pK(A) in proteins solving the Poisson-Boltzmann equation with finite elements

Area of Science:

• Computational Biology
• Biophysics
• Biochemistry

Background:

• Understanding protein pK(A) values is crucial for elucidating protein function in biological systems.
• The finite difference (FD) method is a well-established approach for calculating these values.

Purpose of the Study:

• To introduce and validate a novel finite element (FE) method for computing protein pK(A) values.
• To compare the accuracy and performance of the FE method against the traditional FD method.

Main Methods:

• Implementation of the molecular Finite Element Solver (mFES) software within the Karlsberg+ program.
• Solving the linearized Poisson-Boltzmann equation (lPBE) using both FE and FD methods on protein crystal structures.
• Setting up accurate and coarse model systems with comparable numbers of unknowns for both methods.

Main Results:

• The FE method (mFES) achieves high accuracy in computing protein pK(A) values, comparable to the FD method.
• The FE method provides accurate computations for interaction energies of titratable groups.
• Analysis demonstrates the influence of various parameters on the accuracy of FE-computed pK(A) values.

Conclusions:

• The finite element (FE) method offers a viable and accurate alternative to the finite difference (FD) method for pK(A) calculations in proteins.
• The mFES software provides a powerful tool for accurate pK(A) and interaction energy computations.
• This work advances computational approaches for studying protein electrostatics and function.