Collective Variable-based Calculations¹

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:

$$\xi(t) \; = \xi\left({\mbox{\boldmath {$x$}}}_{i}(t), {\mbox{\bol... ...mbox{\boldmath {$x$}}}_{k}(t), \ldots \right)\;, \;\; 1 \leq i,j,k\ldots \leq N$$ (35)

The colvars module in NAMD may be used in both MD simulation and energy minimization runs (except free energy methods). It 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 10.1);

• 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 10.2.2);

• 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 10.3.1), metadynamics (see 10.3.2), Steered Molecular Dynamics (SMD) and Umbrella Sampling (US) via a flexible harmonic restraint bias (see 10.3.3);

• 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.

• compute collective variable values from existing coordinates (e.g. an MD trajectory): use NAMD's coorfile read command, and perform a 0-timestep run for each set of coordinates, as illustrated in 16.