Accurate treatments of electrostatics for computer simulations of biological systems: A brief survey of developments and existing problems

Abstract

Sha-Sha(衣沙沙) a)b) , Pan Cong(潘 聪) a)b) , and Hu Zhong-Han(胡中汉) a)b) † a)

Analytic theory of finite-size effects in supercell modeling of charged interfaces

“…Reliable all-atom molecular dynamics or Monte-Carlo simulations of condensed phases require a careful treatment of the long-ranged electrostatic interactions among full or partial atomic charges [1]. As the range of the coulomb force is greater than the box length of a typical simulation cell containing N < 10 7 charges, truncation methods often produce unacceptable artifacts [1][2][3][4].…”

“…Reliable all-atom molecular dynamics or Monte-Carlo simulations of condensed phases require a careful treatment of the long-ranged electrostatic interactions among full or partial atomic charges [1]. As the range of the coulomb force is greater than the box length of a typical simulation cell containing N < 10 7 charges, truncation methods often produce unacceptable artifacts [1][2][3][4]. Instead, the routinely used Ewald3D sum with the tinfoil boundary condition (e3dtf) method [5][6][7] or its various computationally efficient implementations [8] include interactions of the charges with all their periodic images in a supercell.…”

“…For any nonuniform charge density, ν e3dtf (r) produces a periodic electric field that explicitly depends on L x , L y and L z . Unless the simulation is carried out in an infinitely large unit cell for which the difference between ν e3dtf (r) and ν 0 (r) vanishes, one may expect strong finite-size effects on simulated quantities of nonuniform polar/charged systems, which however is commonly ignored in the literature [1]. * zhonghanhu@jlu.edu.cn It turns out that the spatial symmetry of a nonuniform system plays a crucial role in determining the effect imposed by the finiteness of the simulation box [12].…”

Three‐site and five‐site fixed‐charge water models compatible with AMOEBA force field

“…To develop these water models, the truncation-type method was applied to compute the electrostatic interactions, and this simple treatment often causes errors such as energy divergence for systems of highly charged DNA/RNA molecules in aqueous solution. [21][22][23][24] If one directly uses these water models with a more accurate way to compute electrostatic interactions [25][26][27] such as the Particle Mesh Ewald (PME) [25] method, other issues may arise such as lower densities and larger diffusion constants. [28] To alleviate these issues, many of these water models have been reparametrized [9,28,29] using the PME method.…”

Note: A pairwise form of the Ewald sum for non-neutral systems

“…Other efficient and accurate methods using mean-field ideas or the 2D periodic Ewald sum for such systems have been recently developed [10][11][12][13][14]. Relations among them have been discussed [15,16]. Moreover, it has been clarified that U e3d p is in fact an accurate mean-field approximation to the 2D periodic Ewald sum [17].…”