genetic nets

genetic nets

0.1

Introduction

Genetic ‘nets’, or

networks

,

G

⁢

N

– that

represent

a living organism’s genome –are mathematical models of

functional

genes linked through their non-linear, dynamic interactions.

A simple genetic (or gene) network

G

⁢

N

s

may be thus represented by a

directed graph

G

D

whose nodes (or vertices) are the genes

g

i

of a cell or a multicellular organism and whose edges (arcs) are arrows representing the actions of a gene

a

g

i

on a linked gene or genes; such a directed graph representing a gene network has a canonically associated

biogroupoid

𝒢

B

which is generated or directly computed from the directed graph

G

D

.

0.2

Boolean vs. N-state models of genetic networks in

L

⁢

M

n

- logic algebras

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,

𝐆𝐍

Ł

⁢

M

n

that operate on the basis of a Łukasiewicz-Moisil

n-valued logic

algebra

L

⁢

M

n

. Then, the category of genetic networks,

𝐆𝐍

Ł

⁢

M

n

was shown in ref.

[

2

]

to form a subcategory of the

algebraic category

of Łukasiewicz algebras (

http://planetmath.org/AlgebraicCategoryOfLMnLogicAlgebras

),

ℒ

⁢

ℳ

[

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 automata

(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

𝐆𝐍

Ł

⁢

M

n

. The latter corresponds to

organismic sets

of zero-th order

S

0

in the simpler, Rashevsky’s theory of organismic sets.

References

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 algebra

and Łukasiewicz-Moisil topos:

transformations

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

Characterization

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

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