Multilayered Computational Framework for Designing Peptide Inhibitors of HVEM-LIGHT Interaction.

The herpesvirus entry mediator (HVEM) and its ligand LIGHT play crucial roles in immune system regulation, including T-cell proliferation, B-cell differentiation, and immunoglobulin secretion. However, excessive T-cell activation can lead to chronic inflammation and autoimmune diseases. Thus, inhibiting the HVEM-LIGHT interaction emerges as a promising therapeutic strategy for these conditions and in preventing adverse reactions in organ transplantation. This study focused on designing peptide inhibitors, targeting the HVEM-LIGHT interaction, using molecular dynamics (MD) simulations of 65 peptides derived from HVEM. These peptides varied in length and disulfide-bond configurations, crucial for their interaction with the LIGHT trimer. By simulating 31 HVEM domain variants, including the full-length protein, we assessed conformational changes upon LIGHT binding to understand the influence of HVEM segments and disulfide bonds on the binding mechanism. Employing multitrajectory microsecond-scale, all-atom MD simulations and molecular mechanics with generalized Born and surface area (MM-GBSA) binding energy estimation, we identified promising CRD2 domain variants with high LIGHT affinity. Notably, point mutations in these variants led to a peptide with a single disulfide bond (C58-C73) and a K54E substitution, exhibiting the highest binding affinity. The importance of the CRD2 domain and Cys58-Cys73 disulfide bond for interrupting HVEM-LIGHT interaction was further supported by analyzing truncated CRD2 variants, demonstrating similar binding strengths and mechanisms. Further investigations into the binding mechanism utilized steered MD simulations at various pulling speeds and umbrella sampling to estimate the energy profile of HVEM-based inhibitors with LIGHT. These comprehensive analyses revealed key interactions and different binding mechanisms, highlighting the increased binding affinity of selected peptide variants. Experimental circular dichroism techniques confirmed the structural properties of these variants. This study not only advances our understanding of the molecular basis of HVEM-LIGHT interactions but also provides a foundation for developing novel therapeutic strategies for immune-related disorders. Furthermore, it sets a gold standard for peptide inhibitor design in drug development due to its systematic approach.

Peptide-based inhibitors targeting the PD-1/PD-L1 axis: potential immunotherapeutics for cancer.

The PD-1/PD-L1 complex belongs to the group of inhibitory immune checkpoints and plays a critical role in immune regulation. The PD-1/PD-L1 axis is also responsible for immune evasion of cancer cells, and this complex is one of the main targets of immunotherapies used in oncology. Treatment using immune checkpoint inhibitors is mainly based on antibodies. This approach has great therapeutic potential; however, it also has major drawbacks and can induce immune-related adverse events. Thus, there is a strong need for alternative, non-antibody-based therapies using small molecules, peptides, or peptidomimetics. In the present study, we designed, synthesized, and evaluated a set of PD-1-targeting peptides based on the sequence and structure of PD-L1. The binding of these peptides to PD-1 was investigated using SPR and ELISA. We also assessed their ability to compete with PD-L1 for binding to PD-1 and their inhibitory properties against the PD-1/PD-L1 complex at the cellular level. The best results were obtained for the peptide PD-L1(111-127)(Y112C-I126C), named (L11), which displaced PD-L1 from binding to PD-1 in the competitive assay and inhibited the formation of the PD-1/PD-L1 complex. The (L11) peptide also exhibited strong affinity for PD-1. NMR studies revealed that (L11) does not form a well-defined secondary structure; however, MD simulation indicated that (L11) binds to PD-1 at the same place as PD-L1. After further optimization of the structure, the peptide inhibitor obtained in this study could also be used as a potential therapeutic compound targeting the PD-1/PD-L1 axis.

Mechanical Stability of Ribonuclease A Heavily Depends on the Redox Environment.

