Chaotic Spike Patterns Evoked by Periodic Inhibition of Rat Cortical Neurons

Abstract

We use methods of nonlinear dynamics to describe the effect of periodic inhibition on the patterns of action potentials generated by regular spiking rat cortical neuron in vitro. Both direct measurements and our mathematical model reveal that chaotic patterns of discharge can be evoked at certain frequencies of inhibitory stimulation. We use detailed biophysical simulation of a cortical neuron to explain the firing patterns in terms of known membrane ionic conductances.There is a small voltage difference across the outer membrane of every living cell [1]. Neurons make use of this membrane voltage to perform their computations and to communicate with one another. One very common neuronal communication signal is the action potential, a brief regenerative voltage spike that can travel long distances along the cell membrane without attenuation [2]. The time between spikes (interspike interval duration) may encode information, since the form and distribution of these intervals reflect excitatory and inhibitory signals reaching the nerve cells.In this paper, we investigate the effect of periodic inhibitory pulses on the output pattern of rat cortical neurons that usually generate a regular train of spikes in response to intracellular injection of a constant stimulating current. The experiments were performed in a brain slice preparation, and also in a simulated cortical pyramidal neuron. We analyze the data using methods of nonlinear dynamics, which are emerging as powerful tools for understanding the behavior of biological systems [3]. We develop and enhance an approach of Glass and Guevara et al. [4], which they used to describe the changes in instantaneous firing rate of embryonic chicken heart cells.Slices of somatosensory cortex from Sprague-Dawley rat were prepared by standard procedures [5]. We used sharp electrodes to record membrane potentials from neurons (n = 20) in the first third of the cortex adjacent to cerebral white matter. Intracellular injection of constant current evoked regular spiking behavior in these neurons. To simulate inhibitory input we superimposed negative rectangular current pulses of 5 ms duration at time t t ,i= 1, 2,... (c.f. Fig. 1 tive to the preceding spike. When we applied the current pulse soon after a spike, we observed a shortening of the interspike interval, while late application lengthened the interval, as shown in Figure 1. The effect of a stimulus arriving at time r, after the preceding spike, on the interspike interval length T, was described in terms of phase. The phase </ > of the applied stimulus is defined as tJT 0 , where T 0 is the unperturbed interspike interval (c.f. Figure 1). Plotting T/T 0 versus </ > yields the phase response curve (see Fig. 2) which shows how the interspike interval length depends on the exact arrival time of the stimulus. From the phase </> ; of the last stimulus, the phase of the next stimulus </> i + 1 can be predicted by a Poincare map P: 0,--0 1 + j. This claim can be confirmed from Fig. 1, which shows that the following relation holds:D...

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