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COLLECTIVE VARIABLES MODULE

Reference manual for VMD

Code version: 2019-05-22

Alejandro Bernardin, Jeﬀrey R. Comer, Giacomo Fiorin, Haohao Fu, Jérôme Hénin, Axel Kohlmeyer, Fabrizio Marinelli, Joshua V. Vermaas, Andrew D. White

### 1 Overview

In 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’, often shortened to colvar, to indicate any diﬀerentiable function of atomic Cartesian coordinates, ${\text{}x\text{}}_{i}$, with $i$ between $1$ and $N$, the total number of atoms:

 $\xi \left(t\right)\phantom{\rule{3.04074pt}{0ex}}=\xi \left(\text{}X\text{}\left(t\right)\right)\phantom{\rule{3.04074pt}{0ex}}=\xi \left({\text{}x\text{}}_{i}\left(t\right),{\text{}x\text{}}_{j}\left(t\right),{\text{}x\text{}}_{k}\left(t\right),\dots \right)\phantom{\rule{3.04074pt}{0ex}},\phantom{\rule{3.04074pt}{0ex}}\phantom{\rule{3.04074pt}{0ex}}1\le i,j,k\dots \le N$ (1)

This manual documents the collective variables module (Colvars), a software that provides an implementation for the functions $\xi \left(\text{}X\text{}\right)$ with a focus on ﬂexibility, robustness and high performance. 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 variables, 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 variables, 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 variables, such as running averages and standard deviations, correlation functions of pairs of variables, 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.

Detailed explanations of the design of the Colvars module are provided in reference [1]. Please cite this reference whenever publishing work that makes use of this module.

Using the Colvars Module in VMD Within VMD, the Colvars Module can be accessed in two ways:

• Using the Colvars dashboard, an intuitive, but partial interface to the Colvars module, to easily deﬁne and analyze collective variables, but not biases (section 3).
• Using the full-featured Tcl scripting interface as documented in section 4.1; see in particular the example in section 4.1.1.

### 2 Writing a Colvars conﬁguration: a crash course

The Colvars conﬁguration is a plain text ﬁle or string that deﬁnes collective variables, biases, and general parameters of the Colvars module. It is passed to the module using back-end-speciﬁc commands documented in section 4. Writing the conﬁguration for a collective variable in VMD is made much easier using the dashboard and its conﬁguration editor (section 3). However, note that the dashboard does not handle biases: if necessary, they should be managed separately using the scripting interface.

Now let us look at a complete, non-trivial conﬁguration. Suppose that we want to run a steered MD experiment where a small molecule is pulled away from a protein binding site. In Colvars terms, this is done by applying a moving restraint to the distance between the two objects. The conﬁguration will contain two blocks, one deﬁning the distance variable (see section 5 and 5.2.1), and the other the moving harmonic restraint (7.4). Note that in VMD, no biasing forces are applied, but biases may be useful in the context of an analysis script, e.g. to collect histograms or to compute bias energies.

colvar {
name dist
distance {
group1 { atomNumbersRange 42-55 }
group2 {
psfSegID PR
atomNameResidueRange CA 15-30
}
}
}

harmonic {
colvars dist
forceConstant 20.0
centers 4.0         # initial distance
targetCenters 15.0  # final distance
targetNumSteps 500000
}

Reading this input in plain English: the variable here named dist consists in a distance function between the centers of two groups: the ligand (atoms 42 to 55) and the $\alpha$-carbon atoms of residues 15 to 30 in the protein (segment name PR). To the “dist” variable, we apply a harmonic potential of force constant 20 kcal/mol/Å${}^{2}$, initially centered around a value of 4 Å, which will increase to 15 Å over 500,000 simulation steps.

The atom selection keywords are detailed in section 6.

### 3 The Colvars dashboard

The Colvars dashboard is a graphical interface for interactive visualization and reﬁnement of collective variables aided by molecular structures and trajectories. It is accessible in VMD’s Main Menu under “Extensions/Analysis/Colvars Dashboard”. Throughout the interface, keyboard shortcuts for common operations are indicated in square brackets.

