Chapter I: Part 1

Transcriber’s Notes:

Underscores “_” before and after a word or phrase indicate _italics_
in the original text.
Equal signs “=” before and after a word or phrase indicate =bold= in
the original text.
A single underscore after a symbol indicates a subscript.
Carat symbol “^” designates a superscript.
A bold arrow in front of a letter indicates a vector,
e.g. ⮕M means “the vector M”.
Small capitals have been converted to SOLID capitals.
Illustrations have been moved so they do not break up paragraphs.
Typographical and punctuation errors have been silently corrected.

SELF-ORGANIZING
SYSTEMS
1963

=Edited By=

=JAMES EMMETT GARVEY=
_Office of Naval Research
Pasadena, California_

=ACR-96=

=OFFICE OF NAVAL RESEARCH
DEPARTMENT OF THE NAVY
WASHINGTON, D.C.=

For sale by the Superintendent of Documents.
U.S. Government Printing Office
Washington, D.C., 20402—Price $1.50

CONTENTS

Foreword iv

The Ionic Hypothesis and Neuron Models 1
—E. R. Lewis

Fields and Waves in Excitable Cellular Structures 19
—R. M. Stewart

Multi-Layer Learning Networks 37
—R. A. Stafford

Adaptive Detection of Unknown Binary Waveforms 46
—J. J. Spilker, Jr.

Conceptual Design of Self-Organizing Machines 52
—P. A. Kleyn

A Topological Foundation for Self-Organization 65
—R. I. Ścibor-Marchocki

On Functional Neuron Modeling 71
—C. E. Hendrix

Selection of Parameters for Neural Net Simulations 76
—R. K. Overton

Index of Invited Participants 77

FOREWORD

The papers appearing in this volume were presented at a Symposium on Self-Organizing Systems, which was sponsored by the Office of Naval Research and held at the California Institute of Technology, Pasadena, California, on 14 November 1963. The Symposium was organized with the aim of providing a critical forum for the presentation and discussion of contemporary significant research efforts, with the emphasis on relatively uncommon approaches and methods in an early state of development. This aim and nature dictated that the Symposium be in effect a Working Group, with numerically limited invitational participation.

The papers which were presented and discussed did in fact serve to introduce several relatively unknown approaches; some of the speakers were promising young scientists, others had become known for contributions in different fields and were as yet unrecognized for their recent work in self-organization. In addition, the papers as a collection provided a particularly broad, cross-disciplinary spectrum of investigations which possessed intrinsic value as a portrayal of the bases upon which this new discipline rests. Accordingly, it became obvious in retrospect that the information presented and discussed at the Symposium was of considerable interest—and should thus receive commensurate dissemination—to a much broader group of scientists and engineers than those who were able to participate directly in the meeting itself. This volume is the result of that observation; as an edited collection of the papers presented at the Symposium, it forms the Proceedings thereof. If it provides a useful reference for present and future investigators, as well as documenting the source of several new approaches, it will have fulfilled its intended purpose well.

A Symposium which takes the nature of a Working Group depends for its utility especially upon effective commentary and critical analysis, and we commend all the participants for their contributions in this regard. It is appropriate, further, to acknowledge the contributions to the success of the Symposium made by the following: The California Institute of Technology for volunteering to act as host and for numerous supporting services; Professor Gilbert D. McCann, Director of the Willis Booth Computing Center at the California Institute of Technology, and the members of the technical and secretarial staffs of the Computing Center, who assumed the responsibility of acting as the immediate representatives of the Institute; the members of the Program Committee, who organized and led the separate sessions—Harold Hamilton of General Precision, Joseph Hawkins of Ford Motor Company, Robert Stewart of Space-General, Peter Kleyn of Northrop, and Professor McCann; members of the Technical Information Division of the Naval Research Laboratory, who published these Proceedings; and especially the authors of the papers, which comprised the heart of the Symposium and subsequently formed this volume. To all of these the sponsors wish to express their very sincere appreciation.

JAMES EMMETT GARVEY
_Office of Naval Research Branch Office
Pasadena, California_

MARGO A. SASS
_Office of Naval Research
Washington, D.C._

The Ionic Hypothesis and Neuron Models

E. R. LEWIS

_Librascope Group, General Precision, Inc.
Research and Systems Center
Glendale, California_

The measurements of Hodgkin and Huxley were aimed at
revealing the mechanism of generation and propagation
of the all-or-none spike. Their results led to the
Modern Ionic Hypothesis. Since the publication of
their papers in 1952, advanced techniques with
microelectrodes have led to the discovery of many
modes of subthreshold activity not only in the axon
but also in the somata and dendrites of neurons. This
activity includes synaptic potentials, local response
potentials, and pacemaker potentials.

