System Biology Modeling of Protein Process using Deterministic Finite Automata (DFA)

A Mathematical Model of Central Dogma of Molecular Biology Employing a Novel Irrational-Integral-Imaginary (I3) Encoding and Numerical Approximation Based on Cellular Automaton

“…, where % stands for the modulo operator. It may be noted that (b % 1) = 0 in all the four possible cases of the column state variables since 1 being the "Multiplicative Identity" leaves a remainder of 0 irrespective of whatever natural number it divides; hence the dual exceptions of 'serine' and 'stop codons' being distributed across two different columns (2,4) and (3,4) respectively; counted from left-to-right in the standard genetic code system tablecf. http://en.wikipedia.org/wiki/DNA_codon_table) is handled evidently.…”

“…Finite automata are a family of mathematical constructs that are defined by a finite set of states, an output alphabet, and the rules that take the automaton from its current state to next state [1]. There are several evidences where principle of finite automaton has been utilized for various biological applications such as systems biology simulation [2], recognition of restriction endonucleases for a given DNA sequence [3], exact string matching [4] and protein structure classification [5]. Based upon the theory of coherent electronic states in nucleotide chains proposed by Achimowicz et al [6], we arrive at an optimum codon length well in agreement (as a numerical approximation to) with the same.…”