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Robustness and parameter geography in post-translational modification systems.

Kee-Myoung Nam1, Benjamin M Gyori2, Silviana V Amethyst3

  • 1Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America.

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|May 5, 2020
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Summary
This summary is machine-generated.

Biological systems exhibit robustness, but understanding it is challenging. This study reveals that realistic enzyme mechanisms, unlike simplified models, show bistability is rarer in post-translational modification systems.

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Area of Science:

  • Systems Biology
  • Biochemistry
  • Mathematical Biology

Background:

  • Biological systems are known for robustness to perturbations, yet a deep understanding remains elusive.
  • Parameter regions in mathematical models offer insights into robustness, termed 'parameter geography'.

Purpose of the Study:

  • To explore the parameter geography of bistability in post-translational modification (PTM) systems.
  • To investigate the impact of enzyme mechanism complexity on the robustness of PTM systems.

Main Methods:

  • Utilized a linear framework for timescale separation to model steady-states of a two-site PTM system.
  • Employed numerical algebraic geometry tools (Bertini, Paramotopy, alphaCertified) to analyze solutions across approximately 10^9 parameter points.
  • Incorporated complex enzyme mechanisms beyond the Michaelis-Menten scheme, including product rebinding.

Main Results:

  • Bistability was absent below a substrate concentration threshold relative to enzyme amounts.
  • The bistable region's 8-dimensional volume increased monotonically and sigmoidal with substrate concentration.
  • Realistic enzyme mechanisms revealed bistability to be rarer and compromised by product rebinding compared to simplified models.

Conclusions:

  • Unrealistic assumptions in enzyme mechanisms, like those in the Michaelis-Menten scheme, have overestimated the prevalence of bistability in PTM systems.
  • Product rebinding significantly compromises bistability, highlighting the importance of detailed mechanistic modeling.
  • High-dimensional analysis of parameter geography offers novel insights into biological system robustness.