Abstract
The Ramachandran map consisting of the dihedral angles ϕ and ψ has been an object of study for 50 years, since its presentation by Ramachandran, Ramakrishnan, and Sasisekharan in July 1963. As the number of structures has grown, it has become possible to apply modem non-parametric statistics to develop proper probability density estimates for the Ramachandran distribution for each amino acid type and different input data sets. It has also become possible to derive classification functions and regressions as a function of ϕ and ψ If. For example our most recent backbone-dependent rotamer library consists of the classification probability of the side-chain rotamers and a regression of the mean dihedral angles and variances. The backbone and side-chain bond angles of amino acids also vary with ϕ,ψ, as observed in non-parametric regressions from sub-Angstrom crystal structme data. This variation confirms Ramachandran's early work that some regions of the Ramachandran map are only accessible with larger values of the backbone bond angle N-Cα-C. Most non-parametric statistical methods can be appropriately modified for pairs of angles and applied to the Ramachandran variables, including kernel density estimates and kernel regressions with the bivariate von Mises distribution, hieraiChi.cal Dirichlet processes, and Gaussian processes.
Original language | English |
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Title of host publication | Biomolecular Forms And Functions: A Celebration Of 50 Years Of The Ramachandran Map |
Subtitle of host publication | A Celebration of 50 Years of the Ramachandran Map |
Editors | M Bansal, N Srinivasan |
Publisher | World Scientific Publishing Co. |
Pages | 76-94 |
Number of pages | 19 |
ISBN (Electronic) | 9789814449144 |
ISBN (Print) | 9789814449137 |
DOIs | |
State | Published - 2013 |