Disulfide bonds are covalent bonds that connect nonlocal fragments of proteins, and they are unique post-translational modifications of proteins. They require the oxidizing environment to be stable, which occurs for example during oxidative stress; however, in a cell the reductive environment is maintained, lowering their stability. Despite many years of research on disulfide bonds, their role in the protein life cycle is not fully understood and seems to strictly depend on a system or process in which they are involved. In this article, coarse-grained UNited RESidue (UNRES), and all-atom Assisted Model Building with Energy Refinement (AMBER) force fields were applied to run a series of steered molecular dynamics (SMD) simulations of one of the most studied, but still not fully understood, proteins─ribonuclease A (RNase A). SMD simulations were performed to study the mechanical stability of RNase A in different oxidative-reductive environments. As disulfide bonds (and any other covalent bonds) cannot break/form in any classical all-atom force field, we applied additional restraints between sulfur atoms of reduced cysteines which were able to mimic the breaking of the disulfide bonds. On the other hand, the coarse-grained UNRES force field enables us to study the breaking/formation of the disulfide bonds and control the reducing/oxidizing environment owing to the presence of the designed distance/orientation-dependent potential. This study reveals that disulfide bonds have a strong influence on the mechanical stability of RNase A only in a highly oxidative environment. However, the local stability of the secondary structure seems to play a major factor in the overall stability of the protein. Both our thermal unfolding and mechanical stretching studies show that the most stable disulfide bond is Cys65-Cys72. The breaking of disulfide bonds Cys26-Cys84 and Cys58-Cys110 is associated with large force peaks. They are structural bridges, which are mostly responsible for stabilizing the RNase A conformation, while the presence of the remaining two bonds (Cys65-Cys72 and Cys40-Cys95) is most likely connected with the enzymatic activity rather than the structural stability of RNase A in the cytoplasm. Our results prove that disulfide bonds are indeed stabilizing fragments of the proteins, but their role is strongly redox environment-dependent.

Design, synthesis and biological evaluation of PD-1 derived peptides as inhibitors of PD-1/PD-L1 complex formation for cancer therapy.

Over the past few years, many molecules such as monoclonal antibodies, affibodies, nanobodies, and small compounds have been designed and tested as inhibitors of PD-1/PD-L1 complex formation. Some of them have been successfully implemented into clinical oncology practice. However, the majority of these compounds have disadvantages and limitations, such as high production price, potential for immunogenicity and/or prolonged clearance. Thus, new inhibitors of the PD-1/PD-L1 immune checkpoints are needed. Recently, peptides emerged as potential novel approach for blocking receptor/ligand interaction. In the presented studies we have designed, synthesised and tested peptides, which are potential inhibitors of the PD-1/PD-L1 axis. The amino acid sequences of the designed peptides were based on the binding sites of PD-1 to PD-L1, as determined by the crystal structure of the protein complex and also based on MM/GBSA analysis. Interactions of the peptides with PD-L1 protein were confirmed using SPR, while their inhibitory properties were studied using cell-based PD-1/PD-L1 immune checkpoint blockade assays. The characterization of the peptides has shown that the peptides PD-1(119-142)T120C-E141C, PD-1(119-142)C123-S137C and PD-1(122-138)C123-S137C strongly bind to PD-L1 protein and disrupt the interaction of the proteins. PD-1(122-138)C123-S137C peptide was shown to have the best inhibitory potential from the panel of peptides. Its 3D NMR structure was determined and the binding site to PD-L1 was established using molecular modelling methods. Our results indicate that the PD-1 derived peptides are able to mimic the PD-1 protein and inhibit PD-1/PD-L1 complex formation.

Mitochondrial potassium channels: A novel calcitriol target.

BACKGROUND: Calcitriol (an active metabolite of vitamin D) modulates the expression of hundreds of human genes by activation of the vitamin D nuclear receptor (VDR). However, VDR-mediated transcriptional modulation does not fully explain various phenotypic effects of calcitriol. Recently a fast non-genomic response to vitamin D has been described, and it seems that mitochondria are one of the targets of calcitriol. These non-classical calcitriol targets open up a new area of research with potential clinical applications. The goal of our study was to ascertain whether calcitriol can modulate mitochondrial function through regulation of the potassium channels present in the inner mitochondrial membrane. METHODS: The effects of calcitriol on the potassium ion current were measured using the patch-clamp method modified for the inner mitochondrial membrane. Molecular docking experiments were conducted in the Autodock4 program. Additionally, changes in gene expression were investigated by qPCR, and transcription factor binding sites were analyzed in the CiiiDER program. RESULTS: For the first time, our results indicate that calcitriol directly affects the activity of the mitochondrial large-conductance Ca2+-regulated potassium channel (mitoBKCa) from the human astrocytoma (U-87 MG) cell line but not the mitochondrial calcium-independent two-pore domain potassium channel (mitoTASK-3) from human keratinocytes (HaCaT). The open probability of the mitoBKCa channel in high calcium conditions decreased after calcitriol treatment and the opposite effect was observed in low calcium conditions. Moreover, using the AutoDock4 program we predicted the binding poses of calcitriol to the calcium-bound BKCa channel and identified amino acids interacting with the calcitriol molecule. Additionally, we found that calcitriol influences the expression of genes encoding potassium channels. Such a dual, genomic and non-genomic action explains the pleiotropic activity of calcitriol. CONCLUSIONS: Calcitriol can regulate the mitochondrial large-conductance calcium-regulated potassium channel. Our data open a new chapter in the study of non-genomic responses to vitamin D with potential implications for mitochondrial bioenergetics and cytoprotective mechanisms.

