[Chimera-users] measurement of arc-length (geodesic distance) between atoms on a protein surface?

[Tom Goddard]

Hi Michael,

  A few years ago I was curious to look at geodesic paths on an electron microscopy map surface, so I wrote a little ChimeraX Python code to do that.  My code just started at a point and headed in a direction on the surface taking a locally minimal path.  You want to get a geodesic between two specified points on a surface.  That is harder and for a surface with hole there will be infinitely many such paths that have different number of turns through a hole, so finding the globally shortest between two points which I guess is what you want is difficult.

  As Elaine pointed out you cannot find a single point on the solvent excluded surface calculated by Chimera/ChimeraX for an atom because a whole spherical patch on the surface is equidistance from the atom (at a distance equal to the atom radius).  You could of course define the point you want, maybe the furthest of the equidistant points from all other atoms, but that would take some tricky code to calculate.

  For your and my amusement I ran that ChimeraX geodesic code to make some paths each 100 Angstroms long on an alpha helix surface (1fav, chain A), image below.  Straight lines on curved surfaces are pretty.  A 1 micron long geodesic on this 78 amino acid alpha helix danced all over the surface .

	Tom

Geodesics on an alpha helix (C-alpha atoms in pink),



A micron long straight line on the alpha helix surface:



Geodesics on electron microscopy surface of a GroEL:



> On Sep 17, 2020, at 4:12 PM, Wiener, Michael C (mcw2s) <mcw2s at virginia.edu> wrote:
> 
> New subscriber here, with a question about whether Chimera currently can measure arc-length (geodesic distance) between atoms on a protein surface (or, for example, generate a Calpha-Calpha distance matrix of this). 
>  
> I am (very) interested in measuring/obtaining distances between pairs of Calpha carbons (or pairs of other atoms, I suppose) of different amino acids that are on the surface of a protein. While the difference between arc-length (geodesic) distance and cartesian/Euclidean distance will be negligible if, for example, the two solvent-exposed Calpha atoms are on the same solvent-exposed face of an alpha-helix, the difference could be significant for residues on opposite “sides” of the protein. I did see that there are ways in Chimera to get distances between an atom and a molecular surface, or to place markers on the surface & obtain the lengths between these for a distance, but I am VERY interested in whether one can simply select two atoms and get the arc-length (geodesic) distance or generate an arc-length (geodesic distance) matrix of all surface-exposed Calpha pairs.
>  
> Several computational methods have been developed for this sort of thing, via graph theoretical or other approximation method, and have been published (Hall et al., Biophysical Chemistry 190-191 [2014] 50-55). However, I have not yet (?) found this to be in any graphics/analysis program. I’m thinking that this could perhaps be useful to someone besides me?
>  
> Any assistance would be greatly appreciated. My lab and I are (much) more on the user side than the developer side, so are not currently well-positioned to code it in-lab.
>  
> Regards,
>  
> -MW
>  
> (btw, if anyone in the “Chimera Group” wants to know more about why I am interested in this, don’t hesitate to send me an email. This type of distance calculation is related to some experimental technology/assay development that we are doing.)
>  
> -----
> Michael C. Wiener. Ph.D., Professor
> Department of Molecular Physiology and
>                 Biological Physics
> University of Virginia
> Charlottesville, VA 22908-0886
> 434-243-2731 (office); 434-243-2730 (lab)
>  
>  
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