Question

The addition and subtraction of charge to biological molecules such as proteins is critical to the conformational changes that drive essential biological processes. A prime example of this is found in the Sodium-Potassium Pump that maintains imbalances in the concentration of sodium and potassium ions across the cell membrane. A simple model of this pump is shown in the figure below. In the second panel of the figure we see a configuration of ions that generates an attractive electric force between the captured sodium ions (purple) and the phosphorylation site (blue). This causes the pump to change confirmation moving sodium ions to the outside of the cell and letting it collect the potassium ions that need to be transported into the cell. Assuming that the group of three sodium ions can be treated as a single +3e point charge, the phosphate ion as single -2e point charge, and that their separation is ~7 nm, calculate the magnitude of the attractive electric force generated in this configuration

Answer 1

Electric force is given by:

F = k*q1*q2/r^2

k = electrostatic constant = 9*10^9

q1 = Charge on three sodium ion = +3e

q2 = charge on phosphate ion = -2e

e = charge on single electron = 1.6*10^-19 C

r = distance between sodium ion and phosphate ion = 7 nm = 7*10^-9 m

Using these values:

|F| = k*|q1|*|q2|/r^2

|F| = 9*10^9*3*1.6*10^-19*2*1.6*10^-19/(7*10^-9)^2

|F| = 2.82*10^-11 N

Please Upvote.