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Improvements to the APBS biomolecular solvation software suite
Elizabeth Jurrus, Dave Engel, Keith Star, Kyle Monson, Juan Brandi, Lisa E. Felberg, David H. Brookes, Leighton Wilson, Jiahui Chen, Karina Liles, Minju Chun, Peter Li, David W. Gohara, Todd Dolinsky, Robert Konecny, David R. Koes, Jens Erik Nielsen, Teresa Head-Gordon, Weihua Geng, Robert Krasny, Guo Wei Wei, Michael J. Holst, J. Andrew McCammon, Nathan A. Baker
TL;DR
Explicit electrostatic models require extensive equilibration and sampling, motivating efficient continuum approaches for biomolecular solvation. This paper reviews APBS-PDB2PQR improvements spanning structure preparation, multiple Poisson-Boltzmann solvers, solvation models, titration-state prediction, visualization, and extensible workflows. The updated suite supports a wide range of computational-biology users and workflows.
Problem
Explicit electrostatic models generally require extensive equilibration and sampling, motivating continuum approaches for efficient biomolecular solvation calculations.
Method
The paper reviews APBS-PDB2PQR capabilities including structure preparation, numerical and analytical solvers, geometric-flow solvation, graph-based pKa prediction, visualization, and framework development.
Results
The updated APBS-PDB2PQR suite provides a wide range of features for users across computational biology expertise levels.
Takeaways & Limitations
APBS-PDB2PQR offers integrated tools for preparing biomolecules, calculating electrostatics, visualizing results, and incorporating new models and workflows.
Abstract
from arXiv · showhide
The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining p$K_a$ values, and an improved web-based visualization tool for viewing electrostatics.
1 Introduction
APBS uses continuum electrostatics to provide efficient, qualitatively accurate biomolecular solvation models while avoiding the extensive equilibration and sampling required by explicit models. This article reviews expanded APBS-PDB2PQR capabilities for structure preparation, electrostatics calculation, and visualization.
- Continuum models eliminate solvent and solute degrees of freedom, exchanging numerical precision for robust qualitative accuracy and efficiency without explicit-model equilibration and sampling.
- The Poisson-Boltzmann equation is a widely used implicit-solvent model that computes the global electrostatic potential within and around biomolecules.
- APBS-PDB2PQR supports biomolecular structure preparation, electrostatics calculations, and web-based workflows for sharing and analyzing results.
- The updated suite adds PB-AM, PB-SAM, an optimized boundary element solver, geometric-flow solvation, graph-based pKa determination, and improved web visualization.
2 Preparing biomolecular structures
PDB2PQR prepares biomolecular structures for Poisson-Boltzmann calculations by converting PDB files to PQR and optimizing structural, titration, hydrogen, charge, and radius information. Its graph-cut method enables polynomial-time titration-state optimization for larger proteins.
- PQR replaces PDB temperature and occupancy columns with per-atom charge and radius values, preserving compatibility with widely used biomolecular workflows.
- PDB2PQR converts PDB structures into PQR files and automatically sets up, executes, and optimizes them for Poisson-Boltzmann calculations.
- PDB2PQR rebuilds missing heavy atoms using amino-acid topologies and existing coordinates, then performs limited sidechain minimization to reduce steric clashes.
- PDB2PQR supports empirical and implicit-solvent methods for estimating amino-acid titration states and pKa values.
- The graph-cut method transforms titratable-group interaction energies into a flow network and has polynomial-time O(N^4) behavior for larger proteins.
- After titration assignment, PDB2PQR adds and optimizes hydrogens and assigns force-field-dependent atomic charges and radii.
3 Solving the Poisson-Boltzmann and related solvation equations
APBS provides finite-difference, finite-element, boundary-element, geometric-flow, analytical, and semi-analytical approaches for solving Poisson-Boltzmann and related solvation equations. These methods trade accuracy, geometric detail, computational focus, and efficiency across biomolecular applications.
- 3.1 Finite difference and finite element solvers: APBS includes finite-element and finite-difference solvers, with FEtk resolving fine features across large domains and PMG providing coarse-grained solutions for many users.
- The geometric-flow formulation couples polar and nonpolar solvation components while optimizing the solute-solvent interface during the calculation.
- 3.3 Boundary element methods: TABI-PB uses a treecode-accelerated boundary integral formulation that concentrates numerical effort on the solute-solvent interface.
- 3.3 Boundary element methods: APBS visualization examples compare multigrid and TABI-PB potentials using a red-white-blue [−4, 4] kJ/mol/e color map under specified ionic and dielectric conditions.
