TB5

Question 1

Define molecular mechanics

Answer 1

method by which molecular systems are modelled using classical mechanics, as there is no explicit representation of electrons as seen in quantum mechanics

Question 2

Define the energy surface

Answer 2

The multidimensional surface upon which you can see changes in the energy of a system

Question 3

Define force field

Answer 3

A set of bonded and non-bonded parameters that are used to describe molecules

Question 4

Give the equation for the potential energy of a molecule

Answer 4

U-total = U-bonded + U-non-bonded

Question 5

List the bonded terms in a force field

Answer 5

Bond lengths, bond angles, dihedrals (torsion)

Question 6

List the non-bonded terms in a force field

Answer 6

Electrostatics and Van der Waals

Question 7

Define a harmonic potential

Answer 7

A second-order differential equation used to describe the interaction between pairs of bonded atoms and the summation over all valence angles in a molecule

Question 8

Describe the Lennard Jones potential

Answer 8

Describes non-bonded, short range interactions such as VdW forces

Question 9

Describe the Coulomb potential

Answer 9

Describes electrostatic, long range interactions

Question 10

Define the Lorenz-Berthelot mixing rules

Answer 10

(Size of AB) = 1/2 (size of AA + size of BB)
ϵ_AB=√(ϵ_AA ϵ_BB )

Question 11

Define well depth parameter

Answer 11

Controls the ‘stickiness’ of the potential; larger well-depth means greater attraction between atoms

Question 12

Describe energy minimisation via the steepest descents

Answer 12

The mathematical function trying to be minimized is the force-field of every atom in the molecule. To do this, we take the first derivative of the function of the force-field, allowing us to go ‘down’ the slope.
i.e., imagine standing at the top of a hill and looking for the steepest slope that takes you down. At each step, the direction is taken as the negative gradient of the function (negative gradient will go down, positive will go up).
If we go too far, we may start going up again, so you also need to know how far to go. This is achieved using either line search or arbitrary steps (the point where the energy starts gong up, stop!). Or rather than taking arbitrary steps, you fit a quadratic for the location and solve (i.e., if the step forward results in the energy going up, you know the minima is around where you last were and so would fit a quadratic there).

Question 13

Describe conjugate gradients

Answer 13

an alternative method to steepest descents which is more efficient near to the minimum as direction of travel doesn’t zig-zag by using information from the previous step.

Question 14

Describe the many body problem

Answer 14

the movement of one atom will impact the movement of other molecules such that you cannot take the movements of each molecule in isolation. This leads to the many body problem that cannot be solved precisely analytically. Consequently, the solution is approximated numerically.

Question 15

Describe leapfrog algorithms

Answer 15

Integration is broken down into many times-steps. The system will be at some time, t. In the leapfrog method, for a given time, the velocities are calculated for half a step behind and half a step forward, while the positions are calculated for a full step forward in time. Thus, the positions and velocities keep leapfrogging over each other. NB: you will never have the velocities of where you are now, only the position.

Question 16

Define RMSD

Answer 16

measure of accuracy and the average distance between atoms

Question 17

Describe systematic sources of error

Answer 17

o Rounding in math of the algorithms
o Machine precision – the cpu (central processing unit) can only compute to a certain number of decimal points (another rounding error)
o Parameters that aren’t well described

Question 18

Describe statistical sources of error

Answer 18

These are errors dependent on simulation time and are often reported as standard deviations, estimated using block averaging.

Question 19

Describe block averaging

Answer 19

Take blocks of simulation time and estimate the error of the property (e.g., dihedral angle) for each block. This can be split up into either small blocks, giving strong correlations, or large blocks, giving weak correlations among blocks. However, small blocks will look similar to one another which means showing strong correlations that don’t exist.
- Large blocks (weak correlations among blocks) will give a better reflection of the property

Question 20

Define stratified systematic sampling

Answer 20

take single value from each block (used for structural properties)

Question 21

Define stratified random sampling

Answer 21

single value from each block at random (used for structural properties)

Question 22

Define course-graining

Answer 22

average for each block determined and then the average of those averages is taken (used for thermodynamic properties)

Question 23

Compare course-grained at united atom level to MARTINI level

Answer 23

UAL: non-polar, aliphatic hydrogens are combined with associated carbons into a single particle
ML: groups of 4 or 5 heavy atoms and associated hydrogens are combined together

Question 24

Define the ergodic principle

Answer 24

The time average of a property is the same as the ensemble average

Question 25

Describe the following ensembles: microcanonical, canonical, isothermal-isobaric

Answer 25

micro: fixed N, V, E canon: fixed N, V, T iso: fixed N, P, T

Question 26

Define potential of mean force

Answer 26

The free energy surface of a chosen coordinate

Question 27

Describe umbrella sampling

Answer 27

Umbrella sampling is used to improve sampling of a system where ergodicity is hindered by the form of the system’s energy landscape, caused by normal MD simulation samples being in system equilibrium. E.g., systems in which an energy barrier separates two regions of configuration space may suffer from poor sampling.

