The Glial membrane-fluid cleft-neural membrane arrangement cuts effective neural capacitance, greatly increasing signal conduction velocity and greatly reducing the energy requirement per action potential.

July 14, 1997                M.R. Showalter

Unmyelinated axons and dendrites are not bathed by open volumes of grounded fluid. Instead, they are closely surrounded by the membranes of other cells, separated by thin fluid clefts that are 2-4 times the neural membrane thickness. It has been assumed that the fluid clefts act as perfect neural membrane capacitor grounds. The assumption has been that the clefts have such high effective conductance that they act in the same way as an open volume of grounded fluid would do. For very slow voltage fluctuations, this would be true enough. However, for voltage fluctuation frequencies of neural interest, the fluid clefts are ungrounded.

Considering cleft resistance alone, conduction in the plane of the fluid cleft would be badly and inconsistently grounded. Cleft resistance is typically very much higher than neural line conductance. When cleft R2C effective inductance is also taken into account, and clefts are seen to be ungrounded for signal propagation purposes. Voltage fluctuation propagation velocities in the plane of the cleft are about 1/(R2C2).5 meters/sec (about .0001 meters/sec) - much slower than action potentials and other signals in the neuron. The fluid cleft acts as a dielectric layer, surrounded by two dielectric membranes, not as a ground. The R2C effective inductance does not reduce smooth cleft current flows, which are dominated by cleft resistance, and does not reduce molecular diffusion through the clefts.

Analysis indicates that ion flows in and out of a fluid cleft during action potentials are capacitive, and do not involve significant conductance along the plane of the fluid cleft. The membrane-fluid cleft-membrane assembly has a much larger effective capacitance with respect to charged ion flows between cleft and neuron than it does between neuron and effective neuron capacitance ground. The effective capacitance for charged ion flows across the cleft is about the same as the capacitance of a membrane surrounded by a large volume of grounded fluid would be. This means that much less ion flow is required with the membrane-cleft-membrane assembly than would be required otherwise for a given change in axolemma voltage. At the same time the capacitance between neural membrane and cleft provides an ample source of ions for the action potential at a nearly steady voltage.

A neural membrane-fluid cleft-glial membrane assembly reduces the effective capacitance of the neural membrane by about two orders of magnitude, compared to the capacitance of the neural membrane surrounded by a large volume of grounded fluid. A neural membrane-fluid cleft-neural membrane assembly in the cerebral parallel fibers and similar structures reduces effective capacitance for the same reasons and in similar proportion.

The effectively ungrounded fluid clefts have strong physiological effects and advantages.

The energy requirement (ion flow) per action potential is proportional to the effective neural membrane capacitance. Therefore, the fluid cleft assembly reduces energy consumption per action potential about 100 fold.

Ion flow required to produce a unit of axolemma voltage change is proportional to the effective neural membrane capacitance. Therefore, the fluid cleft assembly cuts the time to equilibration for a set number of channels and a set initial voltage difference across the membrane.

The velocity of action potential conduction and passive conduction is inverse with assembly capacitance (according to Showalter-Kline theory), so that the fluid cleft increases conduction velocity about 100 fold.

Thin fluid clefts essentially always surround unmyelinated neural membrane. This seems to be consistently true for all animals that have nerves. It is suggested that the important energy conservation and conduction facilitation that these clefts provide is the biological reason for their consistent occurrence through phylogeny.


Ideal capacitor grounds have high conductance to ground on the time scales where they are used. Visual inspection of the fluid clefts shown between neural membranes in electron micrographs makes the ideality of these clefts as grounds at least questionable. Current paths through the clefts are generally restrictive and appear to vary over a wide range from cleft to cleft. Nor can the clefts be simple resistive conductors. Charges in the clefts are strongly coupled with the capacitance of the neural and glial membranes that are the walls of the cleft. Even so, the idea of the cleft as ideal ground has been accepted.

I was forced to question this ideality when my theoretical work calculated conduction velocities about 100-fold too slow. According to the Showalter-Kline conduction theory, conduction velocity for frequencies of neural interest(1), for the case of low membrane conductance, is predicted by equation (1). Conduction velocities at higher membrane conductances are proportional to (1).

