Discrete versus continuum modeling of a charged dielectric interface: A first grade test

Two main treatments within classical simulations for modeling a charged surface are using explicit, discrete charges and continuous, uniform charges. The computational cost can be substantially reduced if, instead of discrete surface charges, one uses an electric field to represent continuous surface charges. In addition, many electrolyte theories, including the Poisson--Boltzmann theory, are developed on the assumption of uniform surface charge. However, recent simulations have demonstrated with discrete surface charges, one observes much stronger charge reversal, compared to the surfaces with continuous surface charges, when the lattice constant becomes notably larger than the ion diameter. These examples show that the two treatments for modeling a charged dielectric interface can lead to substantially different results. In this short note, we calculate the electrostatic force for a single point charge above an infinite plane, and compare the differences between discrete and continuous representations of surface charges. Our results show that while the continuous, uniform surface charge model gives a quite simple picture, the discrete surface charge model can offer several different cases even for such a simple problem, depending on the respective values of ion size versus lattice spacing and a self-image interaction parameter.Comment: 3 pages, 3 figure

Molecular Characterization of the 14-3-3 Gene Family in Brachypodium distachyon L. Reveals High Evolutionary Conservation and Diverse Responses to Abiotic Stresses

The 14-3-3 gene family identified in all eukaryotic organisms is involved in a wide range of biological processes, particularly in resistance to various abiotic stresses. Here, we performed the first comprehensive study on the molecular characterisation, phylogenetics and responses to various abiotic stresses of the 14-3-3 gene family in Brachypodium distachyon L.. A total of seven 14-3-3 genes from B. distachyon and 120 from five main lineages among 12 species were identified, which were divided into five well-conserved subfamilies. The molecular structure analysis showed that the plant 14-3-3 gene family is highly evolutionarily conserved, although certain divergence had occurred in different subfamilies. The duplication event investigation revealed that segmental duplication seemed to be the predominant form by which the 14-3-3 gene family had expanded. Moreover, seven critical amino acids were detected, which may contribute to functional divergence. Expression profiling analysis showed that BdGF14 genes were abundantly expressed in the roots, but showed low expression in the meristems. All seven BdGF14 genes showed significant expression changes under various abiotic stresses, including heavy metal, phytohormone, osmotic, and temperature stresses, which might play important roles in responses to multiple abiotic stresses mainly through participating in ABA-dependent signalling and reactive oxygen species-mediated MAPK cascade signalling pathways. In particular, BdGF14 genes generally showed upregulated expression in response to multiple stresses of high temperature, heavy metal, abscisic acid (ABA), and salicylic acid (SA), but downregulated expression under H2O2, NaCl, and polyethylene glycol (PEG) stresses. Meanwhile, dynamic transcriptional expression analysis of BdGF14 genes under longer treatments with heavy metals (Cd2+, Cr3+, Cu2+, and Zn2+) and phytohormone (ABA) and recovery revealed two main expression trends in both roots and leaves: up-down and up-down-up expression from stress treatments to recovery. This study provides new insights into the structures and functions of plant 14-3-3 genes