Chapter 8: Brownian Motors

Question 1

Give 2 examples of the functions of molecular motors

Answer 1

• Brownian ratchets: using energy in the form of ATP to change the molecular conformation of a ligand to move it along a template.
• Movement along a template without changing molecular conformation; they do not consume energy as obviously.

Question 2

Define ligand

Answer 2

A protein that can bind to another molecular structure.

Question 3

Describe how a Brownian ratchet can be modelled using a template with a periodic, asymmetric function to describe the binding energy in the x-direction

Answer 3

A ligand molecule, L, moves along a molecular template, P, by attaching to a series of successive binding sites. The ligand starts at minimum binding free energy before time, τ = 0, then can move in either the positive or negative direction from τ = 0 due to energy fluctuations. The ligand will either move to the next positive or negative maximum and rebind or not reach it and return to the original site. Overall, the ligand will move in the direction with the shortest distance between the minimum and maximum as it is more likely to reach the maximum before reattaching.

Question 4

What is the normal distribution function for the mathematical model of a Brownian ratchet?

Answer 4

p( ) = probability function
x = displacement
µ = mean
σ = standard deviation
D = diffusion constant

Question 5

Describe the graph of the normal distribution function for the mathematical model of a Brownian ratchet

Answer 5

Question 6

Give the equation for the net velocity of a ligand to the right in a model for a Brownian ratchet, assuming that the rms diffusion distance is not large

Answer 6

a = distance (to the right) to the next maxima
b = distance (to the left) to the next maxima
τ_off = time detached
τ_on = time attached
p_right = probability ligand moves right
p_left = probability ligand moves left