Buried volume

Buried volumes are implemented as described by Cavallo and co-workers [1].

Module

The BuriedVolume class calculates the buried volume. Steric maps can also be plotted.

Example

>>> from morfeus import BuriedVolume, read_xyz
>>> elements, coordinates = read_xyz("1.xyz")
>>> bv = BuriedVolume(elements, coordinates, 1, excluded_atoms=[2, 3, 4, 5, 6, 7])
>>> print(bv.fraction_buried_volume)
0.2962110976518822
>>> bv.print_report()
V_bur (%): 29.6

By default, hydrogen atoms are excluded in the calculation. They can be added by giving the keyword argument indclude_hs=True. The metal atom is also excluded, while the atoms of other ligands need to be given in the excluded_atoms list. The default sphere radius is 3.5 Å, but can be changed with radius=<float>. Default radii type is Bondi which are scaled by a factor of 1.17. This can be changed with radii_type=<str> and radii_scale=<float>. Custom radii can be supplied as a list with radii=<list>.

For more information, use help(BuriedVolume) or see the API: BuriedVolume

Quadrants and octants

The buried volume can be decomposed into contributions from quadrants and octants using the octant_analysis method. To get meaningful results, the system should to be oriented in a reproducible way. Orientation is acheived by specifiying the z_axis_atoms=<list>``and ``xz_plane_atoms=<list> keyword arguments. For more information on the orientation convention, see the original reference [1].

z-axis orientation

The list of atom indices from z_axis_atoms is used to define the direction of the z axis. The axis will be oriented from the geometric center of the atoms in the list to the metal atom.

xz-plane orientation

The list of atom indices from xz_plane_atoms is used to define the orientation of the xz-plane. The coordinate system will be rotateed so that the geometric mean of the given atoms lies in the xz plane.

The results of the octant analysis is stored in the octants attribute, giving percent buried volume, buried volume (in ų) and the free volume (in ų) for each octant.

Quadrant and octant analysis

>>> bv = BuriedVolume(elements, coordinates, 1,
... excluded_atoms=[2, 3, 4, 5, 6, 7],
... z_axis_atoms=[14],
... xz_plane_atoms=[11])
>>> bv.octant_analysis()
>>> bv.octants
{'percent_buried_volume': {0: 0.0, ...},
 'buried_volume': {0: 0.0, ...},
 'free_volume': {0: 22.449297503777064, ...}}
>>> bv.quadrants
{'percent_buried_volume': {1: 27.53214685054044, ...},
 'buried_volume': {1: 12.361547111309221, ...},
 'free_volume': {1: 32.53704789624491, ...}}

The octants are numbered from 0–7 according to the Gray code and their signs are given by the OCTANT_SIGNS dictionary. The quadrants are numbered from 1–4 corresponding to the Roman numerals I–V and the corresponding signs are given in the QUADRANT_SIGNS dictionary.

Distal volume

The distal volume is the volume of the ligand beyond the sphere. It can be computed with the compute_distal_volume method. Using method="sasa" is faster, while method="buried_volume" allows octant and quadrant decompositon of the distal volume. This will add the entries distal_volume and molecular_volume to the results.

Distal volume

>>> bv = BuriedVolume(elements, coordinates, 1,
... excluded_atoms=[2, 3, 4, 5, 6, 7],
... z_axis_atoms=[14],
... xz_plane_atoms=[11])
>>> bv.distal_volume
273.2150492473022
>>> bv.octant_analysis()
>>> bv.compute_distal_volume(method="buried_volume", octants=True)
>>> bv.octants
{'percent_buried_volume': {0: 0.0, ...},
 'buried_volume': {0: 0.0, ...},
 'free_volume': {0: 22.449297503777064, ...},
 'distal_volume': {0: 0.0, ...},
 'molecular_volume': {0: 0.0, ...}}

Plotting

A steric map can be plotted with plot_steric_map if the z_axis_atoms=<list> keyword has been given.

Steric map

>>> from morfeus import BuriedVolume, read_xyz
>>> elements, coordinates = read_xyz("1.xyz")
>>> bv = BuriedVolume(elements, coordinates, 1, excluded_atoms=[2, 3, 4, 5, 6, 7], z_axis_atoms=[2])
>>> bv.plot_steric_map()

Plots can be saved by passing the filename=<str> keyword argument. draw_3D gives a three-dimensional representation of the buried volume.

Command line script

The basic functionality is available through the command line script.

Example

$ morfeus buried_volume 1.xyz - 1 --excluded_atoms='[2,3,4,5,6,7]' - print_report
V_bur (%): 29.6

Background

The percent of buried volume is a measure of the steric hindrance induced by a ligand of a transition metal complex [1]. A web tool to calculate buried volumes, SambVca, was made available for scientific purposes by Cavallo and co-workers in 2009 [2] with version 2 in 2016 [1]. .

The approach of ᴍᴏʀғᴇᴜs differs somewhat from that in ref. [1] in that points are generated uniformly in the test sphere rather than considering voxels. The numerical results with standard settings are the same though as shown by benchmarks on complexes 1-18 from ref. [1]. Steric maps also match those in ref. [1].

References

[1] (1,2,3,4,5,6,7)

Laura Falivene, Raffaele Credendino, Albert Poater, Andrea Petta, Luigi Serra, Romina Oliva, Vittorio Scarano, and Luigi Cavallo. SambVca 2. A web tool for analyzing catalytic pockets with topographic steric maps. Organometallics, 35(13):2286–2293, 2016. doi:10.1021/acs.organomet.6b00371.

[2]

Albert Poater, Biagio Cosenza, Andrea Correa, Simona Giudice, Francesco Ragone, Vittorio Scarano, and Luigi Cavallo. SambVca: A web application for the calculation of the buried volume of N-heterocyclic carbene ligands. European Journal of Inorganic Chemistry, 2009(13):1759–1766, 2009. doi:10.1002/ejic.200801160.