Question

The average thermal energy of a particle is ~ k_BT where k_B is Boltzmann’s constant and T is the temperature in degrees Kelvin. At room temperature, k_BT = 25 meV = 4.1 x 10-21 J = 4.1 pN – nm =0.6 kcal/mole (eV = electron volts; J = Joules, N = Newtons; kcal = kilocalories).

a. A typical molecular motor uses 100 to 1000 ATP molecules per second. Calculate how much energy is dissipated in the motor (in Watts, or J/s). Call this power quantity M.

b. Nuclear vibrations occur on the time scale of 10^-13 sec. Compute the scale of power input to a molecular motor from random collisions with surrounding water and call it R, assuming that the collisions transfer about k_BT of energy each. Estimate the ratio R/M.

c. How does your estimate differ if you assume that water molecules require a diffusion time given by Δx²/D to transfer k_BT of energy to the motor, where Δx is the average distance between water molecules in solution?

Answer 1