Umbrella Sampling and the Potential of Mean Force

Umbrella sampling has been found to be especially useful in simulations where the changes are of a local character, such as in the calculation of the potential of mean force (PMF) along a reaction coordinate. The general definition of the PMF, W(x, x ) (see Chapter 5 of Ref. 80), is 

In practice, one must estimate the PD of Eq. [47] at several values of around P(4) can be written as 

A well-studied system is alanine dipeptide (AcAlaNHMe). The relative stability of different conformational states in vacuum - and in water were obtained from PMF calculations, ° and again different models and simulation parameters were applied. In a recent study Marrone, Gilson, and McCammon calculated the PMF of alanine dipeptide by using the Pois-son-Boltzmann method with a hydrophobic term and by using explicit water and found comparable results. Fraternali and van Gunsteren studied PMFs of glycine dipeptide in water for two reaction coordinates. Tobias and Brooks used their own technique to calculate the PMF of the central torsional angle 

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