Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models

I Baianu

doi:10.1038/npre.2011.6206.1

Abstract

AbstractOperational logic and bioinformatics models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes are proposed. Łukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Łukasiewicz Topos with an n-valued Łukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.

Highlights

The assumption was made (Baianu,1977) that certain genetic activities have n levels of intensity, and this assumption is justified both by the existence of epigenetic controls, as well as by the coupling of the genome to the rest of the cell through specific signaling pathways that are involved in the modulation of both translation and transcription control processes
Łukasiewicz algebras were introduced by Moisil (1940) as algebraic models of n-valued logics: further improvements are here made by utilizing categorical constructions of Łukasiewicz Logic algebras (Georgescu and Vraciu, 1970)
One of the first successful applications of Logics to Biology was the use of predicate calculus for a dynamical description of activities in neural nets (McCulloch and Pitts, 1943), That was subsequently further developed by several neural network theorists

Summary

Introduction

The assumption was made (Baianu,1977) that certain genetic activities have n levels of intensity, and this assumption is justified both by the existence of epigenetic controls, as well as by the coupling of the genome to the rest of the cell through specific signaling pathways that are involved in the modulation of both translation and transcription control processes. Had the structural genes presented an "all-or-none" type of response to the action of regulatory genes, the neural nets might be considered to be dynamically analogous to the corresponding genetic networks, especially since the former have coupled , intra-neuronal signaling pathways resembling-but distinct- from those of other types of cells in higher organisms. Sub-case (IIa) states that the dynamics of the genetic net is such that it maintains the genes structurally unchanged It does not allow for mutations which would alter the lowest and 'the highest levels of activities if the genetic net, and which would, change the whole net. In order to characterized mutations of genetics networks one has to consider mappings on n-valued Lukasiewicz algebras. If the activity of genes would be of the “all or none” type we would have to consider genetic nets as represented by Boolean algebra. The above algebraic result shows that he particular case n=2 (that is “all or none” response) can be treated by means of centered Łukasiewicz algebras

Categories of Genetic Networks

Discussion and Conclusions