(1)$R_g ~=~ \left({\frac{\sum_i \|{\bf r}_i\|^2 m_i}{\sum_i m_i}}\right)^{{\frac{1}{2}}}$
where $$m_i$$ is the mass of atom $$i$$ and $${\bf r}_i$$ the position of atom $$i$$ with respect to the center of mass of the molecule. It is especially useful to characterize polymer solutions and proteins. The program will also provide the radius of gyration around the coordinate axis (or, optionally, principal axes) by only summing the radii components orthogonal to each axis, for instance
(2)$R_{g,x} ~=~ \left({\frac{\sum_i \left( r_{i,y}^2 + r_{i,z}^2 \right) m_i}{\sum_i m_i}}\right)^{{\frac{1}{2}}}$
• 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 $$r_{max}$$.
• 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. 56.