB: 2BL2) using microcanonical and canonical molecular dynamics simulations with the coarse-grained UNRES force field, including a lipid-membrane model, on a millisecond laboratory time scale. Our results demonstrate that rotational motion can occur with zero total angular momentum in the microcanonical regime and that thermal motions can be converted into net rotation in the canonical regime, as previously observed in simulations of smaller cyclic molecules. For 6SD5 and 2BL2, net rotation (with a ratcheting pattern) occurring only about the pivot of the respective system was observed in canonical simulations. The extent and direction of the rotation depended on the initial conditions. This result suggests that rotatory molecular motors can convert thermal oscillations into net rotational motion. The energy from ATP hydrolysis is required probably to set the direction and extent of rotation. Our findings highlight the importance of molecular-motor structures in facilitating movement and transportation within living organisms.

UNRES-GPU for physics-based coarse-grained simulations of protein systems at biological time- and size-scales.

SUMMARY: The UNited RESisdue (UNRES) package for coarse-grained simulations, which has recently been optimized to treat large protein systems, has been implemented on Graphical Processor Units (GPUs). An over 100-time speed-up of the GPU code (run on an NVIDIA A100) with respect to the sequential code and an 8.5 speed-up with respect to the parallel Open Multi-Processing (OpenMP) code (run on 32 cores of 2 AMD EPYC 7313 Central Processor Units (CPUs)) has been achieved for large proteins (with size over 10 000 residues). Due to the averaging over the fine-grain degrees of freedom, 1 time unit of UNRES simulations is equivalent to about 1000 time units of laboratory time; therefore, millisecond time scale of large protein systems can be reached with the UNRES-GPU code. AVAILABILITY AND IMPLEMENTATION: The source code of UNRES-GPU along with the benchmarks used for tests is available at https://projects.task.gda.pl/eurohpcpl-public/unres.

Long-time scale simulations of virus-like particles from three human-norovirus strains.

The dynamics of the virus like particles (VLPs) corresponding to the GII.4 Houston, GII.2 SMV, and GI.1 Norwalk strains of human noroviruses (HuNoV) that cause gastroenteritis was investigated by means of long-time (about 30 µs in the laboratory timescale) molecular dynamics simulations with the coarse-grained UNRES force field. The main motion of VLP units turned out to be the bending at the junction between the P1 subdomain (that sits in the VLP shell) and the P2 subdomain (that protrudes outside) of the major VP1 protein, this resulting in a correlated wagging motion of the P2 subdomains with respect to the VLP surface. The fluctuations of the P2 subdomain were found to be more pronounced and the P2 domain made a greater angle with the normal to the VLP surface for the GII.2 strain, which could explain the inability of this strain to bind the histo-blood group antigens (HBGAs).

Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins.

We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 µs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.

Origin of Correlations between Local Conformational States of Consecutive Amino Acid Residues and Their Role in Shaping Protein Structures and in Allostery.

By analyzing the Kubo-cluster-cumulant expansion of the potential of mean force of polypeptide chains corresponding to backbone-local interactions averaged over the rotation of the peptide groups about the Cα···Cα virtual bonds, we identified two important kinds of "along-chain" correlations that pertain to extended chain segments bordered by turns (usually the ß-strands) and to the folded spring-like segments (usually α-helices), respectively, and are expressed as multitorsional potentials. These terms affect the positioning of structural elements with respect to each other and, consequently, contribute to determining their packing. Additionally, for extended chain segments, the correlation terms contribute to propagating the conformational change at one end to the other end, which is characteristic of allosteric interactions. We confirmed both findings by statistical analysis of the virtual-bond geometry of 77 950 proteins. Augmenting coarse-grained and, possibly, all-atom force fields with these correlation terms could improve their capacity to model protein structure and dynamics.

A coarse-grained approach to NMR-data-assisted modeling of protein structures.

