Resolving coupled pH titrations using alchemical free energy calculations

Area of Science:

• Biochemistry
• Computational Biology
• Physical Chemistry

Background:

• Titratable sites in proteins, such as amino acid residues, can influence each other's protonation states.
• Understanding these coupled interactions is crucial for predicting protein behavior and function, especially concerning pH-dependent processes.

Purpose of the Study:

• To develop and validate a computational method for accurately quantifying the pKa values of coupled titratable residues in proteins.
• To improve the accuracy of pKa calculations by accounting for residue coupling, which is often neglected in simpler models.

Main Methods:

• Derivation of a formalism based on double free energy differences to quantify individual site pKa values of coupled residues.
• Application of alchemical free energy calculations to estimate these pKa values.
• Validation using toy models, molecular dynamics simulations (regular and constant-pH), and experimental data.

Main Results:

• The proposed formalism, combined with alchemical free energy calculations, effectively resolves pH-dependent protein pKa values.
• Accounting for coupling significantly improves the accuracy of calculated pKa values, reducing errors by up to half compared to naive methods.
• The approach provides insights into coupling and microstate probabilities, applicable to complex enzymatic systems.

Conclusions:

• Alchemical free energy methods offer a robust way to determine pKa values for both uncoupled and coupled residues.
• This work enhances the predictive power of computational methods for understanding protein electrostatics and pH-dependent functions.
• The developed approach facilitates more accurate modeling of biological systems where protonation states are critical.