We considered the question, “Can this activity also
be explained in terms of the Hodgkin-Huxley Model?”
To seek an answer, we have constructed an electronic
analog based on the ionic hypothesis and designed
around the data of Hodgkin and Huxley. Synaptic
inputs were simulated by simple first-order or
second-order networks connected directly to simulated
conductances (potassium or sodium). The analog has,
with slight parameter adjustments, produced all modes
of threshold and subthreshold activity.

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)):

1. Synaptic Potentials
a. Excitatory or inhibitory
b. Facilitated, antifacilitated, or neither
c. With excitatory aftereffect, inhibitory aftereffect,
neither, or both

2. Pacemaker Potentials
a. Relaxation type, undulatory type, or none at all
b. Producing single spike, spike burst, or no spikes
c. Rhythmic or sporadic

3. Graded Response (rate sensitive)

4. Spike Initiation

THE MODERN IONIC HYPOTHESIS

Hodgkin, Huxley, and Katz (3) and Hodgkin and Huxley (14), (15), (16), in 1952, published a series of papers describing detailed measurements of voltage, current, and time relationships in the giant axon of the squid (_Loligo_). Hodgkin and Huxley (17) consolidated and formalized these data into a set of simultaneous differential equations describing the hypothetical time course of events during spike generation and propagation. The hypothetical system which these equations describe is the basis of the Modern Ionic Hypothesis.

The system proposed by Hodgkin and Huxley is basically one of dynamic opposition of ionic fluxes across the axon membrane. The membrane itself forms the boundary between two liquid phases—the intracellular fluid and the extracellular fluid. The intracellular fluid is rich in potassium ions and immobile organic anions, while the extracellular fluid contains an abundance of sodium ions and chloride ions. The membrane is slightly permeable to the potassium, sodium, and chloride ions; so these ions tend to diffuse across the membrane. When the axon is inactive (not propagating a spike), the membrane is much more permeable to chloride and potassium ions than it is to sodium ions. In this state, in fact, sodium ions are actively transported from the inside of the membrane to the outside at a rate just sufficient to balance the inward leakage. The relative sodium ion concentrations on both sides of the membrane are thus fixed by the active transport rate, and the net sodium flux across the membrane is effectively zero. The potassium ions, on the other hand, tend to move out of the cell; while chloride ions tend to move into it. The inside of the cell thus becomes negative with respect to the outside. When the potential across the membrane is sufficient to balance the inward diffusion of chloride with an equal outward drift, and the outward diffusion of potassium with an inward drift (and possibly an inward active exchange), equilibrium is established. The equilibrium potential is normally in the range of 60 to 65 millivolts.

The resting neural membrane is thus polarized, with the inside approximately 60 millivolts negative with respect to the outside. Most of the Hodgkin-Huxley data is based on measurements of the transmembrane current in response to an imposed stepwise reduction (depolarization) of membrane potential. By varying the external ion concentrations, Hodgkin and Huxley were able to resolve the transmembrane current into two “active” components, the potassium ion current and the sodium ion current. They found that while the membrane permeabilities to chloride and most other inorganic ions were relatively constant, the permeabilities to both potassium and sodium were strongly dependent on membrane potential. In response to a suddenly applied (step) depolarization, the sodium permeability rises rapidly to a peak and then declines exponentially to a steady value. The potassium permeability, on the other hand, rises with considerable delay to a value which is maintained as long as the membrane remains depolarized. The magnitudes of both the potassium and the sodium permeabilities increase monotonically with increasing depolarization. A small imposed depolarization will result in an immediately increased sodium permeability. The resulting increased influx of sodium ions results in further depolarization; and the process becomes regenerative, producing the all-or-none action potential. At the peak of the action potential, the sodium conductance begins to decline, while the delayed potassium conductance is increasing. Recovery is brought about by an efflux of potassium ions, and both ionic permeabilities fall rapidly as the membrane is repolarized. The potassium permeability, however, falls less rapidly than that of sodium. This is basically the explanation of the all-or-none spike according to the Modern Ionic Hypothesis.

By defining the net driving force on any given ion species as the difference between the membrane potential and the equilibrium potential for that ion and describing permeability changes in terms of equivalent electrical conductance changes, Hodgkin and Huxley reduced the ionic model to the electrical equivalent in Figure 5. The important dynamic variables in this equivalent network are the sodium conductance (G{Na}) and the potassium conductance (G{K}). The change in the sodium conductance in response to a step depolarization is shown in Figure 6B. This change can be characterized by seven voltage dependent parameters:

1. Delay time—generally much less than 1 msec
2. Rise time—1 msec or less
3. Magnitude of peak conductance—increases
monotonically with increasing depolarization
4. Inactivation time constant—decreases
monotonically with increasing depolarization.
5. Time constant of recovery from
inactivation—incomplete data
6. Magnitude of steady-state conductance—increases
monotonically with increasing depolarization
7. Fall time on sudden repolarization—less than 1 msec.

