Dynamical Relation of Poisson Spike Trains In Hodkin-Huxley Neural Ion Current Model and Formation of Non-Canonical Bases, Islands, and G-quadruplexes in DNA, mRNA, and RNA at or near the Transcription.

“Thousands of diseases are produced by genetic defects in channels, including many diseases of profound importance, like cystic fibrosis, epilepsy, atrial and ventricular fibrillation, and so on, as documented in many papers …. among thousands of others. Many of these diseases are caused by problems in the construction of channels, or the insertion of channels in the wrong places in the wrong cells, or in the regulation and control of channels.” (Bob Eisenberg “Crowded Charges in Ion Channels”).

Abstract

Ground breaking application of mathematics and biochemistry to explain formation of non-canonical bases, islands, G-quadruplex structures, and analog bases in DNA and mRNA at or near the transcription with connection to neural networks is implemented using statistical and stochastic methods apparatus with the addition of quantum principles. As a result the usual transience of Poisson spike trains (PST) becomes very instrumental tool for finding periodical type of solutions to Fokker-Plank (FP) stochastic differential equation (SDE). The present study develops new multidimensional methods of finding solutions to SDE. This is based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem (KCCT) that allows the stochastic processes with jumps under certain conditions to have -Holder continuous modification, which is used as basis for finding analogous parallels in neural networks and dynamics of formation of CpG and non-CpG islands (CpGI or non CpGI), non-canonical bases, and structures involving G-quadruplexes during DNA transcription.