# Continuum Electrostatics

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## Introduction

Continuum electrostatics models parts of the system as a dielectric and other parts atomistically.

## Solvation Free Energy

The solvation free energy is the energy required to submerge a system in water. In continuum electrostatic calculations, the water is approximated as a dielectric.

### Solvation Energy of a Proteins

For a protein, the protein is modeled atomistically, with each atom having a radius and charge. The radii are used to determine the solvent accessible surface area (the region at which protein volume transitions to water). The solvation free energy is then the energy to dunk the atomic partial charges in the water. Two calculations are done, one for charges in vacuum and one for charges in a dielectric of water. The difference in energy is the solvation free energy of the protein.

### Binding Energy

The binding free energy of a molecule to a protein can also be calculated using continuum electrostatics. The binding free energy is the change in solvation energy between the protein and ligand separately and the solvation energy of the protein and ligand complex.

## Poisson-Boltzmann Equation

Poisson-Boltzmann equation is a method for calculating the solvation energy of a system.

### Calculation Parameters

Finite-difference methods for solving the Poisson-Boltzmann equation involve extrapolating the system to a grid and solving for the discretized system.

| Atomic Partial Charges and Radii

Each atom is given a partial atomic charge and a radii. The sum of the partial atomic charges for a molecule should sum to a net integer. If not, you did something wrong.

| Dielectric Constants

The polarizability of a system is modeled by dielectric constant. The dielectric constant for water is 78 or 80 and the dielectric constant for a protein is anywhere between 2 and 20. This is pretty controversial.

| Grid Definition

The grid is defined as a set of points in the x, y, and z direction. One can define the grid by defining two the these three parameters: number of grid point in each of the x, y, and z direction, grid spacing between grid points in each direction, and length of the calculation grid. The center of the grid must also be defined.

| Charge Extrapolation to Grid

There are several methods in which charges can be placed onto the grid.

## Reduction Potential Calculations

To calculate the reduction potential of a redox protein, the change in solvation free energy of the redox site in the protein is calculated.