Predicted velocities were gratifyingly congruent with measurements when calculations were done in centimeter-gram-second-coulomb-volt units. CGS units are the customary units in neural studies. However, thanks to an incisive question from a reviewer, it became clear that the CGS unit system did not correctly account for crossterms in the Showalter-Kline theory. The fully dimensionally consistent Meter-Kilogram-Second-Coulomb-Second (MKS-Georgi) unit system was necessary instead. For the nonlinear terms in the Showalter-Kline theory, a change of unit systems is an integration scale correction that changes magnitudes. I found that in the MKS-Georgi unit system, (1) was predicting conduction velocities about a factor of 100 too slow. Either the Showalter-Kline theory was wrong, or one or more of the parameters used to calculate (1) had to be wrong, or (1) had to be an incorrect representation of neural circumstances.

Resistivity could not be changed much. On first inspection, the calculation for membrane capacitance seemed solid also.

I was therefore forced to look hard at the role of the fluid clefts in determining effective neural capacitance, for the neuron as it actually was in tissue. If the cleft was part of a neural membrane-fluid cleft-glial membrane assembly with a capacitance per unit area Ca, then (2) should be substituted for (1):

The cleft IS part of an assembly that is more complicated than the single membrane capacitor we have assumed in our models of neural capacitance.

Fig. 1 shows how glial membrane surrounds almost all unmyelinated neural membrane. (Parallel fibers in cerebellum, and some similar structures, are an exception, but have fluid clefts that are similar.) The fluid in the cleft is much like plasma or cerebrospinal fluid. Dielectric constant of the membranes is about 2, and the dielectric constant of (pure) water is about forty times higher, about 80.

Fig. 1 is a crossection of the membranes as a planar structure. Length and depth of the planar membranes is very large with respect to 20 nanometers.

How does this assembly act as a capacitor, with respect to the neural axolemma (with charge differentials perpendicular to the plane)? It is useful to think of the two polar cases, one corresponding to effectively infinite cleft conductance in the plane, and the other to effectively zero cleft conductance in the plane.

Polar Case 1. For charge fluctuations so slow that the electrical conductance of the fluid cleft is asymptotically large, THE FLUID CLEFT IS THE CAPACITOR GROUND with respect to both neural and glial membrane. In this "infinite cleft conductance" case, the capacitance with respect to the neural membrane is no different than it would be for a single membrane - the potential the neural membrane "sees" does not depend at all on the glial membrane.

Polar Case 2. For charge fluctuations in the neuron so fast that the electrical conductance of the fluid cleft is asymptotically small, THE FLUID CLEFT IS UNGROUNDED. The effective capacitor ground of the neural axolemma is the glial axolemma (or vice versa). The dielectric properties of the ungrounded fluid cleft will be nearly the same as they would be for pure water (an ion does not move more than half a water molecule length because polar water molecules around it rotate with uniform statistics.)

(Example for polar case 2, for 30 nm cleft thickness, and dielectric constants of 2 for the membrane and 80 for the cleft fluid. Capacitance would be 1/152nd (.0066) of the capacitance for the unshielded single membrane.)

In terms of Showalter-Kline theory, the fluid cleft is effectively ungrounded at action potential and neural signal frequencies. An exact quantitative model of cleft conductance as a function of frequency and the (extremely variable) cleft geometry that occurs in neural tissue would be daunting to do and to read. No such model is offered here. It should suffice to know that the conduction velocity of a voltage disturbance in the cleft (along the plane of the cleft) depends on cleft thickness and cleft fluid resistivity, and is about 10-5 meter/sec (or .001 cm/sec) or less. (See Appendix.). (Velocity perpendicular to the plane of the cleft will be a factor >108 faster.) The planar cleft signal velocity is far too low to carry much of the charge flux involved in

the action potential or passive signal propagation in the neuron. RAPID charge equilibration across the neural membrane must come from assembly capacitance, not from charge flows along the cleft plane. For dynamic purposes, the cleft is ungrounded.

The assembly capacitance is amply large to supply the charge flows needed for signal propagation and action potentials. To see this, it is useful to review the electrochemistry of action potentials and other neural potentials. Levitan and Kaczmarek phrase the central fact of electrochemistry nicely:

The Nernst equilibrium potential. Assume the membrane is permeable to a single charged ion, X+, which is asymmetrically distributed on the two sides of the membrane. The counterion, Y-, cannot cross the membrane. X+ will flow across the membrane from the side of high concentration to the side of low concentration, until the buildup of charge is sufficient to (generate a voltage that is sufficient to) oppose net ion flow. The transmembrane voltage (Vm) is 0 before X+ begins to flow. At equilibrium Vm = Ex+ (2)

Suppose that the charge flow sufficient to buildup voltage Ex changes by a factor of N (suppose that capacitance changes by a factor of N). Even if N is a large number, the equilibrium voltage itself does not change. The charge flow (and the energy consumption that charge flow represents) changes in proportion to the capacitance. Equilibration becomes faster as the charge flow required for equilibration becomes smaller. From both these points of view, reducing the net neural membrane capacitance is an advantage. Reduced capacitance cuts energy requirements and speeds performance.

