A Biological Solution to a Fundamental Distributed Computing Problem

Modeling of development in the fruit fly yields an algorithm useful in designing wireless communication networks. Computational and biological systems are often distributed so that processors (cells) jointly solve a task, without any of them receiving all inputs or observing all outputs. Maximal independent set (MIS) selection is a fundamental distributed computing procedure that seeks to elect a set of local leaders in a network. A variant of this problem is solved during the development of the fly’s nervous system, when sensory organ precursor (SOP) cells are chosen. By studying SOP selection, we derived a fast algorithm for MIS selection that combines two attractive features. First, processors do not need to know their degree; second, it has an optimal message complexity while only using one-bit messages. Our findings suggest that simple and efficient algorithms can be developed on the basis of biologically derived insights.

[1]  Peng-Jun Wan,et al.  Distributed Construction of Connected Dominating Set in Wireless Ad Hoc Networks , 2004, Mob. Networks Appl..

[2]  P. Simpson,et al.  Notch signalling in development: on equivalence groups and asymmetric developmental potential. , 1997, Current opinion in genetics & development.

[3]  Thomas L. Madden,et al.  Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. , 1997, Nucleic acids research.

[4]  Roger Wattenhofer,et al.  Initializing newly deployed ad hoc and sensor networks , 2004, MobiCom '04.

[5]  M. Elowitz,et al.  Cis Interactions between Notch and Delta Generate Mutually Exclusive Signaling States , 2010, Nature.

[6]  Noga Alon,et al.  A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem , 1985, J. Algorithms.

[7]  A. Mccarthy.  Development , 1996, Current Opinion in Neurobiology.

[8]  Amir Pnueli,et al.  Symmetric and Economical Solutions to the Mutual Exclusion Problem in a Distributed System , 1984, Theor. Comput. Sci..

[9]  A. Tero,et al.  Rules for Biologically Inspired Adaptive Network Design , 2010, Science.

[10]  P. Simpson,et al.  Movement of bristle precursors contributes to the spacing pattern in Drosophila , 2002, Mechanisms of Development.

[11]  Scott Barolo,et al.  Lateral inhibition in proneural clusters: cis-regulatory logic and default repression by Suppressor of Hairless , 2005, Development.

[12]  Seif Haridi,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.

[13]  P. Maini,et al.  Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling. , 1996, Journal of theoretical biology.

[14]  Uri Alon,et al.  An Introduction to Systems Biology , 2006 .

[15]  Adam C. Miller,et al.  cis-Inhibition of Notch by Endogenous Delta Biases the Outcome of Lateral Inhibition , 2009, Current Biology.

[16]  Paul Flicek,et al.  Sense from sequence reads: methods for alignment and assembly , 2009, Nature Methods.

[17]  M. Fortini,et al.  Notch signaling: the core pathway and its posttranslational regulation. , 2009, Developmental cell.

[18]  David Peleg,et al.  Distributed Computing: A Locality-Sensitive Approach , 1987 .

[19]  Yves Métivier,et al.  An optimal bit complexity randomized distributed MIS algorithm , 2011, Distributed Computing.

[20]  A. E. Fincham,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[21]  B. Bainbridge,et al.  Genetics , 1981, Experientia.

[22]  Roger Wattenhofer,et al.  Maximal independent sets in radio networks , 2005, PODC '05.

[23]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[24]  Richard M. Karp,et al.  A fast parallel algorithm for the maximal independent set problem , 1985, JACM.

[25]  Naama Barkai,et al.  Error Minimization in Lateral Inhibition Circuits , 2010, Science Signaling.

[26]  Michael Luby,et al.  A simple parallel algorithm for the maximal independent set problem , 1985, STOC '85.

[27]  Scott Barolo,et al.  New Drosophila transgenic reporters: insulated P-element vectors expressing fast-maturing RFP. , 2004, BioTechniques.

[28]  J M Rendel,et al.  Canalisation of development of scutellar bristles in Drosophila by control of the scute locus. , 1965, Genetics.

[29]  S. Bray.  Notch signalling: a simple pathway becomes complex , 2006, Nature Reviews Molecular Cell Biology.

[30]  Ian M. Mitchell,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[31]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[32]  K. Kimura,et al.  Sequential emergence of the evenly spaced microchaetes on the notum of Drosophila , 1993, Roux's archives of developmental biology.

[33]  A. Parks,et al.  The dynamics of neurogenic signalling underlying bristle development in Drosophila melanogaster , 1997, Mechanisms of Development.

[34]  E. Plahte.  Pattern formation in discrete cell lattices , 2001, Journal of mathematical biology.