Question 28

Describe steered MD

Answer 28

SMDs apply forces to a protein in order to manipulate its structure by pulling it along desired degrees of freedom. These experiments can be used to reveal structural changes in a protein at the atomic level.

Question 29

Define the Jarzynski equality

Answer 29

states that the average work is equal to the change in free energy between two states

Question 30

Describe metadynamics

Answer 30

Metadynamics is used to estimate the free energy and other state functions of a system, where ergodicity is hindered by the form of the system’s energy landscape

Question 31

Describe thermodynamic cycles

Answer 31

Thermodynamic cycles can be used to compare known data (e.g., Gibbs free energy) for protein A with the unknown data of protein A*. This is achieved by ‘converting’ protein A to A*: the MD simulation is started and over a number of steps, * is introduced. At each step, the system is allowed to equilibrate, and the energy released is summed.

Question 32

Define normal mode analysis

Answer 32

form of MD; rather than atomistic/course-grained using force fields, it focuses on the basic structure modelled on an elastic network. Good at predicting dominant motions from a crystal structure.

Question 33

Describe molecular dynamics flexible fitting

Answer 33

used to fit static crystal structures to cryo-EM structures via morphing. This is MD driven, rather than normal modes analysis. It takes a solved crystal structure and a cryo-EM structure and fits the cryo-EM structure to the crystal structure.

Question 34

Describe native mass spectrometry

Answer 34

Partially de-solvate the protein/complex, meaning the native bonds continue to exist. As you increase the energy of the mass spectrometer, you can dissociate systems in real time. This is useful to dissect proteins by different components and is very useful for studying membrane proteins – you can pull off lipids one by one to find which are important to protein function, etc.

Question 35

Describe the relaxation phenomenon

Answer 35

Over time, the frequency decays as a result of M moving back into the z-plane to be parallel with B0 once again. This is called relaxation

Question 36

What is the decay rate of a 90 degree pulse?

Answer 36

1/T-2 (transverse)

Question 37

What is the decay rate of a 180 degree pulse?

Answer 37

1/T-1 (longitudinal)

Question 38

Describe spin echo

Answer 38

1. A 90° RF pulse puts two nuclei into the xy-plane 2. The two nuclei are in different local fields, experiencing different environments, and so they’re going to fan out over a time, τ. 3. 180° pulse swaps the two nuclei positions, but they’re still feeling the same field. This means that they have the same relative precession to one another and will come back together. 4. Record several experiments with increasing number of spin echoes (fixed τ) to map out the T2 decay. Spin echo cannot affect T1 because this relaxation rate is only focused on the z-plane, not the xy-plane.

Question 39

Describe spin inversion

Answer 39

Mz is inverted 180° at t=0, and is then allowed to recover along the external magnetic field axis (z-axis). We can’t detect along z, only in the xy-plane, so at each time point a 90° pulse is applied to move it back into the xy-plane and check on it. Like with T2 measurements, this is combined with a 1H, 15N HSQC experiment to measure 15N T1 for every residue in the protein.

Question 40

Define the squared order parameter

Answer 40

the magnitude of flexibility (1=no movement, 0=total freedom)

Question 41

Describe exchange processes in NMR

Answer 41

protein X can be in either state A or state B, each with its own resonance. If the barrier between the two states is very high, then k is very low (k << Δv). This means exchange between these two states is very slow and we can see two signals. The appearance of the spectrums depends on k and the separation Δv, such that 2 signals shows slow exchange and 1 signal shows fast exchange. Line broadening is observed when k is approximately equal to Δv.

Question 42

Describe CMPG experiments

Answer 42

Measure the exchange by recording a series of similar experiments with a fixed total time, but each time you increase the number of 180° pulses which refocuses the magnetization. CMPG is basically a competition experiment – it measures what value of 1/τ (rate of refocusing) is sufficient to refocus the exchange process with a rate of k.