#### 3.1 A mini-tutorial

Here are the steps for a quick ﬁrst tour of the Dashboard:

1. load an MD trajectory into VMD;
2. open the Dashboard;
3. click “New” to create a new collective variable;
4. in the Editor window, click “Apply” to accept the dein the Dashboard window, fault template;
5. in the Dashboard window, click “Show atoms” to display the two atom groups involved in this distance coordinate;
6. click “Timeline plot”;
7. click anywhere in the timeline plot to navigate in the trajectory.

Now, clicking “Edit” in the Dashboard window, you can modify the collective variable to reﬂect interesting geometric properties of the system. The power of the collective variables approach lies in the variety of geometric functions (“components”) and their combinations. The editor window provides a number of helpers to make it easy and quick to deﬁne the most relevant variables. See section 3.4 for details.

#### 3.2 The Dashboard window

The Dashboard window displays a table listing currently deﬁned variables, and their values for the current frame indicated at the bottom of the window. By default the frame is updated to track VMD’s currently displayed frame, but that can be changed by toggling the “Track frame” checkbox, e.g. to animate the trajectory without recomputing expensive variables. Vector-values variables can be expanded to list their scalar components. This is necessary when individual scalar quantities have to be selected for plotting. Other operations act on variables as a whole and ignore speciﬁc selected scalar components.

Buttons above the table allow for general operations on the state of the Colvars Module. Buttons below the table oﬀer operations on selected variables.

If several molecules are loaded, the dashboard only interacts with the molecule labeled ”top” (T in VMD’s main window). If the top molecule is changed, the Colvars Module needs to be reset using the Reset button. This will remove all current deﬁnitions, so make sure to save the variables to a ﬁle beforehand.

If variables are modiﬁed, added or deleted interactively or by an external script, hit “Refresh” or press F5 to update the displayed variables and values. Starting the dashboard also enables trajectory animation using the left/right arrow keys within VMD’s graphical window. Atomic coordinates can be modiﬁed using VMD’s “Mouse/Move” functions, and the Colvars Module can then be updated by pressing F5 directly from the graphical window.

This saves the conﬁguration of all deﬁned collective variables to a ﬁle. Neither biases, nor general parameters of the Colvars Module are saved: editing them is beyond the scope of the dashboard. We recommend keeping them in separate conﬁguration ﬁles, and reading them separately in biased MD simulations.

#### 3.4 The conﬁguration editor

The conﬁguration editor can be started with the “Edit” or “New” buttons. Using the “Edit” button, the conﬁguration of selected variables is loaded, and those variables will be replaced when applying the new conﬁguration.

The editor window oﬀers links to online documentation, as well as helpers to write correct conﬁguration ﬁles.

As a ﬁrst step, the most useful helper is the collection of template ﬁles. Parameters that must be supplied are indicated by the symbol @. Colvar templates can be inserted at the beginning of the conﬁguration, whereas “component” templates found in the directory of the same name deﬁne basis functions that belong inside a colvar block. Templates are indented using 4 spaces per level to indicate their position in the nested structure of the conﬁguration: general options, colvars and biases at level 0, bias and colvar parameters like components at level 1, component parameters such as atom groups at level 2, and atom group parameters at level 3.

The next helper buttons allow importing atom selections from VMD, either typing a VMD atom selection text, by copying the selection of an existing graphical representation, or by inserting the list of atoms currently labeled in VMD using the “Pick atom” feature. Atom selections should be inserted within an atom group block, within a component block (such as distance).

The “Insert labeled...” button combined with the selection box allows for inserting components matching VMD’s geometry measurements: Bonds (distances), angles, and dihedrals.

#### 3.5 Plotting and visualizing collective variables

Timeline plots show the selected variables as a function of time. A vertical bar indicates the current frame, which can be changed either using VMD’s trajectory animation controls, or directly in the plot window by clicking the mouse inside the graph, or using the keyboard left/right arrows. Shift+arrow skips frames for faster animation, and Ctrl+arrow skips more frames. The up/down arrows operate a zoom/unzoom along the time axis. Visible data can be ﬁtted vertically using the h key. All data can be ﬁtted horizontally using the h key.

