Stable and unstable attractors in Boolean networks

Konstantin Klemm, Stefan Bornholdt

Research output: Contribution to journalArticle

92 Citations (Scopus)

Abstract

Boolean networks at the critical point have been a matter of debate for many years as, e.g., the scaling of numbers of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We point out here that these results are obtained using deterministic parallel update, where a large fraction of attractors are an artifact of the updating scheme. This limits the significance of these results for biological systems where noise is omnipresent. Here we take a fresh look at attractors in Boolean networks with the original motivation of simplified models for biological systems in mind. We test the stability of attractors with respect to infinitesimal deviations from synchronous update and find that most attractors are artifacts arising from synchronous clocking. The remaining fraction of attractors are stable against fluctuating delays. The average number of these stable attractors grows sublinearly with system size in the numerically tractable range.

Original languageEnglish
Article number055101
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume72
Issue number5
DOIs
Publication statusPublished - Nov 2005
Externally publishedYes

Fingerprint

Boolean Networks
Attractor
Unstable
Biological Systems
artifacts
Update
Scaling
scaling
Updating
Critical point
critical point
Deviation
deviation
Range of data

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Stable and unstable attractors in Boolean networks. / Klemm, Konstantin; Bornholdt, Stefan.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 72, No. 5, 055101, 11.2005.

Research output: Contribution to journalArticle

@article{df5fd70cb3c347e08935deea653c493e,
title = "Stable and unstable attractors in Boolean networks",
abstract = "Boolean networks at the critical point have been a matter of debate for many years as, e.g., the scaling of numbers of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We point out here that these results are obtained using deterministic parallel update, where a large fraction of attractors are an artifact of the updating scheme. This limits the significance of these results for biological systems where noise is omnipresent. Here we take a fresh look at attractors in Boolean networks with the original motivation of simplified models for biological systems in mind. We test the stability of attractors with respect to infinitesimal deviations from synchronous update and find that most attractors are artifacts arising from synchronous clocking. The remaining fraction of attractors are stable against fluctuating delays. The average number of these stable attractors grows sublinearly with system size in the numerically tractable range.",
author = "Konstantin Klemm and Stefan Bornholdt",
year = "2005",
month = "11",
doi = "10.1103/PhysRevE.72.055101",
language = "English",
volume = "72",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "5",

}

TY - JOUR

T1 - Stable and unstable attractors in Boolean networks

AU - Klemm, Konstantin

AU - Bornholdt, Stefan

PY - 2005/11

Y1 - 2005/11

N2 - Boolean networks at the critical point have been a matter of debate for many years as, e.g., the scaling of numbers of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We point out here that these results are obtained using deterministic parallel update, where a large fraction of attractors are an artifact of the updating scheme. This limits the significance of these results for biological systems where noise is omnipresent. Here we take a fresh look at attractors in Boolean networks with the original motivation of simplified models for biological systems in mind. We test the stability of attractors with respect to infinitesimal deviations from synchronous update and find that most attractors are artifacts arising from synchronous clocking. The remaining fraction of attractors are stable against fluctuating delays. The average number of these stable attractors grows sublinearly with system size in the numerically tractable range.

AB - Boolean networks at the critical point have been a matter of debate for many years as, e.g., the scaling of numbers of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We point out here that these results are obtained using deterministic parallel update, where a large fraction of attractors are an artifact of the updating scheme. This limits the significance of these results for biological systems where noise is omnipresent. Here we take a fresh look at attractors in Boolean networks with the original motivation of simplified models for biological systems in mind. We test the stability of attractors with respect to infinitesimal deviations from synchronous update and find that most attractors are artifacts arising from synchronous clocking. The remaining fraction of attractors are stable against fluctuating delays. The average number of these stable attractors grows sublinearly with system size in the numerically tractable range.

UR - http://www.scopus.com/inward/record.url?scp=28844465824&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844465824&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.72.055101

DO - 10.1103/PhysRevE.72.055101

M3 - Article

VL - 72

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5

M1 - 055101

ER -