Comparison of dielectric response models for simulating electrostatic effects in proteins

Area of Science:

• Biophysics
• Computational Chemistry

Background:

• Accurate calculation of pK shifts in proteins is crucial for understanding protein function and stability.
• Existing methods for calculating pK shifts include empirical models and numerical solutions to electrostatic equations.

Purpose of the Study:

• To compare the accuracy and efficiency of two methods for calculating pK shifts in proteins: Coulomb's law with distance-dependent dielectric permittivity and a finite difference approach to Poisson's equation.
• To evaluate the behavior of dielectric permittivity at different charge separations.

Main Methods:

• Application of Coulomb's law with a distance-dependent dielectric permittivity (ε(r)).
• Implementation of a finite difference method to solve Poisson's equation.
• Statistical analysis of errors in calculated pK shifts for charge separations > 10 Å.

Main Results:

• The distance-dependent dielectric permittivity ε(r) exhibits nonlinear behavior for charge separations greater than 10 Å.
• For charge separations > 10 Å, both methods show marginal differences in reliability for calculating pK shifts.
• Coulomb's law with an appropriate ε(r) provides comparable accuracy to the finite difference approach.

Conclusions:

• Coulomb's law with a distance-dependent dielectric permittivity is a reliable and computationally less intensive method for calculating protein pK shifts.
• The choice of ε(r) is critical, especially for larger charge separations where nonlinearity becomes significant.