Self-assembly, modularity, and physical complexity

S. E. Ahnert, I. G. Johnston, T. M. A. Fink, J. P. K. Doye, and A. A. Louis
Phys. Rev. E 82, 026117 – Published 27 August 2010

Abstract

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus, to any given type of physical structure that can be divided into building blocks. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favored in biological self-assembly, for example in protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful quantitative measure of the difference between physical structures.

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  • Received 12 October 2009

DOI:https://doi.org/10.1103/PhysRevE.82.026117

©2010 American Physical Society

Authors & Affiliations

S. E. Ahnert1, I. G. Johnston2, T. M. A. Fink3,4,5, J. P. K. Doye6, and A. A. Louis2

  • 1Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom
  • 3Institut Curie, INSERM U900, CNRS UMR144, 26 rue d’Ulm, Paris F-75248, France
  • 4Mines ParisTech, Fontainebleau F-77300, France
  • 5London Institute for Mathematical Sciences, 22 South Audley Street, London W1K 2NY, United Kingdom
  • 6Physical & Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom

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Issue

Vol. 82, Iss. 2 — August 2010

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