genetic nets

0.1 Introduction

Genetic ‘nets’, or networks, GN – that represent a living organism’s genome –are mathematical models of functionalPlanetmathPlanetmathPlanetmath genes linked through their non-linear, dynamic interactions.

A simple genetic (or gene) network GNs may be thus represented by a directed graphMathworldPlanetmath GD whose nodes (or vertices) are the genes gi of a cell or a multicellular organism and whose edges (arcs) are arrows representing the actions of a gene agi on a linked gene or genes; such a directed graph representing a gene network has a canonically associated biogroupoid 𝒢B which is generated or directly computed from the directed graph GD.

0.2 Boolean vs. N-state models of genetic networks in LMn- logic algebras

The simplest, Boolean, or two-state models of genomes represented by such directed graphs of gene networks form a proper subcategoryMathworldPlanetmath of the categoryMathworldPlanetmath of n-state genetic networks, 𝐆𝐍ŁMn that operate on the basis of a Łukasiewicz-Moisil n-valued logic algebraPlanetmathPlanetmathPlanetmath LMn. Then, the category of genetic networks, 𝐆𝐍ŁMn was shown in ref. [2] to form a subcategory of the algebraic categoryPlanetmathPlanetmathPlanetmath of Łukasiewicz algebras (, [1, 2]. 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. [2]. 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 automataPlanetmathPlanetmath (or sequential machines based on Chrysippean or Boolean logic) and the category of (M,R)-systems (which can be realized as concrete metabolic-repair biosystems of enzymes, genes, and so on) are subcategories of the category of gene nets 𝐆𝐍ŁMn. The latter corresponds to organismic sets of zero-th order S0 in the simpler, Rashevsky’s theory of organismic sets.


  • 1 Baianu, I.C. (1977). A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory., Bulletin of Mathematical Biology, 39:249-258.
  • 2 Baianu, I.C., Brown, R., Georgescu, G., Glazebrook, J.F. (2006). Complex nonlinear biodynamics in categories, higher dimensional algebraPlanetmathPlanetmath and Łukasiewicz-Moisil topos: transformationsPlanetmathPlanetmath of neuronal, genetic and neoplastic networks. Axiomathes 16(1-2):65-122.
  • 3 Baianu, I.C., J. Glazebrook, G. Georgescu and R.Brown. (2008). A Novel Approach to Complex Systems Biology based on Categories, Higher Dimensional Algebra and Łukasiewicz Topos. Manuscript in preparation, 16 pp.
  • 4 Georgescu, G. and C. Vraciu (1970). On the CharacterizationMathworldPlanetmath of Łukasiewicz Algebras., J. Algebra, 16 (4), 486-495.
Title genetic nets
Canonical name GeneticNets
Date of creation 2013-03-22 18:11:28
Last modified on 2013-03-22 18:11:28
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 50
Author bci1 (20947)
Entry type Topic
Classification msc 55U99
Classification msc 92D15
Classification msc 03B50
Classification msc 92B20
Classification msc 92B05
Synonym genome network
Synonym genome
Synonym entity of all interacting genes in a living organism
Related topic DirectedGraph
Related topic AlgebraicCategoryOfLMnLogicAlgebras
Related topic OrganismicSets3
Related topic OrganismicSets2
Related topic JanLukasiewicz
Related topic SupercategoriesOfComplexSystems
Related topic MolecularSetTheory
Related topic CategoryTheory
Related topic OrganismicSetTheory
Related topic FunctionalBiology
Defines gene net
Defines Bayesian model
Defines genetic network
Defines N-state net models
Defines two-state models
Defines genome Boolean models
Defines category of genetic nets