A minimal single-channel model for the regularity of beating in the sinoatrial node

It has been suggested that the normal irregular beating of the heart is a manifestation of deterministically chaotic dynamics. Evidence proffered in support of this hypothesis includes a 1/f-like power spectrum, a small noninteger correlation dimension, and self-similarity of the time series. The major cause of the normal fluctuations in heart rate is the impingement of several neural and hormonal control systems upon the sinoatrial node, the natural pacemaker of the heart. However, intrinsic fluctuations of beat rate can be seen in the isolated node, devoid of all neural and hormonal inputs, and even in a single cell isolated from the node. The electrical activity in such a single cell is generated by ions flowing through discrete channels in the cell membrane.We decided to test the hypothesis that the fluctuations in beat rate in a single cell might be due to the fluctuations in the activity of this population of single channels. We thus assemble a model consisting of 6000 channels and probe its dynamics. Each channel has one or more gates, all of which must be open to allow current to flow through the channel. Since these gates are thought to open and close in a random manner, we model each gate by a Markov process, assigning a pseudorandom number to each gate every time that it changes state from open to closed or vice versa. This number, in conjunction with the classical voltage-dependent Hodgkin-Huxley-like rate constants that control the speed with which a gate will open or close, then determines when that gate will next change state. We also employ a second method that is much more efficient computationally, in which one computes the lifetime of the ensemble of 6000 channels. We show that the Monte Carlo model has behavior consistent with the hypothesis that the irregular beating seen experimentally in single nodal cells is due to the (pseudo)random opening and closing of single channels. However, since the pseudorandom number generator used in the simulations is deterministic, one cannot state that the activity in the model is random (or stochastic). Thus, it would be premature to claim that the irregularity of beating in a single nodal cell is accounted for by the stochastic behavior of a population of a few thousand single channels lying in the membrane of the cell. Finally, we consider some implications of our work for the naturally occurring in situ fluctuations in heart rate ("heart rate variability"). (c) 1995 American Institute of Physics.