- 3.4 Analytical and semi-analytical methods: PB-AM provides a fully analytical linearized Poisson-Boltzmann solution for multiple macromolecules represented as coarse-grained low-dielectric spheres.
- 3.4 Analytical and semi-analytical methods: PB-SAM extends PB-AM with boundary integrals and overlapping spherical cavities, representing complex molecular boundaries while maintaining computational efficiency.
- 3.4 Analytical and semi-analytical methods: PB-AM and PB-SAM examples compare electrostatic potentials around barnase and barstar using isosurfaces and surface or planar representations.
4 Using APBS results
APBS tools generate electrostatic potentials for biomolecular visualization and support diverse analysis applications. Web-based 3Dmol.js integration broadens access to interactive molecular viewing and calculation workflows.
- Visualization: APBS tools generate electrostatic potentials for visualization software and support graphical interfaces for setting up calculations.Supported visualization packages include PyMOL, VMD, PMV, Chimera, Jmol, and 3Dmol.js.
- Visualization: 3Dmol.js combines desktop-like performance with web-based accessibility for displaying APBS results.The integration extends output formats and adds a customized interface for surfaces, color schemes, cartoons, and spheres.
- Other applications: APBS-PDB2PQR has been used to analyze molecular dynamics trajectories, protein–nanoparticle interactions, nucleic acid–ion interactions, docking, ligand binding, coarse-grained models, and membrane protein simulations.
- Visualization: Figure 4 displays fasciculin-2 (1FAS) with a translucent solvent-accessible surface, stick representation, and red-green-blue coloring.
5 The future of APBS
APBS is being extended through a modular software architecture and a framework intended to integrate existing capabilities with user-defined models and workflows. The future direction emphasizes portability, extensibility, testing, documentation, and cloud-based resources.
- Architecture: APBS uses a Clean OO C architecture that combines object-oriented design with ANSI-C portability and speed.This framework has made it relatively straightforward to extend functionality and incorporate new features.
- Architecture: The Clean OO C design continues to support many APBS and PDB2PQR modules after 17 years.
- Future framework: The planned framework will integrate APBS-PDB2PQR components around common user workflows and map them to cloud-based resources.
- Future framework: APBS aims to provide a well-designed, well-tested, and well-documented framework for incorporating new features, models, methods, and workflows.
A Appendix
The appendix provides limited configuration guidance for APBS electrostatics calculations, focusing on input keywords directly related to solvation setup and execution rather than duplicating the online manual.
- Scope: The appendix focuses on input-file keywords directly related to configuring and executing solvation calculations.
- Scope: It provides basic configuration information rather than reproducing the full APBS user manual.
- Documentation: More detailed APBS documentation is available on the APBS website.
A.1 General keywords for implicit solvent calculations
General ELEC keywords configure ionic species, equation linearization, molecule selection, dielectric properties, temperature, and input data for implicit-solvent calculations across APBS solver types.
- General configuration: The general keywords apply to all solver types described for implicit-solvent calculations.
- Ionic species: The ion keyword specifies each mobile species’ charge qi, concentration ci, and ionic radius used to calculate Vi.The line may be repeated for multiple ionic species.
- Equation choice: The lpbe and npbe keywords select the linearized or full nonlinear Poisson–Boltzmann equation.
- Molecule selection: The mol keyword selects the molecule ID on which calculations are performed.The ID is assigned by READ statements importing molecular data.
- Dielectric properties: The pdie and sdie keywords set dielectric coefficients for the biomolecular interior and bulk solvent, respectively.A typical sdie value is 78.54, while pdie commonly ranges from 2 to 40.
- Temperature: The temp keyword sets calculation temperature in kelvin, with 298 K given as a typical value.
- Input data: READ statements load molecule information, parameter sets, and finite-element meshes.Additional command details are provided on the APBS website.
A.2 Finite element and finite difference calculations in APBS
APBS’s finite difference and finite element methods were documented previously; this section instead addresses how users configure and use them.
- Scope: APBS’s finite difference and finite element methods are described extensively in earlier publications.The section cites prior work for methodological descriptions.
- Scope: The section focuses on configuring and using these methods within APBS.It is not intended as a full re-description of the underlying numerical methods.
- Scope: Both finite difference and finite element calculations are covered as APBS capabilities.The section title and passage jointly establish the two-method scope.
A.2.1 Finite difference calculation configuration
APBS finite difference calculations expose configurable solver, boundary, grid, charge-discretization, and surface-definition options through the input configuration.
- Solver configuration: APBS invokes finite difference calculations through keywords in the ELEC block, including manual, automatic, and parallel multigrid modes.mg-auto and mg-para use focusing to increase resolution in areas of interest.
