Self-referring DNA and protein: a remark on physical and geometrical aspects

All known life forms are based upon a hierarchy of interwoven feedback loops, operating over a cascade of space, time and energy scales. Among the most basic loops are those connecting DNA and proteins. For example, in genetic networks, DNA genes are expressed as proteins, which may bind near the same genes and thereby control their own expression. In this molecular type of self-reference, information is mapped from the DNA sequence to the protein and back to DNA. There is a variety of dynamic DNA-protein self-reference loops, and the purpose of this remark is to discuss certain geometrical and physical aspects related to the back and forth mapping between DNA and proteins. The mappings are examined as dimensional reductions and expansions between high- and low-dimensional manifolds in molecular spaces. The discussion raises basic questions regarding the nature of DNA and proteins as self-referring matter, which are examined in a simple toy model.