Pathways Plugin for VMD

Background and theory

Downloading and installing

Getting started

Usage notes

Parameters

Licensing and acknowledgments

Background and theory. The Pathways plugin for VMD provides the functionality to identify dominant electron transfer (ET) pathways and estimate the donor-to-acceptor electronic tunneling coupling in biological redox reactions as well as ET reactions in engineered biomolecular systems. Since those reactions typically occur in the weak-coupling tunneling regime, their rates are reasonably well described by the Fermi Golden rule (R. A. Marcus and N. Sutin, Biochim. Biophys. Acta 811, 265-322 (1985)):

,

where is the donor-to-acceptor tunneling coupling, and the middle term in the right hand side is the Franck-Condon factor (the probability of the donor and acceptor to form a resonance activated complex), which is controlled by two energy parameters, (the driving force) and (the reorganization energy). While the Franck-Condon factor plays an important role, the overall usually-exponential dependence of on the tunneling distance is primarily controlled by .

The Pathways plugin is based on the Pathways model (D. N. Beratan, J. N. Betts, and J. N. Onuchic, Science 252, 1285-1288 (1991)), the first theoretical framework to characterize the influence of the protein structure on in biological ET reactions. It assumes that ET from the donor to the acceptor occurs via pathways -- sequences of steps from one electronic state (usually atom-centered one) to another. The steps can be mediated by covalent bonds, hydrogen bonds, or through-space jumps, all characterized by different tunneling barriers. Each step is assigned a penalty: the softest ones describe covalent bond-nediated steps (lower tunneling barriers), the steepest distance-dependent ones describe through-space jumps (higher tunneling barriers), and hydrogen bond-mediated steps are treated as combinations of a covalent bond-mediated step and a through-space jump. The overall penalty for ET along the pathway is then calculated as a product of penalties for each step:

where is the penalty for propagation through covalent bond , is the penalty for propagation through hydrogen bond , and is the penalty for through-space jump . In the most common parameterization (see the above reference), the penalty for any covalent bond-mediated step is , the penalty for a hydrogen bond-mediated step is , and the penalty for a through-space jump is , where is the step distance in Angstroms. In this parameterization, hydrogen atoms are not included explicitly in the model, and hydrogen bond lengths are measured between heavy atoms. Several other parameterizations of the Pathways model exist, providing similar estimates.

The Pathways plugin provides four key functionalities:

Starting from version 1.1, the Pathways plugin includes the capability to describe collective electronic states, in which electrons are delocalized over several atoms, as in protein amino acid side chains (His, Phe, Trp, and Tyr) or nucleic acid bases. These states are abundant in some redox proteins (e.g., cryptochromes or photolyase) as well as engineered molecular complexes based on nucleic acid templates. Because of electron delocalization, these states may essentially influence ET pathways and redox reaction rates, thereby regulating protein biological function or operation of molecular electronic devices. The Pathways plugin accounts for these states by assigning no penalty to electron propagation within each state.

Downloading and installing. The Pathways plugin consists of two components: Tcl scripts and the graph search utility pathcore. The Tcl scripts are common for all platform/OS combinations. The pathcore utility is provided in several forms: as statically compiled binaries for 64-bit or 32-bit x86 platforms running Linux, and as source code (that needs compiling) for all other platforms. Providing pathcore binaries for Mac OS X and Windows is planned for future releases.

Version Tcl scripts Pathcore

Pathways 1.1 (recommended)

Tcl scripts (tar.gz)

Pathways 1.0

Tcl scripts (tar.gz)

To install Pathways on any UNIX-like platform, including Mac OS X, follow the following steps:

  1. Create a personal VMD plugin directory, for example:

    mkdir ~/vmd/plugins

  2. Download the Tcl scripts archive and extract it in the above directory:

    cd ~/vmd/plugins; tar -xvzf pathways.tgz

  3. Create a personal VMD configuration file ~/.vmdrc and add the following lines there:

    global env
    l
    append auto_path $env(HOME)/vmd/plugins

  4. Install the pathcore binary:

    a) For 64-bit or 32-bit Linux on x86 platforms, download the appropriate static binary, rename it to pathcore, add the executing permissions (chmod a+x pathcore), and place it into a directory in your path.

    b) For other platforms, or if you want to modify the code, download the pathcore source code and compile it as follows:


Getting started.
Like any other VMD plugin, Pathways needs to be loaded into VMD before using. To do that, run the following command in the VMD console (better yet, Tk console):

package require pathways

If the plugin installation was successful, you will see the plugin version. If you plan on using the plugin on a regular basis, you might wish to add the above command to your $HOME/.vmdrc file.

To get the list of available commands, run 'pathways' with no parameters. Then, run each listed command with no parameters to see brief usage help.

