18. Vesicles and Membrane Fluctuations

Question 1

What determines the curvature of bi-layers or membranes?

Answer 1

• Packing constraints
• Elasticity of the bi-layer

Question 2

What shape is a bi-layer in when it is in its lowest state of free energy?

Answer 2

It is a flat surface

Question 3

Describe the graph of how the free energy of a bi-layer changes with its curvature

Answer 3

a0 + ∆a = head groups pushed apart
a0 - ∆a = head groups pushed together

Question 4

Why does the free energy increase when the outside heads of a bilayer are pushed apart?

Answer 4

Because water is admitted into the bilayer which reaches the hydrophobic tail groups.

Question 5

Why does the free energy increase when the inside heads of a bilayer are pushed together?

Answer 5

Because there is a repulsive force between the head groups that is pushing them apart again.

Question 6

The change in free energy with curvature gives the bi-layer _________.

Answer 6

Elasticity

Question 7

Give the equation for the pressure experienced by a bi-layer due to bending

Answer 7

∆U/A = pressure
κ = bending modulus
k = spring constant
R = bilayer radius
lc = critical chain length
∆a = change in bi-layer length due to bending

Question 8

Give the equation for the pressure experienced by a bi-layer due to undulation

Answer 8

P = pressure
kB = Boltzmann’s constant
T = temperature
κ = bending modulus
D = bi-layer separation distance

Question 9

Give the equation for the total pressure experienced by a bi-layer

Answer 9

P = pressure
kB = Boltzmann’s constant
T = temperature
κ = bending modulus
D = bi-layer separation distance

Question 10

The pressure between both parts of a bi-layer is either always _________ or always _________.

Answer 10

Attractive
Repulsive

Question 11

Bi-layer pressure is usually ________.

Answer 11

Repulsive

Question 12

Give 2 ways that bi-layers stick together to produce cell membranes

Answer 12

1. The presence of other molecules in the cell wall to suppress thermal fluctuations.
2. Special transmembrane proteins to provide additional bonds.

Question 13

What causes undulations in a bi-layer membrane?

Answer 13

Thermal fluctuations

Question 14

What inhibits undulation in a bi-layer membrane?

Answer 14

When 2 membranes are brought a distance, D, apart. This inhibits the undulations as the number of available microstates decreases.

Question 15

What causes 2 undulating bi-layers to push one another apart?

Answer 15

The entropic repulsion force

Question 16

What determines whether 2 membranes will stay together or push one another apart?

Answer 16

The stiffness of the membrane- a more flexible membrane will be repulsive.

Question 17

What is the equipartition principle?

Answer 17

Every ‘mode’ of an undulating bilayer has 1/2kT of energy

Question 18

Describe the shape of the DLVO potential

Answer 18

Question 19

Why do membranes/bi-layers often curve into vesicles?

Answer 19

To prevent hydrophobic tails from being exposed to the liquid

Question 20

The elasticity/stiffness of a membrane is proportional to 1/R_ where R is the radius of curvature of the bend.

Answer 20

² (squared)