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07:35
Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess
Published on: June 1, 2022
Stability of open pathways
Edward H Flach1, Santiago Schnell
1Integrated Mathematical Oncology, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL, USA. edward.flach@gmail.com
Mathematical Biosciences
|September 30, 2010
Summary
Simple open biochemical pathways, including chains, branches, and loops, consistently exhibit stable steady states. This finding supports the reliability of analyzing these systems, unlike previously observed unstable enzyme-catalyzed reactions.
Area of Science:
- Biochemistry
- Systems Biology
- Mathematical Biology
Background:
- Previously, the steady state of open enzyme-catalyzed reactions was shown to be potentially unstable.
- This instability discourages the use of the quasi-steady-state approximation (QSSA) in certain biochemical pathway analyses.
Purpose of the Study:
- To investigate the stability of steady states in basic open biochemical pathway structures.
- To determine if simple pathway configurations inherently possess stable steady states.
Main Methods:
- Utilized the Gershgorin circle theorem for stability assessment.
- Employed a linear stability matrix derived from pathway structures.
- Followed established mathematical approaches for biochemical system analysis.
Main Results:
- Analysis revealed that simple open biochemical pathways, including chains, branches, and loops, consistently demonstrate stable steady states.
- The Gershgorin circle theorem provided an elegant and straightforward method for stability assessment.
Conclusions:
- Simple open biochemical pathways are inherently stable.
- The stability of these basic structures contrasts with potential instabilities in more complex enzyme-catalyzed reactions, validating their analysis.
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