Difference between revisions of "Discontinuous system"
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|description=In a '''discontinuous system''', gradients in [[continuous system]]s | |description=In a '''discontinuous system''', gradients in [[continuous system]]s 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<sup>-3</sup>]. 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. | ||
|info=[[ | |info=<u>[[System]]</u> | ||
}} | }} | ||
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 == | == Compartmental description of diffusion (d): vectorial flux and force in a discontinuous system == | ||
::: '''Three compartments''' | ::: '''Three compartments''' [1] | ||
::::* ''J''<sub>d</sub> = -''u''·''α''·Δ<sub>d</sub>''F'' = -''u''·Δ<sub>d</sub>''Π''/''l'' | ::::* ''J''<sub>d</sub> = -''u''·''α''·Δ<sub>d</sub>''F'' = -''u''·Δ<sub>d</sub>''Π''/''l'' | ||
::::::::* Force: Δ<sub>d</sub>''F'' = Δ''μ''/''l'' | ::::::::* Force: Δ<sub>d</sub>''F'' = Δ''μ''/''l'' | ||
::::::::* Pressure: ''α''<sub>3</sub>·Δ''μ'' = ''RT·Δ''c'' | ::::::::* Pressure: ''α''<sub>3</sub>·Δ''μ'' = ''RT·Δ''c'' | ||
::::* Free activity: ''α''<sub>3</sub> = ''RT''·Δ''c''/Δ''μ'' = Δ''c''/Δln''c'' | ::::* Free activity: ''α''<sub>3</sub> = ''RT''·Δ''c''/Δ''μ'' = Δ''c''/Δln''c'' | ||
::: '''Two compartments''' | ::: '''Two compartments''' [1] | ||
::::* ''J''<sub>d</sub> = -''b''·''α''·Δ<sub>d</sub>''F'' = -''b''·Δ<sub>d</sub>''Π'' | ::::* ''J''<sub>d</sub> = -''b''·''α''·Δ<sub>d</sub>''F'' = -''b''·Δ<sub>d</sub>''Π'' | ||
::::::::* Force: Δ<sub>d</sub>''F'' = Δ''μ'' | ::::::::* Force: Δ<sub>d</sub>''F'' = Δ''μ'' | ||
::::::::* Pressure: ''α''·Δ''μ'' = ''RT·Δ''c'' | ::::::::* Pressure: ''α''·Δ''μ'' = ''RT·Δ''c'' | ||
::::* Free activity: ''α'' = ''RT''·Δ''c''/Δ''μ'' = Δ''c''/Δln''c'' (Gnaiger 1989) | ::::* Free activity: ''α'' = ''RT''·Δ''c''/Δ''μ'' = Δ''c''/Δln''c'' (Gnaiger 1989) | ||
== References == | |||
::::# 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. - [[Gnaiger 1989 Energy Transformations |»Bioblast link«]] | |||
{{MitoPedia concepts | {{MitoPedia concepts | ||
|mitopedia concept=Ergodynamics | |mitopedia concept=Ergodynamics | ||
}} | }} | ||
Revision as of 22:14, 5 January 2019
- high-resolution terminology - matching measurements at high-resolution
Discontinuous system
Description
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·Δc/Δμ = Δc/Δlnc
- Three compartments [1]
- Two compartments [1]
- Jd = -b·α·ΔdF = -b·ΔdΠ
- Force: ΔdF = Δμ
- Pressure: α·Δμ = RT·Δc
- Free activity: α = RT·Δc/Δμ = Δc/Δlnc (Gnaiger 1989)
- Two compartments [1]
References
- 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
