Root Mean Square Deviation Rmsd
The residual function used to measure the similarity between two protein structures following rigid body superposition is typically the root mean square deviation between the structures (RMSD).
The RMSD between two structures is quite simply the square root of the average squared distance between equivalent atoms, defined by the equation:
The distances (di) can be visualized as:
manual inspections of the structures or by identifying residues binding common ligands in the active-sites of the two proteins.
Once the optimal superposition has been determined the difference between the structures is commonly measured by the Root Mean Square Deviation (RMSD) shown in equation (1), Box 6.1. Structures having a similar fold typically give values below 3.5A although there is a size dependence to this measure. For example, distant homologs with more than 400 residues may return an RMSD above 4.0A compared to a value of<3.0A for smaller proteins with less than 100 residues, but of comparable evolutionary distance.
Sometimes RMSD is only measured over those residues which have a higher probability of being equivalent, that is residues within a certain intermolecular distance from each other after superposition, typically<3.0A. It is obviously important to consider both the value of the RMSD and the number of equivalent pairs identified, when considering the significance of a similarity. For example, an RMSD of<3A over 20 residues of a 200-residue protein would not constitute a very significant global similarity between two proteins.
RMSD is a very commonly cited measure describing structural similarity and methods which align structures using other protocols often include a final step to superpose equivalent residues by rigid body techniques, and determine the RMSD value. More recently, statistical approaches have also been developed for assessing the significance of structural similarity detected between protein pairs. These are often more reliable as they are independent of protein size and are described in more detail below.
Rigid body superposition methods are highly effective for exploring structural changes occurring on co-factor or substrate binding and also for analyzing the structural effects of point mutations in the sequence as in both these cases equivalent residues between the structures are already known. Similarly, NMR structure determination typically generates many very similar structural models, which are alternative solutions to the distance constraints obtained from
Figure 6.5
Schematic representation of the steps involved in rigid body superposition of two protein structures. (a) Translation of the centers of mass of both protein structures to the origin of a common co-ordinate frame of reference. (b) Rotation of one structure relative to the other to minimize the 'distance' between the superposed structures measured by the RMSD (see Box 6.1).
the experimental measurements. Again, because the equivalent positions are already known, the structures can be superposed very easily. However, for comparing more distant protein relatives, having substantial insertions or deletions additional strategies must be incorporated to help determine the initial sets of equivalences for superposing the structures. These are discussed below.
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