The logic of the action potential, and its dependency on the opening and closing of potassium and sodium channels, does not change when the neuron is surrounded by a fluid cleft (rather than by an infinite bath of grounded fluid) except that energy efficiency and dynamic response are much improved by the capacitive reduction of the cleft. The effective capacitance of a neuron in the course of the action potential has two parts:

a: First, the capacitance from neural axolemma to glial axolemma (from 1-4 on Fig 1) for the full voltage difference v1 - v4.

b: Second, the capacitance across the neural membrane from neural axolemma to cleft, for a voltage difference of about 1/100th v1 - v4.

The net result is an effective capacitance about half of the capacitance from 1 to 4 in Fig. 1.

According to Showalter-Kline theory, in the very low g state, signal forms can propagate passively down neural lines. For such propagations, the effective capacitance is the capacitance between 1 and 4 in Fig. 1.


History shows that it is dangerous to suggest an essential role for glial cells(3) (4). Even so, the role of glia in forming the fluid clefts around neurons seems apparent from these calculations. The clefts reduce energy consumption (and increase conduction velocity) by about two orders of magnitude - enough to make them biologically worthwhile, enough to make them as conserved as they are throughout taxonomy and phylogeny.

Perhaps, with benefit of hindsight, this is not so surprising. From an engineer's perspective, the ability of glia to wrap around neurons and form fluid clefts is wonderful. It is nearly impossible to model the geometry of single neurons in three dimensional detail. There are billions of neurons, and they lie together in an ordered but still much tangled three dimensional array. How would you design a cell type that would wrap all the neurons, wrap them everywhere, and wrap them in a way that forms such consistent fluid clefts? Glia do wrap the neurons, excepting myelinated neural lines, and some bundles such as the parallel fibers. In electron micrographs, which are crossections, one simply expects a thin fluid cleft surrounding axons and dendrites.

Glial geometries seem haphazard or semichaotic in many other ways, but glia wrap neurons with stark precision. Thin fluid clefts essentially always surround unmyelinated neural membrane. This seems to be consistently true for all animals that have nerves. Since the glia do such a difficult thing when then they form the clefts so consistently, must not the cleft geometries formed be very important? The calculations here show that the clefts ARE very important in neural transmission.

The fluid clefts between parallel fibers in cerebellum and elsewhere should act similarly to increase conduction velocity and reduce neural energy consumption.

This paper has assumed the correctness of the Showalter-Kline neural conduction model, and found that predicted characteristics of the fluid cleft strongly reinforce that model. The combination of Showalter-Kline with the clefts forms a functionally neat package, well adapted for precision neural transmission and resonance, and energetically efficient.

In contrast, the clefts make Kelvin-Rall, already very implausible, more implausible still. Strong reasons to doubt Kelvin-Rall have been reviewed elsewhere(5) Without considering the clefts, Kelvin-Rall has the following problems. In Kelvin-Rall, electrical propagation velocity goes as the square root of fourier frequency, and so a coherent waveform such as an action potential waveform would be impossible. Some unexplained mechanism whereby channel-generated voltage changes travel down the neuron at a speed different from other voltage changes has to be posited. Velocities are also much too high. Kelvin-Rall lacks any mechanism for the coordinated firing of many neurons over large distances that is observed. Kelvin-Rall predicts that neurons are much slower than they are. For these reasons, the sophisticated information processing brains do seems impossible under Kelvin-Rall. When the effects of clefts are added, under the Kelvin-Rall assumption of no effective inductance in the clefts, the model becomes much more complicated, and more statistically varied, because of wide ranges of resistivity from cleft to cleft, or along a single cleft. Such a muddy system does not fit the requirements of know patterns of information processing.

Under Showalter-Kline theory, the fluid clefts ubiquitously observed around neurons are part of an efficient neural conduction assembly capable of precision function.

APPENDIX 1: Cleft Velocity, Showalter-Kline theory

Conduction velocity of fluctuating voltage in the cleft is much smaller than line action potential velocity or passive conduction velocity, so that conduction along the plane of the cleft cannot carry a significant fraction of the current flow necessary to support either sort of neural line conduction.

