Chapter 1 has introduced the basic concepts, units and laws of electrical theory and electromagnetism and explained how the construction and properties of common components of electrical and electronic circuitry, such as conductors, insulators, switches, semiconductors, resistors and capacitors are designed and connected in accordance with the appropriate theory.
Biological tissues seem so different in their wet and salty nature compared, for example, to the metallic wiring of a television set, that they would appear to have nothing in common. Yet the astonishing fact is that living cells are dependent upon electrical activity for their very existence and the tissues that they make, such as bone and fascia, exhibit a wide range of electrical properties. The same theory applies to their use of electrical components. They obey the same laws and use the same units of, for example, voltage, capacitance, current flow, and resistance.
As will be seen, the main difference between electricity in biological tissues and electricity in equipment is that cells and tissues use charged atoms, or ions, for the movement of charge whereas electrical and electronic systems use electrons.
With this relationship between
biological tissues and electrical circuitry in mind, the rest of this chapter
will be devoted to biological electricity, or bioelectricity.
Cells as Electrical Systems
Living cells employ many of the properties of electrical systems. For example, they generate electromotive force (e.m.f.), maintain a required potential difference (p.d.) between two points, increase or decrease that p.d. as necessary, use varying resistances in series and in parallel, switch current on and off, control current flow, rectify current flow, possess impedance and, of crucial importance, store charge (i.e. exhibit capacitance; The average body cell, with all of its ordered complexity and function (Figure 2.1), is between 10 and 50 ,um in diameter (,um = 1 micrometer = 1 millionth, or 10^6 of a metre; This means that it is some 520 times smaller than the smallest particle that the eye can see - a scale
Figure 2.1 Composite diagram of main cell structures which will vary according to cell type. Named structures are discussed in text. (After Gray's Anatomy.)
Of miniaturization approached only by very advanced microchip construction.
Cells are wet circuits that operate in a salty, conductive, medium. In electrical terms, cells have the great advantage of being very compact and thus having extremely short conducting pathways (about 10-20 nanometres; 1 nm = 10^-9m) but, against that, they work under some major disadvantages when compared to ordinary electrical and electronic circuitry, they must:
The ceaseless work involved in achieving and maintaining these essential electrical needs consumes some 50-60% of the metabolic activity of a cell (Alberts et al., 1989).
In marked contrast, ordinary circuits are dry circuits, so there is a clear distinction between conducting and non-conducting components. They carry the advantages that:
For example, no work is required to resist an externally applied e.m.f. (such as the mains supply) when the circuit is switched off because the e.m.f. is passively resisted by the nonconducting properties of the 'off' switch insulator. In contrast, cells have to use active electrical pumps against the e.m.f. in order to maintain the desired p.d. and prevent current leakage.
Another major difference lies in the type of charge used: ordinary circuits use electrons, which have negligible mass, are highly mobile, and have a diameter some 100 000 times smaller than an atom (1015 m compared to 10-1deg. m). Cells use atoms that have become charged as a result of gaining, or losing, valency shell electrons. Compared to an electron, charged atoms (i.e. ions), are very 'heavy', because of the masses of the protons and neutrons found in each ion's nucleus. For example, the single proton nucleus of the hydrogen ion (H+, mass lu; u = I atomic mass unit) has about 2000 times the mass of an electron, and the two main ions used by cells to store charge and generate e.m.f., namely sodium ions (Na+, mass 23u) and potassium ions (K+, mass 39u), are some 46,000 times and 78,000 times, respectively, more massive than an electron, yet possess only the same unit charge as a single electron (as they have each lost only one electron from their outer electron shell)
Another disadvantage for the cell is that all ions in solution are hydrated ions. This means that each ion is surrounded by polar water molecules (H20) that are attracted to the ion by their own, very weak polarity. For cations (which are positive), such as N+ and K+, water molecules orientate themselves so that the weak negativity of their oxygen atoms are closest to the positive ion; for anions (which are negative), the weak positivity of the water molecule's hydrogen atoms lies closest to the negative ion. Thus every hydrated ion, whether positive or negative, is closely surrounded by a cluster of water molecules. When ions pass through the very narrow ion channels in the cell membrane, whether by diffusion along electrochemical gradients or by active transport, the weak hydration bonds of the water cluster are broken as th H20 molecules are 'scraped off' the ion as it moves through the membrane channel (alberts et al.,1989).
