.. _rmsd: Root mean square deviations in structure ---------------------------------------- | :ref:gmx rms , :ref:gmx rmsdist  | The *root mean square deviation* (:math:RMSD) of certain atoms in a molecule with respect to a reference structure can be calculated with the program :ref:gmx rms  by least-square fitting the structure to the reference structure (:math:t_2 = 0) and subsequently calculating the :math:RMSD (:eq:eqn. %s ). .. math:: RMSD(t_1,t_2) ~=~ \left[\frac{1}{M} \sum_{i=1}^N m_i \|{\bf r}_i(t_1)-{\bf r}_i(t_2)\|^2 \right]^{\frac{1}{2}} :label: eqnrmsd | where :math:M = \sum_{i=1}^N m_i and :math:{\bf r}_i(t) is the position of atom :math:i at time :math:t. **Note** that fitting does not have to use the same atoms as the calculation of the :math:RMSD; *e.g.* a protein is usually fitted on the backbone atoms (N,C:math:_{\alpha},C), but the :math:RMSD can be computed of the backbone or of the whole protein. Instead of comparing the structures to the initial structure at time :math:t=0 (so for example a crystal structure), one can also calculate :eq:eqn. %s  with a structure at time :math:t_2=t_1-\tau. This gives some insight in the mobility as a function of :math:\tau. A matrix can also be made with the :math:RMSD as a function of :math:t_1 and :math:t_2, which gives a nice graphical interpretation of a trajectory. If there are transitions in a trajectory, they will clearly show up in such a matrix. Alternatively the :math:RMSD can be computed using a fit-free method with the program :ref:gmx rmsdist : .. math:: RMSD(t) ~=~ \left[\frac{1}{N^2}\sum_{i=1}^N \sum_{j=1}^N \|{\bf r}_{ij}(t)-{\bf r}_{ij}(0)\|^2\right]^{\frac{1}{2}} :label: eqnrmsdff where the *distance* **r**\ :math:_{ij} between atoms at time :math:t is compared with the distance between the same atoms at time :math:0.