A Mathematical Model of Central Dogma of Molecular Biology employing a Novel Irrational-Integral-Imaginary (i3) Encoding and Numerical Approximation based on Cellular Automation

Abstract

Cellular Automaton (CA) is usually used to model the spatio-temporal evolution of dynamical systems. In this work, a special class of the same known as 'Outer-totalistic' Cellular Automaton is applied to examine if there is a rationale behind the correlation between 64 possible codons and the resulting 20 amino-acids. Also, an attempt is made to mathematically model the central dogma of molecular biology in an intelligible format, including transcription and translation. Results suggest that our irrational-integral-imaginary (i3) encoding approach forms not only a satisfactory basis for a mathematical model of translation of mRNA to protein but also that of transcription from ssDNA (single stranded DNA) to mRNA (messenger RNA).