Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

Area of Science:

• Biophysical modeling
• Computational chemistry
• Numerical analysis

Background:

• Surface formulations in biophysical modeling offer computational advantages.
• Numerical simulations often use approximate surface discretizations, impacting accuracy.
• Curved surfaces with complex structures and singularities pose challenges for standard methods.

Purpose of the Study:

• To develop methods for exact surface discretizations in biophysical modeling.
• To assess the impact of surface representation fidelity on simulation accuracy.
• To compare the accuracy of exact curved-element methods versus approximate planar-triangle methods.

Main Methods:

• Defined two classes of curved elements for exact discretization of molecular surfaces (van der Waals, solvent-accessible, solvent-excluded).
• Developed numerical integration techniques for accurate evaluation of integrals over curved surfaces.
• Compared approximate planar-triangle discretizations with exact curved-element simulations for sGB, scvdW, and BEM electrostatics.

Main Results:

• Continuum electrostatic calculations using BEM with curved elements were nearly ten times more accurate than planar-triangle BEM.
• sGB and scvdW calculations showed exceptional accuracy even with coarse discretizations.
• Approximate integration on exact geometry proved more accurate than exact integration on approximate geometry.

Conclusions:

• Exact surface discretizations using curved elements significantly enhance the accuracy of biophysical simulations.
• The precise representation of the solute-solvent interface is crucial for accurate electrostatic calculations.
• The developed methods offer a more accurate and potentially efficient approach to surface-based biophysical modeling.