Kinetic Analysis of Ca 2+ /K + Selectivity of an Ion Channel by Single-Binding-Site Models D. Gradmann 1 , E. Johannes 2 , U.-P. Hansen 3 1 Biophysical Laboratory, A.-v.-Haller-Institute for Plant Sciences, University of Go ¨ttingen, Untere Karspu ¨le 2, D-37073 Go ¨ttingen, Germany 2 The Plant Laboratory, Biology Department, University of York, P.O. Box 373, York YO1 5YW, UK 3 Institut fu ¨r Angewandte Physik der Universita ¨t, Olshausenstr. 40, D-24098 Kiel, Germany Received: 19 February 1997/Revised: 19 May 1997 Abstract. Current-voltage relationships of a cation chan- nel in the tonoplast of Beta vulgaris, as recorded in so- lutions with different activities of Ca 2+ and K + (from Johannes & Sanders 1995, J. Membrane Biol. 146:211– 224), have been reevaluated for Ca 2+ /K + selectivi- ty. Since conversion of reversal voltages to permeability ratios by constant field equations is expected to fail be- cause different ions do not move independently through a channel, the data have been analyzed with kinetic chan- nel models instead. Since recent structural information on K + channels show one short and predominant con- striction, selectivity models with only one binding site are assumed here to reflect this region kinetically. The rigid-pore model with a main binding site between two energy barriers (nine free parameters) had intrinsic prob- lems to describe the observed current-saturation at large (negative) voltages. The alternative, dynamic-pore model uses a selectivity filter in which the binding site alternates its orientation (empty, or occupied by either Ca 2+ or K + ) between the cytoplasmic side and the lu- minal side within a fraction of the electrical distance and in a rate-limiting fashion. Fits with this model describe the data well. The fits yield about a 10% electrical dis- tance of the selectivity filter, located about 5% more cytoplasmic than the electrical center. For K + transloca- tion, reorientation of the unoccupied binding site (with a preference of about 6:5 to face the lumenal side) is rate limiting. For Ca 2+ , the results show high affinity to the binding site and low translocation rates (<1% of the K + translocation rate). With the fitted model Ca 2+ entry through the open channel has been calculated for physi- ological conditions. The model predicts a unitary open channel current of about 100 fA which is insensitive to cytoplasmic Ca 2+ concentrations (between 0.1 and 1 M) and which shows little sensitivity to the voltage across the tonoplast. Key words: Calcium — Channel — Current-voltage curves — Selectivity filter — Rate theory — Kinetic model Introduction Entry of Ca 2+ into the cytoplasm through ion channels is an important subject in contemporary physiology. Strictly Ca 2+ -selective channels have not been identified in plants yet. There are, however, many reports about channels in plant membranes which allow Ca 2+ perme- ation to a small but sufficient extent. For a quantitative estimate of this portion, it was common usage to measure current-voltage relationships (IV-curves) in the presence of K + and Ca 2+ and to convert the obtained reversal voltages to relative permeabilities by constant field equa- tions (e.g., Bertl & Slayman, 1992; Johannes, Brosnan & Sanders, 1992; Ding & Pickard, 1993; Gelli & Blum- wald, 1993; Pin ˜eros & Tester, 1994; Allen & Sanders, 1995, 1996; Schulz-Lessdorf & Hedrich, 1995; Ward, Pei & Schroeder, 1995). This approach is based on the assumption of independent movement of different ion species (Goldman, 1943), which has been questioned to be valid for individual channels where competition be- tween various transportees can rather be expected (Hille, 1992; Gradmann, 1996). An explicit treatment, based on rate-theory, suffered from complexity, because channels have widely been accepted to have several binding sites in series (Hille & Schwarz, 1978). This notion was mainly based on flux-coupling ratios and anomalous mole fraction effects. Nevertheless, the rigid-pore model with several binding sites (energy wells) separated by Correspondence to: D. Gradmann J. Membrane Biol. 159, 169–178 (1997) The Journal of Membrane Biology © Springer-Verlag New York Inc. 1997