- Configuration options: APBS documents the numerous finite difference calculation keywords and highlights settings that govern solver configuration and numerical representation.The configuration includes solver type, boundary conditions, grid parameters, charge mapping, and surface definition.
- Boundary conditions: Dirichlet boundary conditions set exterior-domain potential values to asymptotically correct approximations, while zero-potential Dirichlet conditions are not recommended for typical calculations.Other available boundary-condition forms have approximately equal accuracy when the calculation domain is sufficiently large.
- Grid configuration: Grid setup depends on domain lengths Li, grid-point counts ni, and spacings hi = Li/(ni −1), with spacings below 0.5 Å generally recommended.The grid dimensions, center, and spacing are configured for rectangular finite difference domains.
- Charge discretization: Charge-discretization choices trade grid sensitivity against stencil extent and resolution requirements, from spl0 through spl2 to spl4.spl4 distributes charge density to 125 grid points and generally requires smaller spacing for accurate charge-position representation.
- Surface definitions: Surface definitions control dielectric and ion-accessibility coefficients using molecular, smoothed, spline, or polynomial constructions.Spline-based definitions are stable with respect to grid parameters and support force calculations, but may require force-field reparameterization; spl4 provides higher-order continuity for multipole force fields.
A.2.2 Finite elements calculation configuration
APBS finite element calculations begin from an imported or generated mesh and use iterative solve-estimate-refine procedures to reduce solution error under configured limits.
- Invocation: Users invoke APBS’s FEtk finite element solver with the fe-manual keyword in the ELEC input section.Finite element configuration shares many aspects with finite difference configuration but also has unique options.
- Mesh construction: APBS generates an initial mesh from a coarse 8-tetrahedron mesh or imports one externally, then refines it near molecular surfaces and charge locations.Initial refinement continues until targetNum vertices or targetRes edge length is reached.
- Adaptive refinement: The FEtk solve-estimate-refine iteration first solves the problem on the current finite element mesh.This is the first stage of the adaptive finite element workflow.
- Adaptive refinement: APBS then estimates position-dependent solution error using a configured criterion such as simplex, global, or fractional error selection.The ekey setting determines which simplices are flagged for refinement.
- Adaptive refinement: The mesh is adaptively refined to reduce error until the target etol is reached or maxsolve or maxvert limits are met.These stopping conditions bound the number of solve-estimate-refine iterations and mesh vertices.
A.3 Geometric flow calculations in APBS
APBS’s geometric flow implementation is presented as a configuration-and-use section that supplements previously published descriptions of the method.
- Scope: The section provides additional information about APBS’s implementation of the geometric flow equation.It follows the method’s introduction in Section 3.2.
- Scope: Earlier publications describe the geometric flow methods extensively, while this section emphasizes their configuration and use in APBS.The section cites multiple prior references for the underlying methods.
- Scope: The geometric flow calculations are treated as an APBS implementation capability rather than reintroduced from first principles.The passage frames the section as implementation-specific documentation.
A.3.1 Geometric flow calculation configuration
APBS geometric flow calculations are invoked with the geoflow-auto keyword and configured through parameters linking nonpolar and polar implicit-solvent models. The supplied material also documents related boundary-element and analytical solver settings and outputs.
- Geometric flow configuration: The geoflow-auto keyword activates APBS geometric flow calculations in the ELEC input section.Its configuration shares many finite-difference solver keywords and adds parameters for coupling nonpolar and polar solvent models.
- Geometric flow parameters: 0.431 kJ mol−1 Å−2 is the recommended small-molecule solvent surface tension gamma value.Gamma specifies solvent surface tension.
- Geometric flow parameters: 0.104 kJ mol−1 Å−3 is the recommended small-molecule internal solvent pressure value for press.The press parameter specifies internal solvent pressure.
- Geometric flow parameters: 0.0334 Å−3 is the recommended bulk water density for bconc, which specifies bulk solvent concentration.The vdwdisp option separately controls inclusion of van der Waals interactions and requires force-field van der Waals terms when enabled.
- Related solver configuration: TABI-PB discretizes the solute–solvent boundary into surface elements and uses treecode-accelerated matrix-vector products for the resulting dense system.The solver outputs surface potential, its normal derivative, and electrostatic solvation energy; mesh choices include MSMS and NanoShaper implementations.
- Analytical solver formulation: PB-AM represents charge distributions with effective multipole expansions, whose solved coefficients support interaction energies, forces, and torques.The linear system combines dielectric boundary crossing, cavity polarization, coordinate transformation, and fixed-charge operators.