A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. II. Backbone-local potentials of coarse-grained O1 → 4-bonded polyglucose chains

Based on the theory of the construction of coarse-grained force fields for polymer chains described in our recent work [A. K. Sieradzan et al., J. Chem. Phys. 146, 124106 (2017)], in this work effective coarse-grained potentials, to be used in the SUGRES-1P model of polysaccharides that is being developed in our laboratory, have been determined for the O...O...O virtual-bond angles (theta) and for the dihedral angles for rotation about the O...O virtual bonds (gamma) of 1 -> 4-linked glucosyl polysaccharides, for all possible combinations of [alpha, beta]-[D, L]-glucose. The potentials of mean force corresponding to the virtual-bond angles and the virtual-bond dihedral angles were calculated from the free-energy surfaces of [alpha, beta]-[D, L]-glucose pairs, determined by umbrella-sampling molecular-dynamics simulations with the AMBER12 force field, or combinations of the surfaces of two pairs sharing the overlapping residue, respectively, by integrating the respective Boltzmann factor over the dihedral angles lambda for the rotation of the sugar units about the O...O virtual bonds. Analytical expressions were subsequently fitted to the potentials of mean force. The virtual-bond-torsional potentials depend on both virtual-bond-dihedral angles and virtual-bond angles. The virtual-bond-angle potentials contain a single minimum at about theta = 140 degrees for all pairs except beta-D-[alpha, beta]-L-glucose, where the global minimum is shifted to theta = 150 degrees and a secondary minimum appears at theta = 90 degrees. The torsional potentials favor small negative gamma angles for the alpha-D-glucose and extended negative angles lambda for the beta-D -glucose chains, as observed in the experimental structures of starch and cellulose, respectively. It was also demonstrated that the approximate expression derived based on Kubo's cluster-cumulant theory, whose coefficients depend on the identity of the disugar units comprising a trisugar unit that defines a torsional potential, fits simultaneously all torsional potentials very well, thus reducing the number of parameters significantly. Published by AIP Publishing.