Walkers Metadynamics

P. Raiteri, A. Laio, F. L. Gervasio, C. Micheletti, and M. Parrinello (2006) Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics. J. Phys. Chem. B 110, pp. 3533-3539... 

In multiple walkers metadynamics there is no efficiency gain in computing time, as the same accuracy could be obtained by performing just a single simulation Nj, -times longer. However, because the walkers are weakly coupled, this algorithm can be run easily on a parallel machine or even on a weakly inter-coimected cluster. Only a shared file system is required to allow interwalker commuitication in typical implementations. Moreover, it is not even necessary to start all the walkers at the same time, and there is no practical problem if one or more of the simulations is interrupted at some point. 

Multiple walkers metadynamics can also be used in the well-tempered algorithm. In the long time fimit the error prefactor will be decreased when increasing the number of walkers because the walkers will provide independent statistics biased by the same potential. 

As a final remark, we note that the theoretically perfect scaling of multiple walkers metadynamics can be reached only if the walkers are started from independent configurations taken from the proper equilibrium distribution. This can be a difficult task, as the free-energy landscape is not known a priori. 

The parameters w and 5s determine the accuracy and efEciency of the free energy reconstruction, as we will discuss in Sects. 1.1 and 3. After the collective coordinates are updated using (3), an ensemble with values is prepared, and the new forces are evaluated in another MD or MC run. In this manner the collective variables will perform a metadynamics in the CV space, visiting configurations very different from the ones they would have explored under the action of the thermodynamic force alone. In the following we refer to the point that explores the CV space as a walker. 

If the aim is to estimate the free energy in a predefined region in the CV space, metadynamics should be stopped when the walker has explored this whole region and its motion becomes diffusive. This can be detected by... 

The parameters w and Gq set the strength and the width of the bias potential, respectively. By iterating the sequence of force calculations from a constrained MD simulation (or from a MC simulation) and the propagation step of (13) one obtains the time evolution of the collective variables. In the metadynamics terminology one then speaks of a walker traveling through the low-dimensional space of the collective variables on the FES F q). 

As the walker leaves free energy minima most easily through saddle points in the free energy landscape, the metadynamics method is also capable of discovering new pathways between stable states and it can help to identify the respective mechanisms. Of course, the method is successful only if the space of the collective variables includes the degrees of freedom, which properly characterize the... 

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