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Measuring Eccentricity

Introduction

Eccentricity is a measure of how much a protein or complex's shape deviates from a sphere, or its roundness.

Eccentricity (e) is calculated using the moments of inertia (I) from the three principal axes (x, y, z). Values of e closer to 0 are considered more spherical, while values closer to 1 are more ellipsoid.

e can be calculated using the following equation1:

Equation for eccentricity. Eccentricity = sqrt(1 - ((Ix + Iy - Iz) / (-Ix + Iy + Iz)))

I for each axis can be calculated using gmx gyrate with the -moi option. Note that gmx principal may also be used to determine I, but gmx gyrate is currently supported in scripts used by our lab.

You should have the following files:

  • Trajectory files (.xtc)
  • Topology file (.tpr)

Note

gmx gyrate was changed in the 2024 version of GROMACS. This page references the command as it was in prior releases.

Using gmx gyrate

To calculate moments of inertia using gmx gyrate:

gmx gyrate -f trajectory.xtc -s topology.tpr -o moi.xvg -moi
Other options you may find useful

Warning

You MUST use the -moi option, otherwise GROMACS will calculate radius of gyration instead.

When prompted, select the atom group you wish to analyze. Special groups will require a custom index file to be supplied with -n.

This will output an XVG file of I versus time. This file can be processed to extract each value and calculate the eccentricity of your protein. Alternatively, it can also be visualized using Grace or Python, as is.

Additional Resources

  1. This is the equation used in the lab to determine e. Occasionally, you will find literature that also uses a more simplified equation of e = 1 - (Imin/Iavg). ↩