The Fibonacci sequence
From Biomatics.org
The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of the double helix spiral. 34 and 21 are Fibonacci numbers. DNA has two grooves in its spirals, with a ratio between the major groove and the minor groove (roughly 21 angstroms to 13 angstroms) approximating the so-called golden ratio.
The microtubule lattice features a series of helical winding patterns which repeat on longitudinal protofilaments at 3, 5, 8, 13, 21 and higher numbers of subunit dimers (tubulins). These particular winding patterns (whose repeat intervals match the Fibonacci series) define attachment sites of the microtubule-associated proteins (MAPs), and are found in simulations of self-localized phonon excitations in microtubules (Samsonovich, 1992: These suggest topological global states in microtubules which may be resistant to local decoherence. Penrose has suggested the Fibonacci patterns on microtubules may be optimal for error correction.
The organization of mammalian microtubules is interesting from a mathematical point of view. The number 13 might seem to have no particular mathematical significance,but this is not entirely so. It is a Fibonacci number
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