Genetic `nets', or networks, - that form a living organism's genome -are mathematical models of functional genes linked through their non-linear, dynamic
interactions.
A simple genetic (or gene) network may be thus represented by a
directed graph
-the gene net digraph- whose nodes (or vertices) are the genes
of a cell or a multicellular organism and whose edges (arcs) are arrows representing the actions of a gene
on a linked gene or genes; such a directed graph
representing a gene network has a canonically associated biogroupoid
which is generated or directly computed from the directed graph
.
The simplest, Boolean, or two-state models of genomes represented by such directed graphs of gene networks form a proper subcategory of the category
of n-state genetic networks,
that operate on the basis of a Łukasiewicz-Moisil n-valued logic algebra
. Then, the category of genetic networks,
was shown in ref. [7] to form a subcategory of the
algebraic category of Łukasiewicz algebras,
[,7]. There are several published, extensive computer simulations
of Boolean two-state models of both genetic and neuronal networks (for a recent summary of such computations
see, for example, ref. [7]. Most, but not all, such mathematical models are Bayesian, and therefore involve computations for random networks that may have limited biological relevance as the topology of genomes, defined as their connectivity, is far from being random.
The category of automata
(or sequential machines
based on Chrysippean or Boolean logic) and the category of -systems (which can be realized as concrete metabolic-repair biosystems of enzymes, genes, and so on) are subcategories of the category of gene nets
. The latter corresponds to organismic sets
of zero-th order
in the simpler, Rashevsky's theory of organismic sets.
As of this snapshot date, this entry was owned by bci1.