Pairwise scatterplots are useful to identify correlation between variables. To create a pairwise plot, select exactly two scalar variables (or scalar components of vector variables), and click “Pairwise plot”. Frames are represented by circles, and lines connect consecutive frames. The blue dot tracks the current frame. Arrow keys animate the trajectory as in the timeline plot. Clicking a circle jumps to the corresponding frame.

“Show atoms” creates representations of the atoms involved in the deﬁnition of the selected colvars. Each atom group is shown in a diﬀerent color. “Show gradient” is available for scalar variables only. It creates a graphical representation of the atomic gradients of the selected variables, visualizing how the value of the collective variable would vary in response to a change in atomic coordinates.

### 4 General parameters

Here, we document the syntax of the commands and parameters used to set up and use the Colvars module in VMD. One of these parameters is the conﬁguration ﬁle or the conﬁguration text for the module itself, whose syntax is described in 4.2 and in the following sections.

#### 4.1 Using the cv command

At any moment during the execution of VMD, several options in the Colvars module can be read or modiﬁed by the command cv with the following syntax:
cv $<$subcommand$>$ [args...]
For example, to record the value of a collective variable named myVar into the Tcl variable value, use the following syntax:
set value [cv colvar myVar value]
All subcommands of cv are documented below.

Note: in VMD, Colvars must be attached to one molecule (system). Therefore, the cv command must be used for the ﬁrst time as cv molid $<$molid$>$ to set up the Colvars module for the molecule identiﬁed by $<$molid$>$. In all following invocations, the cv command will continue operating on the same molecule, regardless of its “top” status. To use the cv command on a diﬀerent molecule, use cv delete ﬁrst and then cv molid $<$molid$>$. Invoking the cv command with no arguments prints a help screen.

##### 4.1.1 Example use of the cv command: analyze a trajectory

By far the most typical use of Colvars in VMD is computing the values of one or more variables along an existing trajectory:
# Activate the module on the current VMD molecule
cv molid top
# Load a Colvars config file
cv configfile test.in
set out [open "test.colvars.traj" "w"]
# Write the labels to the file
puts -nonewline ${out} [cv printframelabels] for { set fr 0 } {${fr} < [molinfo top get numframes] } { incr fr } {
# Point Colvars to this trajectory frame
cv frame ${fr} # Recompute variables and biases cv update # Print variables and biases to the file puts -nonewline${out} [cv printframe]
}

##### 7.9.1 Grid deﬁnition for multidimensional histograms

Like the ABF and metadynamics biases, histogram uses the parameters lowerBoundary, upperBoundary, and width to deﬁne its grid. These values can be overridden if a conﬁguration block histogramGrid { } is provided inside the conﬁguration of histogram. The options supported inside this conﬁguration block are:

• lowerBoundaries $⟨\phantom{\rule{0.3em}{0ex}}$Lower boundaries of the grid$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramGrid
Acceptable values: list of space-separated decimals
Description: This option deﬁnes the lower boundaries of the grid, overriding any values deﬁned by the lowerBoundary keyword of each colvar. Note that when gatherVectorColvars is on, each vector variable is automatically treated as a scalar, and a single value should be provided for it.
• upperBoundaries: analogous to lowerBoundaries
• widths: analogous to lowerBoundaries

#### 7.10 Probability distribution-restraints

The histogramRestraint bias implements a continuous potential of many variables (or of a single high-dimensional variable) aimed at reproducing a one-dimensional statistical distribution that is provided by the user. The $M$ variables $\left({\xi }_{1},\dots ,{\xi }_{M}\right)$ are interpreted as multiple observations of a random variable $\xi$ with unknown probability distribution. The potential is minimized when the histogram $h\left(\xi \right)$, estimated as a sum of Gaussian functions centered at $\left({\xi }_{1},\dots ,{\xi }_{M}\right)$, is equal to the reference histogram ${h}_{0}\left(\xi \right)$:

 $V\left({\xi }_{1},\dots ,{\xi }_{M}\right)=\frac{1}{2}k\int {\left(h\left(\xi \right)-{h}_{0}\left(\xi \right)\right)}^{2}\mathrm{d}\xi$ (28)
 $h\left(\xi \right)=\frac{1}{M\sqrt{2\pi {\sigma }^{2}}}\sum _{i=1}^{M}exp\left(-\frac{{\left(\xi -{\xi }_{i}\right)}^{2}}{2{\sigma }^{2}}\right)$ (29)

When used in combination with a distancePairs multi-dimensional variable, this bias implements the reﬁnement algorithm against ESR/DEER experiments published by Shen et al [26].