The relatively unwieldy masses and sizes of ions mean that they require far more energy to control their movement, and accelerate much more slowly along a given p.d. gradient than do electrons. This is one reason why cellular ionic changes tend to have submillisecond to millisecond (10-3 s) response times, in contrast to the nanosecond (10-9 s) to attosecond (10-18 s] response times achievable in electronic circuitry.
Cell membranes are between 5 and 7.5 nm thick, and are composed of a highly mobile but closely packed array of proteolipid molecules arranged as a bilayer, with thier lipid tails forming a central zone figure (2.2) that is resistant to the passage of electricity and can act as an insulator. The plasma membrane forms the surface boundary of the cell, and the intracellular membranes enclose each of the cell s organelles, with a double membrane being present around the nucleus. A cell membrane, by means of selective permeability to Na+ and K+ ions (being relatively impermeable to Na+ ions but more permeable to K+ ions), causes its outer surface to have a higher positive charge than its inner surface - there are greater numbers, or densities, of Na+ and other cations per unit area on the outside surface than there are K+ on the inner surface. This charge separation results in an average p.d. across the membrane of 80 mV, with the inner surface being relatively negatively charged in comparison to the outer surface.
Figure 2.2 Fluid mosaic of cell membrance. Note the transmembrane receptor protein, attached to the branched glycolipid array, and the charged surface. (After Thibodeau, 1987.)
Figure 2.3 illustrates the relative differences indication concentrations on either side of the cell membrane; the 80 mV e.m.f. across the mem brane as shown by the arrow.
Figure 2.3 Schematic diagram illustrating the relative negativity of cations inside the plasma membrane compared to cations on the outside,m the resulting transmembrane e.m.f. at a given p.d. in millivolts, and the resistance offered by the central lipid layer acting as an insulator and the Na+ force of the Na+/K+ pump.
'Positive' and 'negative' are relative terms in electricity. They can mean either a difference of separate positive charge and negative charge concentrations between two points in a circuit, or a relative difference in concentration of the same type of charge between two points in a circuit, one point having less charge per unit volume or area than another and therefore being relatively less positive or negative. In ordinary electrical circuits, an e.m.f. is created by a difference of electron [i.e. negative charge] concentration between two points because electrons are the only type of charge that can travel along metal conductors. In cells, the gradient difference is created by separating cations into different concentration strengths either side of a membrane. This separation is also backed up by differences in negatively charged ions inside and outside of the cell.
Because fluid filled ion channels are relatively leaky, ion separation across a membrane is controlled by directional ion pumps, Such as the Na+ / K+ pumps that eject two Na+ ions out of the cell for every K+ ion coming into the cell, to maintain the charge separation across the width of the membrane. Another vitally important ion pump is the Ca2+ ion pump that keeps Ca2+ ions outside the cell at a concentration some 10000 greater than inside the cell. Passive ion diffusion channels are controlled by varying the diameter and lining charge of the ion channel as necessary. Figure 2.4 summarizes the activity of these ion channels and pumps and is best read by starting at A' on the left-hand side of the diagram, where potassium ions are moving down an electrical gradient into the cell, and moving clockwise through the alphabet to K, where representative passive ion channels are shown. The transmembrane 75 mV p.d. shown here is the resulting average e.m.f. generated by these ionic movements and acts, in effects as a capacitor's store of charge that is available to do work. The 'bound cations in the cell form a thin layer of potassium cations that are held to the boundary surface of the negatively charged cytosol by mutual attraction, and do not play any part in membrane ion-pump exchange.
In summary, cell membranes act as capacitor plates when they hold a difference in ion charge concentration across their width. The charge is held on the continuous insulator surface of plasma membranes between the pores of the ion pump channels that help to maintain it. Cell membrane charge is measured in picofarads (1 pF = 10-12 F) and/or picocoulombs (pC).
Figure 2.4 Diagram summarizing plasma membrane K+ leak channels, ion pumps, and ion channels. Total electrochemical equilibrium acts as an ion battery creating a resting potential across the membrane which is internally negative.
