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

Abstract

A method for the estimation of coordinates of atoms in proteins from coarse-grained geometry by simple analytical formulas (ESCASA), for use in nuclear-magneticresonance (NMR) data-assisted coarse-grained simulations of proteins is proposed. In this paper, the formulas for the backbone H α and amide (H N ) protons, and the sidechain H β protons, given the C α -trace, have been derived and parameterized, by using the interproton distances calculated from a set of 140 high-resolution nonhomologous 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.

A coarse‐grained approach toNMR‐data‐assisted modeling of protein structures

“…We have developed a multiscale approach to NMR-data-assisted modeling of protein structures, in which the main part of the conformational search is carried out at the coarse-grained level, with explicit NMR-based restraints imposed at simulation time. We have implemented with UNRES the ESCASA algorithm for calculating the approximate positions of the backbone and H β protons from the coarse-grained geometry, 30 extended in this work to other side-chain protons. To handle inaccurate and ambiguous restraints, we have implemented the "intersecting-gorge-like" function (Equation (3) and Figure 2), 37 which is based on the flat-bottom Lorentz-like penalty function introduced in our earlier work 36,47 modified in this work to provide a mild slope at large distances (Equation ( 4)).…”

“…To estimate the positions of the backbone-α (H α ), backbone-amide (HN), and sidechain-β (H β ) protons, we use our recently developed ESCASA algorithm. 30 This algorithm calculates proton positions in the local-coordinate system of the respective C α Á Á ÁC α Á Á ÁC α frame, using approximate analytical formulas. The coordinates of a given H α or H β proton depend on the respective backbone-virtual-bond angle θ, while those of a given HN proton depend on the backbonevirtual-bond-dihedral-angle γ whose axis is the C α Á Á ÁC α axis of the peptide group that contains that proton and the two adjacent virtual-bond angles θ (see Figure 1 for the definition of these angles).…”

“…Therefore, recently, we developed an analytical approach for the estimation of proton coordinates in proteins from the CG geometry (ESCASA), 30 with which the analytical derivatives of the estimated proton positions in the coarse-grained coordinates and, consequently, the analytical forces due to the atom-based restraints are available.…”

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

“…With canonical simulations, it is straightforward to perform cluster analysis of the resulting ensemble and select the mean structures from the clusters as candidate models, ranking them according to decreasing cluster populations; this approach has also been carried over to extended canonical ensemble simulations [231]. We have developed a fully energy-based method of protein structure modeling [79,156], which we used in the CASP exercises [155][156][157][158]232,233]. The method consists of four basic stages.…”

Recent Developments in Data-Assisted Modeling of Flexible Proteins

“…However, this method is not suitable for restrained MD simulations, because it does not provide the forces due to restraints. Recently, we developed ESCASA (Lubecka and Liwo, 2021), an analytical approach to calculating approximate positions of the protons from C α -trace geometry, thus enabling us to compute the forces due to the penalty function and, consequently, to use the method with coarse-grained MD.…”