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  • C.L. Nehaniv
  • John Rhodes
  • Attila Egri-Nagy
  • Paolo Dini
  • Eric Rothstein Morris
  • Gabor Horvath
  • Fariba Karimi
  • Daniel Schreckling
  • M. Schilstra
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Original languageEnglish
Article number20140223
Number of pages51
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Journal publication date28 Jul 2015
Volume373
Early online date15 Jun 2015
DOIs
StatePublished - 28 Jul 2015

Abstract

Interaction Computing (IC) 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 (1) to identify and understand mathematically the natural subsystems and hierarchical relations in natural systems enabling this, and (2) to 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, Krebs cycle, and p53-mdm2 genetic regulation constructed from Systems Biology models have canonically associated algebraic structures { 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 (SNAGs) are found in biological examples and can be harnessed to realize nitary 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.

Notes

Date of Acceptance: 27/04/2015. © 2015 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited

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