In round figures, the quantity of electrons, or equivalent univalent (single charge) ions, in one coulomb (C] is 6 x 1018. A farad is the equivalent unit of capacitance where one coulomb of charge creates a p.d. of 1 volt. This is a very large quantity of charge, and capacitors in ordinary circuits are usually rated in microfarads (uF) or picofarads (pF). A quantity of 1 pF is 6 x 106 univalent I charges and cells operate in quantities of a few L pC of ions stored upon their membranes, and z around 0.01-0.001 pC flowing through individual ion channels. The rate of ion flow (amperage] through individual ion channels is measured in nanoamperes (nA), and the sum rates of ion channel flow across all the membranes of a cell at any given moment, acting as resistances in parallel, is measured in microamperes (uA).
Charge separation creates a p.d.
and a resulting e.m.f. between the two areas of charge on either side of
the plasma membrane. As this cannot discharge through the middle lipid
layer of the membrane, it can be used to create a controlled driving force
of ionic flow through the ionic channels. This force can be used as a transport
system, and Na+ -ion exclusion from the cell helps to control cytoplasm
osmolarity and cell volume. In neurones, the voltage-gated Na+ pumps are
used to transmit impulses. Depending upon the type of cell, membrane p.d.s
range from between 10 and 200 m\/ across their diameter. These are very
high voltages to sustain across an incredibly thin membrane of some 7.5
nm width, without breakdown, when the membrane consists only of freely
mobile lipid molecules at 37deg.C undergoing constant thermal agitation.
Scaled up into round figures by assuming a central lipid diameter of 5
nm, and an average membrane p.d. of ~~(90 mV; this is the equivalent of
an e.m.f. of 2 x 104 V/ mm. One millimetre is the average thickness of
the insulation sleeves around the live, neutral and earth wires inside
13 A cabling. At equivalent cell membrane voltages, their sleeve insulator
atoms would have to withstand an electron shell deformation force of some
20 000 \/ without breakdown by shorting, compared to the 230 V mains e.m.f.
distortion force that they normally withstand.
The Cell as an Electrified System
This sounds very similar to discussing cells as electrical systems, and the phenomenon is based partly upon active charge separation as discussed in the previous section, but carries a more extended meaning and involves additional components of charge.
To consider the cell as an electrified system means considering it as an electrified, or charged, body with a surrounding electrical field that can influence other charged bodies, or objects. It also means looking at cell structure to see whether different components of the cell act as collective wholes that create clearly defined sub zones of particular charge, or sign.
Every cell is an electrified resultant of two types of electrical phenomena. One has already been discussed, and this is the active creation by the cell of charged capacitor-like membrane surfaces through selective ion channel diffusion and ion pump maintenance. The second type concerns electrostatics: cell membranes can be considered in terms of electrostatics as their stored charge of inorganic ions creates an electrical field, consisting of an electric flux, or lines of force, radiating outwards from their surfaces. To this actively maintained surface charge must be added any organic molecules and compounds, such as proteins, amino acids, polysaccharides and simple sugars in the cytoplasm of the cell, that carry an overall charge and act collectively as an ionic mass. Some organic ions carry a positive charge but the majority are negative (Alberts, 1989). Furthermore, to these must be added those compound molecules that are electrically neutral, but carry charges of opposite sign at their ends - these are dipoles. Dipoles tend to rotate about their centre in response to an alternating field, and orientate themselves anti-parallel to a site of opposite charge, as if pointing at it like a stick.
When the cell is considered in these terms it is found to possess an external charge relative to other charged bodies, and is cross-sectionally divided into four charged zones, two of relatively steady charge strength, and two that vary about a mean value. Figure 2.5 shows the cell as an electrified system and should be referred to when reading the following description as it is a rather unusual way of looking at the cell. From the centre zone outwards, these four electrified zones are as follows:
1 Central negative zone (steady charge) This zone is the negatively charged mass of cytoplasm that includes negatively charged proteins, amino acids and other organic molecules, and maintains a steady bulk negativity.
2 Inner positive zone (variable charge). This consists of a thin zone of cations, mainly K+ ions, which both 'coats' the outer surface of the central negative zone with a thin layer of cations (bound cations), and clusters along the inner surface of the plasma membrane as freely mobile cations that are available for transport in and out of the cell as required.
3 Outer positive zone(variable charge]. This consists of a more extended, and more dense, zone of mobile cations, mainly Na+ ions and Ca2+
Figure 2.5 Schematic diagram of electrical zones of a cell. The membrane is relatively impermeable to Na+ and Ca2+ ions, so the membrane p.d. has a relative inner negative.
ions, with some K+ ions, that cluster along the outer surface of the plasma membrane and are therefore extracellular.
