Evaluation of the scale-consistent UNRES force field in template-free prediction of protein structures in the CASP13 experiment

Integrating Explicit and Implicit Fullerene Models into UNRES Force Field for Protein Interaction Studies

Fullerenes, particularly C60, exhibit unique properties that make them promising candidates for various applications, including drug delivery and nanomedicine. However, their interactions with biomolecules, especially proteins, remain not fully understood. This study implements both explicit and implicit C60 models into the UNRES coarse-grained force field, enabling the investigation of fullerene-protein interactions without the need for restraints to stabilize protein structures. The UNRES force field offers computational efficiency, allowing for longer timescale simulations while maintaining accuracy. Five model proteins were studied: FK506 binding protein, HIV-1 protease, intestinal fatty acid binding protein, PCB-binding protein, and hen egg-white lysozyme. Molecular dynamics simulations were performed with and without C60 to assess protein stability and investigate the impact of fullerene interactions. Analysis of contact probabilities reveals distinct interaction patterns for each protein. FK506 binding protein (1FKF) shows specific binding sites, while intestinal fatty acid binding protein (1ICN) and uteroglobin (1UTR) exhibit more generalized interactions. The explicit C60 model shows good agreement with all-atom simulations in predicting protein flexibility, the position of C60 in the binding pocket, and the estimation of effective binding energies. The integration of explicit and implicit C60 models into the UNRES force field, coupled with recent advances in coarse-grained modeling and multiscale approaches, provides a powerful framework for investigating protein-nanoparticle interactions at biologically relevant scales without the need to use restraints stabilizing the protein, thus allowing for large conformational changes to occur. These computational tools, in synergy with experimental techniques, can aid in understanding the mechanisms and consequences of nanoparticle-biomolecule interactions, guiding the design of nanomaterials for biomedical applications.

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.

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.

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).

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 β and the α+β 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.

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 β-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.

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.

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.

Modeling protein structures with the coarse-grained UNRES force field in the CASP14 experiment

The UNited RESidue (UNRES) force field was tested in the 14th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP14), in which larger oligomeric and multimeric targets were present compared to previous editions. Three prediction modes were tested (i) ab initio (the UNRES group), (ii) contact-assisted (the UNRES-contact group), and (iii) template-assisted (the UNRES-template group). For most of the targets, the contact restraints were derived from the server models top-ranked by the DeepQA method, while the DNCON2 method was used for 11 targets. Our consensus-fragment procedure was used to run template-assisted predictions. Each group also processed the Nuclear Magnetic Resonance (NMR)- and Small Angle X-Ray Scattering (SAXS)-data assisted targets. The average Global Distance Test Total Score (GDT_TS) of the 'Model 1' predictions were 29.17, 39.32, and 56.37 for the UNRES, UNRES-contact, and UNRES-template predictions, respectively, increasing by 0.53, 2.24, and 3.76, respectively, compared to CASP13. It was also found that the GDT_TS of the UNRES models obtained in ab initio mode and in the contact-assisted mode decreases with the square root of chain length, while the exponent in this relationship is 0.20 for the UNRES-template group models and 0.11 for the best performing AlphaFold2 models, which suggests that incorporation of database information, which stems from protein evolution, brings in long-range correlations, thus enabling the correction of force-field inaccuracies.

Pseudopotentials for coarse-grained cross-link-assisted modeling of protein structures

Pseudopotentials for the chemical cross-links comprising the glutamic- and aspartic-acid side chains bridged with adipic- (ADH) or pimelic-acid hydrazide (PDH), and the lysine side chains bridged with glutaric (BS² G) or suberic acid (BS³ ) for coarse-grained cross-link-assisted simulations were determined by canonical molecular dynamics with the Amber14sb force field. The potentials depend on the distance between side-chain ends and on side-chain orientation, this preventing from making cross-link contacts across the globule in simulations. The potentials were implemented in the UNRES coarse-grained force field and their effect on the quality of models was assessed with 11 monomeric and 1 dimeric proteins, using synthetic or experimental cross-link data. Simulations with the new potentials resulted in improvement of the generated models compared to unrestrained simulations in more instances compared to those with the statistical potentials.

ESCASA: Analytical estimation of atomic coordinates from coarse-grained geometry for nuclear-magnetic-resonance-assisted protein structure modeling. I. Backbone and Hβ protons

A method for the estimation of coordinates of atoms in proteins from coarse-grained geometry by simple analytical formulas (ESCASA), for use in nuclear-magnetic-resonance (NMR) data-assisted coarse-grained simulations of proteins is proposed. In this paper, the formulas for the backbone H^α and amide (H^N ) protons, and the side-chain H^β protons, given the C^α -trace, have been derived and parameterized, by using the interproton distances calculated from a set of 140 high-resolution non-homologous protein structures. The mean standard deviation over all types of proton pairs in the set was 0.44 Å after fitting. Validation against a set of 41 proteins with NMR-determined structures, which were not considered in parameterization, resulted in average standard deviation from average proton-proton distances of the NMR-determined structures of 0.25 Å, compared to 0.21 Å obtained with the PULCHRA all-atom-chain reconstruction algorithm and to the 0.12 Å standard deviation of the average-structure proton-proton distance of NMR-determined ensembles. The formulas provide analytical forces and can, therefore, be used in coarse-grained molecular dynamics.

