ESCASA: Analytical estimation of atomic coordinates from coarse-grained geometry for nuclear-magnetic-resonance-assisted protein structure modeling. I. Backbone and Hβ protons.

A method for the estimation of coordinates of atoms in proteins from coarse-grained geometry by simple analytical formulas (ESCASA), for use in nuclear-magnetic-resonance (NMR) data-assisted coarse-grained simulations of proteins is proposed. In this paper, the formulas for the backbone Hα and amide (HN ) protons, and the side-chain Hβ protons, given the Cα -trace, have been derived and parameterized, by using the interproton distances calculated from a set of 140 high-resolution non-homologous protein structures. The mean standard deviation over all types of proton pairs in the set was 0.44 Å after fitting. Validation against a set of 41 proteins with NMR-determined structures, which were not considered in parameterization, resulted in average standard deviation from average proton-proton distances of the NMR-determined structures of 0.25 Å, compared to 0.21 Å obtained with the PULCHRA all-atom-chain reconstruction algorithm and to the 0.12 Å standard deviation of the average-structure proton-proton distance of NMR-determined ensembles. The formulas provide analytical forces and can, therefore, be used in coarse-grained molecular dynamics.