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. 2004 Jun;86(6):3510-8.
doi: 10.1529/biophysj.103.038679.

How to impose microscopic reversibility in complex reaction mechanisms

David Colquhoun  1 , Kathryn A Dowsland, Marco Beato, Andrew J R Plested
Affiliations

How to impose microscopic reversibility in complex reaction mechanisms

David Colquhoun et al. Biophys J. 2004 Jun.

Abstract

Most, but not all, ion channels appear to obey the law of microscopic reversibility (or detailed balance). During the fitting of reaction mechanisms it is therefore often required that cycles in the mechanism should obey microscopic reversibility at all times. In complex reaction mechanisms, especially those that contain cubic arrangements of states, it may not be obvious how to achieve this. Three general methods for imposing microscopic reversibility are described. The first method works by setting the 'obvious' four-state cycles in the correct order. The second method, based on the idea of a spanning tree, works by finding independent cycles (which will often have more than four states) such that the order in which they are set does not matter. The third method uses linear algebra to solve for constrained rates.

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Figures

FIGURE 1
FIGURE 1
A four-state cyclic reaction mechanism. The names of the states in this example are intended to indicate that R is a receptor with two different binding sites; either (states 2 and 4) may become occupied before both are occupied (state 1). The labels on the arrows indicate the transition rates and the corresponding equilibrium constants are shown as K1 = k12/k21, K2 = k23/k32, K3 = k43/k34, K4 = k14/k41.
FIGURE 2
FIGURE 2
Representation of a two-dimensional reaction scheme with 16 states (one at each vertex). It contains nine four-membered cycles (numbered 1–9 in the diagram).
FIGURE 3
FIGURE 3
A reaction mechanism with eight states (vertices) in a cubic arrangement.
FIGURE 4
FIGURE 4
The 16-state mechanism in Fig. 2, with two examples of the many possible spanning trees shown, as thick lines.
FIGURE 5
FIGURE 5
The cubic mechanism in Fig. 3 is shown projected in two dimensions, with thick lines indicating one of the many possible spanning trees.
See this image and copyright information in PMC

Comment in

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