Nasser Hassan Sweilam (N. H. Sweilam)

In this article, numerical study for the fractional Cable equation which is fundamental equations for modeling neuronal dynamics is introduced by using weighted average of finite difference methods. The stability analysis of the proposed methods is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. A simple and an accurate stability criterion valid for different discretization schemes of the fractional derivative and arbitrary weight factor is introduced and checked numerically. Numerical results, figures, and comparisons have been presented to confirm the theoretical results and efficiency of the proposed method.

A theoretical study is performed of the possible role of the methyl-directed mismatch repair system in the ultraviolet-induced mutagenesis of Escherichia coli bacterial cells. For this purpose, mathematical models of the SOS network, translesion synthesis and mismatch repair are developed. Within the proposed models, the key pathways of these repair systems were simulated on the basis of modern experimental data related to their mechanisms. Our model approach shows a possible mechanistic explanation of the hypothesis that the bacterial mismatch repair system is responsible for attenuation of mutation frequency during ultraviolet-induced SOS response via removal of the nucleotides misincorporated by DNA polymerase V (the UmuD'2C complex).