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.

Structural Characterization of Covalently Stabilized Human Cystatin C Oligomers.

Human cystatin C (HCC), a cysteine-protease inhibitor, exists as a folded monomer under physiological conditions but has the ability to self-assemble via domain swapping into multimeric states, including oligomers with a doughnut-like structure. The structure of the monomeric HCC has been solved by X-ray crystallography, and a covalently linked version of HCC (stab-1 HCC) is able to form stable oligomeric species containing 10-12 monomeric subunits. We have performed molecular modeling, and in conjunction with experimental parameters obtained from atomic force microscopy (AFM), transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) measurements, we observe that the structures are essentially flat, with a height of about 2 nm, and the distance between the outer edge of the ring and the edge of the central cavity is ~5.1 nm. These dimensions correspond to the height and diameter of one stab-1 HCC subunit and we present a dodecamer model for stabilized cystatin C oligomers using molecular dynamics simulations and experimentally measured parameters. Given that oligomeric species in protein aggregation reactions are often transient and very highly heterogeneous, the structural information presented here on these isolated stab-1 HCC oligomers may be useful to further explore the physiological relevance of different structural species of cystatin C in relation to protein misfolding disease.

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

The recent NEWCT-9P version of the coarse-grained UNRES force field for proteins, with scale-consistent formulas for the local and correlation terms, has been tested in the CASP13 experiment of the blind-prediction of protein structure, in the ab initio, contact-assisted, and data-assisted modes. Significant improvement of the performance has been observed with respect to the CASP11 and CASP12 experiments (by over 10 GDT_TS units for the ab initio mode predictions and by over 15 GDT_TS units for the contact-assisted prediction, respectively), which is a result of introducing scale-consistent terms and improved handling of contact-distance restraints. As in previous CASP exercises, UNRES ranked higher in the free modeling category than in the general category that included template based modeling targets. Use of distance restraints from the predicted contacts, albeit many of them were wrong, resulted in the increase of GDT_TS by over 8 units on average and introducing sparse restraints from small-angle X-ray/neutron scattering and chemical cross-link-mass-spectrometry experiments, and ambiguous restraints from nuclear magnetic resonance experiments has also improved the predictions by 8.6, 9.7, and 10.7 GDT_TS units on average, respectively.

Introduction of Phosphorylated Residues into the UNRES Coarse-Grained Model: Toward Modeling of Signaling Processes.

Phosphorylated proteins take part in many signaling pathways and play a key role in homeostasis regulation. The all-atom force fields enable us to study the systems containing phosphorylated proteins, but they are limited to short time scales. In this paper, we report the extension of the physics-based coarse-grained UNRES force field to treat systems with phosphorylated amino-acid residues. To derive the respective potentials, appropriate physics-based analytical expressions were fitted to the potentials of mean force of systems modeling phosphorylated amino-acid residues computed in our previous work and implemented in UNRES. The extended UNRES performed well in ab initio simulations of two miniproteins containing phosphorylated residues, strongly suggesting that realistic large-scale simulations of processes involving phosphorylated proteins, especially signaling processes, are now possible.

A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains.

A general and systematic method for the derivation of the functional expressions for the effective energy terms in coarse-grained force fields of polymer chains is proposed. The method is based on the expansion of the potential of mean force of the system studied in the cluster-cumulant series and expanding the all-atom energy in the Taylor series in the squares of interatomic distances about the squares of the distances between coarse-grained centers, to obtain approximate analytical expressions for the cluster cumulants. The primary degrees of freedom to average about are the angles for collective rotation of the atoms contained in the coarse-grained interaction sites about the respective virtual-bond axes. The approach has been applied to the revision of the virtual-bond-angle, virtual-bond-torsional, and backbone-local-and-electrostatic correlation potentials for the UNited RESidue (UNRES) model of polypeptide chains, demonstrating the strong dependence of the torsional and correlation potentials on virtual-bond angles, not considered in the current UNRES. The theoretical considerations are illustrated with the potentials calculated from the ab initiopotential-energysurface of terminally blocked alanine by numerical integration and with the statistical potentials derived from known protein structures. The revised torsional potentials correctly indicate that virtual-bond angles close to 90° result in the preference for the turn and helical structures, while large virtual-bond angles result in the preference for polyproline II and extended backbone geometry. The revised correlation potentials correctly reproduce the preference for the formation of ß-sheet structures for large values of virtual-bond angles and for the formation of α-helical structures for virtual-bond angles close to 90°.

