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Given the 3D structure of a molecule (e.g. as *.mol) and a probe radius r, I want to calculate the solvent excluded surface (SES) and the excluded volume enclosed by it. Note the difference between SAS and SES:

enter image description here

I'm looking for a command line program, C/C++ or Python library that can accomplish such a task.

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MSMS

MSMS is a rather old (1996) command line tool that computes the Solvent Excluded Surface (SES). It is wrapped in a python module in mgtool or in openstructure which may be more convenient to use.

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    $\begingroup$ Includes everything I was looking for and the Python bindings is a neat plus. You set the bar very high for potential competing answers. $\endgroup$ – Kexanone Mar 15 at 19:57
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    $\begingroup$ Nice to hear you got an answer that you like! The other answer is substantially longer, was that suggestion not useful for you? $\endgroup$ – Nike Dattani Mar 19 at 16:24
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    $\begingroup$ I personally went for MSMS, but I will give him the bounty for his effort. $\endgroup$ – Kexanone Mar 21 at 20:21
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EDTSurf

EDTSurf[1] is a common and reasonably well regarded approach. The source code is available at https://zhanglab.ccmb.med.umich.edu/EDTSurf/

I tested the mac version and it worked with the following:

./EDTSurf_mac -i kras.pdb

which outputs kras.ply. A slight hiccup is the website describes different command line arguments - but the default is the SES. You'll see they have windows and linux versions, too.

Assuming you're comfortable with python, you could then visualize the output with Open3D:

import open3d as o3d
mesh = o3d.io.read_triangle_mesh("./kras.ply")
o3d.visualization.draw_geometries([mesh])

Now, for volume. Volume of the SES is difficult to calculate exactly, but the volume of a mesh is trivial to calculate. Open3D has a get_volume method:

mesh.get_volume()

unfortunately that froze my jupyter notebook every time - you may have better luck with a fresh install.

But the following will also work:

import numpy as np

verts = np.array(mesh.vertices)
faces = np.array(mesh.triangles)

def signed_vol_of_triangle(p1, p2, p3):
    v321 = p3[0]*p2[1]*p1[2]
    v231 = p2[0]*p3[1]*p1[2]
    v312 = p3[0]*p1[1]*p2[2]
    v132 = p1[0]*p3[1]*p2[2]
    v213 = p2[0]*p1[1]*p3[2]
    v123 = p1[0]*p2[1]*p3[2]
    return (1 / 6)*(-v321 + v231 + v312 - v132 - v213 + v123)


def make_vol(pts):
    return signed_vol_of_triangle(pts[0], pts[1], pts[2])

print(sum([make_vol(v) for v in verts[faces]]))

In short, this loops through each triangle in the mesh and calculates the signed volume of the triangular prism with the fourth point at the origin. The theory behind this is in [2], and I used the implementation in this SO answer which you might want to also consult: https://stackoverflow.com/a/1568551/3089865

While I haven't rigorously tested that volume-calculating approach for correctness, it returns 21058.959617488006 angstrom cubed, which seems reasonable to me (~21 nm^3) given KRAS fits in a ~4x3x3nm box.

[1] Xu, Dong, Hua Li, and Yang Zhang. "Protein depth calculation and the use for improving accuracy of protein fold recognition." Journal of Computational Biology 20.10 (2013): 805-816.

[2]Zhang, Cha, and Tsuhan Chen. "Efficient feature extraction for 2D/3D objects in mesh representation." Proceedings 2001 International Conference on Image Processing (Cat. No. 01CH37205). Vol. 3. IEEE, 2001.

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