Figure 6B shows the potassium conductance change in response to an imposed step depolarization. Four parameters are sufficient to characterize this response:

1. Delay time—decreases monotonically with
increasing depolarization
2. Rise time—decreases monotonically with increasing
depolarization
3. Magnitude of steady-state conductance—increases
monotonically with increasing depolarization
4. Fall time on sudden repolarization—8 msec
or more, decreases slightly with increasing
depolarization.

In addition to the aforementioned parameters, the transient portion of the sodium conductance appears to exhibit an accommodation to slowly varying membrane potentials. The time constants of accommodation appear to be those of inactivation or recovery from inactivation—depending on the direction of change in the membrane potential (18). The remaining elements in the Hodgkin-Huxley model are constant and are listed below:

1. Potassium potential—80 to 85 mv (inside negative)
2. Sodium potential—45 to 50 mv (inside positive)
3. Leakage potential—38 to 43 mv (inside negative)
4. Leakage conductance—approx. 0.23 millimhos/cm²
5. Membrane capacitance—approx. 1 μf/cm²
6. Resting potential—60 to 65 mv
7. Spike amplitude—approx. 100 mv

ELECTRONIC SIMULATION OF THE HODGKIN-HUXLEY MODEL

Given a suitable means of generating the conductance functions, G_{Na}(v,t) and G_{K}(v,t), one can readily stimulate the essential aspects of the Modern Ionic Hypothesis. If we wish to do this electronically, we have two problems. First, we must synthesize a network whose input is the membrane potential and whose output is a voltage or current proportional to the desired conductance function. Second, we must transform the output from a voltage or current to an effective electronic conductance. The former implies the need for nonlinear, active filters, while the latter implies the need for multipliers. The basic block diagram is shown in Figure 7. Several distinct realizations of this system have been developed in our laboratory, and in each case the results were the same. With parameters adjusted to closely match the data of Hodgkin and Huxley, the electronic model exhibits all of the important properties of the axon. It produces spikes of 1 to 2 msec duration with a threshold of approximately 5% to 10% of the spike amplitude. The applied stimulus is generally followed by a prepotential, then an active rise of less than 1 msec, followed by an active recovery. The after-depolarization generally lasts several msec, followed by a prolonged after-hyperpolarization. The model exhibits the typical strength-duration curve, with rheobase of 5% to 10% of the spike amplitude. For sufficiently prolonged sodium inactivation (long time constant of recovery from inactivation), the model also exhibits an effect identical to classical Wedensky inhibition (18). Thus, as would be expected, the electronic model simulates very well the electrical properties of the axon.

In addition to the axon properties, however, the electronic model is able to reproduce all of the somatic and dendritic activity outlined in the section on subthreshold activity. Simulation of the pacemaker and graded-response potentials is accomplished without additional circuitry. In the case of synaptically induced potentials, however, auxiliary networks are required. These networks provide additive terms to the variable conductances in accordance with current notions on synaptic transmission (19). Two types of networks have been used. In both, the inputs are simulated presynaptic spikes, and in both the outputs are the resulting simulated chemical transmitter concentration. In both, the transmitter substance was assumed to be injected at a constant rate during a presynaptic spike and subsequently inactivated in the presence of an enzyme. One network simulates a first-order chemical reaction, where the enzyme concentration is effectively constant. The other simulates a second-order chemical reaction, where the enzyme concentration is assumed to be reduced during the inactivation process. For simulation of an excitatory synapse, the output of the auxiliary network is added directly to G_{Na} in the electronic model. For inhibition, it is added to G_{K}. With the parameters of the electronic membrane model set at the values measured by Hodgkin and Huxley, we have attempted to simulate synaptic activity with the aid of the two types of auxiliary networks. In the case of the simulated first-order reaction, the excitatory synapse exhibits facilitation, antifacilitation, or neither—depending on the setting of a single parameter, the transmitter inactivation rate (_i.e._, the effective enzyme concentration). This parameter would appear, in passing, to be one of the most probable synaptic variables. In this case, the mechanisms for facilitation and antifacilitation are contained in the simulated postsynaptic membrane. Facilitation is due to the nonlinear dependence of G_{Na} on membrane potential, while antifacilitation is due to inactivation of G_{Na}. The occurrence of one form of response or the other is determined by the relative importance of the two mechanisms (18). Grundfest (20) has mentioned both of these mechanisms as potentially facilitory and antifacilitory, respectively. The simulated inhibitory synapse with the first order input is capable of facilitation (18), but no antifacilitation has been observed. Again, the presence or absence of facilitation is determined by the inactivation rate.

