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:

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

• apply restraints or biasing potentials to multiple colvars, tailored on the system by choosing from a wide set of basis functions, without limitations on their number or on the number of atoms involved;

• calculate potentials of mean force (PMFs) along any set of colvars, using different enhanced sampling methods, such as Adaptive Biasing Force (ABF), metadynamics, steered MD and umbrella sampling; variants of these methods that make use of an ensemble of replicas are supported as well;

• calculate statistical properties of the colvars, such as running averages and standard deviations, correlation functions of pairs of colvars, and multidimensional histograms: this can be done either at run-time without the need to save very large trajectory files, or after a simulation has been completed using VMD and the cv command.

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.

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.