Topic 5 Flashcards
Learning objectives -Outline the Monte Carlo methods for sampling configurational states of a system of particles. -Briefly describe the REMD method -Explain the advantages and disadvantages of REMD compared to regular MD and other advanced sampling methods. -Discuss the practical aspects of setting up and running a REMD calculation.
1
Q
Describe the Monte Carlo (MC) method and how does it contrast to MD method?
A
- MC simulations are an alternative method to sampling accessible microstates of the ensemble, generally used for smaller systems. Uses orthogonal techniques
- MD used Netwon EOM to predict positions of atoms at a future time, taking a time average to find property of interest
- MC generates configurations through random numbers that are unconnected in a timescale, using an ensemble average to investigate a property
2
Q
What is the general principle in Metropolis MC?
A
- The probability of a transition from configuration 1 to 2 is a function of the change in ΔU between those states.
- The probability of a configuration can be written in terms of the Boltzmann distribution where the ideal partition function is a normalizing factor
3
Q
What makes QNVT ideal in metropolis MC?
A
The ideal partition function old depends on positions, r and not momenta, which is an excess
4
Q
How is MC implemented?
A
- Move a random particle in a predefined way (e.g along z-axis), with an acceptable dr
- Calculate U of new configuration. If lower than original, new configuration is accepted and replaces old.
- A trajectory-esque profile forms as we move to lower energy configurations.
5
Q
What if the energy of the new configuration is greater than or equal to (≥) original configuration?
A
- Boltzmann probability is compared to a random number between 0 and 1
- If #rand < p(new), confuguration accepted, allowing an increase in energy
- If #rand > p(new), new configuration rejected and have another copy of original microstate set
6
Q
How does the size of ΔU affect the acceptance ratio?
A
- Unew > Uold : Boltzmann factor of energy difference closer to 1. More likely to be greater than random # from 0 -> 1. High probability uphill likely favourable) move accepted and added to growing ensemble of microstates
- Unew >> Uold (e.g a steric clash): less random #’s likely to be lower than Boltzmann factor of ΔU. Low probability large uphill move accepted.
- Low energy states are general preferred in this algorithm
7
Q
What are some advantages of MC? Give examples and comparisons to MD
A
- MC does not need to follow realistic pathways, so can explore conformations more rapidly. E.g. a protein folding event in MD would have to physically fold realistically – slow process. MC could randomly rotate an important dihedral to quickly generate states on interest
- MC doesn’t require calculation of force, whereas in MD, the differentiation of the potential (=F), using Verlet, can be very costly. In MC this isn’t required, allowing for more unphysical models to be used.
8
Q
What is a disadvantage of MC?
A
- Sampling efficiency depends strongly on move set choice. Poor choice may limit transfer to other unknown configurations, preventing access to all regions of phase space (poor sampling).
- For example, the choice of certain dihedral to sample be our change to sample around, but it may in fact prevent certain configurations from being explored due to unknown factors.
9
Q
What are some examples of moves we could use in our MC steps?
A
- Random displacements
- Dihedral angle displacements
- Rigid body translations and rotations of sets of atoms (e.g binding configuration studies)
- Particle insertion/deletion (constant chemical potential)
10
Q
What is constant chemical potential used for?
A
- Uses the grand canonical ensemble (µPT) to investigate change in free energy as a function of properties like density
11
Q
What is an example of an MD-MC combined simulation? Why must they be used toghether? How? What is the advantage or combining both methods?
A
- A mixed lipid-membrane of chains differing by 4C’s in their tail.
- MD would be too slow to see lipid diffusion
- MC would converge too slowly with a system this complex
- Instead a trail MC move follows each MD step, removing/adding 4C atoms, evaluating E of exchange to see if favourable
- Sampling more efficient as removed dependency on starting configuration, which can trap system in very low energy configurations surrounded by high.
12
Q
Why is it difficult to enhance sampling with a biasing potential?
A
- The timescale problem in MD makes in difficult to overcome kinetic barriers in our simulation time.
- To enhance the sampling of this phase space we could use a biasing potential to explore unfavourable configuration but requires knowledge of important factor in pathways.
13
Q
What is Replica Exchange Molecular dynamics (REMD)?
A
- REMD is an alternative method of overcoming (or removing) kinetic barriers, allowing more rapid sampling of phase space.
- Can either change the potential via alteration of the forcefield to change the curve we are sampling (H-REMD)
- Or change the temperature we sample at (T-REMD).
14
Q
What is the problem with simply changing the temperature we sample at?
A
- The conditions in which we have chosen to investigate are now different, which can complicate the system of interest, if an event is temperature dependent (e.g a phase change)
15
Q
- How can we change the temperature more suitably in T-REMD?
A
- Use Temperature Replica Exchange Molecular Dynamics
- Run an MD simulation of different replicas of the system at different temperatures in parallel (parallel tempering = replicas are generated through MC instead)
- Our temperature of interest is the lowest.
- Exchange configurations between replicas using MC (in both methods)
- Continue simulation
- Repeat step 2 until converged.
16
Q
What would the probability distribution of simulation done at varying temperatures look like?
A
- Regions of higher potential energy will be sampled much less at lower temperatures leading to lower probability of finding a particle at those distances. This means probability distribution will be concentrated to a more limited region of phase space, as the simulation is stuck in that low energy minima.
18
Q
How would a T-REMD probability distribution compare to that of one where the overall simulation temperature was simply adjusted completely?
A
- Probability of finding particle at a given position fairly equal at all temperatures, as simulations have been able to exchange configurations freely as they progress, allowing better sampling of phase space, and exploration across kinetic barriers. (swap of configurations indicated by jump in graph)
26
Q
What is the process of H-REMD? Give a biological example of where this may be useful
A
- Temperature across simulations is constant
- Instead a soft-core potential is used to across replicas, where Lennard Jones potential gradually softened meaning that atoms can sit on top of one another while still remaining in certain conformations
- Useful in ligand binding, where certain bound conformations can be locked in deep minima.
- H-REMD allows ligand to rotate in pocket and explore different orientations while still being bound.
- These can then be swapped in to a correct LJP, giving an indicator to the transitions in between them
