The aim of this project is (i) to determine how long-range correlations between amino-acid residues sitting on distant parts of the polypeptide chain, which do not interact with each other directly, contribute to the formation of protein tertiary structure, (ii) to use the obtained results in enriching the coarse-grained UNited RESidue (UNRES) force field in the respective effective energy terms, which will presumably enhance its power to correctly predict global complicated folds, (iii) to investigate if and how these correlations contribute to the protein dynamics, especially to allosteric communication and to the the exceptional performance of molecular rotatory motors. The basis of the research is the scale-consistent theory of coarse graining developed in our laboratory which enables us to derive, based on the Kubo cluster-cumulant expansion, the terms that account for the mean-field coupling between the backbone-local, backbone-local and backbone-electrostatic, as well as backbone-local and sidechain-sidechain interactions. Application of this theory resulted in the development of the physics-based UNRES model of polypeptide chains that is capable of ab initio folding simulations of proteins. Preliminary studies strongly suggest that long-range coupling terms exist, which particularly propagate through regular (helical, strand, and beta-sheet) structures. These terms seem to determine the direction of the chain immediately following the regular elements. The project will consist of (i) parameterization of the already derived and derivation and parameterization of the new cluster-cumulant terms corresponding to long-range correlations, based on the potential-energy surfaces of model compounds with ab initio and semiempirical methods of molecular quantum mechanics, in which the the Fragment Molecular Orbital method will be used that enables us to partition the energy of a molecule into contributions corresponding to fragments, thus facilitating the definition of coarse-grained centers (ii) statistical analysis of protein structures from Protein Data Bank and those of the AlphaFold (Google DeepMind; the winner group in the CASP14 experiment) database to find how the coupling terms are reflected in the statistics (iii) implementation of the new energy terms in UNRES and calibration of the upgraded force field, (iv) testing UNRES with the new terms with known protein structures and in the CASP16 and CASP17 blind-prediction experiments, (v) running all-atom and UNRES molecular dynamics simulations of proteins with allosteric communication and analyzing their results to relate the correlation terms to allosteric phenomena and (vi) running all-atom and UNRES molecular dynamics simulations of selected rotatory molecular motors and finding out if and how the indirect interactions along polypeptide chains contribute to the highly-concerted motions of molecular rotatory motors (e.g., those of bacterial flagella), which exhibit exceptional efficiency in converting energy into motion. If successful, the project will result in a version of UNRES capable of physics-based modeling the structure and dynamics of proteins with complex folds and will make a breakthrough in the understanding of the principles of organized structure formation in proteins and other bio- as well-as man-made polymers and in the design of polymer structures, as well as of the dynamics of such systems, and in the design of force fields to model the structure and dynamics of biological macromolecules.