Here is the standard formula for line propagation velocity. We can treat a strip of cleft as a line.

we interpret R, L, G, C including crossproducts, taking hatted values as below(6)

It is useful to consider the case where G is negligibly small, so that only the R2C crossterm has to be included in the modelling. Then we can write

n subscripts emphasize that we are dealing with numerical values (and keeping track of units implicitly.) In the neural range this simplifies(7) to

including units, this equation is

Consider a cleft one unit of length deep (1 meter deep). In MKS-Georgi units resistance and capacitance are

Capacitance is proportional to width, and resistance is inversely proportional to width: the RC product is independent of width, as it must be.

We can now calculate conduction velocity in a cleft for reasonable values of the dimensional parameters. We'll choose

c = .01 farad/meter2 (1 microfarad/cm2) = .55 ohm-meter

t = 3 x 10-8 meter

The velocity is 3.86 x 10-6 meters/second, or 3.86 microns/second. We've made assumptions (particularly, that of small G) in this calculation. Even going back and accounting for them, cleft conduction velocity remains very slow, far slower than the speed of neural line conduction.

This result does not effect molecular diffusion in the clefts. It does not effect the steady current flow capacity of the clefts, which is controlled by resistance alone, not by effective inductance. HOWEVER, THE RESULT SHOWS THAT THE CLEFTS ARE UNGROUNDED TO GOOD APPROXIMATION SO FAR AS ACTION POTENTIALS OR OTHER RAPID LINE CONDUCTANCES ARE CONCERNED.

APPENDIX 2: Cleft Conduction Velocity - standard theory

According to Showalter-Kline conduction theory, conduction velocity of fluctuating voltage in the cleft is much smaller than line action potential velocity or passive conduction velocity. According to conventional conduction theory, calculated cleft conduction velocity is orders of magnitude faster.

Here again is the standard formula for line propagation velocity. We can treat a strip of cleft as a line.

In Appendix 1, we interpreted R, L, G, C including crossproducts. In this appendix, we neglect the crossproducts, and compute cleft velocity according to the old standard theory.

Again, we consider the case where G is negligibly small, and electromagnetic inductance is also negligible, so that we can write

n subscripts emphasize that we are dealing with numerical values (and keeping track of units implicitly.) R and C are the same as in Appendix 1. As before, capacitance is proportional to width, and resistance is inversely proportional to width, so that the RC product is independent of width, as it must be, since velocity must not vary with width.

We can now calculate conduction velocity according to the standard theory using the same parameters as in Appendix 1. The calculated old-theory velocity varies with the square root of frequency, and would be

for a fourier component of 5,000 hz, this would be .29 meters/sec, or 29 cm/sec, about 75,000 times faster than velocity calculated accoding to the Showalter-Kline theory. This old theory velocity (for a 30 nm fluid cleft) is about twice as fast as the conduction velocity Sakmann et al measured for a 6 micron (200 x 30 nm) diameter dendrite.


1. Showalter, M.R. A Passive Neural Conduction Equation: Part a: derivation p. 10 and A Passive Neural Conduction Equation: Part b. neural conduction properties. p. 7 available FTP

2. Levitan, I.B. and Kaczmarek, L.K. THE NEURON: Cell and Molecular Biology Oxford U. Press (1991) pp 54, 55

3. "There are between 10 and 50 times more glial cells than neurons in the central nervous system of vertebrates. Glial cells are probably not essential for processing information . . . "

Kandel, E.R. Nerve Cells and Behavior p 23 in Principles of Neural Science 3d ed Kandel, E.R., Schwartz, J.H., and Jessell, T.M., eds. Elsevior, 1991

4. "Studies of glial cells are in a peculiar state. . . . It is remarkable that one should have to discuss the performance of the brain in terms of neurons only, as if glial cells did not exist. Even if in the end this neglect should turn out to be correct, which we doubt, one ought to be able to justify the reasons for ignoring the most numerous cell types in the nervous system."

(the "peculiar state" Kuffler et al speaks of persists.)

in Kuffler, S.W. Nicholls, J.G. and Martin, A.R. FROM NEURON TO BRAIN: A Cellular Approach to the Function of the Nervous System 2d ed Sinauer Associates, Sunderland, Mass 1984 p 324

5. Showalter, M.R. Reasons to Doubt the Current Neural Conduction Model available FTP\pub2\showalt

6. reference 1, part a p.3

7. reference 1, part a, pp 8-9 reference 1, part b, p. 7