Protein pKa calculations

In computational biology, protein pKa calculations are used to estimate the pKa values of amino acids as they exist within proteins. These calculations complement the pKa values reported for amino acids in their free state, and are used frequently within the fields of molecular modeling, structural bioinformatics, and computational biology.

Amino acid pKa values
pKa values of amino acid side chains play an important role in defining the pH-dependent characteristics of a protein. The pH-dependence of the activity displayed by enzymes and the pH-dependence of protein stability, for example, are properties that are determined by the pKa values of amino acid side chains.

The pKa values of an amino acid side chain in solution is typically inferred from the pKa values of model compounds (compounds that are similar to the side chains of amino acids). (''See Amino acid for the pKa values of all amino acid side chains inferred in such a way.) The table below lists the model pKa values that are normally used in a protein pKa calculation.

The effect of the protein environment
When a protein folds, the titratable amino acids in the protein are transferred from a solution-like environment to an environment determined by the 3-dimensional structure of the protein. For example, in an unfolded protein an Aspartic acid typically is in an environment which exposes the titratable side chain to water. When the protein folds the Aspartic acid could find itself buried deep in the protein interior with no exposure to solvent. Furthermore, in the folded protein the Aspartic acid will be closer to other titratable groups in the protein and will also interact with permanent charges (e.g. ions) and dipoles in the protein. All of these effects alter the pKa value of the amino acid side chain, and pKa calculation methods generally calculate the effect of the protein environment on the model pKa value of an amino acid side chain.

Typically the effects of the protein environment on the amino acid pKa value are divided into pH-independent effects and pH-depenent effects. The pH-independent effects (desolvation, interactions with permanent charges and dipoles) are added to the model pKa value to give the intrinsic pKa value. The pH-dependent effects cannot be added in the same straight-forward way and have to be accounted for using Boltzmann summation, Tanford-Roxby iterations or other methods.

The interplay of the intrinsic pKa values of a system with the electrostatic interaction energies between titratable groups can produce quite spectacular effects such as non-Henderson-Hasselbalch titration curves and even back-titration effects. pKaTool provides an easy interactive and instructive way of playing around with these effects.

The image below shows a theoretical system consisting of three acidic residues. One group is displaying a back-titration event (blue group).

pKa calculation methods
Several software packages and webserver are available for the calculation of protein pKa values. See links below or this table

Using the Poisson-Boltzmann equation
Some methods are based on solutions to the Poisson-Boltzmann equation (PBE), often referred to as FDPB-based methods (FDPB is for "finite difference Poisson-Boltzmann"). The PBE is a modification of Poisson's equation that incorporates a description of the effect of solvent ions on the electrostatic field around a molecule.

The H++ web server, the pKD webserver and MCCE use the FDPB method to compute pKa values of amino acid side chains.

FDPB-based methods calculate the change in the pKa value of an amino acid side chain when that side chain is moved from a hypothetical fully solvated state to its position in the protein. To perform such a calculation, one needs theoretical methods that can calculate the effect of the protein interior on a pKa value, and knowledge of the pKa values of amino acid side chains in their fully solvated state.

Theoretical methods
The pKa values of amino acid side chains in their fully solvated state are often inferred from comparisons with pKa values of so-called model compounds.

Empirical methods
A set of empirical rules relating the protein structure to the pKa values of ionizable residues have been developed by Li, Robertson, and Jensen. These rules form the basis for the web-accessible program called PROPKA for rapid predictions of pKa values.

Molecular dynamics (MD)-based methods
Molecular dynamics methods of calculating pKa values involve computationally measuring the free energy difference between the protonated and deprotonated forms of the molecule. This free energy differences is measured using methods such as free-energy perturbation, thermodynamic integration and the Bennett acceptance ratio.

Molecular dynamics is typically a much more computationally expensive way to predict pKa's than using the Poisson-Boltzmann equation. Furthermore, it is currently much less accurate. This is because currently used molecular force fields do not take polarisability into account. Polarisability is an important property for protonation energies.

Using titration curves to determine pKa values
The pH value where the titratable group is half-protonated is equal to the pKa if the titration curve follows the Henderson-Hasselbalch equation. Most pKa calculation methods silently assume that all titration curves are Henderson-Hasselbalch shaped, and pKa values in pKa calculation programs are therefore often determined in this way.

Software For Protein pKa Calculations

 * H++ Poisson-Boltzmann based pKa calculations
 * MCCE Multi-Conformation Continuum Electrostatics
 * pKD server pKa calculations and pKa value re-design
 * PROPKA Empirical calculation of pKa values
 * WHAT IF pKa calculation package

Analysis and teaching software

 * pKaTool