Enhanced sampling techniques

Many chemical systems, notably those in condensed matter and in biology, are characterized by the presence of multiple low energy states which are separated by large barriers. The presence of these barriers prevents exploration of all of configuration space during the relatively short timescales accessible in molecular dynamics (MD) simulations. Typically this means that only those configurations in a small, locally ergodic region in the vicinity of the input structure are visited.

One trick that is commonly used to resolve this problem is to add a simulation bias in order to force the interesting, rarer events to occur. This simulation bias forces the value of some particularly interesting collective variable (CV) to change more rapidly than it otherwise would. This is a very good strategy when you have a reasonable understanding of what occurs during your rare event and when you can encode what happens mathematically. For instance, to study a process such as nucleation you simply have to find a differentiable quantity that distinguishes between configurations where the ions are distributed uniformly across the simulation cell from those in which the ions are bunched together in a crystalline nucleus. To develop coordinates for complicated problems such as these we are involved with the development of a code called plumed 2.0. Already we are using this code to find new CVs that can be used to study nucleation and to study how water molecules enter the ionic channels in large protein molecules.

2d-scheme Contour plots showing the potential energy + the current bias at selected points along a Reconnaissance Metadynamics trajectory for a particle diffusing about a 2D potential energy surface. The black dots indicate the positions of the snapshots accumulated from the trajectory while the red ellipses indicate the basins found using the PPCA algorithm. Blue ellipses are those basins, found during previous PPCA analyses, to which hills are being added.

We are also working on methods where you do not have an accurate description of the rare events in advance. In particular, we have a method called reconnaissance metadynamics [1] that finds CVs automatically and have applied it to problems in protein folding [1], drug docking [2] and cluster physics [3].

fes_lj_3d.png The locations of the various basins found during a reconnaissance metadynamics simulation of the Lennard-Jones 7 cluster plotted as a function of the second and third moments of the distribution of coordination numbers and the index of the atom with the highest coordination number. Also shown is a free energy surface calculated using a well- tempered metadynamics simulation that employed the second and third moments of the distribution as collective coordinates. Each basin is represented by a circle with an area that is proportional to the bias at its center.

The code we use to do these sorts of calculations can be downloaded from www.plumed-code.org.

References:

[1] G. A. Tribello, M. Ceriotti and M. Parrinello. Proceedings of the National Academy of Sciences, 107(41), 17509–17514 (2010).

[2] P. Soderhjelm, G. A. Tribello and M. Parrinello. Proceedings of the National Academy of Sciences, 109(14), 5170–5175 (2012).

[3] G. A. Tribello, J. Cuny, H. Eshet and M. Parrinello. Journal of Chemical Physics, 135(11), 114109 (2011).

Staff involved

Gareth Tribello