A simple recipe for setting up the flux equations of cyclic and linear reaction schemes of ion transport with a high number of states: The arrow scheme

Abstract

The calculation of flux equations or current-voltage relationships in reaction kinetic models with a high number of states can be very cumbersome. Here, a recipe based on an arrow scheme is presented, which yields a straightforward access to the minimum form of the flux equations and the occupation probability of the involved states in cyclic and linear reaction schemes. This is extremely simple for cyclic schemes without branches. If branches are involved, the effort of setting up the equations is a little bit higher. However, also here a straightforward recipe making use of so-called reserve factors is provided for implementing the branches into the cyclic scheme, thus enabling also a simple treatment of such cases.

Site-specific ion occupation in the selectivity filter causes voltage-dependent gating in a viral K+ channel

“… 43 and those used in the Eqs S15 to S17 in the Supplementary material. In the model in ( c ), two reactions from the original scheme 43 are merged according to the theory of reserve factors 36 because they are not affected separately by the experimental conditions. All models in ( a – c ) are permeation models representing the open state.…”

“…Here, we employ a novel approach to determine ion distribution in the selectivity filter from single-channel recordings using a model-based IV curve analysis 36 . This is encouraged by previous studies, where simple Markov models for ion transport comprising loading, translocation and recycling steps have yielded important insights such as the binding order in cotransporters 37 or the effect of internal pH on H + pump stoichiometry 38 .…”