Topic 4 Flashcards
-Give examples of reaction coordinates commonly used to study free energy changes in biophysical systems -Explain why the use of biased potential could offer a strategy for dealing with the timescale problem in MD. -Give a basic overview of the umbrella sampling and metadynamics methods. -Describe the pros and cons of umbrella sampling with each other and with other methods covered in this course -Be aware of how these techniques may be used to study biophysical systems.
1
Q
What is biased sampling?
A
- Where a biasing potential is used that can be used to force the system to explore unfavourable configurations, leading to enhanced sampling of phase space
- This means we are more likely to overcome kinetic barriers that trap us in local minima of our PES for our entire simulation time
2
Q
What is a key condition of biased sampling?
A
Need to know something about pathways as a starting point as this is what we are defining
3
Q
What are reaction coordinates and briefly give two examples? (also known as collective variables and order parameters)
A
- Characterise a process in terms of a small set of properties of a system that are a function of atomic coordinates.
- Also known as collective variables and order parameters
- Distance/separation, r
- Dihedral angle
4
Q
- Give an example of how distance can be used as a reaction coordinate
A
- Potential mean force (PMF), which is the free energy along a chosen reaction coordinate, can be simulated using the distance between an Na+-Cl- ion pair in electrolyte solution.
5
Q
- Give an example of how bond and dihedral angle can be used as a reaction coordinate. What is the output of using two coordinates in this way
A
- Investigate free energy change of valine dipeptide as it is rotated.
- One can even make 2D plots, investigating multiple rotation sites to see how energy changes couple to one another.
6
Q
- Give an example of how radius of gyration (Rgyr) can be used as a reaction coordinate. What must be assumed?
A
- Rgyr gives an indication of the expansion/contraction of a globular structure through the average of the distance each atom is from the centre of mass. More expanded = higher Rgyr
- The transformation of a β hairpin peptide to unfolded random coil state’s free energy landscape can be investigated
- Choosing appropriate set of reaction coordinates is difficult so must guess generally
7
Q
Choosing appropriate set of reaction coordinates is difficult so must … generally
A
Choosing appropriate set of reaction coordinates is difficult so must guess generally
8
Q
- How could the example given in investigating the hairpin peptide free energy change through Rgyr be improved?
A
- Could introduce a second reaction coordinate, number of hydrogen bonds, which introduces cut-off indicators for hydrogen bond probability
9
Q
Give an advantages and disadvantages of using multiple reaction coordinates
A
Pros
- A combination of variables allows important structures across high energy barriers to be sampled, giving a larger indication of the greater free energy landscape.
- If our single reaction coordinate output poorly maps experimental results, a second coordinate can be introduced to form a 2D plot that may give a different minimum energy pathway to before.
Cons
- However, in combination, outputs of these reaction coordinates can lead to many different structures which must all be considered
- Certain structures may even be resritcted via specific choice of a given set of coordinates
- Large computational cost
10
Q
- Give an example of how root mean squared distance (RMSD) can be used as a reaction coordinate
- WHat must one be careful of?
A
- RMSD is the difference between atomic positions at time t and the starting positions of the simulation, t0.
- Can be averaged over all atoms of interest, e.g. carbons in a protein backbone chain
- Similarly, with Rgyr, must be careful with choice of reaction coordinate to pair with as may not be unique function of rN.
11
Q
- Free energy is a … function so the free energy change is independent of the …. This means we can create unrealistic … if …/… are not of importance to us.
A
- Free energy is a state function, so the free energy change is independent of the path. This means we can create unrealistic pathways if mechanism/kinetics are not of importance to us.
12
Q
- Outline the basic principles of umbrella sampling
A
- System is restrained (through tethering to a spring) to a small region along the reaction coordinate ξ using a biasing potential.
- If the system deviates too far from this small region, an energy penalty restores the region.
- This is repeated at different target values of ξ. The system is forced to explore small unfavourable regions along a certain channel until full reaction coordinate is explored.
- All simulations are stitched together to produce an unweighted underlying free energy profile.
13
Q
- Biasing potential V is usually a …
- Total forcefield potential then = … + …
A
- Biasing potential V is usually a harmonic potential
- Total forcefield potential then = U(r) + V(f1(r), s)
14
Q
What factors control the overlap sampling between adjacent simulations and how fine grained our sampling of our free energy profile is in umbrella sampling?
A
- Force constant
- Too low: biasing insufficient to explore high energy regions (wide harmonic)
- Too high: insufficient overlap between windows (narrow (harmonic)
- Frequency of window spacing
- Choosing these values is largely trial and error
15
Q
- How is the free energy of our reaction (FES -F[ξ]) coordinate related weighted ensemble distribution?
A
- Each biased simulation used to plot a histogram showing weighted ensemble distribution, which is an estimate of F(ξ) at that moment using given reaction coordinates.
- We force the system to span the full range of ξ, then stitching simulations together to find full FES.
18
Q
There is poor overlap between these histograms, indicating not all values of r are sampled well. How should this simulation protocol be modified to give better overall sampling?
A
Do additional simulations, increasing sampling in-between values of r
19
Q
Still poor sampling in central region. How can this be improved further?
A
- Inserted peaks move to the right of left of poorly sampled space, indicating a high energy region of tethered phase space, hence why not exploring it.
- Must to additional simulations at that space, with a higher K threshold.