With the simulated second-order reaction, both excitatory and inhibitory synapses exhibit facilitation. In this case, two facilitory mechanisms are present—one in the postsynaptic membrane and one in the nonconstant transmitter inactivation reaction. The active membrane currents can, in fact, be removed; and this system will still exhibit facilitation. With the second-order auxiliary network, the presence of excitatory facilitation, antifacilitation, or neither depends on the initial, or resting, transmitter inactivation rate. The synaptic behavior also depends parametrically on the simulated enzyme reactivation rate. Inhibitory antifacilitation can be introduced with either type of auxiliary network by limiting the simulated presynaptic transmitter supply.

Certain classes of aftereffects are inherent in the mechanisms of the Ionic Hypothesis. In the electronic model, aftereffects are observed following presynaptic volleys with either type of auxiliary network. Following a volley of spikes into the simulated excitatory synapse, for example, rebound hyperpolarization may or may not occur depending on the simulated transmitter inactivation rate. If the inactivation rate is sufficiently high, rebound will occur. This rebound can be monophasic (inhibitory phase only) or polyphasic (successive cycles of excitation and inhibition). Following a volley of spikes into the simulated inhibitory synapse, rebound depolarization may or may not occur depending on the simulated transmitter inactivation rate. This rebound can also be monophasic or polyphasic. Sustained postexcitatory depolarization and sustained postinhibitory hyperpolarization (2) have been achieved in the model by making the transmitter inactivation rate sufficiently low.

The general forms of the postsynaptic potentials simulated with the electronic model are strikingly similar to those published in the literature for real neurons. The first-order auxiliary network produces facilitation of a form almost identical to that shown by Otani and Bullock (8) while the second-order auxiliary network produces facilitation of the type shown by Chalazonitis and Arvanitake (2). The excitatory antifacilitation is almost identical to that shown by Hagiwara and Bullock (1) in both form and dependence on presynaptic spike frequency. In every case, the synaptic behavior is determined by the effective rate of transmitter inactivation, which in real neurons would presumably be directly proportional to the effective concentration of inactivating enzyme at the synapse.

Pacemaker potentials are easily simulated with the electronic model without the use of auxiliary networks. This is achieved either by inserting a large, variable shunt resistor across the simulated membrane (see Figure 5) or by allowing a small sodium current leakage at the resting potential. With the remaining parameters of the model set as close as possible to the values determined by Hodgkin and Huxley, the leakage current induces low-frequency, spontaneous spiking. The spike frequency increases monotonically with increasing leakage current. In addition, if the sodium conductance inactivation is allowed to accumulate over several spikes, periodic spike pairs and spike bursts will result. Subthreshold pacemaker potentials have also been observed in the model, but with parameter values set close to the Hodgkin-Huxley data these are generally higher in frequency than pacemaker potentials in real neurons. It is interesting that a pacemaker mode may exist in the absence of the simulated sodium conductance. It is a very high-frequency mode (50 cps or more) and results from the alternating dominance of potassium current and chloride (or leakage ion) current in determining the membrane potential. The significance of this mode cannot be assessed until better data is available for the potassium conductance at low levels of depolarization in real neurons. In general, as far as the model is concerned, pacemaker potentials are possible because the potassium conductance is delayed in both its rise with depolarization and its fall with repolarization.

Rate sensitive graded response has also been observed in the electronic model. The rate sensitivity—or accommodation—is due to the sodium conductance inactivation. The response of the model to an imposed ramp depolarization was discussed in Reference 18. At this time, several alternative model parameters could be altered to bring about reduced electrical excitability. None of the parameter changes was very satisfying, however, because none of them was in any way justified by physiological data. We have since found that the membrane capacitance, a plausible parameter in view of recent physiological findings, can completely determine the electrical excitability. Thus, with the capacitance determined by Hodgkin and Huxley (1 microfarad per cm²), the model exhibits excitability characteristic of the axon. As the capacitance is increased, the model becomes less excitable until, with 10 or 12 μμf, it is effectively inexcitable. Thus, with an increased capacitance—but with all the remaining parameters set as close as possible to the Hodgkin-Huxley values—the electronic model exhibits the characteristics of Bullock’s graded-response regions.

Whether membrane capacitance is the determining factor in real neurons is, of course, a matter of speculation. Quite a controversy is raging over membrane capacity measurements (see Rall (21)), but the evidence indicates that the capacity in the soma is considerably greater than that in the axon (6), (22).

It should be added that increasing the capacitance until the membrane model becomes inexcitable has little effect on the variety of available simulated synaptic responses. Facilitation, antifacilitation, and rebound are still present and still depend on the transmitter inactivation rate. Thus, in the model, we can have a truly inexcitable membrane which nevertheless utilizes the active membrane conductances to provide facilitation or antifacilitation, and rebound. The simulated subthreshold pacemaker potentials are much more realistic with the increased capacitance, being lower in frequency and more natural in form.

