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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
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Noise in random Boolean networks.

Tiago P Peixoto1, Barbara Drossel

  • 1Institut für Festkörperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt, Germany. tiago@fkp.tu-darmstadt.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 28, 2009
PubMed
Summary
This summary is machine-generated.

Noise impacts random Boolean networks differently based on connectivity. Networks with fewer inputs show smooth transitions, while more connected networks exhibit abrupt changes in dynamics when noise is introduced.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Computational Biology

Background:

  • Random Boolean networks (RBNs) are models for complex systems.
  • Understanding the impact of noise on RBN dynamics is crucial for biological and computational applications.
  • Previous studies have explored RBN behavior under deterministic conditions.

Purpose of the Study:

  • To investigate the effect of noise on the dynamics of random Boolean networks.
  • To characterize the transitions between deterministic and stochastic behaviors in RBNs.
  • To analyze the influence of network connectivity (number of inputs, K) on noise-induced transitions.

Main Methods:

  • Simulating RBNs with varying levels of noise (probability p).
  • Defining and calculating order parameters: average Hamming distance and average frozenness.
  • Employing analytical methods, including annealed approximation and self-consistent calculations.
  • Evaluating order parameters as a function of noise strength and number of inputs (K).

Main Results:

  • A smooth transition from deterministic to stochastic dynamics for K <= 2.
  • A first-order transition at p=0 for K > 2.
  • Analytical derivation of average Hamming distance using annealed approximation.
  • Frozenness distribution shows delta peaks for K=1, fractal structure for K>1, approaching continuous for large K.

Conclusions:

  • Noise induces distinct phase transitions in RBNs depending on network connectivity.
  • The nature of the transition (smooth vs. first-order) is critically dependent on the number of inputs per node.
  • Analytical and computational results provide a comprehensive understanding of noise effects in RBNs.