The ESCASA algorithm for analytical estimation of proton positions from coarse-grained geometry developed in our recent work has been implemented in modeling protein structures with the highly coarse-grained UNRES model of polypeptide chains (two sites per residue) and nuclear magnetic resonance (NMR) data. A penalty function with the shape of intersecting gorges was applied to treat ambiguous distance restraints, which automatically selects consistent restraints. Hamiltonian replica exchange molecular dynamics was used to carry out the conformational search. The method was tested with both unambiguous and ambiguous restraints producing good-quality models with GDT_TS from 7.4 units higher to 14.4 units lower than those obtained with the CYANA or MELD software for protein-structure determination from NMR data at the all-atom resolution. The method can thus be applied in modeling the structures of flexible proteins, for which extensive conformational search enabled by coarse-graining is more important than high modeling accuracy.

Prediction of Aggregation of Biologically-Active Peptides with the UNRES Coarse-Grained Model.

The UNited RESidue (UNRES) model of polypeptide chains was applied to study the association of 20 peptides with sizes ranging from 6 to 32 amino-acid residues. Twelve of those were potentially aggregating hexa- or heptapeptides excised from larger proteins, while the remaining eight contained potentially aggregating sequences, functionalized by attaching larger ends rich in charged residues. For 13 peptides, the experimental data of aggregation were used. The remaining seven were synthesized, and their properties were measured in this work. Multiplexed replica-exchange simulations of eight-chain systems were conducted at 12 temperatures from 260 to 370 K at concentrations from 0.421 to 5.78 mM, corresponding to the experimental conditions. The temperature profiles of the fractions of monomers and octamers showed a clear transition corresponding to aggregate dissociation. Low simulated transition temperatures were obtained for the peptides, which did not precipitate after incubation, as well as for the H-GNNQQNY-NH2 prion-protein fragment, which forms small fibrils. A substantial amount of inter-strand ß-sheets was found in most of the systems. The results suggest that UNRES simulations can be used to assess peptide aggregation except for glutamine- and asparagine-rich peptides, for which a revision of the UNRES sidechain-sidechain interaction potentials appears necessary.

Theoretical Investigation of the Coronavirus SARS-CoV-2 (COVID-19) Infection Mechanism and Selectivity.

The SARS-CoV-2 virus, commonly known as COVID-19, first occurred in December 2019 in Wuhan, Hubei Province, China. Since then, it has become a tremendous threat to human health. With a pandemic threat, it is in the significant interest of the scientific world to establish its method of infection. In this manuscript, we combine knowledge of the infection mechanism with theoretical methods to answer the question of the virus's selectivity. We proposed a two-stage infection mechanism. In the first step, the virus interacts with the ACE2 receptor, with the "proper strength". When the interaction is too strong, the virus will remain in an "improper position"; if the interaction is too weak, the virus will "run away" from the cell. We also indicated three residues (positions 30, 31, and 353) located on the ACE2 protein-binding interface, which seems to be crucial for successful infection. Our results indicate that these residues are necessary for the initiation of the infection process.

Probing Protein Aggregation Using the Coarse-Grained UNRES Force Field.

Protein aggregation is the cause of many, often lethal, diseases, including the Alzheimer's, Parkinson's, and Huntington's diseases, and familial amyloidosis. Theoretical investigation of the mechanism of this process, including the structures of the oligomeric intermediates which are the most toxic, is difficult because of long time scale of aggregation. Coarse-grained models, which enable us to extend the simulation time scale by three or more orders of magnitude, are, therefore, of great advantage in such studies. In this chapter, we describe the application of the physics-based UNited RESidue (UNRES) force field developed in our laboratory to study protein aggregation, in both free simulations and simulations of aggregation propagation from an existing template (seed), and illustrate it with the examples of Aß-peptide aggregation and Aß-peptide-assisted aggregation of the peptides derived from the repeat domains of tau (TauRD).

Influence of Temperature and Salt Concentration on the Hydrophobic Interactions of Adamantane and Hexane.

