Chapter 6: Protein Folding

Question 1

When does a protein become functional?

Answer 1

When it has been folded into the correct 3D conformation.

Question 2

Define Levinthal’s paradox

Answer 2

A simple calculation that demonstrates how amino acid chains bust fold in a predetermined manner rather than following a trial and error process.

Question 3

Describe the assumptions of Levinthal’s paradox

Answer 3

• For each amino acid there are only two degrees of freedom, found in the φ and ψ angles in the peptide bond.
• There are only three stable values that either of these angles can take on (3^2N possible conformations for a protein if N is the number of amino acids in the chain).
• That 10^13 conformations can be explored per second.
• That an amino acid chain has 100 amino acids.

Question 4

How long would an amino acid chain take to explore all conformations if the assumptions of Levinthal’s paradox were followed?

Answer 4

3^200 / 10^13 = 2.6 x 10^82 s = 8 x 10^74 years

Question 5

How long does a polypeptide chain actually take to fold?

Answer 5

1µs to a few seconds

Question 6

Why do proteins take such a short time to fold?

Answer 6

• The method involves cooperativity
• There is a global phase transition into the folded state
• Many processes act simultaneously
• The open amino acid chains fold into the conformation of minimal energy

Question 7

Give the equation for the expectation distance between two ends of a randomly coiled polymer chain

Answer 7

N = number of subunits
b = length of subunits (represented by vector, a)
r = vector connecting two ends

Question 8

If the equation for the projection of each amino acid subunit in a random polymer chain on the x-axis

Answer 8

x = length along x-axis
b = subunit length
θ = angle a forms with the x-axis

Question 9

What is the rms of the x-component of a randomly coiled polymer chain length?

Answer 9

rms(r) = root mean square
b = subunit length
θ = distribution of all possible angles
N = number of subunits

Question 10

How is the orientation of each amino acid in a randomly coiled polypeptide chain found (aka the average orientation)?

Answer 10

It is assumed that ‘a’ orients uniformly so has an equal probability of being in any direction about a sphere. A strip of this sphere is then taken and the average of cos^2 θ is obtained via an integration and probability calculations.

Question 11

Derive the average of cos^2 θ in order to find the x-component of the from for a randomly coiled polypeptide chain

Answer 11

Question 12

What is the rms value for the x-component of a randomly coiled polypeptide chain?

Answer 12

rms(r) = root mean square
b = subunit length
N = number of subunits

Question 13

The frequency of chains with a length, N, that begin at the origin of the x-axis and end at the position, r, is given following a _______ distribution where the central value is the rms. (EXTRA: give the formula for this distribution)

Answer 13

Gaussian

Question 14

What are the model stipulations for energy calculations of an amino acid chain?

Answer 14

• Modelled as being pulled apart along x-axis
• Constant intermolecular interactions (U = 0)

Question 15

Give the equation for Helmholtz free energy of a polymer chain

Answer 15

F = Helmoltz free energy
U = potential energy
T = temperature
S = entropy

Question 16

Give the equation for Helmholtz free energy in terms of entropy, S, when S = k_B ln(W) and W represents the number of micro states

Answer 16

F = Helmholtz free energy
k_B = Boltzmann’s constant
T = temperature
S = entropy
P(r, N) = probability of each microstate
N = number of subunits
r = separation distance between ends of the chain
b = length of each subunit

Question 17

Force is the ________ ________ of Helmholtz free energy.

Answer 17

negative gradient

Question 18

Give the equation for force on a polymer chain

Answer 18

F_elastic = force
F = Helmholtz free energy
x = displacement
N = number of subunits
r = separation distance between ends of the chain
b = length of each subunit

Question 19

Elastic force has a ______ displacement meaning that it can be compared to the equation for _______ law.

Answer 19

Linear
Hooke’s

Question 20

Stretching the chain _______ the number of possible conformations because the elastic force is an example of an _______ force.

Answer 20

Reduces
Entropic

Question 21

Give the equation for the probability that a molecular shape is generated by random fluctuations at a given internal energy

Answer 21

n = number of conformations with the same internal energy (degenerate states)
Z = partition function
U = potential energy of molecular interactions

Question 22

What is the equation for the partition function (polypeptide conformations)?

Answer 22

Z = partition function
U = potential energy of molecular interactions

Question 23

It is common to have molecular conformations where the interaction energy, U_i, _______ _____ the thermal energy, k_B x T. It is less common to have them with _____ energy

Answer 23

Approximately equals
Higher

Question 24

Is U_i positive or negative for attractive interactions between molecules in a polypeptide chain?

Answer 24

Negative

Question 25

What two things do the conformations depend on?

Answer 25

• Temperature variations
• Whether there is any potential energy to produce a ‘binding’ energy

Question 26

At low temperatures, the _______ state has the favourable ‘binding’ energy, whereas, at high temperatures the _____ state has the favourable entropy so the chain unfolds.

Answer 26

Closed
Open

Question 27

What are the key requirements to consider when determining the probability of different polypeptide chain conformations?

Answer 27

• Sums of changes in internal energy from bond stretching.
• Changes of bond angles.
• Changes in dihedral/ tetrahedral angles.
• Coulomb potential between charges.
• Van der Waals potential describing induced dipoles and other interactions between neutral atoms.

Question 28

What process initiates protein folding? (EXTRA: why?)

Answer 28

Hydrophobic effects

EXTRA: because the interactions between hydrophobic functional groups in the amino acids that draw them to the centre of the molecule.

Question 29

The movement of hydrophobic functional groups is a ________ process so the movement of some amino acids impacts that of others.

Answer 29

Cooperative

Question 30

What is the most stable conformation for a polypeptide chain?

Answer 30

The conformation with the lowest potential energy (this state is not always assumed).

Question 31

What are the uses of determining how a protein can fold?

Answer 31

• Prediction of their 3D structure which in turn predicts their function.
• Finding diseases caused by the misfolding of proteins.