Fields and Waves in ExcitableCellular Structures

R. M. STEWART

Space General CorporationEl 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)

J. Z. Young (24)

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.

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 ofsmall 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 agoSperry (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 cellularstructures 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.

(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:

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 withgrossly 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.

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.”

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 notconceivably 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. AsHebb (9)stated, “A reverbratory trace might cooperate with a structural change and carry the memory until the growth change is made.”

The current most highly regarded specific conception of the synapse is largely due to and has been best described byEccles (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 byHebb (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 thedischarge 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).

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 ofGesell (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.

Most modern theories of semipermanent structural change (orengrams, 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 byKonorski (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 asYoung (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.”

First, fromBoycott 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 distressand of success seem to exert a lasting influence on behavior only in relation tosimultaneoussensory events or, better yet, sensory events just immediatelyprecedingin 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.

In almost all experiments, the basic signal-energy mechanism employed has been essentially that one studied most extensively byLillie (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 inFigure 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.

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.

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.

Figure 1—Test chamber andfluid exchanger

Coupling between isolated excitable (iron) sites is greatly affected by the fine structure and effective bulk resistivity of the glass and fluid medium which supports and fills the space between such sites. In general (see Section 3, following) it is necessary, to promote strong coupling between small structures, to impede the “short-circuit” return flow of current from an active or excited surface, through the electrolyte and back through the dendritic structure attached to the same excitable site. This calls for control (increase) of the bulk resistivity, preferably by means specifically independent of electrolyte composition, which relates to and affects surface phenomena such as recovery (i.e., the “refractory” period).Figure 2illustrates the way in which this is being done,i.e., by appropriate choice of particle size distributions. The case illustrated shows the approximate proper volume ratios for maximum resistivity in a two-size-phase random mixture of spheres.

Figure 3shows an iron loop (about 2-inch diameter) wrapped with a silver wire helix which is quite stable in 53-55% acid and which will easily support a circulating pattern of three impulses. For demonstration, unilateral waves can be generated by first touching the iron with a piece of zinc (which produces two oppositely travelling waves) and then blocking one of them with a piece of platinum or a small platinum screen attached to the end of a stick or wand. Carbon blocks may also be used for this purpose.

The smallest regenerative or reverberatory loop which we are at present able to devise is about 1 mm in diameter. Multiple waves, as expected, produce stable patterns in which all impulses are equally spaced. This phenomenon can be related to the slightly slower speed characteristic of the relative refractory period as compared with a more fully recovered zone.

Figure 2—Conductivity control—mixed pellet-size aggregates

Figure 3—Regenerative or reverberatory loop

If two touching pieces of iron are placed in a bath of nitric acid, a wave generated on one will ordinarily spread to the other. As is to be expected, a similar result is obtained if the two pieces are connected through an external conducting wire. However, if they are isolated, strong coupling does not ordinarily occur, especially if the elements are small in comparison with a “critical size,” σ/ρ where σ is the surface resistivity of passive iron surface (in Ω-cm²) and ρ is the volume resistivity of the acid (in Ω-cm). A simple and informative structure which demonstrates the essential conditions for strong electrical coupling between isolated elements of very small size may be constructed as shown inFigure 4. The dielectric barrier insures that charge transfer through one dipole must be accompanied by an equal and opposite transfer through the surfaces of the other dipole. If the “inexcitable” silver tails have sufficiently high conductance (i.e., sufficiently large surface area, hence preferably, dendrites), strong coupling will occur, just as though the cores of the two pieces of iron were connected with a solid conducting wire.

Figure 4Figure 5—Electrochemical excitatory-inhibitoryinteraction cell

Figure 4

Figure 5—Electrochemical excitatory-inhibitoryinteraction cell

If a third “dipole” is inserted through the dielectric membrane in the opposite direction, then excitation of this isolated element tends to inhibit the response which would otherwise be elicited by excitation of one of the parallel dipoles.Figure 5shows the first such “logically-complete” interaction cell successfully constructed and demonstrated. It may be said to behave as an elementary McCulloch-Pitts neuron(15). Further analysis shows that similar structures incorporating many dipoles (both excitatory and inhibitory) can be made to behave as general “linear decision functions” in which all input weights are approximately proportional to the total size or length of their corresponding attached dendritic structures.

Figure 6shows a sample gold dendrite grown by electrodeposition (actual size, about 1 mm) from a 54% nitric acid solution to which gold chloride was added. When such a dendrite is attached to a piece of iron (both submerged), activation of the excitable element produces a field in such a direction as to promote further growth of the dendritic structure. Thus, if gold chloride is added to the solution used in the elementary interaction cells described above, all input influence “weights” tend to increase with use and, hence, produce a plasticity of function.

Our measurements indicate that, during the refractory period following excitation, the surface resistance of iron in nitric acid drops to substantially less than 1% of its resting value in a manner reminiscent of nerve membranes(4). Thus, if a distributed or gross field exists at any time throughout a complex cellular aggregate, concomitant current densities in locally-refractive regions will be substantially higher than elsewhere and, if conditions appropriate to dendrite growth exist (as described above) growth rates in such regions will also be substantially higher than elsewhere. It would appear that, as a result, recently active functional couplings (in contrast to those not associated with recent neural activity) should be significantly altered by widely distributed fields or massive peripheral shocks. This mechanism might thus explain the apparent ability of the brain to form specific temporal associations in response to spatially-diffuse effects such as are generated, for example, by the pain receptors.

(a)(b)Figure 6—Dendritic structures, living and non-living.(a)Cat dendrite trees (from Bok, “Histonomy of the Cerebral Cortex,” Elsevier, 1959);(b)Electrodeposited gold dendrite tree.

(a)

(b)

Figure 6—Dendritic structures, living and non-living.(a)Cat dendrite trees (from Bok, “Histonomy of the Cerebral Cortex,” Elsevier, 1959);(b)Electrodeposited gold dendrite tree.

An attempt is being made to develop meaningful electrochemical model techniques which may contribute toward a clearer understanding of cortical function. Two basic phenomena are simultaneously employed which are variants of (1) the Lillie iron-wire nerve model, and (2) growth of metallic dendrites by electrodeposition. These phenomena are being induced particularly within dense cellular aggregates of various materials whose interstitial spaces are flooded with liquid electrolyte.

REFERENCES

This paper summarizes work carried out during 1941-1946 at the University of Leipzig, and published during the war years in German periodicals.

organized by the Council for International Organizations of Medical Science, Oxford:Blackwell Scientific Publications, 1961

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