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.
A. 18 pN, toward the cell interior
B. 18 pN, toward the cell exterior
C. 90 pN, toward the cell interior
D. 90 pN, toward the cell exterior
E. 45 pN, toward the cell interior

Answer 1

Each of the four S4 helices in a voltage-gated cation channel experiences a collective force due to the electric field changes during depolarization. The force is approximately 45 picoNewtons (pN) in the direction toward the cell exterior when the voltage threshold is reached.

Step-by-step explanation:

The question involves calculating the collective force experienced by the S4 helices in voltage-gated cation channels when the neuron reaches threshold depolarization. Each S4 helix has seven positively charged residues, and the charge per residue is 1.6 × 10-19 coulombs. Given that there are seven residues per helix and four helices, we calculate the total charge (q) as 7 × 4 × 1.6 × 10-19 coulombs. The change in electric field (E) provided is about 4 × 106 N/C. By using the formula F = q × E, we can find the magnitude of the force.

Plugging in the numbers: F = (7 × 4 × 1.6 × 10-19) × (4 × 106) N/C, which equals approximately 1.792 × 10-12 N, or 1.792 pN (picoNewtons) per charged residue. Since there are 28 such residues in total (7 residues × 4 helices), we multiply 1.792 pN by 28, giving a collective force of 50.176 pN. The channels will experience this force in the direction of the electric field, which we can infer to be toward the cell exterior when the membrane depolarizes.

Given the choices provided and rounding to the closest option, the correct answer is 45 pN, toward the cell exterior.