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Adaptive Cartesian and torsional restraints for interactive model rebuilding.

ABSTRACT: When building atomic models into weak and/or low-resolution density, a common strategy is to restrain their conformation to that of a higher resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of `top-out' potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviation between the model and reference grows beyond that range. In each current implementation the rate at which the potential flattens at large deviations follows a fixed form, although the form chosen varies among implementations. A restraint potential with a tuneable rate of flattening would provide greater flexibility to encode the confidence in any given restraint. Here, two new such potentials are described: a Cartesian distance restraint derived from a recent generalization of common loss functions and a periodic torsion restraint based on a renormalization of the von Mises distribution. Further, their implementation as user-adjustable/switchable restraints in ISOLDE is described and their use in some real-world examples is demonstrated.

SUBMITTER: Croll TI

PROVIDER: S-EPMC8025879 | biostudies-literature | 2021 Apr

REPOSITORIES: biostudies-literature

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Adaptive Cartesian and torsional restraints for interactive model rebuilding.

Croll Tristan Ian TI Read Randy J RJ

Acta crystallographica. Section D, Structural biology 20210330 Pt 4

When building atomic models into weak and/or low-resolution density, a common strategy is to restrain their conformation to that of a higher resolution model of the same or similar sequence. When doing so, it is important to avoid over-restraining to the reference model in the face of disagreement with the experimental data. The most common strategy for this is the use of `top-out' potentials. These act like simple harmonic restraints within a defined range, but gradually weaken when the deviati ...[more]

PMID: 33825704

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Project description:An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous assessment of the solution accuracy; (ii) a pair of low dielectric charged spheres embedded in a ionic solvent to compute electrostatic interaction free energies as a function of the distance between sphere centers; (iii) surface potentials of proteins, nucleic acids and their larger-scale assemblies such as ribosomes; and (iv) electrostatic solvation free energies and their salt sensitivities - obtained with both linear and nonlinear Poisson-Boltzmann equation - for a large set of proteins. These latter results along with timings can serve as benchmarks for comparing the performance of different PBE solvers.

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Adaptive Cartesian and torsional restraints for interactive model rebuilding.

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Adaptive Cartesian and torsional restraints for interactive model rebuilding.

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