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Figure 8 | Theoretical Biology and Medical Modelling

Figure 8

From: A symmetry model for genetic coding via a wallpaper group composed of the traditional four bases and an imaginary base E: Towards category theory-like systematization of molecular/genetic biology

Figure 8

Example of a category theory-like scheme on canonical “central dogma” and reference chart. The features of DNA sequencing involving changes, insertion/deletion, and recombination, can receive a group theoretic treatment. A single-stranded ‘Dj’ (“sense” of double-stranded DNA) is transformed into its complementary sequence ‘Dj’ (same as its ‘anti-sense’) or remains in the same ‘Dj’ by morphism ρ. A single-stranded ‘Dj’ (same as the “anti-sense” of ‘Dj’) without discrimination for directions (<5’ → 3’ > or <3’ → 5’>) is transformed into its pre-messenger RNA (pre-mRNA; ‘Rj’) containing ‘introns’ that are not used in protein synthesis, or remains in the same ‘Dj’ by morphism τ. Then, ‘Dj’ is transcribed into mature RNA (mRNA; ‘Rsj’) through RNA splicing. After either the simultaneous deletion of all explicit ‘E’s from ‘Rsj’s, <Rsj > 1 (= < Rsj>), or through a sequence of deletions, <Rsj > t (t = 0, 1, 2,…) with additional idels, protein synthesis can be described in subsequent procedures of this scheme. Objects X and Y are in set D, and object Z is in set R; however, object Zs is in set Rs, which is a part of set Z. Over set Rs, group operations are not definable at present.

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