Chapter 6: Protein Folding Flashcards
When does a protein become functional?
When it has been folded into the correct 3D conformation.
Define Levinthal’s paradox
A simple calculation that demonstrates how amino acid chains bust fold in a predetermined manner rather than following a trial and error process.
Describe the assumptions of Levinthal’s paradox
- 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.
How long would an amino acid chain take to explore all conformations if the assumptions of Levinthal’s paradox were followed?
3^200 / 10^13 = 2.6 x 10^82 s = 8 x 10^74 years
How long does a polypeptide chain actually take to fold?
1µs to a few seconds
Why do proteins take such a short time to fold?
- 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
Give the equation for the expectation distance between two ends of a randomly coiled polymer chain
N = number of subunits
b = length of subunits (represented by vector, a)
r = vector connecting two ends
If the equation for the projection of each amino acid subunit in a random polymer chain on the x-axis
x = length along x-axis
b = subunit length
θ = angle a forms with the x-axis
What is the rms of the x-component of a randomly coiled polymer chain length?
rms(r) = root mean square
b = subunit length
θ = distribution of all possible angles
N = number of subunits
How is the orientation of each amino acid in a randomly coiled polypeptide chain found (aka the average orientation)?
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.
Derive the average of cos^2 θ in order to find the x-component of the from for a randomly coiled polypeptide chain
What is the rms value for the x-component of a randomly coiled polypeptide chain?
rms(r) = root mean square
b = subunit length
N = number of subunits
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)
Gaussian
What are the model stipulations for energy calculations of an amino acid chain?
- Modelled as being pulled apart along x-axis
- Constant intermolecular interactions (U = 0)
Give the equation for Helmholtz free energy of a polymer chain
F = Helmoltz free energy
U = potential energy
T = temperature
S = entropy
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
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
Force is the ________ ________ of Helmholtz free energy.
negative gradient
Give the equation for force on a polymer chain
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
Elastic force has a ______ displacement meaning that it can be compared to the equation for _______ law.
Linear
Hooke’s
Stretching the chain _______ the number of possible conformations because the elastic force is an example of an _______ force.
Reduces
Entropic
Give the equation for the probability that a molecular shape is generated by random fluctuations at a given internal energy
n = number of conformations with the same internal energy (degenerate states)
Z = partition function
U = potential energy of molecular interactions
What is the equation for the partition function (polypeptide conformations)?
Z = partition function
U = potential energy of molecular interactions
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
Approximately equals
Higher
Is U_i positive or negative for attractive interactions between molecules in a polypeptide chain?
Negative
What two things do the conformations depend on?
- Temperature variations
- Whether there is any potential energy to produce a ‘binding’ energy
At low temperatures, the _______ state has the favourable ‘binding’ energy, whereas, at high temperatures the _____ state has the favourable entropy so the chain unfolds.
Closed
Open
What are the key requirements to consider when determining the probability of different polypeptide chain conformations?
- 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.
What process initiates protein folding? (EXTRA: why?)
Hydrophobic effects
EXTRA: because the interactions between hydrophobic functional groups in the amino acids that draw them to the centre of the molecule.
The movement of hydrophobic functional groups is a ________ process so the movement of some amino acids impacts that of others.
Cooperative
What is the most stable conformation for a polypeptide chain?
The conformation with the lowest potential energy (this state is not always assumed).
What are the uses of determining how a protein can fold?
- Prediction of their 3D structure which in turn predicts their function.
- Finding diseases caused by the misfolding of proteins.