Residue-Level Contact Reveals Modular Domain Interactions of PICK1 Are Driven by Both Electrostatic and Hydrophobic Forces

PICK1 is a multi-domain scaffolding protein that is uniquely comprised of both a PDZ domain and a BAR domain. While previous experiments have shown that the PDZ domain and the linker positively regulate the BAR domain and the C-terminus negatively regulates the BAR domain, the details of internal regulation mechanisms are unknown. Molecular dynamics (MD) simulations have been proven to be a useful tool in revealing the intramolecular interactions at atomic-level resolution. PICK1 performs its biological functions in a dimeric form which is extremely computationally demanding to simulate with an all-atom force field. Here, we use coarse-grained MD simulations to expose the key residues and driving forces in the internal regulations of PICK1. While the PDZ and BAR domains do not form a stable complex, our simulations show the PDZ domain preferentially interacting with the concave surface of the BAR domain over other BAR domain regions. Furthermore, our simulations show that the short helix in the linker region can form interactions with the PDZ domain. Our results reveal that the surface of the βB-βC loop, βC strand, and αA-βD loop of the PDZ domain can form a group of hydrophobic interactions surrounding the linker helix. These interactions are driven by hydrophobic forces. In contrast, our simulations reveal a very dynamic C-terminus that most often resides on the convex surface of the BAR domain rather than the previously suspected concave surface. These interactions are driven by a combination of electrostatic and hydrophobic interactions.

Atomistic detailed free-energy landscape of intrinsically disordered protein studied by multi-scale divide-and-conquer molecular dynamics simulation

Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca²⁺ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α-helix form in the presence Ca²⁺ -loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca²⁺ -loaded CaM must be simultaneously treated. However, it is time-consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi-scale divide-and-conquer MD (MSDC-MD), which combines AAM-MD and coarse-grained model MD (CGM-MD). To speed up the conformation sampling, MSDC-MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM-MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC-MD; the root-mean-square distance (RMSD) with respect to the experimental structure was 2.23 Å.

Prediction of CD28-CD86 protein complex structure using different level of resolution approach

Immune system plays essential role in functioning of higher organisms. Its hyperactivity can lead to autoimmune diseases or even anaphylactic shock while hypoactivity leads to proneness to infections or even cancer. T-cells play crucial role in immunity mechanisms and their activation and inhibition is strictly controlled by the regulatory proteins, such as CD28 and CTLA-4. Activity of these proteins is controlled by a pair of ligands, named CD80 and CD86, which can non-covalently bound to their receptors. While structure of human CTLA-4-CD86 complex in known, there is still no available structure for the CD28-CD86 system. To obtain the reliable structure of CD28-CD86 complex we first validated our methodology on the CTLA-4-CD86 system. Then coarse-grained UNRES-dock molecular docking simulation was performed followed by all-atom molecular dynamics simulations. As a result, we obtained a complete CD28-CD86 complex structure on atomistic level, in which interaction interface is consistent with available data. We also determined the kinetic properties for CTLA4-CD86 and CD28-CD86 complexes with use of coarse-grained model and determined the key residues for complex formation with use of Robetta, PPCheck and HawkDock servers. Our results not only verify high accuracy of the UNRES-dock method, but also provide a highly reliable model of the CD28-CD86 complex, which can be used in further studies and drug design.

Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers

In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.

Improved Consensus-Fragment Selection in Template-Assisted Prediction of Protein Structures with the UNRES Force Field in CASP13

The method for protein-structure prediction, which combines the physics-based coarse-grained UNRES force field with knowledge-based modeling, has been developed further and tested in the 13th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP13). The method implements restraints from the consensus fragments common to server models. In this work, the server models to derive fragments have been chosen on the basis of quality assessment; a fully automatic fragment-selection procedure has been introduced, and Dynamic Fragment Assembly pseudopotentials have been fully implemented. The Global Distance Test Score (GDT_TS), averaged over our “Model 1” predictions, increased by over 10 units with respect to CASP12 for the free-modeling category to reach 40.82. Our “Model 1” predictions ranked 20 and 14 for all and free-modeling targets, respectively (upper 20.2% and 14.3% of all models submitted to CASP13 in these categories, respectively), compared to 27 (upper 21.1%) and 24 (upper 18.9%) in CASP12, respectively. For oligomeric targets, the Interface Patch Similarity (IPS) and Interface Contact Similarity (ICS) averaged over our best oligomer models increased from 0.28 to 0.36 and from 12.4 to 17.8, respectively, from CASP12 to CASP13, and top-ranking models of 2 targets (H0968 and T0997o) were obtained (none in CASP12). The improvement of our method in CASP13 over CASP12 was ascribed to the combined effect of the overall enhancement of server-model quality, our success in selecting server models and fragments to derive restraints, and improvements of the restraint and potential-energy functions.