3 Radius of gyration and distances
4 --------------------------------
6 | :ref:`gmx gyrate <gmx gyrate>`, :ref:`gmx distance <gmx distance>`,
7 :ref:`gmx mindist <gmx mindist>`, :ref:`gmx mdmat <gmx mdmat>`,
8 :ref:`gmx pairdist <gmx pairdist>`, :ref:`gmx xpm2ps <gmx xpm2ps>`
9 | To have a rough measure for the compactness of a structure, you can
10 calculate the *radius of gyration* with the program
11 :ref:`gmx gyrate <gmx gyrate>` as follows:
13 .. math:: R_g ~=~ \left({\frac{\sum_i \|{\bf r}_i\|^2 m_i}{\sum_i m_i}}\right)^{{\frac{1}{2}}}
16 | where :math:`m_i` is the mass of atom :math:`i` and :math:`{\bf r}_i`
17 the position of atom :math:`i` with respect to the center of mass of
18 the molecule. It is especially useful to characterize polymer
19 solutions and proteins. The program will also provide the radius of
20 gyration around the coordinate axis (or, optionally, principal axes)
21 by only summing the radii components orthogonal to each axis, for
24 .. math:: 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}}}
27 Sometimes it is interesting to plot the *distance* between two atoms, or
28 the *minimum* distance between two groups of atoms (*e.g.*: protein
29 side-chains in a salt bridge). To calculate these distances between
30 certain groups there are several possibilities:
32 * The *distance between the geometrical centers* of two groups can be
33 calculated with the program :ref:`gmx distance <gmx distance>`, as explained in
36 * The *minimum distance* between two groups of atoms during time can
37 be calculated with the program :ref:`gmx mindist <gmx mindist>`. It also calculates the
38 *number of contacts* between these groups within a certain radius
41 * :ref:`gmx pairdist <gmx pairdist>` is a selection-enabled version of :ref:`gmx mindist <gmx mindist>`.
43 * To monitor the *minimum distances between amino acid residues*
44 within a (protein) molecule, you can use the program :ref:`gmx mdmat <gmx mdmat>`. This
45 minimum distance between two residues A\ :math:`_i` and
46 A\ :math:`_j` is defined as the smallest distance between any pair
47 of atoms (i :math:`\in` A\ :math:`_i`, j :math:`\in` A\ :math:`_j`).
48 The output is a symmetrical matrix of smallest distances between all
49 residues. To visualize this matrix, you can use a program such as
50 ``xv``. If you want to view the axes and legend or if you want to print
51 the matrix, you can convert it with :ref:`xpm2ps <gmx xpm2ps>` into a Postscript
52 :numref:`Fig. %s <fig-distm>`.
56 .. figure:: plots/distm.*
59 A minimum distance matrix for a
60 peptide \ :ref:`168 <refSpoel96b>`.
62 * Plotting these matrices for different time-frames, one can analyze
63 changes in the structure, and *e.g.* forming of salt bridges.