Stability of open pathways
Related Experiment Video
Updated: Jun 8, 2026

Assessment of Open Probability of the Mitochondrial Permeability Transition Pore in the Setting of Coenzyme Q Excess
Published on: June 1, 2022
Edward H Flach1, Santiago Schnell
1Integrated Mathematical Oncology, H. Lee Moffitt Cancer Centre and Research Institute, Tampa, FL, USA. edward.flach@gmail.com
Abstract:
We consider the steady state of an open biochemical pathway, with controlled flow. Previously we have shown that the steady state of open enzyme catalysed reactions may be unstable, which discourages the application of the quasi-steady-state approximation (QSSA) [IEE Proc.-Syst. Biol. 153 (2006) 187]. Here we examine basic open biochemical pathway structures, to see the stability of their steady states. Following De Leenheer et al. [J. Math. Chem. 41 (2007) 295], we employ the Gershgorin circle theorem, which elegantly assesses stability. This is the key tool for our analysis. Once we have the linear stability matrix laid out in a suitable form, the application of the method is straightforward. We find that in open biochemical pathways, simple chains, branches and loops always have stable steady states. We conclude that simple open pathways are stable.
Related Concept Videos
Stability of structures
Stability of Equilibrium Configuration
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Control System Problem
When forming a closed-loop system, issues can arise if the poles cross into the unstable region, leading to potential...
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