To get started, load your ET-mediating molecule into VMD and run a command similar to the following one (make sure to replace these donor and acceptor names with the actual ones):

pathways -d "name CU" -a "name RU" -b "segid A RBU"

This command calculates and displays the strongest ET pathway and prints a list of pathway steps (atoms, step type, step distance, and distance along the pathway).

Now, it is time to try some advanced commands - for example, run Pathways using a molecular dynamics trajectory or estimate importance of individual atoms for mediating the electronic coupling. Try changing some parameters (see the complete list below) and find out how they influence the ET pathways and the electronic donor-to-acceptor coupling.

Usage notes. These aspects of Pathways operation are relevant for obtaining the correct and meaningful results:

Chemical structure. In the pathway search, Pathways essentially depends on bond information, and missing even a single bond may lead to grossly incorrect results. Since Pathways receives bond information from VMD, it is helpful to understand how VMD identifies bonds.

If a structure file was loaded, VMD reads the covalent bond list from that file. A structure file in the PSF format can be generated by one of VMD plugins, psfgen or autopsf, using a coordinate file (e.g., PDB) and one of Charmm topology files. While generating a structure file, VMD plugins also add hydrogen atoms needed to identify hydrogen bonds. An example of structure file generation is available from the NAMD2 user's guide. Note that the topology files only describe common biomolecular fragments such as amino acids, nucleic acids, and lipids. If the molecule includes an uncommon group (e.g., a metal cofactor), one needs to use psfgen (and not autopsf!) in order to manually define covalent bonds in that group using patches (see the above example).

If a structure file was not loaded, VMD attempts to guess covalent bonds using interatomic distances and a set of empiric rules for common biomolecular fragments. For VMD to identify hydrogen bonds, hydrogens should be already added to the structure using the above VMD plugins or 3rd party tools (e.g., Pymol). Again, if an uncommon group is present in the molecule, one needs to manually define covalent bonds in that group using addbond and delbond commands described in the Pathways built-in help. In addition, Pathways requires segment IDs to be assigned, which can be done by setseg command.

Summarizing the above, here is a brief description of possible ways to prepare molecules for calculations with Pathways, in order of preference:

  1. Generate a PSF structure file using psfgen, the coordinate file, and a Charmm topology file and manually define uncommon covalent bonds, if any, using patches. Load the molecule in VMD as the structure file and the coordinate file.
  2. Generate a PSF structure using autopsf, the coordinate file, and a Charmm topology file. Load the molecule in VMD as the structure file and the coordinate file. Use addbond and/or delbond commands to correct bond structure, if needed, and use setseg command to assign segment IDs, if needed.
  3. Add hydrogen atoms using any tool. Load the molecule into VMD as the coordinate file alone. Use addbond and/or delbond commands to correct bond structure, if needed, and use setseg command to assign segment IDs, if needed.

Internal limitations. The Pathways model has been designed and parameterized to describe the weak-coupling tunneling regime typical for many biological ET reactions, in which the tunneling coupling is dominated by the strongest pathways. Whereas it provides reasonable qualitative coupling estimates for these reactions, other ET reactions occur in essentially different regimes, most notably:

Using the Pathways model for estimating rates of these reactions might lead to grossly incorrect results. Nevertheless, even in these systems, the Pathways model may provide valuable qualitative insights into ET reaction mechanisms when (and if) the above factors are properly addressed. For example, a statistical analysis of the coupling fluctuations along a molecular dynamics trajectory may help to incorporate effects of destructive electronic interference (e.g., Balabin, Skourtis, and Beratan, Phys. Rev. Lett. 101, 158102 (2008)). Renormalizing decays per step could help describe hopping-dominated transport (e.g., ET in nucleic acids) or water-mediated tunneling. However, while these modifications appear feasible, they have not been properly tested yet. As such, Pathways-based estimates for the above reactions should be taken with care.

Parameters. Using Pathways is simple: there are only two required parameters, atom selection strings for the donor and the acceptor. At the same time, Pathways accepts a large number of parameters that make it fully configurable. These parameters, however, can (and some of them should!) be safely left at their default values. The following is the complete parameter list; the parameter values are for illustration only:

Mandatory parameters:

Marcus ET rate estimate parameters:

Generic parameters:

Pathways model parameters:

Output parameters:

Graphics parameters:

Experimental parameters (version 1.1 and newer):

Contributions and licensing. The Pathways plugin is created by Ilya Balabin (project design and management, VMD integration, user interfaces, graphics, animation), Xiangqian Hu (graph search wrapper), and David Beratan (overall management) at Duke University. The work was funded by the NIH grant GM-048043.

The Pathways plugin is released under the GNU public license version 3 or later.

Please send your comments, suggestions, and bug reports to Ilya Balabin.


(C) Ilya A. Balabin ilya dot balabin at duke dot edu Modified on 2012-03-08