# Radius of gyration and distances¶

*radius of gyration*with the program gmx gyrate as follows:

(456)¶\[R_g ~=~ \left({\frac{\sum_i \|{\bf r}_i\|^2 m_i}{\sum_i m_i}}\right)^{{\frac{1}{2}}}\]

(457)¶\[R_{g,x} ~=~ \left({\frac{\sum_i \left( r_{i,y}^2 + r_{i,z}^2 \right) m_i}{\sum_i m_i}}\right)^{{\frac{1}{2}}}\]

Sometimes it is interesting to plot the *distance* between two atoms, or
the *minimum* distance between two groups of atoms (*e.g.*: protein
side-chains in a salt bridge). To calculate these distances between
certain groups there are several possibilities:

The

*distance between the geometrical centers*of two groups can be calculated with the program gmx distance, as explained in sec. Bonds/distances, angles and dihedrals.The

*minimum distance*between two groups of atoms during time can be calculated with the program gmx mindist. It also calculates the*number of contacts*between these groups within a certain radius \(r_{max}\).gmx pairdist is a selection-enabled version of gmx mindist.

To monitor the

*minimum distances between amino acid residues*within a (protein) molecule, you can use the program gmx mdmat. This minimum distance between two residues A\(_i\) and A\(_j\) is defined as the smallest distance between any pair of atoms (i \(\in\) A\(_i\), j \(\in\) A\(_j\)). The output is a symmetrical matrix of smallest distances between all residues. To visualize this matrix, you can use a program such as`xv`

. If you want to view the axes and legend or if you want to print the matrix, you can convert it with xpm2ps into a Postscript Fig. 58.

Plotting these matrices for different time-frames, one can analyze changes in the structure, and

*e.g.*forming of salt bridges.