4 Outermost negative calyx zone (steady charge) This outermost zone of steady negativity is separated from the outer positive zone of the plasma membrane by a distance of some 20 ,um. It is created by negatively charged sialic acid molecules that tip many of the glycolipid arrays that project outwards from the surface of the cell like cactus branches. Many of these glycolipid structures are attached through the plasma membrane to the cell's micro tubular framework (Figure 2.6). Microtubules are flexible hollow tubes, built from dipole-charged protein blocks like chimney bricks, that have an overall oppositely signed charge at each end, and are, therefore bipolar (i.e. dipoles). They radiate outwards from their centriole base near the central nucleus to the plasma membrane, and sometimes beyond. They help to give the cell shape, provide sites for enzymes, support the membrane, and act as active transport systems throughout the cytoplasm. In neurones they are the channels for axoplasmic flow.
It is this outermost calyx zone of steady negativity that makes each cell act as a negatively charged body; every cell creates a negatively charged field around itself that influences any other charged body close to it. This electrostatic field has important consequences. Although the field is very weak, cell calyx fields repulse each other, thus tending to maintain a 40 ,um space between cells, except where there is actual junctional contact. All cellular tissue surfaces, such as the endothelial lining of the vascular system for example, carry a steady negative charge on their surfaces. In this example, the endothelial surface charge repulses the negatively charged blood cells, platelets and plasma proteins so that they are separated from the endothelium by a thin zone of pure plasma fluid. If the endothelium is damaged, the damaged area loses its negativity, allowing the platelets to adhere with consequent risk of thrombus formation (Marino, 1988).
Figure 2.6 Schematic of a cellular cytoskeleton membrane. M - cell membrane potential; GP - glycoprotein extending into extracellular space; MT - microtubule; MF - microfilaments [actin filaments or intermediate filaments); MTL microtrabecular lattice. Cytoskeletal proteins that connect MT and membrane proteins include spectrin, fodrin, and ankyrin (Hameroff, 1987.)
In addition to these four zones,
it should be noted that the immediate inner surface of the plasma membrane
carries an overall negative charge that holds an important enzyme, protein
kinase C, against its surface until it is activated and released by an
influx of Ca2+ ions to initiate cascade reactions within the cell.
The Electrical Properties of Tissues
All soft tissues include long-chain
protein molecules such as collagen, elastin, and keratin in their structure;
these molecules have a regular, repeating, subunit structure. Connective
tissues, such as capsules, ligaments, fascia and tendon, consist of dense
sheets of these molecules, especially collagen. Cartilage consists of collagen
and proteoglycans, and bone is a calcified collagenous structure. All such
tissue proteins possess one electrical feature in common: when they are
mechanically distorted (strained) by an applied mechanical stress they
develop piezoelectric type p.d.s upon their external and internal surfaces
(Becker and Marino, 1982; Black, 1989). Bone can be taken as a typical
example of a tissue developing piezoelectric-like potentials when it is
deformed, as shown in Figure 2.7. Surface voltages range from 10-150 mV
and are proportional to the degree of strain deformation resulting from
a given stress force acting upon the tissue.
Figure 2.7 Apparent piezoelectricity in bone. al Typical piezocrystal response to momentary deformation; b) Similar transducing response in bone. c) Tension/compression surface potentials of opposite sign to resulting bone cell response. [After Becker and Selden, 1985.]
Many regular, lattice-type structures, such as the crystals used in ultrasound equipment and protein molecules, exhibit a piezo (pressure) - electric (surface potential) effect because the mechanical distortion of strain displaces some electrons towards the compressed surfaces (negative) and away from the stretched surfaces (positive} This phenomenon is more fully explained in the chapter on ultrasound therapy, where the crystal transduction of electrical and acoustic energy is discussed. This surface charge exists as long as there is distortion, and disappears when the stress is removed. If the stress force varies over time, so does the strength of the surface charge, so it will be synchronous with it
Each time a bone, such as the femur, takes a weightbearing load it bends slightly. The compressed concave surface generates a negative p.d., and the stretched convex surface generates a positive p.d. The point charges are measured in pico coulombs as shown in Figure 2.8. A similar
Figure 2.8 Charge distribution (pC/crn2) along femoral surfaces on loading. Hatched outline k theoretical profile change of growth and resorption proportional to charge strength. (After Becker and Marino, 1982.)
