Electrical insulation · Lobeworks/17

Electrical insulation is the property of a material that lets almost no current through, because it has almost no free charges to carry one, and in the nervous system it is what the lipid membrane and, many times over, myelin provide: a wall that ions cannot cross, across which a voltage can be held.

Electrical insulation. Electrical insulation is the property of a material that lets almost no current through, because it has almost no free charges to carry one, and in the nervous system it is what the lipid membrane and, many times over, myelin provide: a wall that ions cannot cross, across which a voltage can be held.

How well a material insulates is measured by its resistivity ρ\rhoρ, in ohm metres: a block of length LLL and cross-section AAA has a resistance R=ρL/AR = \rho L / AR=ρL/A. Copper sits near 1.7×10−81.7 \times 10^{-8}1.7×10−8 Ω·m, the cytoplasm of an axon near 1 Ω·m, glass around 10910^{9}109 to 101210^{12}1012 and PTFE (Teflon) above 101810^{18}1018: some twenty-six orders of magnitude separate a good conductor from a good insulator, one of the widest ranges of any physical quantity. The difference is in the charge carriers. In a metal electrons move freely; in an insulator they are bound behind an energy gap (about 9 eV in silicon dioxide) that heat cannot lift them across. Body fluids conduct with ions instead of electrons, so for a neuron an insulator is anything ions cannot enter, above all the oily core of the lipid bilayer, where an ion pulled out of water would cost far more energy than the membrane voltage can supply.

An insulator between two conductors also stores charge. A thin layer of permittivity ε\varepsilonε and thickness ddd is a capacitor,

C=εAdC = \frac{\varepsilon A}{d}C=dεA​

which is why every cell membrane carries about 1 µF/cm² and why charging it is part of the cost of every change of voltage.

The membrane holds an enormous field. A resting potential of 70 mV across about 5 nm is E=V/d≈1.4×107E = V/d \approx 1.4 \times 10^{7}E=V/d≈1.4×107 V/m, some five times the field at which air breaks down into a spark (about 3 MV/m); only a very thin and very good insulator survives it.

Myelin stacks the insulator. Wrapping the axon in nnn layers of membrane puts nnn resistors and nnn capacitors in series, so the wall's resistance grows about nnn times and its capacitance falls about nnn times, R≈nR1R \approx nR_1R≈nR1​ and C≈C1/nC \approx C_1/nC≈C1​/n. Less current leaks out and less charge moves the voltage, so the length constant of axonal conduction grows and the spike leaps from node to node in saltatory conduction. With tens to over a hundred layers, made mostly of lipid (about 70 to 85 % of myelin's dry mass), a sheath a micrometre thick does the work of a much wider axon.

Electrodes need it too. A recording electrode must touch the tissue only at its tip, or it averages the voltage along its whole length, so the shafts of the Utah array are coated in parylene and only the tips are left bare; the slow failure of that coating in the body is one of the ways implants lose their signal over years.

An insulator is a place charges cannot go, and so a place where a voltage can be kept.

The membrane is a battery because it insulates, and myelin is speed bought with more layers of the same insulation.

Questions: If the lipid membrane insulates, how do ions cross it at all? Through proteins that make holes in the insulator: ion channels and transporters. The oily core of the bilayer keeps ions out because leaving water for a hydrocarbon would cost them far more energy than the membrane voltage supplies, so the membrane's resistance is set by how many channels are open. Opening voltage-gated sodium channels is, in electrical terms, punching thousands of tiny holes in the insulation for a millisecond. How strong is the electric field across a resting membrane, and how does it compare with the field that makes air spark? About 14 million volts per metre: E=V/d≈0.07 V/5 nm=1.4×107E = V/d \approx 0.07\ \text{V} / 5\ \text{nm} = 1.4\times10^{7}E=V/d≈0.07 V/5 nm=1.4×107 V/m. Air breaks down into a spark at about 3 MV/m, so the resting membrane holds some five times that field, and only because it is so thin and so good an insulator. Mica, one of the best solid insulators, holds about 200 MV/m before it fails. What quantity measures how well a material insulates, and where do copper, an axon's cytoplasm and Teflon fall on it? Resistivity, ρ\rhoρ, in ohm metres: a block of length LLL and cross-section AAA has resistance R=ρL/AR = \rho L/AR=ρL/A. Copper is about 1.7×10−81.7\times10^{-8}1.7×10−8 Ω·m, an axon's cytoplasm about 1 Ω·m and PTFE (Teflon) above 101810^{18}1018 Ω·m, so a good insulator resists some 102610^{26}1026 times more than a good conductor. The cytoplasm's resistance per unit length is the rir_iri​ of the cable equations, the term a wider axon lowers. Why must a recording electrode be insulated everywhere but its tip? So that it reads the voltage at one point instead of an average along its whole length. A bare shaft would touch tissue all the way down and pick up every neuron it passes; insulating it confines the contact to the tip, near one or a few cells. The shafts of the Utah array are coated in parylene-C with only the tips left bare, and the slow failure of that coating in the body is one of the ways implants lose their signal over years. Why does wrapping an axon in more layers of membrane insulate it better, in numbers? Because the layers act in series. Each layer of membrane is a resistor and a capacitor across the wall; nnn of them stacked add their resistances and divide their capacitance, so R≈nR1R \approx nR_1R≈nR1​ and C≈C1/nC \approx C_1/nC≈C1​/n: a hundred wraps leak about a hundred times less and need about a hundred times less charge to change the voltage. The length constant λ=rm/ri\lambda = \sqrt{r_m/r_i}λ=rm​/ri​​ grows with the resistance, and the spike can jump from node to node.