In one case, the electronic model predicted behavior which was subsequently reported in real neurons. This was in respect to the interaction of synaptic potentials and pacemaker potential. It was noted in early experiments that when the model was set in a pacemaker mode, and periodic spikes were applied to the simulated inhibitory synapse, the pacemaker frequency could be modified; and, in fact, it would tend to lock on to the stimulus frequency. This produced a paradoxical effect whereby the frequency of spontaneous spikes was actually increased by increasing the frequency of inhibitory synaptic stimuli. At very low stimulus frequencies, the spontaneous pacemaker frequency was not appreciably perturbed. As the stimulus frequency was increased, and approached the basic pacemaker frequency, the latter tended to lock on and follow further increases in the stimulus frequency. When the stimulus frequency became too high for the pacemaker to follow, the latter decreased abruptly in frequency and locked on to the first subharmonic. As the stimulus frequency was further increased, the pacemaker frequency would increase, then skip to the next harmonic, then increase again, _etc._ This type of behavior was observed by Moore _et al._ (23) in _Aplysia_ and reported at the San Diego Symposium for Biomedical Electronics shortly after it was observed by the author in the electronic model.

Thus, we have shown that an electronic analog with all parameters except membrane capacitance fixed at values close to those of Hodgkin and Huxley, can provide all of the normal threshold or axonal behavior and also all of the subthreshold somatic and dendritic behavior outlined on page 7. Whether or not this is of physiological significance, it certainly provides a unifying basis for construction of electronic neural analogs. Simple circuits, based on the Hodgkin-Huxley model and providing all of the aforementioned behavior, have been constructed with ten or fewer inexpensive transistors with a normal complement of associated circuitry (18). In the near future we hope to utilize several models of this type to help assess the information-processing capabilities not only of individual neurons but also of small groups or networks of neurons.

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22. Araki, T., and Otani, T.,
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_J. Neurophysiol._ =18=:472-485 (1955)

23. Moore, G. P., Perkel, D. H., and Segundo, J. P.,
“Stability Patterns in Interneuronal Pacemaker Regulation,”
_Proceedings of the San Diego Symposium for Biomedical
Engineering_, San Diego, California, 1963

24. Eccles, J. C.,
_The Neurophysiological Basis of Mind_,
Oxford:Clarendon Press, 1952

Fields and Waves in Excitable Cellular Structures

R. M. STEWART

_Space General Corporation
El Monte, California_

“Study of living processes by the physiological
method only proceeded laboriously behind the study of
non-living systems. Knowledge about respiration, for
instance, began to become well organized as the study
of combustion proceeded, since this is an analogous
operation....”

J. Z. Young (24)

INTRODUCTION

The study of electrical fields in densely-packed cellular media is prompted primarily by a desire to understand more fully the details of brain mechanism and its relation to behavior. Our work has specifically been directed toward an attempt to model such structures and mechanisms, using relatively simple inorganic materials.

The prototype for such experiments is the “Lillie[1] iron-wire nerve model.” Over a hundred years ago, it had been observed that visible waves were produced on the surface of a piece of iron submerged in nitric acid when and where the iron is touched by a piece of zinc. After a short period of apparent fatigue, the wire recovers and can again support a wave when stimulated. Major support for the idea that such impulses are in fact directly related to peripheral nerve impulses came from Lillie around 1920. Along an entirely different line, various persons have noted the morphological and dynamic similarity of dendrites in brain and those which sometimes grow by electrodeposition of metals from solution. Gordon Pask (17), especially, has pointed to this similarity and has discussed in a general way the concomitant possibility of a physical model for the persistent memory trace.

[1] For review articles see: Lillie (13), Franck (6).

By combining and extending such concepts and techniques, we hope to produce a macroscopic model of “gray matter,” the structural matrix of which will consist of a dense, homogeneously-mixed, conglomerate of small pellets, capable of supporting internal waves of excitation, of changing electrical behavior through internal fine-structure growth, and of forming temporal associations in response to peripheral shocks.

A few experimenters have subsequently pursued the iron-wire nerve-impulse analogy further, hoping thereby to illuminate the mechanisms of nerve excitation, impulse transmission and recovery, but interest has generally been quite low. It has remained fairly undisturbed in the text books and lecture demonstrations of medical students, as a picturesque aid to their formal education. On the outer fringes of biology, still less interest has been displayed; the philosophical vitalists would surely be revolted by the idea of such models of mind and memory, and at the other end of the scale, contemporary computer engineers generally assume that a nerve cell operates much too slowly to be of any value. This lack of interest is certainly due, in part, to success in developing techniques of monitoring individual nerve fibers directly to the point that it is just about as easy to work with large nerve fibers (and even peripheral and spinal junctions) as it is to work with iron wires. Under such circumstances, the model has only limited value, perhaps just to the extent that it emphasizes the role of factors other than specific molecular structure and local chemical reactions in the dynamics of nerve action.

