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

Praharshit Sharma, Bhupendra Kumar Pathak, Tiratha Raj Singh


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).

Full Text:



Hopcroft JE, Motwani R, and Ullman JD. Introduction to automata theory, languages and computation. 2nd ed. Massachussets: Addison-Wesley; 1979.

Samarrai W, Yeol JW, Barjis I, and Ryu YS. System biology modeling of protein process using deterministic finite automata (DFA). Proceedings of 9th International Workshop on Cellular Neural Networks and Their Applications, pp. 290-95; 2005.

Singh TR. WebFARM: web server for finite automated restriction mapping. Bioinformation 2010 4(8): 341-343.

Hogeweg P. Multilevel Cellular Automata as a Tool for Studying Bioinformatic Processes. In: Hoekstra AG, Kroc J, Sloot PMA, editors. Simulating complex systems by cellular automata. pp.19-28, Springer; 2010. pp. 19-28.

Singh TR and Pardasani KR. A finite automation model for DNA fragment extraction. GAMS J Math. Biosci. 2007; 3(1) 73-80.

Achimowicz J, Kazimierski K, Wojcik K. Possibility of genetic coding of amino acid sequences by coherent electronic states in nucleotide chains. PhysiolChem Phys. 1981; 13(2):171-3.

Praharshit Sharma. Proof of Achimowicz's result in relation to Genetic Code through a Cellular Automaton Approach. Journal of Errology. Available from: http://www.bioflukes.com/Others/bioflukes/4

Praharshit Sharma. Ab-initio reconstruction of genetic code, prediction of Tm , C-value paradox and correlation with ANISOU data based on cellular automaton theory with further applications to protein secondary structure prediction, codon-bias and degeneracy. F1000Posters 2013, 4: 1315. Available from: http://f1000.com/posters/browse/summary/1094586

Carsten M and Marc TH. Outer-totalistic Cellular Automaton on graphs. Physics Letters: A. 373(5), 2009, 546–549.

SirakoulisGCh, Karafyllidis I, MizasCh, Mardiris V, Thanailakis A, Tsalides P. A cellular

automaton model for the study of DNA sequence evolution. ComputBiol Med. 2003 Sep; 33(5): 439-53.

Robscheit-Robbins FS, Miller LL, Whipple GH. Plasma protein and hemoglobin production : deletion of individual amino acids from growth mixture of ten essential amino acids. Significant changes in urinary nitrogen. J Exp Med. 1947 Feb 28; 85(3):243-65.

George LN. “Essential” and “nonessential” amino acids in the urine of severely burned patients. J Clin Invest. 1954 June; 33(6): 847–8.