Lecture 2 Flashcards
-Know what a collective variable (or order parameter) is -Be familiar with the Forward Flux sampling method
1
Q
- What is an order parameter?
A
- An order parameter or collective variable, allows the different configurations/states of a system to be distinguished
- Allows system to be driven from A to B (or v.v) through application of enhanced sampling method of choice.
2
Q
Give an example of an order parameter to characterise the adsorption of a potassium atom on to a silver surface.
A
- State A: atom not interacting with surface
- State B: K fully adsorbed on to surface
- OP = min | |rAr – rAui,Surf |
3
Q
- What is the problem with the surface adsorption OP?
A
- Only in terms of state A (adsorbed) and state B (free).
- To drive a free energy pathway, OP must recognise intermediate states as well
4
Q
- What order parameter could be used to describe a protein folding event?
A
- Radius of gyration of a protein describes how much an average chain deviate from geometric centre
- Many atoms stay at this mean distance and calculation of them is costly
- May ned to remap values to positive numbers that can be made in to mathematical objects more easily

5
Q
- What may be a more suitable OP for a protein fold? What is the result of this better choice?
A
- Instead coarse grain the protein atoms in to a sub set of chains to save computational time
- Average distance between two chains could be used to give similar indication of fold
- FES remapped in to simpler CG representation (6D –> 2D)

6
Q
- What are the requirements of an OP? what is the difficulty in this requirement?
A
- Must be differentiable with respect to atomic position
- This is simple in the cases illustrated but can be very challenging for complex systems that is simple enough to compute but accurately represents dynamics.
- Can also be difficult when no prior knowledge of configurational space is known.
7
Q
- How many OP’s or collective variables would we need to simulate the nucleation of crystals from molecules in solution.
A
- Need two collective variables to describe 2 step process.
- One describing density difference of un/aggregated particles.
- One describing order of clumped particles.
8
Q
- Choice of order parameter determines the … and … of enhanced sampling results
- For this reason, it may be necessary to use …
A
- Choice of order parameter determines the nature and reliability of enhanced sampling results
- For this reason, it may be necessary to use multiple
9
Q
- What is affected by our OP choice in free energy-based methods.
A
- Our choice of OP determines the resulting free energy surface (FES)
- This multidimensional hyper surface is re-mapped on to a simple coarse-grained FES (1D/2D)
10
Q
- What is problem with this new FES?
A
- Can often be an oversimplification as only representative of the chosen order parameter.
- The true FES, which represents all configurational space does not equal the FES we are sampling, constrained to our OP of choice
11
Q
- (IMP) How does statistical mechanics relate to our FES assumption?
A
- Stat mech confirms true FES ≠ our FES according to this OP, as uses configurational partition function, Z which does not contain info about kinetics/ dynamics of the system and depends only on particles position in the system only.

12
Q
(PPQ) How can we use commitor analysis to probe the accuracy of our OP?
A
- Select a value, OP* of OP corresponding to a putative transition state (maximum)
- Sample an ensemble of configurations characterized by OP*
- Run several MD simulations for each, varying velocity (making them statistically independent)
- Find probability of OP* configuration making to it to B
- Plot histogram of these probabilities.

13
Q
- (PPQ) Which of these histograms indicates a more accurate OP?

A
- (a) indicates no matter where you start you always end up with same probability of ending up in A or B, NO indication this is a TS
- (b) indicates probability of ending up in B increasing as you move further along coordinate, 0.5 at middle. Representative of the putative TS
- Therefore, b is better.
14
Q
- Why can the probability of going from state A to B not always be used?
A
- In ice nucleation the rate is extremely low
- Describing the path in terms of an order parameter would be completely unrealistic time wise
15
Q
(IMP)
- … … … is a path based enhanced sampling method where instead of computing an overall (v.low) … , path is divided into a series of …
- Each … has an increasing value of our …, … each corresponding to a possible … with said value of …
- As λ increases likelihood of going from … to … , rather than back to A, …
A
(IMP)
- Forward flux sampling is a path based enhanced sampling method where instead of computing an overall (v.low) probability, path is divided into a series of interfaces
- Each interface has an increasing value of our OP, λ, each corresponding to a possible configuration with said value of λ
- As λ increases likelihood of going from A to B, rather than back to A, increases

16
Q
- How is the probability of the process overall related to interfaces that make it up?
A
- Sum or product?? of computable windows

17
Q
(IMP) How are trajectories generating in FFS?
A
- Begin by looking at fluctuations of a long unbiased MD run
- At each interface λi large # of trial molecular dynamics runs done
- The few that reach the next interface λi+1 are used as a starting point to reach the following interface.

18
Q
- What is the problem with this trajectory generation? How can it be avoided?
A
- It is technically a bias result as each final trajectory is a function of its starting configuration
- To try and avoid this we must make sure initial simulation is run for the maximum amount of time, to ensure probabilities are correct.
19
Q
- Why is our overall nucleation mechanism not biast?
A
- Information is not biast from A to B as we are not changing system parameters with forces as you do in conventional MD, resulting in a fairly true mechanism.
- Other free E based methods will often add forces which will modify the Hamiltonian giving the correct thermodynamic properties of the system, but not the kinetics or mechanism.