effect occurs within fluid filled
channels, such as the Haversian canals, where the surface p.d. is termed
a streaming potential, as it is the p.d. between the charge generated
on the tissue surface and the ionized fluid that is flowing past it. A
very thin, electrically neutral, interface develops between the two p.d.s
which is called the slip plane. In tendons, the tensile stress exerted
by muscle contraction against the external load carried by the tendon between
the muscle and its skeletal or fascial insertion, generates parallel planes
of surface charge along its stretched length, and the same applies to all
The Electrical Cell and Electrotherapy
The first two sections show how basic electrical theory an be applied to cell structure and function by considering the living cell as an electrical system and as an electrified body, respectively. It helps to provide a framework for understanding how the physical effects of various forms of applied electrical, magnetic, electromagnetic and ultrasonic energy may be converted to physiological effects when absorbed by cells. It is particularly relevant to those modalities that evoke a variety of non-thermal cellular responses, such as low-frequency stimulation, and to those modalities that are claimed to possess, and may indeed possess, nonthermal effects in addition to any physiological effects resulting from tissue temperature rise following energy absorption from them, for example pulsed and continuous high frequency fields.
What must always be borne in mind is that cells are functional wholes. To discuss them only in electrical terms is to abstract one aspect of their function, and any consequences arising from such electrical activity must be considered in their physiological context of change in metabolism and function.
The section on the known electrical properties of bone and soft tissues, as distinct from the living cells that manufacture them, is far less familiar. The probable reason for this is that the biological function and significance of these electrical effects are not known for certain, and many claims are hotly disputed. This uncertainty centres upon highly contentious issues concerning cellular responses to various forms of applied direct current, low-frequency currents and fields, high-frequency currents and fields, ultra sonic vibration, and pulsed low-energy laser radiation. These issues are discussed in more detail in their relevant chapters.
Leaving aside the known and undisputed cellular and body system responses to electrotherapy modalities as a consequence of, for example, heating, cooling, depolarization, mechanical vibration, and photochemical reactions, the unresolved question is whether cells can receive, decode, and act upon, specific frequencies, intensities and waveforms in the same way that they respond to, for example, the arrival of hormone molecules.
There are a number of questions that need to be asked:
Can cells respond to oscillatory electrical and/ or magnetic fields that are emitted from environmental sources, such as mains cables, high tension cables, and electronic equipment, which permeate the body by night and day?
If the answer to these questions is 'yes', then it means that particular forms of electrical and/or magnetic energy can act as incoming first messengers like chemical molecules, and the cell will respond to them in a reasonably consistent way, as it does to, say, insulin or growth hormone. If this could be demonstrated beyond reasonable doubt. then electromagnetic medicine, as electrotherapy would become, would develop as a recognized specialty. It would be able to deliver measured doses of electrotherapy appropriate to the diagnosis of a wide range of disorders, as, for example, it does now when specific J/ cm2 dosages of UV-A radiation are applied to psoriatic skin in conjunction with psoralen drug therapy (PUVA).
A 'yes' answer also has deep implications concerning the possible role of naturally produced (endogenous) electricity. The piezoelectric-type tissue p.d. response to mechanical deformation offers an interesting, and unresolved, test case for discussion.
To those who consider that the evidence supports a working hypothesis that cells can interpret and respond to fluctuating patterns of external e.m.f. impinging upon their charged surfaces, these tissue p.d.s resulting from mechanical deformation are seen as a self-regulatory command system that instructs tissue cells what to do (Bassett, 1982; Becker and Marino, 1982; Becker and Selden, 1985; Becker, 1991; Black, 1989; Frochlich, 1988; Nordenstrom, 1983). According to this view, mechanical stress and the resulting strain distortion is transduced (a process of energy transformation) into patterns and intensities of surface p.d.s proportional to localized strain deformation. These p.d.s act as a signaling system upon adjacent cells, such as fibrocytes in tendons, chondrocytes in cartilage, and osteoblasts and osteoclasts in bone, instructing them to increase/ decrease, tissue formation, or increase/decrease tissue absorption, as a response to the imposed mechanical stress. Thus, bone and tendon becomes proportionally thicker with increased loadbearing stress through exercise because the cells have 'read' the proportional intensity and frequency of tissue generated surface p.d.s. Bone, for example, can undergo extensive remodeling in response to sustained changes in load. Figure 2.9 provides a diagrammatic summary of this hypothesis and should be read clockwise, starting from the initiating agent of mechanical stress.