Role of the sulfur to α-carbon thioether bridges in thurincin H.

Thurincin H is a small protein produced by Bacillus thuringiensis SF361 with gram-positive antimicrobial properties. The toxins produced by B. thuringiensis are widely used in the agriculture as, e.g. natural preservatives in dairy products. The structure of thurincin H possesses four covalent sulfur to [Formula: see text]-carbon bonds that involve the cysteine side-chains; these bonds are probably responsible for the shape and stability of the protein and, thereby, for its antimicrobial properties. To examine the influence of the formation of the sulfur-carbon bonds on the folding pathways and stability of the protein, a series of canonical and multiplexed replica-exchange simulations with the coarse-grained UNRES force field was carried out without and with distance restraints imposed on selected S-C[Formula: see text] atom pairs. It was found that the order of the formation and breaking of the S-C[Formula: see text] thioether bonds significantly impacts on the foldability and stability of the thurincin H. It was also observed that thioether bridges play a major role in stabilizing the global fold of the protein, although it significantly diminishes the entropy of the system. The maximum foldability of thurincin H was observed in the presence of the optimal set of three out of four thioether bridges. Thus, the results suggest that the presence of ThnB enzyme and other agents that catalyze the formation of thioether bridges can be essential for correct folding of thurincin H and that the formation of the fourth bridge does not seem to facilitate folding; instead, it seems to rigidify the loop and prevent proteolysis.

Performance of protein-structure predictions with the physics-based UNRES force field in CASP11.

Participating as the Cornell-Gdansk group, we have used our physics-based coarse-grained UNited RESidue (UNRES) force field to predict protein structure in the 11th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP11). Our methodology involved extensive multiplexed replica exchange simulations of the target proteins with a recently improved UNRES force field to provide better reproductions of the local structures of polypeptide chains. All simulations were started from fully extended polypeptide chains, and no external information was included in the simulation process except for weak restraints on secondary structure to enable us to finish each prediction within the allowed 3-week time window. Because of simplified UNRES representation of polypeptide chains, use of enhanced sampling methods, code optimization and parallelization and sufficient computational resources, we were able to treat, for the first time, all 55 human prediction targets with sizes from 44 to 595 amino acid residues, the average size being 251 residues. Complete structures of six single-domain proteins were predicted accurately, with the highest accuracy being attained for the T0769, for which the CαRMSD was 3.8 Å for 97 residues of the experimental structure. Correct structures were also predicted for 13 domains of multi-domain proteins with accuracy comparable to that of the best template-based modeling methods. With further improvements of the UNRES force field that are now underway, our physics-based coarse-grained approach to protein-structure prediction will eventually reach global prediction capacity and, consequently, reliability in simulating protein structure and dynamics that are important in biochemical processes. AVAILABILITY AND IMPLEMENTATION: Freely available on the web at http://www.unres.pl/ CONTACT: has5@cornell.edu.

Introduction of periodic boundary conditions into UNRES force field.

In this article, implementation of periodic boundary conditions (PBC) into physics-based coarse-grained UNited RESidue (UNRES) force field is presented, which replaces droplet-like restraints previously used. Droplet-like restraints are necessary to keep multichain systems together and prevent them from dissolving to infinitely low concentration. As an alternative for droplet-like restrains cuboid PBCs with imaging of the molecules were introduced. Owing to this modification, artificial forces which arose from restraints keeping a droplet together were eliminated what leads to more realistic trajectories. Due to computational reasons cutoff and smoothing functions were introduced on the long range interactions. The UNRES force field with PBC was tested by performing microcanonical simulations. Moreover, to asses the behavior of the thermostat in PBCs Langevin and Berendsen thermostats were studied. The influence of PBCs on association pattern was compared with droplet-like restraints on the ßßα hetero tetramer 1 protein system.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the UNited RESidue (UNRES) force field for protein simulations.

