Conformational Sampling
Abbreviations
Reviews
Applications
Methods
Systematic search methods
Tag line: Try all combinations of dihedral angles
Normal MD/MC
Tag line: Maxwell daemons on strike!
PES modifications
Tag line: Tweak the PES to accelerate barrier crossing
- General remarks:
- Beware of Hamiltonian lagging: http://dx.doi.org/10.1063/1.457251
- Plain umbrella sampling
- http://dx.doi.org/10.1016/0021-9991(77)90121-8
- see http://molsim.chem.uva.nl/frenkel_smit/
- choice of coordinates is important
- free energy profile
- Metadynamics (based on umbrella sampling)
- http://people.sissa.it/~laio/metadynamics.htm
- http://www.pnas.org/content/99/20/12562.full.pdf+html
- choice of coordinates is important
- free energy profile
- Weighted histogram method (based on umbrella sampling)
- http://dx.doi.org/10.1002/jcc.540130812
- comparable to metadynamics but more robust and less efficient
- choice of coordinates is important
- free energy profile
- Local elevation or Conformational flooding (based on umbrella sampling)
- Metadynamics or Weighted Histogram Method with PCA modes as coordinates (based on umbrella sampling)
- Computationally intensive
- PCA (linear modes) must make sense, not applicable if only dihedrals play a role
- http://www.youtube.com/watch?v=Ur7qo6ILK04
- Mainly applied to proteins
- Computationally intense: PCA must be performed first
- Original paper (no doi found): J. Biom. Str. Dyn. 13(4):615–626, 1996.
- Application: http://dx.doi.org/10.1002/(SICI)1097-0134(199611)26:33.0.CO;2-D
- Puddle skimming and jumping (MC) (based on umbrella sampling)
- http://dx.doi.org/10.1016/S0301-0104(02)00837-6
- http://dx.doi.org/10.1063/1.1469605
- Works with energy cutoffs: Potential energies below Eb are altered and set equal to Eb
- In case of MD: The transition between the original potential energy and the plateau must be smooth.
- Hyperdynamics
- http://dx.doi.org/10.1063/1.473503
- http://dx.doi.org/10.1103/PhysRevLett.78.3908
- Fixed bias potential that does not require prior knowledge
- Accelerates (highly activated) reactions, original rates can be recovered
- Time scale is no longer linear
- Potential scaling
- Example in combination with Replica Exchange to get correct partition functions
- http://dx.doi.org/10.1016/j.cplett.2008.02.055
- Used to improve the sampling of ions in water around protein
- Similar, but for free energy calculations: http://dx.doi.org/10.1063/1.466707
Reduced degrees of freedom
Tag line: Shrink the haystack
- Torsional angle MD
- http://dx.doi.org/10.1002/jcc.20293
- non-trivial implementation
- Coarse grained MD in general
- The setup of a good coarse-grained potential requires a long MD/MC simulation on a small
- representative system.
- Enhanced conformational sampling (MC/MD)
- http://dx.doi.org/10.1006/jmbi.1999.3440
- http://dx.doi.org/10.1529/biophysj.104.041541
- http://dx.doi.org/10.1016/S0006-3495(03)70017-4
- http://dx.doi.org/10.1006/10.1002/jcc.20622
- Small fragments or groups are sampled individually. The free energy surface of the total system is the sum of the fragment contributions.
- Is like a one-time coarse-grained potential
- SHAKE
- Distance constraints in molecular dynamics simulations.
- MILC SHAKE, RATTLE, etc are improved algorithms for solving the eqs of motion.
- Reduce the number of solvent molecules
- Implicit solvent models
- In case of spherical solutes: use a periodic system that is not cubic, but closer to a spherical shape
Altered kinetics
Tag line: Leave the PES untouched, but change the kinetics of the conformational barriers.
- Digitally filtered MD
- http://dx.doi.org/10.1063/1.480832
- Based on averaging forces of last n time steps. (One can also take any other linear combination)
- Same method with a different name: http://dx.doi.org/10.1021/jp9817372
- Mass weighted MD
- http://dx.doi.org/10.1016/S0006-3495(91)82090-2
- Elegant trick and simple to apply.
- Configurational partition functions remain intact.
- Increase mass of hydrogens: also larger time step
- High Temperature MD
- refs?
- Seems straightforward but there is a hidden pitfall. Free energy minima of large systems (e.g. proteins) are very sensitive to temperature. (They have a large entropic penalty at high temperatures.)
- Different thermostats for slow and fast modes: http://dx.doi.org/10.1016/S0006-3495(03)75090-5
- Simulated Annealing
- http://dx.doi.org/10.1126/science.220.4598.671
- Problems
- Not clear how to tune parameters (initial temperature and cooling rate)
- When parameters are wrong, one has to start from zero.
- In combination with Replica Exchange MD: http://dx.doi.org/10.1016/j.jsb.2009.02.015
- Walking-J, complex temperature variations, http://dx.doi.org/10.1063/1.458863
- Activation-relaxation technique for internal coordinate space trajectories (ARTIST)
Clever MC/MD
Tag line: Original PES, different way of exploration
- Parallel tempering
- Replica exchange MD
- http://dx.doi.org/10.1016/S0009-2614(99)01123-9
- http://dx.doi.org/10.1021/ct050250b
- MD counterpart of parallel tempering
- Correct ensemble
- Improved barrier crossing
- Computationally intensive
- Often used in combination with other methods
- Any parameter can be varied over the replica's, not only temperature
- Multidimensional: http://dx.doi.org/10.1063/1.1308516
- SWARM-MD: coupled replicas
- http://dx.doi.org10.1021/jp9806258
- all replica's feel are attracted to the average.
- Genetic algorithms
- Mixed with other techniques: http://dx.doi.org/10.1007/s00500-006-0053-y
- New integrators can handle much larger time steps
- RESPA, different time steps for different types of interactions: http://dx.doi.org/10.1063/1.463137
- http://dx.doi.org/10.1103/PhysRevLett.93.150201 (up to 100 fs)
Spatial Warping
Tag line: Transformation of variables that cancels barriers in partition function
- Spatial warping
- Does assume prior knowledge off the barrier shape and position
- http://dx.doi.org/10.1103/PhysRevLett.88.100201
- Dynamical spatial warping
- http://dx.doi.org/10.1209/0295-5075/19/6/002
- Does require prior knowledge of barrier position
Random generators
Tag line: Don't compute the energy, use simple geometric restrictions/rules instead.
- Common to all variants of this method
- Two types:
- Build each generated conformer from scratch (independent samples)
- Make random modifications iteratively.
- Pro:
- Speed, no kinetics
- Con:
- A large amount of rubbish
- Generating ring structures from scratch is not trivial
- Distance Geometry Methods
- http://www.ti.inf.ethz.ch/ew/courses/GCMB07/material/lecture13/havel-dis...
- Can easily incorporate NMR data
- CONCOORD
- MED-3DMC
- http://dx.doi.org/10.1016/j.ejmech.2008.09.052
- based on random rotations of molecular fragments about (sigma) bonds.
- RAMBLE
- http://dx.doi.org/10.1016/0263-7855(90)80057-M
(1) Assign random dihedral angles and (ii) optimize geometry to have a minimal RMS deviation from these angles
Importance sampling
(not strictly a conformational sampling approach, but a component of such algorithms) see http://en.wikipedia.org/wiki/Importance_sampling
- Example where importance sampling is used: