Collective Variable-based Calculations¹

The collective variables module replaces and greatly extends the functionality of the older freeEnergy module for free energy of conformational change calculations. The older module is still available in the code, but has been removed from the documentation to discourage future use.

In today's molecular dynamics simulations, it is often useful to reduce the great number of degrees of freedom of a into a few parameters which can be either analyzed individually, or manipulated in order to alter the dynamics in a controlled manner. These have been called `order parameters', `collective variables', `(surrogate) reaction coordinates', and many other terms. In this section, the term `collective variable' (shortened to colvar) is used, and it indicates any differentiable function of atomic Cartesian coordinates, ${\mbox{\boldmath {$x$}}}_{i}$, with $i$ between $1$ and $N$, the total number of atoms:

$$\xi(t) \; = \xi\left({\mbox{\boldmath {$x$}}}_{i}(t), {\mbox{\bol... ...mbox{\boldmath {$x$}}}_{k}(t), \ldots \right)\;, \;\; 1 \leq i,j,k\ldots \leq N$$ (11)

The colvars module in NAMD offers several features:

• define an arbitrary number of colvars, and perform a multidimensional analysis or biased simulation by accessing any subset of colvars independently from the rest (see 9.1);

• combine different functions of Cartesian coordinates (herein termed colvar components) into a colvar defined as a polynomial of several such components, thereby implementing new functional forms at runtime; periodic, multidimensional and symmetric components are handled transparently (see 9.2.1);

• calculate potentials of mean force (PMFs) for any set of colvars, using different sampling methods: currently implemented are the Adaptive Biasing Force (ABF) method (see 9.3.1), metadynamics (see 9.3.2), Steered Molecular Dynamics (SMD) and Umbrella Sampling (US) via a flexible harmonic restraint bias (see 9.3.3);

• calculate statistical properties of the colvars, such as their running averages and standard deviations, time correlation functions, and multidimensional histograms, without the need to save very large trajectory files.