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620­4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

A unified coarse-grained model of biological macromolecules based on mean-field multipole-multipole interactions.

A unified coarse-grained model of three major classes of biological molecules--proteins, nucleic acids, and polysaccharides--has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site-site interactions as mean-field dipole-dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo's cluster-cumulant series leads to the appearance of mean-field dipole-dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and ß-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented.

Revised Backbone-Virtual-Bond-Angle Potentials to Treat the l- and d-Amino Acid Residues in the Coarse-Grained United Residue (UNRES) Force Field.

Continuing our effort to introduce d-amino-acid residues in the united residue (UNRES) force field developed in our laboratory, in this work the Cα ··· Cα ··· Cα backbone-virtual-bond-valence-angle (θ) potentials for systems containing d-amino-acid residues have been developed. The potentials were determined by integrating the combined energy surfaces of all possible triplets of terminally blocked glycine, alanine, and proline obtained with ab initio molecular quantum mechanics at the MP2/6-31G(d,p) level to calculate the corresponding potentials of mean force (PMFs). Subsequently, analytical expressions were fitted to the PMFs to give the virtual-bond-valence potentials to be used in UNRES. Alanine represented all types of amino-acid residues except glycine and proline. The blocking groups were either the N-acetyl and N',N'-dimethyl or N-acetyl and pyrrolidyl group, depending on whether the residue next in sequence was an alanine-type or a proline residue. A total of 126 potentials (63 symmetry-unrelated potentials for each set of terminally blocking groups) were determined. Together with the torsional, double-torsional, and side-chain-rotamer potentials for polypeptide chains containing d-amino-acid residues determined in our earlier work (Sieradzan et al. J. Chem. Theory Comput., 2012, 8, 4746), the new virtual-bond-angle (θ) potentials now constitute the complete set of physics-based potentials with which to run coarse-grained simulations of systems containing d-amino-acid residues. The ability of the extended UNRES force field to reproduce thermodynamics of polypeptide systems with d-amino-acid residues was tested by comparing the experimentally measured and the calculated free energies of helix formation of model KLALKLALxxLKLALKLA peptides, where x denotes any d- or l- amino-acid residue. The obtained results demonstrate that the UNRES force field with the new potentials reproduce the changes of free energies of helix formation upon d-substitution but overestimate the free energies of helix formation. To test the ability of UNRES with the new potentials to reproduce the structures of polypeptides with d-amino-acid residues, an ab initio replica-exchange folding simulation of thurincin H from Bacillus thuringiensis, which has d-amino-acid residues in the sequence, was carried out. UNRES was able to locate the native α-helical hairpin structure as the dominant structure even though no native sulfide-carbon bonds were present in the simulation.

Improvement of the treatment of loop structures in the UNRES force field by inclusion of coupling between backbone- and side-chain-local conformational states.

The UNited RESidue (UNRES) coarse-grained model of polypeptide chains, developed in our laboratory, enables us to carry out millisecond-scale molecular-dynamics simulations of large proteins effectively. It performs well in ab initio predictions of protein structure, as demonstrated in the last Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP10). However, the resolution of the simulated structure is too coarse, especially in loop regions, which results from insufficient specificity of the model of local interactions. To improve the representation of local interactions, in this work we introduced new side-chain-backbone correlation potentials, derived from a statistical analysis of loop regions of 4585 proteins. To obtain sufficient statistics, we reduced the set of amino-acid-residue types to five groups, derived in our earlier work on structurally optimized reduced alphabets, based on a statistical analysis of the properties of amino-acid structures. The new correlation potentials are expressed as one-dimensional Fourier series in the virtual-bond-dihedral angles involving side-chain centroids. The weight of these new terms was determined by a trial-and-error method, in which Multiplexed Replica Exchange Molecular Dynamics (MREMD) simulations were run on selected test proteins. The best average root-mean-square deviations (RMSDs) of the calculated structures from the experimental structures below the folding-transition temperatures were obtained with the weight of the new side-chain-backbone correlation potentials equal to 0.57. The resulting conformational ensembles were analyzed in detail by using the Weighted Histogram Analysis Method (WHAM) and Ward's minimum-variance clustering. This analysis showed that the RMSDs from the experimental structures dropped by 0.5 Å on average, compared to simulations without the new terms, and the deviation of individual residues in the loop region of the computed structures from their counterparts in the experimental structures (after optimum superposition of the calculated and experimental structure) decreased by up to 8 Å. Consequently, the new terms improve the representation of local structure.