This bias behaves similarly to the histogram bias with the gatherVectorColvars option, with the important diﬀerence that all variables are gathered, resulting in a one-dimensional histogram. Future versions will include support for multi-dimensional histograms.

The list of options is as follows:

• name: see deﬁnition of name in sec. 7 (biasing and analysis methods)
• colvars: see deﬁnition of colvars in sec. 7 (biasing and analysis methods)
• outputEnergy: see deﬁnition of outputEnergy in sec. 7 (biasing and analysis methods)
• lowerBoundary $⟨\phantom{\rule{0.3em}{0ex}}$Lower boundary of the colvar grid$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramRestraint
Acceptable values: decimal
Description: Deﬁnes the lowest end of the interval where the reference distribution ${h}_{0}\left(\xi \right)$ is deﬁned. Exactly one value must be provided, because only one-dimensional histograms are supported by the current version.
• upperBoundary: analogous to lowerBoundary
• width $⟨\phantom{\rule{0.3em}{0ex}}$Width of the colvar grid$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramRestraint
Acceptable values: positive decimal
Description: Deﬁnes the spacing of the grid where the reference distribution ${h}_{0}\left(\xi \right)$ is deﬁned.
• gaussianSigma $⟨\phantom{\rule{0.3em}{0ex}}$Standard deviation of the approximating Gaussian$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramRestraint
Acceptable values: positive decimal
Default value: 2 $×$ width
Description: Deﬁnes the parameter $\sigma$ in eq. 29.
• forceConstant $⟨\phantom{\rule{0.3em}{0ex}}$Force constant (kcal/mol)$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramRestraint
Acceptable values: positive decimal
Default value: 1.0
Description: Deﬁnes the parameter $k$ in eq. 28.
• refHistogram $⟨\phantom{\rule{0.3em}{0ex}}$Reference histogram ${h}_{0}\left(\xi \right)$$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramRestraint
Acceptable values: space-separated list of $M$ positive decimals
Description: Provides the values of ${h}_{0}\left(\xi \right)$ consecutively. The mid-point convention is used, i.e. the ﬁrst point that should be included is for $\xi$ = lowerBoundary+width/2. If the integral of ${h}_{0}\left(\xi \right)$ is not normalized to 1, ${h}_{0}\left(\xi \right)$ is rescaled automatically before use.
• refHistogramFile $⟨\phantom{\rule{0.3em}{0ex}}$Reference histogram ${h}_{0}\left(\xi \right)$$\phantom{\rule{0.3em}{0ex}}⟩$
Context: histogramRestraint
Acceptable values: UNIX ﬁle name
Description: Provides the values of ${h}_{0}\left(\xi \right)$ as contents of the corresponding ﬁle (mutually exclusive with refHistogram). The format is that of a text ﬁle, with each line containing the space-separated values of $\xi$ and ${h}_{0}\left(\xi \right)$. The same numerical conventions as refHistogram are used.
• writeHistogram $⟨\phantom{\rule{0.3em}{0ex}}$Periodically write the instantaneous histogram $h\left(\xi \right)$$\phantom{\rule{0.3em}{0ex}}⟩$
Acceptable values: boolean
Default value: off
Description: If on, the histogram $h\left(\xi \right)$ is written every colvarsRestartFrequency steps to a ﬁle with the name outputName.$<$name$>$.hist.dat This is useful to diagnose the convergence of $h\left(\xi \right)$ against ${h}_{0}\left(\xi \right)$.

#### 7.11 Deﬁning scripted biases

Rather than using the biasing methods described above, it is possible to apply biases provided at run time as a Tcl script. This option, also available in NAMD, can be useful to test a new algorithm to be used in a MD simulation.

