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 (θ) and for the dihedral angles for rotation about the O⋯O virtual bonds (γ) of 1 → 4-linked glucosyl polysaccharides, for all possible combinations of [α,β]-[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 [α,β]-[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 λ 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 θ=140 for all pairs except β-d-[α,β]-l-glucose, where the global minimum is shifted to θ=150 and a secondary minimum appears at θ=90. The torsional potentials favor small negative γ angles for the α-d-glucose and extended negative angles γ for the β-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.