Abstract
AbstractA mathematical model based on Tlusty's topological deconstruction suggests that multiple punctuated ecosystem shifts in available metabolic free energy, broadly akin to the 'aerobic' transition, enabled a punctuated sequence of increasingly complex genetic codes and protein translators under mechanisms similar to the Serial Endosymbiosis effecting the Eukaryotic transition. These evolved until the ancestor to the present narrow spectrum of nearly maximally robust codes became locked-in by path dependence.
Highlights
The genetic code that maps 64 codons to 20 amino acids is far from random, e.g., figure 1 of Koonin and Novozhilov (2009), and the references therein
Following Tlusty’s equation (2), the ‘free energy’ functional has the form D − T S where D is the average ‘error load’, equivalent to average distortion in a rate distortion problem, S is the entropy due to random drift, and T measures the strength of random drift relative to the selection force that pushes towards fitness maximization
Under the important constraint that the Rate Distortion Function R(D) is always a convex function of D (Cover and Thomas, 1991, Lemma 13.4.1). We extend these considerations both downward and upward in scale, examining the effects of changes in R(D) on internal structure within the genetic code, and studying the effect of available metabolic free energy on R(D) itself, and treat more complicated models as well, recognizing that evolutionary process does not always seem to instantiate Occam’s Razor
Summary
The genetic code that maps 64 codons to 20 amino acids is far from random, e.g., figure 1 of Koonin and Novozhilov (2009), and the references therein. We will take a different route, one in which the rate distortion function R(D) between codon pattern and amino acid pattern plays the role of of a temperature-analog driving phase transitions in a corresponding free-energy analog constructed from the distribution of possible genetic codes, as measured by the source uncertainty of the information sources using them. Phase transitions in physical systems characterized by free energy are ubiquitous, following Landau’s symmetry breaking arguments (Landau and Lifshitz, 2007; Pettini, 2007): Higher temperatures enable higher system symmetries, and, as temperature declines, punctuated shifts to lesser symmetry states occur in characteristic manners Extension of this argument seems direct, to groupoid structures. A full-bore mathematical treatment of these and related matters can be found in Glazebrook and Wallace (2009a, b)
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