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 $\mathrm{O}\cdots \mathrm{O}\cdots \mathrm{O}$ virtual-bond angles ($\theta$) and for the dihedral angles for rotation about the $\mathrm{O}\cdots \mathrm{O}$ virtual bonds ($\gamma$) of $1\to 4$-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 $\mathrm{O}\cdots \mathrm{O}$ 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 $\theta =140^{°}$ for all pairs except $\beta$-d$-[\alpha ,\beta ]$-l-glucose, where the global minimum is shifted to $\theta ={150}^{°}$ and a secondary minimum appears at $\theta ={90}^{°}$. The torsional potentials favor small negative $\gamma$ angles for the $\alpha$-d-glucose and extended negative angles $\gamma$ 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.

中文翻译：

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推导聚合物粗粒度能量函数中有效能量项的功能形式的一般方法。二。粗粒骨干的局部潜力$\mathrm{Ø}\mathrm{1个}\to 4$键合的聚葡萄糖链

基于在我们最近的工作中描述的聚合物链的粗粒力场构造理论[AK Sieradzan等。，J. Chem。物理 [ 146，124106（2017）]，在这项工作中，已经确定了用于我们实验室正在开发的多糖的SUGRES-1P模型的有效粗粒度电势。$\mathrm{Ø}\cdots \mathrm{Ø}\cdots \mathrm{Ø}$ 虚拟键角（$\theta$）以及围绕旋转的二面角 $\mathrm{Ø}\cdots \mathrm{Ø}$ 虚拟债券（$\gamma$） 的 $\mathrm{1个}\to 4$-连接的葡糖基多糖，用于[$\alpha ，\beta$]-[ d，l ]-葡萄糖。从[]的自由能面计算出对应于虚拟键角和虚拟键二面角的平均力的电势。$\alpha ，\beta$通过用AMBER12力场进行伞式采样分子动力学模拟确定的]-[ d，l ]-葡萄糖对，或通过将各自的玻耳兹曼因子积分在二面体上而分别共享重叠残基的两对表面的组合来确定角度$\lambda$ 糖单元围绕的旋转 $\mathrm{Ø}\cdots \mathrm{Ø}$虚拟债券。随后将分析表达式拟合为平均力的潜力。虚拟键扭转势取决于虚拟键二面角和虚拟键角。虚拟键角势包含一个最小值，约为$\theta =140^{°}$ 对于所有对，除了 $\beta$- d$-[\alpha ，\beta ]$-升葡萄糖，其中全球最小的移动到$\theta ={150}^{°}$ 次要最小值出现在 $\theta ={90}^{°}$。扭转势偏小$\gamma$ 的角度 $\alpha$- d -葡萄糖和扩展负角$\gamma$ 为了 $\beta$- ð葡萄糖链，分别如淀粉和纤维素的实验结构中观察到。还证明了基于久保的簇-累积量理论推导的近似表达式，其系数取决于包括定义扭转势的三糖单元的二糖单元的身份，因此非常适合所有扭转势，从而减少了扭转数。参数明显。