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The general theory of the construction of scale-consistent energy terms in the coarse-grained force fields presented in Paper I of this series has been applied to the revision of the UNRES force field for physics-based simulations of proteins. The potentials of mean force corresponding to backbone-local and backbone-correlation energy terms were calculated from the ab initio energy surfaces of terminally blocked glycine, alanine, and proline, and the respective analytical expressions, derived by using the scale-consistent formalism, were fitted to them. The parameters of all these potentials depend on single-residue types, thus reducing their number and preventing over-fitting. The UNRES force field with the revised backbone-local and backbone-correlation terms was calibrated with a set of four small proteins with basic folds: tryptophan cage variant (TRP1; α), Full Sequence Design (FSD; α + β), villin headpiece (villin; α), and a truncated FBP-28 WW-domain variant (2MWD; β) (the NEWCT-4P force field) and, subsequently, with an enhanced set of 9 proteins composed of TRP1, FSD, villin, 1BDC (α), 2I18 (α), 1QHK (α + β), 2N9L (α + β), 1E0L (β), and 2LX7 (β) (the NEWCT-9P force field). The NEWCT-9P force field performed better than NEWCT-4P in a blind-prediction-like test with a set of 26 proteins not used in calibration and outperformed, in a test with 76 proteins, the most advanced OPT-WTFSA-2 version of UNRES with former backbone-local and backbone-correlation terms that contained more energy terms and more optimizable parameters. The NEWCT-9P force field reproduced the bimodal distribution of backbone-virtual-bond angles in the simulated structures, as observed in experimental protein structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The folding of the N-terminal part of the B-domain of staphylococcal protein A (PDB ID: 1BDD, a 46-residue three-α-helix bundle) and the formin-binding protein 28 WW domain (PDB ID: 1E0L, a 37-residue three-stranded anti-parallel β protein) was studied by means of Langevin dynamics with the coarse-grained UNRES force field to assess the influence of hydrodynamic interactions on protein-folding pathways and kinetics. The unfolded, intermediate, and native-like structures were identified by cluster analysis, and multi-exponential functions were fitted to the time dependence of the fractions of native and intermediate structures, respectively, to determine bulk kinetics. It was found that introducing hydrodynamic interactions slows down both the formation of an intermediate state and the transition from the collapsed structures to the final native-like structures by creating multiple kinetic traps. Therefore, introducing hydrodynamic interactions considerably slows the folding, as opposed to the results obtained from earlier studies with the use of G?o-like models. [ABSTRACT FROM AUTHOR]

In this study, we characterize the interactions between the extracellular matrix protein, procollagen C-proteinase enhancer-1 (PCPE-1), and glycosaminoglycans (GAGs), which are linear anionic periodic polysaccharides. We applied molecular modeling approaches to build a structural model of full-length PCPE-1, which is not experimentally available, to predict GAG binding poses for various GAG lengths, types and sulfation patterns, and to determine the effect of calcium ions on the binding. The computational data are analyzed and discussed in the context of the experimental results previously obtained using surface plasmon resonance binding assays. We also provide experimental data on PCPE-1/GAG interactions obtained using inhibition assays with GAG oligosaccharides ranging from disaccharides to octadecasaccharides. Our results predict the localization of GAG-binding sites at the amino acid residue level onto PCPE-1 and is the first attempt to describe the effects of ions on protein-GAG binding using modeling approaches. In addition, this study allows us to get deeper insights into the in silico methodology challenges and limitations when applied to GAG-protein interactions. [ABSTRACT FROM AUTHOR]

Coarse graining is usually considered as a tool to extend the time and size scale of simulations. However, leaving out the atomistic details to keep their fingerprints in a coarse-grained model also enables us to understand better structure formation and dynamics. In this chapter, by using our scale-consistent theory of coarse graining, we demonstrate that the coarse-grained terms corresponding to the coupling between local conformational states of amino-acid residues explain secondary-structure propagation along polypeptide backbone to stabilize α -helices and β -strands in proteins and direct the loops preceding and following such segments of protein structure. These and related correlations are probably the still missing terms in both physics- and knowledge-based approaches to protein-structure modeling, including AlphaFold. We also show that the chirality of coarse-grained torsional potentials and, thereby, that of polypeptide backbone emerge from putting together achiral site-based torsional potentials given the phase shift due to residue chirality, and that the improper-torsional potentials that correspond to the coupling between local conformational states of the sites adjacent to a given α -carbon atom enable us to model amino-acid-residue enantiomerization., (© 2025. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

Secondary structure is a solid scaffold on which the three-dimensional structure of a protein is built. Therefore, care must be taken to reproduce the secondary structure as accurately as possible in the simulations of protein systems. In this chapter, we summarize the physics-based energy terms that govern secondary-structure formation, the auxiliary restraints on secondary structure derived from bioinformatics and from the experimental data, and the role of those in the modeling of protein structures, dynamics, and thermodynamics with the physics-based coarse-grained UNRES force field. Examples illustrating the methodology discussed and further directions of development are presented., (© 2025. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

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., (© 2022. Springer Science+Business Media, LLC, part of Springer Nature.)