STRUCTURE COMPARISION METHODS
Because protein structures are composed of amino acids whose side chains are linked by a common protein backbone a number of different possible subseta of atoms that make up a protein macromolecule can be used in producing a structural aligment & calculating the corresponding RMSD values.when aligning structures with very different sequences,the side chain atoms generally are not taken into account because their identities differ between many aligned residues.For this reason it is common for structural alignment methods to use by default only the back bone atoms included in the peptide bond. For simplicity and efficiency, often only the alpha carbon position are considered, since the peptide bond has a minimally variant conformation.Only when the structures to be aligned are highly similar or even identical is meaningfull to align side chain positions, in which case the RMSD reflects not only the conformation of the protein backbone but also the rotamaric states of the side chains, other comparision criteriathat reduce noise and bolster positive matches which include secondary structural alignment, native contact maps or residue interaction patterns, measures of side chain packing and measures of hydrogen bond retention.
The most basic possible comparision between protein structures makes new attempt to align the input structures and requires a pre calculated alignment as input to determine which of the residues in the sequence are intended to be considered in the RMSD calculations. Structural superposition is commonly used to compare multiple conformation of the same protein and to evaluate the quality of alignments produced using only sequence information between two or more sequences whose structures are known.This method traditionally uses a simple least squares fitting algorithm,in which the optimal rotation and translation are found by minimizing the sum of the squared distances among all structures in the superposition.More recently,maximum likelihood and Bayesian methods have greatly increased the accuracy of the estimated rotation,translations and covariance matrices for the superposition.
Algorithm based on multidimensional rotations and modified quaternions have been developed to identify topological relationship between protein structures without the need for a predetermined aligment.Such algorithm have successfully identified canonical folds such as the four helix bundle.The superpose method is sufficiently extensible to correct for relative domain rotations & other structural pitfalls.
A Ramachandran plot developed by gopalasamudram narayana ramachandran & viswanathan sasisekharan is a way to visualize dihedral angles Ψ against Φ of amino acida residues in protein structure.It shows the possible conformation of Ψ & Φ angles for a polypeptide.Mathematically the ramachadran plot is the visualization of a function f:(-п,п) *(-п,п)=R+.The domain of this function is the torus.Hence the conventional ramachandran plot is a projection ot the torus on the plane,resulting in a distorted view & the presence of discontinuities.One would expect that larger side chains would result in more restrictons & consequently a smaller allowable region in the plot.Only the methylene group at the position has an influence.Glyline has a hydrogen atom.With an smaller vander waals radius,instead of a methyl group at the α-position.IN contrast,the plot for praline shows only a very limited no of possible combination of Ψ &Φ.The plot was calculated just before the first protein structures at atomic resolution were determined.forty years later there were tens of thousands of high resolution protein structures determined by x-ray crystallography & deposited in the protein data bank(PDB).One can plot the dihedral angles in polysaccharides & other polymers in this fasion.For the first two protein side chain dihedral angles a similar plot is the janin plot.