Question

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.

Answer 1

We are asked to find the the magnitude and direction of the change in force

Number of positively charged residues in each S4 helice= 7

Number of sub units of S4 helices= 4:

Therefore total number of positively charged residues = 4*7 =28

Charge on each residue= 1.6*10-19 C, therefore charge on 28 residues(q)= 28*1.6*10-19 C

= 44.8*10-19 C

and as the corresponding change in the magnitude of the electric field (ΔE) is given by 4*106 N/C, the magnitude of the change in force is

F= q* ΔE = 44.8*10-19 C* 4*106 N/C = 179.2*10-13 N

As the membrane potential is slightly depolarized, the change in force is directed outward. The force pushes the positively charged S4 helices towards the extracellular leaflet.