The Charged Membrane

Draft for the author's reading and rewriting. Established science throughout; the framing and the leaps are the author's.

The textbook picture of electromagnetism is the wave in the diagram: electric and magnetic fields at right angles, travelling outward, weakening with distance. That picture is correct far from the source. Life does not happen far from the source. It happens within a few nanometres of charges, where the field is not a travelling wave at all but a standing, stored electrical tension. The cell membrane is the clearest place to see it.

A tenth of a volt, five nanometres

A resting cell holds its inside at roughly seventy thousandths of a volt below its outside. That sounds like nothing; a torch battery is twenty times more. But the membrane that holds the difference is only about five nanometres thick. Divide the one by the other and the field inside the membrane comes out at around ten million volts per metre — the same order as the field at which air breaks down into a spark [1, 5].

The membrane does not spark because the lipid core is an excellent insulator and the distance is tiny. What would be violent across a room is ordinary across a molecule. That is the first way the "simple" physics stops being flat: the same law, at a different scale, becomes a different kind of fact.

Why the field stays close

The water on each side of the membrane is not pure water. It is a salt solution, and its free ions crowd around any charge and cancel it at a distance. The length over which a charge is felt in physiological saline — the Debye length — is under a nanometre [5, 7]. Beyond a few nanometres, a charge is, to the rest of the cell, nearly invisible.

So biology's electricity is a near-field affair by construction. It does not broadcast. Each field is local, steep, and felt only by whatever stands right next to it: a channel, a pump, a protein landing on the surface. The cell can therefore keep thousands of different electrical conversations going side by side without them drowning each other out.

The double layer

The faces of the membrane carry charge of their own, from the headgroups of the lipids — on the inner face especially, where negatively charged lipids gather. Each face draws a cloud of counter-ions out of the water. The result is a structured electrical layer, not a bare surface [5]. A protein approaching the membrane meets this layer first. Whether it binds, and how it lies once bound, is partly decided by the charge pattern it finds there.

Keeping the difference standing

Left alone, the ions would leak until the difference vanished. The sodium–potassium pump prevents it, pushing three sodium ions out and two potassium ions in for each molecule of ATP it spends [2]. The cost is large: in the grey matter of the brain, most of the energy used for signalling goes to restoring ion gradients [3]. A living cell pays continuously to stay charged. The voltage is not a resting state; it is held up.

The voltage as a working part

The charge is not decoration on the biology. It is one of its working parts.

In a nerve, channels open and close in response to the voltage itself, letting sodium rush in and potassium out, and the disturbance travels along the fibre as an impulse [1]. The channels know the voltage because charged segments of the protein sit inside that ten-million-volt field and physically move when it changes [6]. The field reaches into the protein's shape.

In the mitochondrion, the respiratory chain pumps protons across the inner membrane, building a difference of roughly a sixth to a fifth of a volt plus a concentration gradient. The protons flowing back through ATP synthase turn it like a rotor, and that turning makes the cell's ATP [4]. Mitchell's proposal that energy is stored as a charged gradient across a membrane, rather than as a chemical intermediate, was resisted for years and is now the ground of bioenergetics.

What the flat reading drops

The flat reading says: electromagnetism is the waves in the diagram, and biology is chemistry. What it drops is the regime in between — steep, screened, standing fields across molecular distances, where the electrical and the chemical are the same event described two ways. The membrane is where charge, shape, and energy stop being separate subjects.

References (to be checked against the originals)

1. Hodgkin, A. L. & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117, 500–544.
2. Skou, J. C. (1957). The influence of some cations on an adenosine triphosphatase from peripheral nerves. Biochimica et Biophysica Acta 23, 394–401.
3. Attwell, D. & Laughlin, S. B. (2001). An energy budget for signaling in the grey matter of the brain. Journal of Cerebral Blood Flow & Metabolism 21, 1133–1145.
4. Mitchell, P. (1961). Coupling of phosphorylation to electron and hydrogen transfer by a chemi-osmotic type of mechanism. Nature 191, 144–148.
5. McLaughlin, S. (1989). The electrostatic properties of membranes. Annual Review of Biophysics and Biophysical Chemistry 18, 113–136.
6. Bezanilla, F. (2008). How membrane proteins sense voltage. Nature Reviews Molecular Cell Biology 9, 323–332.
7. Israelachvili, J. N. (2011). Intermolecular and Surface Forces, 3rd ed. Academic Press.

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