Discontinuous system

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Discontinuous system


In a discontinuous system, gradients in continuous systems across the length, l, of the diffusion path [m], are replaced by differences across compartmental boundaries of zero thickness, and the local concentration is replaced by the free activity, α [mol·dm-3]. The length of the diffusion path may not be constant along all diffusion pathways, spacial direction varies (e.g., in a spherical particle surrounded by a semipermeable membrane), and information on the diffusion paths may even be not known in a discontinuous system. In this case (e.g., in most treatments of the protonmotive force) the diffusion path is moved from the (ergodynamic) isomorphic force term to the (kinetic) mobility term. The synonym of a discontinuous system is compartmental or discretized system. In the first part of the definition of discontinuous systems, three compartments are considered: (1) the source compartment A, (2) the sink compartment B, and (3) the internal barrier compartment with thickness l. In a two-compartmental description, a system boundary is defined of zero thickness, such that the barrier comparment (e.g., a semipermeable membrane) is either part of the system (internal) or part of the environment (external). Similarly, the intermediary steps in a chemical reaction may be explicitely considered in an ergodnamic multi-comparment system; alternatively, the kinetic analysis of all intermediary steps may be collectively considered in the catalytic reaction mobility, reducing the measurement to a two-compartmental analysis of the substrate and product compartments.

Reference: System

Communicated by Gnaiger E 2018-09-17; last update 2019-01-05

Compartmental description of diffusion (d): vectorial flux and force in a discontinuous system

Three compartments [1]
  • Jd = -u·α·ΔdF = -u·ΔdΠ/l
  • Force: ΔdF = Δμ/l
  • Pressure: α3·Δμ = RT·Δc
  • Free activity: α3 = RT·Δcμ = Δc/Δlnc
Two compartments [1]
  • Jd = -b·α·ΔdF = -b·ΔdΠ
  • Force: ΔdF = Δμ
  • Pressure: α·Δμ = RT·Δc
  • Free activity: α = RT·Δcμ = Δc/Δlnc (Gnaiger 1989)


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  1. Gnaiger E (1989) Mitochondrial respiratory control: energetics, kinetics and efficiency. In: Energy transformations in cells and organisms. Wieser W, Gnaiger E (eds), Thieme, Stuttgart:6-17. - »Bioblast link«

MitoPedia concepts: Ergodynamics