When we leave the questions of impulse transmission on long fibers and peripheral junctions, however, and attempt to discuss the brain, there can be hardly any doubt that the development of a meaningful physical model technique would be of great value. Brain tissue is soft and sensitive, the cellular structures are small, tangled, and incredibly numerous. Therefore (Young (24)), “ ... physiologists hope that after having learned a lot about nerve-impulses in the nerves they will be able to go on to study how these impulses interact when they reach the brain. [But], we must not assume that we shall understand the brain only in the terms we have learned to use for the nerves. The function of nerves is to carry impulses—like telegraph wires. The functions of brains is something else.” But, confronted with such awesome experimental difficulties, with no comprehensive mathematical theory in sight, we are largely limited otherwise to verbal discourses, rationales and theorizing, a hopelessly clumsy tool for the development of an adequate understanding of brain function. A little over ten years ago Sperry (19) said, “Present day science is quite at a loss even to begin to describe the neural events involved in the simplest form of mental activity.” This situation has not changed much today. The development, study, and understanding of complex high-density cellular structures which incorporate characteristics of both the Lillie and Pask models may, it is hoped, alleviate this situation. There would also be fairly obvious technological applications for such techniques if highly developed and which, more than any other consideration, has prompted support for this work.

Experiments to date have been devised which demonstrate the following basic physical functional characteristics:

(1) Control of bulk resistivity of electrolytes containing
closely-packed, poorly-conducting pellets
(2) Circulation of regenerative waves on closed loops
(3) Strong coupling between isolated excitable sites
(4) Logically-complete wave interactions, including facilitation
and annihilation
(5) Dendrite growth by electrodeposition in “closed” excitable
systems
(6) Subthreshold distributed field effects, especially in
locally-refractory regions.

In addition, our attention has necessarily been directed to various problems of general experimental technique and choice of materials, especially as related to stability, fast recovery and long life. However, in order to understand the possible significance of, and motivation for such experiments, some related modern concepts of neurophysiology, histology and psychology will be reviewed very briefly. These concepts are, respectively:

(1) Cellular structure in the central nervous system
(2) Short-term or “ephemeral” memory
(3) The synapse
(4) Inhibition
(5) Long-term memory traces or engram
(6) Spatially-diffuse temporal association and learning.

SOME CONTEMPORARY CONCEPTS

Since we are attempting to duplicate processes other than chemical, per se, we will forego any reference to the extensive literature of neurochemistry. It should not be surprising though if, at the neglect of the fundamental biological processes of growth, reproduction and metabolism, it proves possible to imitate some learning mechanisms with grossly less complex molecular structures. There is also much talk of chemical versus electrical theories and mechanisms in neurophysiology. The distinction, when it can be made, seems to hinge on the question of the scale of size of significant interactions. Thus, “chemical” interactions presumably take place at molecular distances, possibly as a result of or subsequent to a certain amount of thermal diffusion. “Electrical” interactions, on the other hand, are generally understood to imply longer range or larger scale macroscopic fields.

1. Cellular Structure

The human brain contains approximately 10¹⁰ neurons to which the neuron theory assigns the primary role in central nervous activity. These cells occupy, however, a relatively small fraction of the total volume. There are, for example, approximately 10 times that number of neuroglia, cells of relatively indeterminate function. Each neuron (consisting of cell body, dendrites and, sometimes, an axon) comes into close contact with the dendrites of other neurones at some thousands of places, these synapses and “ephapses” being spaced approximately 5μ apart (1). The total number of such apparent junctions is therefore of the order of 10¹³. In spite of infinite fine-structure variations when viewed with slightly blurred vision, the cellular structure of the brain is remarkably homogeneous. In the cortex, at least, the extensions of most cells are relatively short, and when the cortex is at rest, it appears from the large EEG alpha-rhythms that large numbers of cells beat together in unison. Quoting again from Sperry, “In short, current brain theory encourages us to try to correlate our subjective psychic experience with the activity of relatively homogeneous nerve cell units conducting essentially homogeneous impulses, through roughly homogeneous cerebral tissue.”

2. Short-Term Memory

A train of impulses simply travelling on a long fiber may, for example, be regarded as a short-term memory much in the same way as a delay line acts as a transient memory in a computer. A similar but slightly longer term memory may also be thought of to exist in the form of waves circulating in closed loops (23). In fact, it is almost universally held today that most significant memory occurs in two basic interrelated ways. First of all, such a short-term circulating, reverberatory or regenerative memory which, however, could not conceivably persist through such things as coma, anesthesia, concussion, extreme cold, deep sleep and convulsive seizures and thus, secondly, a long-term memory trace which must somehow reside in a semipermanent fine-structural change. As Hebb (9) stated, “A reverbratory trace might cooperate with a structural change and carry the memory until the growth change is made.”

