# mdtraj.shrake_rupley¶

mdtraj.shrake_rupley(traj, probe_radius=0.14, n_sphere_points=960, mode='atom', change_radii=None, get_mapping=False)

Compute the solvent accessible surface area of each atom or residue in each simulation frame.

Parameters
trajTrajectory

An mtraj trajectory.

The radius of the probe, in nm.

n_sphere_pointsint, optional

The number of points representing the surface of each atom, higher values leads to more accuracy.

mode{‘atom’, ‘residue’}

In mode == ‘atom’, the extracted areas are resolved per-atom In mode == ‘residue’, this is consolidated down to the per-residue SASA by summing over the atoms in each residue.

A partial or complete dict containing the radii to change from the defaults. Should take the form {“Symbol” : radii_in_nm }, e.g. {“Cl” : 0.175 } to change the radii of Chlorine to 175 pm.

get_mappingbool, optional

Instead of returning only the areas, also return the indices of the atoms or the residue-to-atom mapping. If True, will return a tuple that contains the areas and the mapping (np.array, shape=(n_atoms)).

Returns
areasnp.array, shape=(n_frames, n_features)

The accessible surface area of each atom or residue in every frame. If mode == ‘atom’, the second dimension will index the atoms in the trajectory, whereas if mode == ‘residue’, the second dimension will index the residues.

Notes

This code implements the Shrake and Rupley algorithm, with the Golden Section Spiral algorithm to generate the sphere points. The basic idea is to great a mesh of points representing the surface of each atom (at a distance of the van der waals radius plus the probe radius from the nuclei), and then count the number of such mesh points that are on the molecular surface – i.e. not within the radius of another atom. Assuming that the points are evenly distributed, the number of points is directly proportional to the accessible surface area (its just 4*pi*r^2 time the fraction of the points that are accessible).

There are a number of different ways to generate the points on the sphere – possibly the best way would be to do a little “molecular dyanmics” : put the points on the sphere, and then run MD where all the points repel one another and wait for them to get to an energy minimum. But that sounds expensive.

This code uses the golden section spiral algorithm (picture at http://xsisupport.com/2012/02/25/evenly-distributing-points-on-a-sphere-with-the-golden-sectionspiral/) where you make this spiral that traces out the unit sphere and then put points down equidistant along the spiral. It’s cheap, but not perfect.

The gromacs utility g_sas uses a slightly different algorithm for generating points on the sphere, which is based on an icosahedral tesselation. roughly, the icosahedral tesselation works something like this http://www.ziyan.info/2008/11/sphere-tessellation-using-icosahedron.html

References

1

Shrake, A; Rupley, JA. (1973) J Mol Biol 79 (2): 351–71.