Local elevation is a technique used in computational chemistry or physics, mainly in the field of molecular simulation (including molecular dynamics (MD) and Monte Carlo (MC) simulations).
It was developed in 1994 by Huber, Torda and van Gunsteren [1] to enhance the searching of conformational space in molecular dynamics simulations and is available in the GROMOS software for molecular dynamics simulation (since GROMOS96).
Many recent methods build on the principles of the local elevation technique, including the Engkvist-Karlström, [3] adaptive biasing force, [4] Wang–Landau, metadynamics, adaptively biased molecular dynamics, [5] adaptive reaction coordinate forces, [6] and local elevation umbrella sampling [7] methods.
The basic principle of the method is to add a memory-dependent potential energy term in the simulation so as to prevent the simulation to revisit already sampled configurations, which leads to the increased probability of discovering new configurations.
of the degrees of freedom, which define the relevant conformational variables.
These are typically a set of conformationally relevant dihedral angles, but can in principle be any differentiable function of the cartesian coordinates
) and is gradually built as a sum of small, repulsive functions, giving where
However, due to the infinite range of the Gaussian as well as the artifacts that can occur with a sum of gridded Gaussians, a better choice is to apply multidimensional truncated polynomial functions [8] .
[9] The local elevation method can be applied to free energy calculations as well as to conformational searching problems.
It has been shown by Engkvist and Karlström [3] that the bias potential built by the local elevation method will approximate the negative of the free energy surface.
The free energy surface can therefore be approximated directly from the bias potential (as done in the metadynamics method) or the bias potential can be used for umbrella sampling (as done in metadynamics with umbrella sampling corrections [10] and local elevation umbrella sampling[7] methods) to obtain more accurate free energies.