One of the definitions of hydrophobic interactions is the aggregation of nonpolar particles in a polar solvent, such as water. While this phenomenon appears to be very simple, it is crucial for many complex processes, such as protein folding, to take place. In this work, the hydrophobic association of adamantane and hexane at various temperatures and ionic strengths was studied using molecular dynamics simulations with the AMBER 16.0 program and the GAFF force field. The potentials of mean force of hydrophobic dimer formation, as well as the excess free energy, excess energy, excess entropy, and excess heat capacity corresponding to the formation of the contact minimum, were determined and analyzed. For both systems, the depth of the contact minimum in the potential of mean force was found to increase with both temperature and ionic strength. The excess heat capacity of the association at the contact minimum and T = 298 K was found to be negative and to decrease, while the excess entropy and energy were found to be positive and to increase for both systems, the changes being more pronounced for the hexane dimer. The excess heat capacity is also greater in absolute value for the hexane dimer.

Improvements and new functionalities of UNRES server for coarse-grained modeling of protein structure, dynamics, and interactions.

In this paper we report the improvements and extensions of the UNRES server (https://unres-server.chem.ug.edu.pl) for physics-based simulations with the coarse-grained UNRES model of polypeptide chains. The improvements include the replacement of the old code with the recently optimized one and adding the recent scale-consistent variant of the UNRES force field, which performs better in the modeling of proteins with the ß and the α+ß structures. The scope of applications of the package was extended to data-assisted simulations with restraints from nuclear magnetic resonance (NMR) and chemical crosslink mass-spectroscopy (XL-MS) measurements. NMR restraints can be input in the NMR Exchange Format (NEF), which has become a standard. Ambiguous NMR restraints are handled without expert intervention owing to a specially designed penalty function. The server can be used to run smaller jobs directly or to prepare input data to run larger production jobs by using standalone installations of UNRES.

Modeling the Structure, Dynamics, and Transformations of Proteins with the UNRES Force Field.

The physics-based united-residue (UNRES) model of proteins ( www.unres.pl ) has been designed to carry out large-scale simulations of protein folding. The force field has been derived and parameterized based on the principles of statistical-mechanics, which makes it independent of structural databases and applicable to treat nonstandard situations such as, proteins that contain D-amino-acid residues. Powered by Langevin dynamics and its replica-exchange extensions, UNRES has found a variety of applications, including ab initio and database-assisted protein-structure prediction, simulating protein-folding pathways, exploring protein free-energy landscapes, and solving biological problems. This chapter provides a summary of UNRES and a guide for potential users regarding the application of the UNRES package in a variety of research tasks.

Extended disorder at the cell surface: The conformational landscape of the ectodomains of syndecans.

Syndecans are membrane proteoglycans regulating extracellular matrix assembly, cell adhesion and signaling. Their ectodomains can be shed from the cell surface, and act as paracrine and autocrine effectors or as competitors of full-length syndecans. We report the first biophysical characterization of the recombinant ectodomains of the four human syndecans using biophysical techniques, and show that they behave like flexible random-coil intrinsically disordered proteins, and adopt several conformation ensembles in solution. We have characterized their conformational landscapes using native mass spectrometry (MS) and ion-mobility MS, and demonstrated that the syndecan ectodomains explore the majority of their conformational landscape, from minor compact, globular-like, conformations to extended ones. We also report that the ectodomain of syndecan-4, corresponding to a natural isoform, is able to dimerize via a disulfide bond. We have generated a three-dimensional model of the C-terminus of this dimer, which supports the dimerization via a disulfide bond. Furthermore, we have mapped the NXIP adhesion motif of syndecans and their sequences involved in the formation of ternary complexes with integrins and growth factor receptors on the major conformations of their ectodomains, and shown that these sequences are not accessible in all the conformations, suggesting that only some of them are biologically active. Lastly, although the syndecan ectodomains have a far lower number of amino acid residues than their membrane partners, their intrinsic disorder and flexibility allow them to adopt extended conformations, which have roughly the same size as the cell surface receptors (e.g., integrins and growth factor receptors) they bind to.