WARNING: the term epigenetics as used on this site means “over and above genetics” and should not be taken to imply chromatin marking.

 

In 1979 Douglas Hofstadter published a book entitled “Gödel Escher Bach: the golden braid”. In it he drew (a fairly lengthy) analogy between those collections of molecules that together comprise a living organism and formalism in mathematics. In the latter he showed how meaning could emerge from purely typographical symbolism, in, for example, the very primitive “-,p,q” system. However, he also illustrated the limitations of formal systems that Gödel and a bit later, Turing, identified much to the distaste of the mathematical establishment of the time. Gödel’s incompleteness bugs any formal system beyond a certain degree of “richness”. Gödel’s subject was number theory and John Barrow in “New theories of everything” explains why number theory is incomplete (namely that the theory can generate statements that cannot be proved true or false): “the axioms of ordinary arithmetic … contain less information than some arithmetical statements and hence those axioms and their associated rules of reasoning cannot determine whether these statements are true or false.” You might think that this regrettable state of affairs for arithmetic has little or no bearing on biology; well Hofstadter thought it did.

 

Chemical reactions are not unlike arithmetical calculations in that certain reactants (in arithmetic starting values) are fed into a reaction vessel (formal equations) and products reliably synthesised (answers produced); the resultant reaction can be written down in a form similar to algebraic equations. Is it not the case that living systems are simply much more complex chemical reactions where the information on the DNA leads to the production of gene products which react one with another to produce the living organism? Indeed, conventionally the cell is regarded by many as some kind of computer that can compute the phenotype (functions) from the genotype (gene coding on DNA) just as computer generates output from axioms fed into it and processed by algorithms.

 

The problems identified by Gödel in number theory concern the possibility of arithmetic to generate self-referential statements equivalent to “this statement cannot be proved”. Working from within number theory Gödel showed that number theory had to be incomplete because it could not prove this statement. To address this kind of self-referential statement one has to exit the formal system and examine it from the outside. As pointed out by the theoretical biologist Robert Rosen a purely syntactic system that can produce self-referential statements requires a semantic component if it is to produce meaning. The algorithmic model of cell function mentioned above is such a syntactic system and the cell it seems must be capable of self-reference because it fabricates itself and investigates itself to prove its output (phenotype). If this were not the case we could not expect the cell to be so reliable in maintaining its phenotype.

 

Unlike a computer the cell requires an environment to operate in and to which it can adapt and, therefore, to which it is “open” to influence. None of these things are remotely typical of computers. On this argument the information coded into the gene sequences of the DNA cannot be sufficient and some form of semantic component is required. I have proposed that the syntactic component of the cell is not the DNA but the dynamics of the cell processes that deploy the gene products and that the information coded on the DNA is the semantic component. They are related as the grammar of a language is related to its vocabulary. Meaning, in terms of phenotype, is a product of the combined action of these two components, the former being represented by an attractor (stable) state of the complex dynamic system that constitutes the cell. In so far as this component “directs” the deployment of gene products, the genetic component, it is epigenetic, i.e., over and above genetics.

 

These ideas are spelled out in formal detail here and in a lighter form as an essay here. Further thoughts on epigenetics can be found here.         

 

Epigenetics I

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