Figure 2.9 Summary of the role of strain-generated potentials in bone and, by implication, cartilage and connective tissue adaptation to mechanical stress - Wolffs Law control system. (From Becker and Marino, 1982)
Conversely, the osteoporosis and connective tissue thinning associated with disuse is interpreted from this viewpoint as a lack of stress-induced p.d. stimulus to the cells, with consequent loss of rate of tissue replacement compared to rate of absorption. The late stage of post-fracture remodeling, in this view, is programmed by the intensity distribution of fracture site p.d.s, as shown in Figure 2.10. The important point here is that the remodelling in this case straightens the femoral shaft against the compressional forces of weight bearing that should, by mechanical loading, increase the deformity of the malleable bone. The argument of those who consider that these tissue p.d.s act as an important information and control system is that the cells, as in this example, are responding to the p.d. intensity gradient created by the stress force and not to the stress force in itself.
Suggested mechanisms whereby tissue p.d.s may act as first messengers are that they may activate ion channels, such as Ca2+, which is an important second messenger that can initiate, through protein kinase C, specific enzyme cascades within the cell, or be picked up by the charged glycolipid strands that project outwards from the cell, and then conveyed into the cell via connecting microtubule dipoles and 'read off' by enzyme systems attached to the microtubules as shown in Figure 2.6.
A recent theory concerning the possibility that very weak signals, such as electromagnetic fields, or cellular emission of biophotons, can be detected by cells is that the intrinsic random 'noise' energy created by the ceaseless activity of membrane ion channels may be entrained by very weak, incoming, oscillatory signals to create strong signals at the same frequency (Wiesenfeld and Moss, 1995). In effect, the random fluctuations of membrane noise energy is converted to strong, regular oscillations that can modify cell behaviour. This random-noise to controlled-signal conversion is known as stochastic(random noise) resonance (oscillatory frequency or SR, and its magnitude can be expressed as a signal strength to-noise ratio, or SNR.) If, for example, these were shown to be at the same resonant frequency as the mechanical, electroconformational, changes of transmembrane proteins that control the movement of charge across the membrane, then they could act as first messengers.
(After Black, 1987.)
Another contentious example is the undoubted evidence that a wide range of microampere currents ebb and flow through the body along tissue channels connecting areas of differing metabolic activity (Becker, 1991; Borgens et al, 1989; Nordenstrom. 1983). Areas of raised metabolic activity are electrically negative relative to areas of low metabolic activity, and currents flow through, and around, localized areas of tissue trauma and healing. Most standard authorities see these currents, if they recognize their existence at all, as byproducts of little significance. Others, as cited above, see them as an essential guiding and regulatory component of body function that works in synergy with the nervous system, vascular system and hormonal system. Nordenstrom (1983), for example, refers to them as a circulatory system that is additional to the former systems. He has modelled the body as an electrical circuit system in which sheets of connective tissue, as in organ capsules, fascial planes, and the vascular system, act as relative insulators, and ionic tissue fluids act as ionic currents that an convey charged substances, such as nutrients and waste products to and fro, and alter tissue osmotic pressures. Nordenstrom considers the enclosed blood circulatory system as at zero electrical potential, analogous to 'earth' in electrical systems, and all other tissues as at a relative positive or negative p.d. to it, according to their level of metabolism. The capillaries are the variable resistance points through which ionic currents between tissues and blood plasma can flow according to their relative difference in potential.
There is considerable evidence (Borgens et al, 1989; O'Connor et al., 1990) to show that electrical tissue gradients during embryonic development act as directional growth markers, that injured tissues generate so called 'injury currents' which stimulate repair processes and that wound healing in skin, as a particular example, is more efficient if the area is kept moist so that microampere currents, driven by e.m.f.s generated by the epidermal layers, can flow across it.
Despite the experimental evidence that seems to support the idea that tissue surface p.d. generation act as a selfregulating control system, most authorities, including, it seems, those who write the standard texts, take a cautious 'non-proven' stance. They are skeptical of theories that equate the properties of recognized cell electrophysiology with ordinary, or solid state, circuitry analogies, and make scant reference to the subject.
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