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Theory and implementation

ROG is the name of several related measures of the size of an object, a surface, or an ensemble of points. It is calculated as the Root Mean Square Distance between the system and a reference that can be either the center of gravity of the system either a given axis. In nMOLDYN, the reference is choosen to be the center of gravity of the system under study. Mathematically, it can be defined as:
\begin{displaymath}
ROG(t) = \sqrt{\frac{\sum_{\alpha = 1}^{N_{\alpha}}({\bf r}_{\alpha}(t) - {\bf r}_{cms}(t))}{N_{\alpha}}}
\end{displaymath} (4.32)

where $N_{\alpha}$ is the number of atoms of the system, and ${\bf r}_{\alpha}(t)$ and ${\bf r}_{cms}(t)$ are respectively the position of atom $\alpha$ and the center of mass of the system at time $t$.

ROG describes the overall spread of the molecule and as such is a good measure for the molecule compactness. For example, it can be useful when monitoring folding process.

In nMOLDYN, ROG is computed using the discretized version of equation 4.32:

\begin{displaymath}
ROG(n\cdot\Delta t) = \sqrt{\frac{\sum_{\alpha = 1}^{N_{\alp...
...- {\bf r}_{cms}(t))}{N_{\alpha}}},
\qquad n = 0\ldots N_t - 1.
\end{displaymath} (4.33)

where $N_t$ is the number of frames and $\Delta t$ is the time step.
next up previous contents
Next: Parameters Up: Radius of gyration Previous: Radius of gyration   Contents
pellegrini eric 2009-10-06