Quantum-Like Environment Adaptive Model for Creation of Phenotype

Abstract

The textbook conceptualization of phenotype creation,  ``genotype (G) + environment (E) + genotype \& environment interactions (GE) $\mapsto$  phenotype (Ph)'', is modeled with open quantum systems theory (OQST) or more generally with adaptive dynamics theory(ADT). The {\it model is quantum-like}, i.e., it isn't about quantum physical processes in biosystems.  Generally such modeling is about applications of the quantum formalism and methodology outside of physics. Macroscopic biosystems, in our case genotypes and phenotypes, are treated as information processors which functioning matches the laws of quantum information theory. Phenotypes are the outputs of     the $E$-adaptation processes described by the quantum master equation, {\it Gorini-Kossakowski-Sudarshan-Lindblad equation} (GKSL). Its stationary states correspond to phenotypes. We highlight the class of GKSL dynamics characterized by the camel-like graphs of (von Neumann) entropy: in the process of $E$-adaptation phenotype's state entropy  (disorder) first increases and then falls down - a stable and well-ordered phenotype is created. Traits, an organism's phenotypic characteristics, are modelled within the quantum measurement theory, as generally unsharp observables given by positive operator valued measures (POVMs. This paper is also a review on the methods and mathematical apparatus of quantum information biology.

Keywords: genotype, phenotype, quantum-like model, open quantum systems, superposition, trait observable, adaptive dynamics