Determination of effective potentials for the stretching of C(α) ⋯ C(α) virtual bonds in polypeptide chains for coarse-grained simulations of proteins from ab initio energy surfaces of N-methylacetamide and N-acetylpyrrolidine.

The potentials of mean force (PMF's) for the deformation of the C(α) ⋯ C(α) virtual bonds in polypeptide chains were determined from the diabatic energy surfaces of N-methylacetamide (modeling regular peptide groups) and N-acetylpyrrolidine (modeling the peptide groups preceding proline), calculated at the Møller-Plesset (MP2) ab initio level of theory with the 6-31G(d,p) basis set. The energy surfaces were expressed in the C(α) ⋯ C(α) virtual-bond length (d) and the H-N-C(α) ⋯ C' improper dihedral angle (α) that describes the pyramidicity of the amide nitrogen, or in the C(α)-C'(O)-N-C(α) dihedral angle (ω) and the angle α. For each grid point, the potential energy was minimized with respect to all remaining degrees of freedom. The PMF's obtained from the (d, α) energy surfaces produced realistic free-energy barriers to the trans-cis transition (10 kcal/mol and 13 kcal/mol for the regular and proline peptide groups, respectively, compared to 12.6 - 13.9 kcal/mol and 17.3 - 19.6 kcal/mol determined experimentally for glycylglycine and N-acylprolines, respectively), while those obtained from the (ω, α) energy maps produced either low-quality PMF curves when direct Boltzmann summation was implemented to compute the PMF's or too-flat curves with too-low free-energy barriers to the trans-cis transition if harmonic extrapolation was used to estimate the contributions to the partition function. An analytical bimodal logarithmic-Gaussian expression was fitted to the PMF's, and the potentials were implemented in the UNRES force field. Test Langevin-dynamics simulations were carried out for the Gly-Gly and Gly-Pro dipeptides, which showed a 10(6)-fold increase of the simulated rate of the trans-cis isomerization with respect to that measured experimentally; effectively the same result was obtained with the analytical Kramers theory of reaction rate applied to the UNRES representation of the peptide groups. Application of Kramers' theory to compute the rate constants from the all-atom ab initio energy surfaces of the model compounds studied resulted in isomerization rates close to the experimental values, which demonstrates that the increase of the isomerization rate in UNRES simulations results solely from averaging out the secondary degrees of freedom.

Extension of UNRES force field to treat polypeptide chains with D-amino-acid residues.

Coarse-grained force fields for protein simulations are usually designed and parameterized to treat proteins composed of natural L-amino-acid residues. However, D-amino-acid residues occur in bacterial, fungal (e.g., gramicidins), as well as human-designed proteins. For this reason, we have extended the UNRES coarse-grained force field developed in our laboratory to treat systems with D-amino-acid residues. We developed the respective virtual-bond-torsional and double-torsional potentials for rotation about the C α · · · C α virtual-bond axis and two consecutive C α · · · C α virtual-bond axes, respectively, as functions of virtual-bond-dihedral angles γ. In turn, these were calculated as potentials of mean force (PMFs) from the diabatic energy surfaces of terminally-blocked model compounds for glycine, alanine, and proline. The potential-energy surfaces were calculated by using the ab initio method of molecular quantum mechanics at the Møller-Plesset (MP2) level of theory and the 6-31G(d,p) basis set, with the rotation angles of the peptide groups about [Formula: see text] and [Formula: see text] used as variables, and the energy was minimized with respect to the remaining degrees of freedom. The PMFs were calculated by numerical integration for all pairs and triplets with all possible combinations of types (glycine, alanine, and proline) and chirality (D or L); however, symmetry relations reduce the number of non-equivalent torsional potentials to 13 and the number of double-torsional potentials to 63 for a given C-terminal blocking group. Subsequently, one- (for torsional) and two-dimensional (for double-torsional potentials) Fourier series were fitted to the PMFs to obtain analytical expressions. It was found that the torsional potentials of the x-Y and X-y types, where X and Y are Ala or Pro, respectively, and a lowercase letter denotes D-chirality, have global minima for small absolute values of γ, accounting for the double-helical structure of gramicidin A, which is a dimer of two chains, each possessing an alternating D-Tyr-L-Tyr sequence, and similar peptides. The side-chain and correlation potentials for D-amino-acid residues were obtained by applying the reflection about the [Formula: see text] plane to the respective potentials for the L-amino-acid residues.