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Johannes Georg Klotz1, Reinhard Heckel, Steffen Schober

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Area of Science:

  • Computational Biology
  • Network Dynamics
  • Signal Processing

Background:

  • Nested canalizing functions (NCFs) are crucial for modeling biological regulatory networks and signal processing applications like stack filters.
  • The stabilizing effect of NCFs on network dynamics has been a long-standing conjecture.
  • Average sensitivity is a key metric for assessing the stability of Boolean networks.

Purpose of the Study:

  • To investigate the conjectured stabilizing effect of NCFs in biological networks.
  • To provide a precise mathematical bound for the average sensitivity of NCFs.
  • To connect NCF properties to their prevalence and function in biological systems.

Main Methods:

  • Derivation of a tight upper bound for the average sensitivity of NCFs.
  • Analysis of NCF average sensitivity as a function of relevant input variables.
  • Comparison of the derived upper bound with existing literature and theoretical lower bounds.

Main Results:

  • A tight upper bound for the average sensitivity of NCFs was established.
  • This upper bound was shown to be less than 4/3, supporting the conjecture.
  • The results indicate that many biological network functions exhibit low average sensitivity, approaching a tight lower bound.

Conclusions:

  • NCFs possess a stabilizing effect on network dynamics, as evidenced by their low average sensitivity.
  • The findings confirm that a significant proportion of functions in biological networks belong to a class with inherently low average sensitivity.
  • This study provides strong mathematical support for the role of NCFs in maintaining stable biological regulatory networks.