Root mean square deviations in structure#

The root mean square deviation (RMSD) of certain atoms in a molecule with respect to a reference structure can be calculated with the program gmx rms by least-square fitting the structure to the reference structure (t2=0) and subsequently calculating the RMSD ((459)).
(459)#RMSD(t1,t2) = [1Mi=1Nmiri(t1)ri(t2)2]12
where M=i=1Nmi and ri(t) is the position of atom i at time t. Note that fitting does not have to use the same atoms as the calculation of the RMSD; e.g. a protein is usually fitted on the backbone atoms (N, Cα, C), but the RMSD can be computed of the backbone or of the whole protein.

Instead of comparing the structures to the initial structure at time t=0 (so for example a crystal structure), one can also calculate (459) with a structure at time t2=t1τ. This gives some insight in the mobility as a function of τ. A matrix can also be made with the RMSD as a function of t1 and t2, 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 RMSD can be computed using a fit-free method with the program gmx rmsdist:

(460)#RMSD(t) = [1N2i=1Nj=1Nrij(t)rij(0)2]12

where the distance rij between atoms at time t is compared with the distance between the same atoms at time 0.