• scriptedColvarForces $⟨\phantom{\rule{0.3em}{0ex}}$Enable custom, scripted forces on colvars $\phantom{\rule{0.3em}{0ex}}⟩$
Context: global
Acceptable values: boolean
Default value: off
Description: If this ﬂag is enabled, a Tcl procedure named calc_colvar_forces accepting one parameter should be deﬁned by the user. It is executed at each timestep, with the current step number as parameter, between the calculation of colvars and the application of bias forces. This procedure may use the cv command to access the values of colvars and apply forces on them, eﬀectively deﬁning custom collective variable biases.

#### 7.12 Performance of scripted biases

If concurrent computation over multiple threads is available (this is indicated by the message “SMP parallelism is available.” printed at initialization time), it is useful to take advantage of the scripting interface to combine many components, all computed in parallel, into a single variable.

The default SMP schedule is the following:

1. distribute the computation of all components across available threads;
2. on a single thread, collect the results of multi-component variables using polynomial combinations (see 5.12), or scripted functions (see 5.13);
3. distribute the computation of all biases across available threads;
4. compute on a single thread any scripted biases implemented via the keyword scriptedColvarForces.
5. communicate on a single thread forces to VMD.

The following options allow to ﬁne-tune this schedule:

• scriptingAfterBiases $⟨\phantom{\rule{0.3em}{0ex}}$Scripted colvar forces need updated biases?$\phantom{\rule{0.3em}{0ex}}⟩$
Context: global
Acceptable values: boolean
Default value: on
Description: This ﬂag speciﬁes that the calc_colvar_forces procedure (last step in the list above) is executed only after all biases have been updated (next-to-last step) For example, this allows using the energy of a restraint bias, or the force applied on a colvar, to calculate additional scripted forces, such as boundary constraints. When this ﬂag is set to off, it is assumed that only the values of the variables (but not the energy of the biases or applied forces) will be used by calc_colvar_forces: this can be used to schedule the calculation of scripted forces and biases concurrently to increase performance.

### 8 Syntax changes from older versions

The following is a list of syntax changes in Colvars since its ﬁrst release. Many of the older keywords are still recognized by the current code, thanks to speciﬁc compatibility code. This is not a list of new features: its primary purpose is to make you aware of those improvements that aﬀect the use of old conﬁguration ﬁles with new versions of the code.

Note: if you are using any of the NAMD and VMD tutorials:
https://www.ks.uiuc.edu/Training/Tutorials/
please be aware that several of these tutorials are not actively maintained: for those cases, this list will help you reconcile any inconsistencies.

• Colvars version 2016-06-09 or later (VMD version 1.9.3 or later).
The legacy keyword refPositionsGroup has been renamed fittingGroup for clarity (the legacy version is still supported).
• Colvars version 2016-08-10 or later (VMD version 1.9.3 or later).
“System forces” have been replaced by “total forces” (see for example outputTotalForce). See the following page for more information:
• Colvars version 2017-01-09 or later (VMD version 1.9.4 or later).
A new type of restraint, harmonicWalls (see 7.6), replaces and improves upon the legacy keywords lowerWall and upperWall: these are still supported as short-hands.
• Colvars version 2018-11-15 or later (VMD version 1.9.4 or later).
The global analysis keyword has been discontinued: speciﬁc analysis tasks are controlled directly by the keywords corrFunc and runAve, which continue to remain off by default.
• Deprecation warning for calculations including wall potentials.
The legacy keywords lowerWall and upperWall will stop having default values and will need to be set explicitly (preferably as part of the harmonicWalls restraint). When using an ABF bias, it is recommended to set the two walls equal to lowerBoundary and upperBoundary, respectively. When using a metadynamics bias, it is recommended to set the two walls within lowerBoundary and upperBoundary. This guarantees that the tails of each Gaussian hill are accounted in the region between the grid boundaries and the wall potentials. See also expandBoundaries for an automatic deﬁnition of the PMF grid boundaries.

Up-to-date documentation can always be accessed at:
https://colvars.github.io/colvars-refman-vmd/colvars-refman-vmd.html

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