A "Reverse-Schur" Approach to Optimization With Linear PDE Constraints: Application to Biomolecule Analysis and...

Area of Science:

• Computational chemistry
• Molecular modeling
• Drug discovery

Background:

• Optimizing molecular electrostatic interactions is crucial for drug design.
• Traditional methods are computationally expensive, limiting their application.
• Linear-response theory and continuum models form the basis of current approaches.

Purpose of the Study:

• To develop a significantly faster computational approach for optimizing molecular electrostatic interactions.
• To enhance the efficiency of ligand design by accelerating electrostatic optimization.
• To explore the implications of electrostatic optimization in molecular binding events.

Main Methods:

• A partial-differential-equation (PDE)-constrained optimization approach named reverse-Schur co-optimization.
• Simultaneous solving of optimization and electrostatic simulation problems.
• Incorporation of regularization using an approximate Hessian calculated via the BIBEE/P method.

Main Results:

• The reverse-Schur co-optimization method is over two orders of magnitude faster than traditional methods.
• The approach demonstrates favorable scaling compared to standard methods for both model and realistic problems.
• The method is applicable to both unconstrained and constrained optimization problems.

Conclusions:

• Reverse-Schur co-optimization offers a substantial computational advantage for electrostatic optimization.
• This efficiency can greatly benefit ligand design by enabling rapid screening and improved binding.
• The method provides a powerful tool for exploring molecular interactions in computational chemistry.