TB5 Flashcards
Define molecular mechanics
method by which molecular systems are modelled using classical mechanics, as there is no explicit representation of electrons as seen in quantum mechanics
Define the energy surface
The multidimensional surface upon which you can see changes in the energy of a system
Define force field
A set of bonded and non-bonded parameters that are used to describe molecules
Give the equation for the potential energy of a molecule
U-total = U-bonded + U-non-bonded
List the bonded terms in a force field
Bond lengths, bond angles, dihedrals (torsion)
List the non-bonded terms in a force field
Electrostatics and Van der Waals
Define a harmonic potential
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
Describe the Lennard Jones potential
Describes non-bonded, short range interactions such as VdW forces
Describe the Coulomb potential
Describes electrostatic, long range interactions
Define the Lorenz-Berthelot mixing rules
(Size of AB) = 1/2 (size of AA + size of BB)
ϵ_AB=√(ϵ_AA ϵ_BB )
Define well depth parameter
Controls the ‘stickiness’ of the potential; larger well-depth means greater attraction between atoms
Describe energy minimisation via the steepest descents
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).
Describe conjugate gradients
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.
Describe the many body problem
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.
Describe leapfrog algorithms
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.
Define RMSD
measure of accuracy and the average distance between atoms
Describe systematic sources of error
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
Describe statistical sources of error
These are errors dependent on simulation time and are often reported as standard deviations, estimated using block averaging.
Describe block averaging
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
Define stratified systematic sampling
take single value from each block (used for structural properties)
Define stratified random sampling
single value from each block at random (used for structural properties)
Define course-graining
average for each block determined and then the average of those averages is taken (used for thermodynamic properties)
Compare course-grained at united atom level to MARTINI level
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
Define the ergodic principle
The time average of a property is the same as the ensemble average
Describe the following ensembles: microcanonical, canonical, isothermal-isobaric
micro: fixed N, V, E
canon: fixed N, V, T
iso: fixed N, P, T
Define potential of mean force
The free energy surface of a chosen coordinate
Describe umbrella sampling
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.
Describe steered MD
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.
Define the Jarzynski equality
states that the average work is equal to the change in free energy between two states
Describe metadynamics
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
Describe thermodynamic cycles
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.
Define normal mode analysis
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.
Describe molecular dynamics flexible fitting
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.
Describe native mass spectrometry
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.
Describe the relaxation phenomenon
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
What is the decay rate of a 90 degree pulse?
1/T-2 (transverse)
What is the decay rate of a 180 degree pulse?
1/T-1 (longitudinal)
Describe spin echo
- A 90° RF pulse puts two nuclei into the xy-plane
- The two nuclei are in different local fields, experiencing different environments, and so they’re going to fan out over a time, τ.
- 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.
- 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.
Describe spin inversion
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.
Define the squared order parameter
the magnitude of flexibility (1=no movement, 0=total freedom)
Describe exchange processes in NMR
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 «_space;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.
Describe CMPG experiments
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.
