Minimal Model for Oscillations of Membrane Voltage in Plant Cells

Major plasmalemma ion transporters in plants are voltage-gated. Such gating behavior can lead to sustained oscillations of membrane voltage, which allows long-term osmotic adjustment by switching between periods of net uptake and net release of salt. The aim of this study was to investigate the mechanisms behind the oscillatory behavior by means of a minimal model. According to general preconditions for sustained oscillations such a model must consist of two ion transporters with very different equilibrium voltage and one of them acting as positive feedback. Such a positive feedback can be detected as negative slope of the steady-state I-V curves. Discussing the stability properties of the main electrogenic ion transporters in plants we found that a membrane with a predominant pump and a predominant channel would be a realistic paradigm for a minimal system with inherent oscillatory characteristics. This two-variable model was examined by phase-plane analysis. Parameter ranges for sustained oscillations could be determined via bifurcation analysis. These parameter ranges include physiologically relevant parameter sets for pump/cation-channel and pump/anion-channel systems. Finally, membrane voltage oscillations in systems without sufficient positive self-coupling mechanisms of the electrogenic ion transporters are discussed.