title: Symmetry structure in discrete models of biochemical systems: natural subsystems and the weak control hierarchy in a new model of computation driven by interactions.
abstract: Interaction computing is inspired by the observation that cell metabolic/regulatory systems construct order dynamically, through constrained interactions between their components and based on a wide range of possible inputs and environmental conditions. The goals of this work are to (i) identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this and (ii) use the resulting insights to define a new model of computation based on interactions that is useful for both biology and computation. The dynamical characteristics of the cellular pathways studied in systems biology relate, mathematically, to the computational characteristics of automata derived from them, and their internal symmetry structures to computational power. Finite discrete automata models of biological systems such as the lac operon, the Krebs cycle and p53-mdm2 genetic regulation constructed from systems biology models have canonically associated algebraic structures (their transformation semigroups). These contain permutation groups (local substructures exhibiting symmetry) that correspond to 'pools of reversibility'. These natural subsystems are related to one another in a hierarchical manner by the notion of 'weak control'. We present natural subsystems arising from several biological examples and their weak control hierarchies in detail. Finite simple non-Abelian groups are found in biological examples and can be harnessed to realize finitary universal computation. This allows ensembles of cells to achieve any desired finitary computational transformation, depending on external inputs, via suitably constrained interactions. Based on this, interaction machines that grow and change their structure recursively are introduced and applied, providing a natural model of computation driven by interactions.
authors.affiliation: Royal Society Wolfson Biocomputation Research Laboratory, University of Hertfordshire, Hatfield AL10 9AB, UK.
authors.forename: Chrystopher L
authors.initials: CL
authors.lastname: Nehaniv
authors.affiliation: Department of Mathematics, University of California Berkeley, Berkeley, CA 94720, USA.
authors.forename: John
authors.initials: J
authors.lastname: Rhodes
authors.affiliation: Royal Society Wolfson Biocomputation Research Laboratory, University of Hertfordshire, Hatfield AL10 9AB, UK Centre for Research in Mathematics, University of Western Sydney, Locked Bag 1797, Penrith, New South Wales 2751, Australia.
authors.forename: Attila
authors.initials: A
authors.lastname: Egri-Nagy
authors.affiliation: Royal Society Wolfson Biocomputation Research Laboratory, University of Hertfordshire, Hatfield AL10 9AB, UK p.dini@herts.ac.uk.
authors.forename: Paolo
authors.initials: P
authors.lastname: Dini
authors.affiliation: Institute of IT Security and Security Law, University of Passau, Passau 94030, Germany.
authors.forename: Eric Rothstein
authors.initials: ER
authors.lastname: Morris
authors.affiliation: Institute of Mathematics, University of Debrecen, Pf. 12. Debrecen, 4010 Hungary.
authors.forename: Gábor
authors.initials: G
authors.lastname: Horváth
authors.affiliation: Royal Society Wolfson Biocomputation Research Laboratory, University of Hertfordshire, Hatfield AL10 9AB, UK.
authors.forename: Fariba
authors.initials: F
authors.lastname: Karimi
authors.affiliation: Institute of IT Security and Security Law, University of Passau, Passau 94030, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Schreckling
authors.affiliation: Royal Society Wolfson Biocomputation Research Laboratory, University of Hertfordshire, Hatfield AL10 9AB, UK.
authors.forename: Maria J
authors.initials: MJ
authors.lastname: Schilstra
mesh_terms: D000818:Animals; D017209:Apoptosis; D002455:Cell Division; D002952:Citric Acid Cycle; D003198:Computer Simulation; D004926:Escherichia coli / Q000378:metabolism; D005786:Gene Expression Regulation; D053263:Gene Regulatory Networks; D006801:Humans; D007763:Lac Operon; D008432:Mathematical Computing; D008954:Models, Biological; D009474:Neurons / Q000502:physiology*; D051736:Proto-Oncogene Proteins c-mdm2 / Q000378:metabolism; D016159:Tumor Suppressor Protein p53 / Q000378:metabolism
chemical_list: D016159:Tumor Suppressor Protein p53; C497206:MDM2 protein, human; D051736:Proto-Oncogene Proteins c-mdm2
keywords: algebraic automata theory; automata networks; interaction computing; systems biology