Abstract
AbstractA spontaneous symmetry lifting model based on Tlusty's elegant topological deconstruction suggests that multiple punctuated ecosystem resilience regime changes in metabolic free energy that were broadly similar to the aerobic transition enabled a punctuated sequence of increasingly complex genetic codes and protein translators. In a manner similar to the Serial Endosymbiosis effecting the Eukaryotic transition, codes and translators coevolved until the ancestor of the present narrow spectrum of protein machineries became locked-in by evolutionary path dependence at a relatively modest level of fitness reflecting a modest embedding metabolic free energy ecology. The simplest coevolutionary model of code-translator interaction has high and low fidelity quasi-equilibria consistent with the 'virus world' hypothesis of Koonin et al. (2006). A more detailed search for empirical evidence of 'preaerobic' ecosystem shifts in metabolic free energy availability or efficiency of use might be surprisingly fruitful.
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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