Voltage-gated cation channels in the plasma membrane of a neuron open when the membrane potential passes a threshold value that is about 20 mV above the resting potential. This corresponds to a change of about 4 × 10⁶ newtons per coulomb in the magnitude of the electric field across the membrane compared to the resting state. The tetrameric channels have a voltage-sensing helix S4 in each of their four subunits. Most S4 helices contain seven residues with positively charged side chains. The charge carried by each such residue is about 1.6 × 10-¹⁹ coulombs. By reaching threshold depolarization, what are the magnitude and the direction of the collective force that the four S4 helices in the channel experience as a result of the change in the electric field? The force that particles of charge q in an electric field E experience is calculated as F = q.E.

Question

Quizplus · Accepted Answer

This is an oversimplified picture of the yet-to-be-elucidated gating process in these channels. There are 4 × 7 (= 28) positively charged residues in the four S4 helices combined, whose total charge would be 28 × 1.6 × 10-¹⁹ coulombs. As a result of the change in the electric field (by 4 × 10⁶ newtons per coulomb), the change in the force would be equal to:
(28 × 1.6 × 10-¹⁹ C) × (4 × 10⁶ N/C) = 1.8 × 10-¹¹ N = 18 pN
Since the membrane potential has become slightly depolarized, the change in the force is directed outward, tending to push the positively charged S4 helices more toward the extracellular leaflet. Note that the membrane is still polarized (negative inside) at the threshold potential and the electric field has not reversed yet.

Voltage-Gated Cation Channels in the Plasma Membrane of a Neuron