3. The Synapse

The current most highly regarded specific conception of the synapse is largely due to and has been best described by Eccles (5): “ ... the synaptic connections between nerve cells are the only functional connections of any significance. These synapses are of two types, excitatory and inhibitory, the former type tending to make nerve cells discharge impulses, the other to suppress the discharge. There is now convincing evidence that in vertebrate synapses each type operates through specific chemical transmitter substances ...”. In response to a presentation by Hebb (10), Eccles was quoted as saying, “One final point, and that is if there is electrical interaction, and we have seen from Dr. Estable’s work the complexity of connections, and we now know from the electronmicroscopists that there is no free space, only 200 Å clefts, everywhere in the central nervous system, then everything should be electrically interacted with everything else. I think this is only electrical background noise and, that when we lift with specific chemical connections above that noise we get a significant operational system. I would say that there is electrical interaction but it is just a noise, a nuisance.” Eccles’ conclusions are primarily based on data obtained in the peripheral nervous system and the spinal cord. But there is overwhelming reason to expect that cellular interactions in the brain are an entirely different affair. For example, “The highest centres in the octopus, as in vertebrates and arthropods, contain many small neurons. This finding is such a commonplace, that we have perhaps failed in the past to make the fullest inquiry into its implications. Many of these small cells possess numerous processes, but no axon. It is difficult to see, therefore, that their function can be conductive in the ordinary sense. Most of our ideas about nervous functioning are based on the assumption that each neuron acts essentially as a link in some chain of conduction, but there is really no warrant for this in the case of cells with many short branches. Until we know more of the relations of these processes to each other in the neuropile it would be unwise to say more. It is possible that the effective part of the discharge of such cells is not as it is in conduction in long pathways, the internal circuit that returns through the same fiber, but the external circuit that enters other processes, ...” (3).

4. Inhibition

The inhibitory chemical transmitter substance postulated by Eccles has never been detected in spite of numerous efforts to do so. The mechanism(s) of inhibition is perhaps the key to the question of cellular interaction and, in one form or another, must be accounted for in any adequate theory.

Other rather specific forms of excitation and inhibition interaction have been proposed at one time or another. Perhaps the best example is the polar neuron of Gesell (8) and, more recently, Retzlaff (18). In such a concept, excitatory and inhibitory couplings differ basically because of a macroscopic structural difference at the cellular level; that is, various arrangements or orientation of intimate cellular structures give rise to either excitation or inhibition.

5. Long-Term Memory

Most modern theories of semipermanent structural change (or _engrams_, as they are sometimes called) look either to the molecular level or to the cellular level. Various specific locales for the engram have been suggested, including (1) modifications of RNA molecular structure, (2) changes of cell size, synapse area or dendrite extensions, (3) neuropile modification, and (4) local changes in the cell membrane. There is, in fact, rather direct evidence of the growth of neurons or their dendrites with use and the diminution or atrophy of dendrites with disuse. The apical dendrite of pyramidal neurones becomes thicker and more twisted with continuing activity, nerve fibers swell when active, sprout additional branches (at least in the spinal cord) and presumably increase the size and number of their terminal knobs. As pointed out by Konorski (11), the morphological conception of plasticity according to which plastic changes would be related to the formation and multiplication of new synaptic junctions goes back at least as far as Ramon y Cajal in 1904. Whatever the substrate of the memory trace, it is, at least in adults, remarkably immune to extensive brain damage and as Young (24) has said: “ ... this question of the nature of the memory trace is one of the most obscure and disputed in the whole of biology.”

6. Field Effects and Learning

First, from Boycott and Young (3), “The current conception, on which most discussions of learning still concentrate, is that the nervous system consists essentially of an aggregate of chains of conductors, linked at key points by synapses. This reflex conception, springing probably from Cartesian theory and method, has no doubt proved of outstanding value in helping us to analyse the actions of the spinal cord, but it can be argued that it has actually obstructed the development of understanding of cerebral function.”

Most observable evidence of learning and memory is extremely complex and its interpretation full of traps. Learning in its broadest sense might be detected as a semipermanent change of behavior pattern brought about as a result of experience. Within that kind of definition, we can surely identify several distinctly different types of learning, presumably with distinctly different kinds of mechanisms associated with each one. But, if we are to stick by our definition of a condition of semipermanent change of behavior as a criterion for learning, then we may also be misled into considering the development of a neurosis, for example, as learning, or even a deep coma as learning.

When we come to consider field effects, current theories tend to get fairly obscure, but there seems to be an almost universal recognition of the fact that such fields are significant. For example, Morrell (16) says in his review of electrophysiological contributions to the neural basis of learning, “A growing body of knowledge (see reviews by Purpura, Grundfest, and Bishop) suggests that the most significant integrative work of the central nervous system is carried on in graded response elements—elements in which the degree of reaction depends upon stimulus intensity and is not all-or-none, which have no refractory period and in which continuously varying potential changes of either sign occur and mix and algebraically sum.” Gerard (7) also makes a number of general comments along these lines. “These attributes of a given cell are, in turn, normally controlled by impulses arising from other regions, by fields surrounding them—both electric and chemical—electric and chemical fields can strongly influence the interaction of neurones. This has been amply expounded in the case of the electric fields.”

