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Describing function-based approximations of biomolecular systems.

Abhishek Dey1, Shaunak Sen2

  • 1Department of Electrical Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110 016, India.

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|May 11, 2018
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Summary

Researchers adapted mathematical describing functions to better analyze biomolecular signaling systems. This approach improves upon standard linearization for understanding complex biological dynamics and oscillations.

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Area of Science:

  • Systems biology
  • Mathematical modeling
  • Biomolecular engineering

Background:

  • Mathematical methods are crucial for analyzing complex systems, but new biological contexts require adapted or novel approaches.
  • Existing methods like linearization may not fully capture the dynamics of biomolecular signaling pathways.

Purpose of the Study:

  • To adapt and develop the method of describing functions for biomolecular signaling systems.
  • To provide more accurate approximations of system dynamics compared to standard linearization.
  • To develop computational error estimates for improved analysis.

Main Methods:

  • Utilized a combination of analytical and computational approaches.
  • Applied the describing function method to approximate systems with saturating and hysteretic dynamics.
  • Developed analytical upper bounds for computational error estimates.

Main Results:

  • Achieved better approximations of biomolecular system input-output responses than standard linearization.
  • Quantified computational errors with analytical upper bounds.
  • Integrated error estimates to bound oscillation amplitudes in limit cycle analysis.

Conclusions:

  • The adapted describing function method offers enhanced insight into local system behavior.
  • This approach enables computation of responses to various periodic inputs.
  • The method provides a robust tool for analyzing limit cycles in biomolecular signaling.