title: 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.
authors.affiliation: a Department of Structural Biology , University of Kiel , Kiel , Germany.
authors.forename: Ulf-Peter
authors.initials: UP
authors.lastname: Hansen
authors.affiliation: b Plant Membrane Biophysics , Technical University of Darmstadt , Darmstadt , Germany.
authors.forename: Oliver
authors.initials: O
authors.lastname: Rauh
authors.affiliation: b Plant Membrane Biophysics , Technical University of Darmstadt , Darmstadt , Germany.
authors.forename: Indra
authors.initials: I
authors.lastname: Schroeder
mesh_terms: D000818:Animals; D001419:Bacteria / Q000378:metabolism*; D001693:Biological Transport, Active; D006801:Humans; D016623:Ion Pumps / Q000378:metabolism*; D017136:Ion Transport; D007700:Kinetics; D008962:Models, Theoretical; D014780:Viruses / Q000378:metabolism*
chemical_list: D016623:Ion Pumps
keywords: IV curves; ion transport; lumped reactions; model reduction; rate constants; reaction kinetics; reserve factors