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Theory and implementation

The RMSD is maybe the most popular estimator of structural similarity. It is a numerical measure of the difference between two structures that can be defined as:
\begin{displaymath}
RMSD(t) = \sqrt{\frac{\sum_{\alpha = 1}^{N_{\alpha}}({\bf r}_{\alpha}(t) - {\bf r}_{\alpha}(t_{ref}))}{N_{\alpha}}}
\end{displaymath} (4.30)

where $N_{\alpha}$ is the number of atoms of the system, and ${\bf r}_{\alpha}(t)$ and ${\bf r}_{\alpha}(t_{ref})$ are respectively the position of atom $\alpha$ at time $t$ and $t_{ref}$ where $t_{ref}$ is a reference time usually choosen as the first step of the simulation. Typically, RMSD is used to quantify the structural evolution of the system during the simulation. It can provide precious information about the system especially if it reached equilibrium or conversely if major structural changes occured during the simulation.

In nMOLDYN, RMSD is computed using the discretized version of equation 4.30:

\begin{displaymath}
RMSD(n\cdot\Delta t) = \sqrt{\frac{\sum_{\alpha = 1}^{N_{\al...
...- {\bf r}_{ref}(t))}{N_{\alpha}}},
\qquad n = 0\ldots N_t - 1.
\end{displaymath} (4.31)

where $N_t$ is the number of frames and $\Delta t$ is the time step.


next up previous contents
Next: Parameters Up: Root Mean-Square Deviation Previous: Root Mean-Square Deviation   Contents
pellegrini eric 2009-10-06