Learning situations involving “punishment” and “reward” or, subjectively, “pain” and “pleasure” may very likely be associated with transient but structurally widespread field effects. States of distress and of success seem to exert a lasting influence on behavior only in relation to _simultaneous_ sensory events or, better yet, sensory events just immediately _preceding_ in time. For example, the “anticipatory” nature of a conditioned reflex has been widely noted (21). From a structural point of view, it is as if recently active sites regardless of location or function were especially sensitive to extensive fields. There is a known inherent electrical property of both nerve membrane and passive iron surface that could hold the answer to this mechanism of spatially-diffuse temporal association; namely, the surface resistance drops to less than 1 per cent of its resting value during the refractory period which immediately follows activation.

EXPERIMENTAL TECHNIQUE

In almost all experiments, the basic signal-energy mechanism employed has been essentially that one studied most extensively by Lillie (12), Bonhoeffer (2), Yamagiwa (22), Matumoto and Goto (14) and others, _i.e._, activation, impulse propagation and recovery on the normally passive surface of a piece of iron immersed in nitric acid or of cobalt in chromic acid (20). The iron we have used most frequently is of about 99.99% purity, which gives performance more consistent than but similar to that obtained using cleaned “coat-hanger” wires. The acid used most frequently by us is about 53-55% aqueous solution by weight, substantially more dilute than that predominantly used by previous investigators. The most frequently reported concentration has been 68-70%, a solution which is quite stable and, hence, much easier to work with in open containers than the weaker solutions, results in very fast waves but gives, at room temperatures, a very long refractory period (typically, 15 minutes). A noble metal (such as silver, gold or platinum) placed in contact with the surface of the iron has a stabilizing effect (14) presumably through the action of local currents and provides a simple and useful technique whereby, with dilution, both stability and fast recovery (1 second) can be achieved in simple demonstrations and experiments.

Experiments involving the growth by electrodeposition and study of metallic dendrites are done with an eye toward electrical, physical and chemical compatibility with the energy-producing system outlined above. Best results to date (from the standpoints of stability, non-reactivity, and morphological similarity to neurological structures) have been obtained by dissolving various amounts of gold chloride salt in 53-55% HNO₃.

An apparatus has been devised and assembled for the purpose of containing and controlling our primary experiments. (See Figure 1). Its two major components are a test chamber (on the left in Figure 1) and a fluid exchanger (on the right). In normal operation the test chamber, which is very rigid and well sealed after placing the experimental assembly inside, is completely filled with electrolyte (or, initially, an inert fluid) to the exclusion of all air pockets and bubbles. Thus encapsulated, it is possible to perform experiments which would otherwise be impossible due to instability. The instability which plagues such experiments is manifested in copious generation of bubbles on and subsequent rapid disintegration of all “excitable” material (_i.e._, iron). Preliminary experiments indicated that such “bubble instability” could be suppressed by constraining the volume available to expansion. In particular, response and recovery times can now be decreased substantially and work can proceed with complex systems of interest such as aggregates containing many small iron pellets.

The test chamber is provided with a heater (and thermostatic control) which makes possible electrochemical impulse response and recovery times comparable to those of the nervous system (1 to 10 msec). The fluid-exchanger is so arranged that fluid in the test chamber can be arbitrarily changed or renewed by exchange within a rigid, sealed, completely liquid-filled (“isochoric”) loop. Thus, stability can be maintained for long periods of time and over a wide variety of investigative or operating conditions.

Most of the parts of this apparatus are made of stainless steel and are sealed with polyethylene and teflon. There is a small quartz observation window on the test chamber, two small lighting ports, a pressure transducer, thermocouple, screw-and-piston pressure actuator and umbilical connector for experimental electrical inputs and outputs.

BASIC EXPERIMENTS

The basic types of experiments described in the following sections are numbered for comparison to correspond roughly to related neurophysiological concepts summarized in the previous section.

1. Cellular Structure

The primary object of our research is the control and determination of dynamic behavior in response to electrical stimulation in close-packed aggregates of small pellets submerged in electrolyte. Typically, the aggregate contains (among other things) iron and the electrolyte contains nitric acid, this combination making possible the propagation of electrochemical surface waves of excitation through the body of the aggregate similar to those of the Lillie iron-wire nerve model. The iron pellets are imbedded in and supported by a matrix of small dielectric (such as glass) pellets. Furthermore, with the addition of soluble salts of various noble metals to the electrolyte, long interstitial dendritic or fibrous structures of the second metal can be formed whose length and distribution change by electrodeposition in response to either internal or externally generated fields.