INTRODUCTION

In recent years physiologists have become quite adept at probing into neurons with intracellular microelectrodes. They are now able, in fact, to measure (a) the voltage change across the postsynaptic membrane elicited by a single presynaptic impulse (see, for examples, references [1] and [2]) and (b) the voltage-current characteristics across a localized region of the nerve cell membrane [(3)], [(4)], [(5)], [(6)]. With microelectrodes, physiologists have been able to examine not only the all-or-none spike generating and propagating properties of axons but also the electrical properties of somatic and dendritic structures in individual neurons. The resulting observations have led many physiologists to believe that the individual nerve cell is a potentially complex information-processing system far removed from the simple two-state device envisioned by many early modelers. This new concept of the neuron is well summarized by Bullock in his 1959 Science article [(10)]. In the light of recent physiological literature, one cannot justifiably omit the diverse forms of somatic and dendritic behavior when assessing the information-processing capabilities of single neurons. This is true regardless of the means of assessment—whether one uses mathematical idealizations, electrochemical models, or electronic analogs. We have been interested specifically in electronic analogs of the neuron; and in view of the widely diversified behavior which we must simulate, our first goal has been to find a unifying concept about which to design our analogs. We believe we have found such a concept in the Modern Ionic Hypothesis, and in this paper we will discuss an electronic analog of the neuron which was based on this hypothesis and which simulated not only the properties of the axon but also the various subthreshold properties of the somata and dendrites of neurons.

We begin with a brief summary of the various types of subthreshold activity which have been observed in the somatic and dendritic structures of neurons. This is followed by a brief discussion of the Hodgkin-Huxley data and of the Modern Ionic Hypothesis. An electronic analog based on the Hodgkin-Huxley data is then introduced, and we show how this analog can be used to provide all of the various types of somatic and dendritic activity.

SUBTHRESHOLD ELECTRICAL ACTIVITY
IN NEURONS

In studying the recent literature in neurophysiology, one is immediately struck by the diversity in form of both elicited and spontaneous electrical activity in the single nerve cell. This applies not only to the temporal patterns of all-or-none action potentials but also to the graded somatic and dendritic potentials. The synaptic membrane of a neuron, for example, is often found to be electrically inexcitable and thus incapable of producing an action potential; yet the graded, synaptically induced potentials show an amazing diversity in form. In response to a presynaptic impulse, the postsynaptic membrane may become hyperpolarized (inhibitory postsynaptic potential), depolarized (excitatory postsynaptic potential), or remain at the resting potential but with an increased permeability to certain ions (a form of inhibition). The form of the postsynaptic potential in response to an isolated presynaptic spike may vary from synapse to synapse in several ways, as shown in [Figure 1]. Following a presynaptic spike, the postsynaptic potential typically rises with some delay to a peak value and then falls back toward the equilibrium or resting potential. Three potentially important factors are the delay time (synaptic delay), the peak amplitude (spatial weighting of synapse), and the rate of fall toward the equilibrium potential (temporal weighting of synapse). The responses of a synapse to individual spikes in a volley may be progressively enhanced (facilitation), diminished (antifacilitation), or neither [(1)], [(2)], [(7)], [(8)]. Facilitation may be in the form of progressively increased peak amplitude, or in the form of progressively decreased rate of fall ([see Figure 2]). The time course and magnitude of facilitation or antifacilitation may very well be important synaptic parameters. In addition, the postsynaptic membrane sometimes exhibits excitatory or inhibitory aftereffects (or both) on cessation of a volley of presynaptic spikes [(2)], [(7)]; and the time course and magnitude of the aftereffects may be important parameters. Clearly, even if one considers the synaptic potentials alone, he is faced with an impressive variety of responses. Examples of the various types of postsynaptic responses may be found in the literature, but for purposes of the present discussion the idealized wave forms in [Figure 2] will demonstrate the diversity of electrical behavior with which one is faced.

Figure 1—Excitatory postsynaptic potentials in response to a single presynaptic spike

Figure 2—Idealized postsynaptic potentials

In addition to synaptically induced potentials, low-frequency, spontaneous potential fluctuations have been observed in many neurons [(2)], [(7)], [(9)], [(10)], [(11)]. These fluctuations, generally referred to as pacemaker potentials, are usually rhythmic and may be undulatory or more nearly saw-toothed in form. The depolarizing phase may be accompanied by a spike, a volley of spikes, or no spikes at all. Pacemaker frequencies have been noted from ten or more cycles per second down to one cycle every ten seconds or more. Some idealized pacemaker wave forms are shown in [Figure 3].

Figure 3—Idealized pacemaker potentials

Figure 4—Graded response

Bullock [(7)], [(10)], [(12)], [(13)] has demonstrated the existence of a third type of subthreshold response, which he calls the graded response. While the postsynaptic membrane is quite often electrically inexcitable, other regions of the somatic and dendritic membranes appear to be moderately excitable. It is in these regions that Bullock observes the graded response. If one applies a series of pulsed voltage stimuli to the graded-response region, the observed responses would be similar to those shown in [Figure 4A]. Plotting the peak response voltage as a function of the stimulus voltage would result in a curve similar to that in [Figure 4B] ([see Ref. 3, page 4]). For small values of input voltage, the response curve is linear; the membrane is passive. As the stimulus voltage is increased, however, the response becomes more and more disproportionate. The membrane is actively amplifying the stimulus potential. At even higher values of stimulus potential, the system becomes regenerative; and a full action potential results. The peak amplitude of the response depends on the duration of the stimulus as well as on the amplitude. It also depends on the rate of application of the stimulus voltage. If the stimulus potential is a voltage ramp, for example, the response will depend on the slope of the ramp. If the rate of rise is sufficiently low, the membrane will respond in a passive manner to voltages much greater than the spike threshold for suddenly applied voltages. In other words, the graded-response regions appear to accommodate to slowly varying potentials.

In terms of functional operation, we can think of the synapse as a transducer. The input to this transducer is a spike or series of spikes in the presynaptic axon. The output is an accumulative, long-lasting potential which in some way (perhaps not uniquely) represents the pattern of presynaptic spikes. The pacemaker appears to perform the function of a clock, producing periodic spikes or spike bursts or producing periodic changes in the over-all excitability of the neuron. The graded-response regions appear to act as nonlinear amplifiers and, occasionally, spike initiators. The net result of this electrical activity is transformed into a series of spikes which originate at spike initiation sites and are propagated along axons to other neurons. The electrical activity in the neuron described above is summarized in the following outline (taken in part from [Bullock (7)]):