Persistent membranous cross correlations due to the multiplicity of gates in ion channels

Abstract

Ion channels in excitable cells reveal spontaneous intermittent opening and closing. As the membrane area reduces, this stochasticity enables spontaneous firing and elevates the cell's ability to fire at weaker stimuli. A multiple number of gates are accommodated in each individual ion channel. Here we investigate the possible impact of that gate multiplicity on the cell's function specifically when the membrane area is of limited size. It is shown that a non-trivially persistent correlation then takes place between the transmembrane voltage fluctuations (also between the fluctuations in the gating variables) and the component of open channel fluctuations attributed to the above gate multiplicity. This cross correlation persistency is found to be playing a major augmentative role in the elevation of the cell's excitability and spontaneous firing; without the persistency, the cell would be much less excitable. The cross correlation persistency is also found to enhance spike coherence. The stochastic Hodgkin-Huxley equations, put forward by Fox and Lu, are addressed in the context of their recognized failure to produce accurate enough statistics of spike generation. Our results indicate that the major source of that inaccuracy is the incapability of the stochastic Hodgkin-Huxley description to reflect the above cross correlation persistency.