A Formal Approach to the Molecular Fuzzy Lock-and-Key
The fuzzy lock-and-key (FLK) powers a vast array of sophisticated logic gates at inter- and intra-cellular levels. We invoke representations of groupoid tiling wreath products analogous to the study of nonrigid molecules – or of related fuzzy symmetry extensions – to build a Morse Function that can describe spontaneous symmetry breaking phase transitions driven by information catalysis. The Function can, however, also be used to construct an Onsager-like stochastic dynamics, linked to the phase transition approach by the rich stability criteria associated with stochastic differential equations. The two methods provide complementary ways of looking at the FLK. A limit condition emerging from the stochastic dynamics gives insight into a cellular ‘generalized inflammation’ requiring progressively higher commitment of metabolic free energy for maintenance of basic FLK processes. These results suggest that more systematic study may illuminate pathologies associated with the failure of the FLK, a centrally-important but enigmatic biological process, as well as providing tools for the construction of extraordinarily subtle and capable automatons.
Keywords: Cellular cognition, diffusion, glycosynapse, information theory, intrinsically disordered protein