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Collective Variables Interface (Colvars)

In today's molecular dynamics simulations, it is often useful to reduce the large number of degrees of freedom of a physical system into few parameters whose statistical distributions can be analyzed individually, or used to define biasing potentials to alter the dynamics of the system in a controlled manner. These have been called `order parameters', `collective variables', `(surrogate) reaction coordinates', and many other terms.

Here we use primarily the term `collective variable' (shortened to colvar), which indicates any differentiable function of atomic Cartesian coordinates, $ {\mbox{\boldmath {$x$}}}_{i}$ , with $ i$ between $ 1$ and $ N$ , the total number of atoms:

$\displaystyle \xi(t) \; = \xi\left({\mbox{\boldmath {$x$}}}_{i}(t), {\mbox{\bol...
...mbox{\boldmath {$x$}}}_{k}(t), \ldots \right)\;, \;\; 1 \leq i,j,k\ldots \leq N$ (13.1)

The Colvars module in VMD may be used to calculate these functions over a molecular structure, and to analyze the results of previous simulations. The module is designed to perform multiple tasks concurrently during or after a simulation, the most common of which are:

Note: although restraints and PMF algorithms are primarily used during simulations, they are also available in VMD to test a new input for a simulation, or to evaluate the relative free energy of a new structure based on data from a previous calculation. Options that only have an effect during a simulation are also included for compatibility purposes.

To briefly illustrate the flexibility of the Colvars module, Figure 13.1 shows an example of a non-trivial configuration (the corresponding input can be found in 13.1.2).

Figure 13.1: Graphical representation of a Colvars configuration. The colvar called ``$ d$ '' is defined as the difference between two distances: the first distance ($ d_{1}$ ) is taken between the center of mass of atoms 1 and 2 and that of atoms 3 to 5, the second ($ d_{2}$ ) between atom 7 and the center of mass of atoms 8 to 10. The difference $ d = d_{1} - d_{2}$ is obtained by multiplying the two by a coefficient $ C = +1$ or $ C = -1$ , respectively. The colvar called ``$ c$ '' is the coordination number calculated between atoms 1 to 10 and atoms 11 to 20. A harmonic restraint is applied to both $ d$ and $ c$ : to allow using the same force constant $ K$ , both $ d$ and $ c$ are scaled by their respective fluctuation widths $ w_d$ and $ w_c$ . A third colvar ``alpha'' is defined as the $ \alpha$ -helical content of residues 1 to 10. The values of ``$ c$ '' and ``alpha'' are also recorded throughout the simulation as a joint 2-dimensional histogram.
\includegraphics[width=12cm]{pictures/colvars_diagram}

Detailed explanations of the design of the Colvars module are provided in reference [44]. Please cite this reference whenever publishing work that makes use of this module.



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