Free Energies by Thermodynamic Integration Relative to an Exact Solution, Used to Find the Handedness-Switching Salt Concentration for DNA

TL;DR

This paper introduces a thermodynamic integration method combining atomistic models and analytical solutions to accurately compute free energy differences, exemplified by determining the salt concentration at which DNA switches handedness.

Contribution

It presents a novel approach for calculating absolute free energies of biomolecules by integrating detailed models with simplified analytical solutions, enabling precise determination of salt-dependent DNA conformational equilibria.

Findings

Accurately determined the coexistence salt concentration for DNA isomers.

Demonstrated the method's effectiveness in biomolecular free energy calculations.

Achieved unprecedented accuracy in free energy difference estimations.

Abstract

Sets of free energy differences are useful for finding the equilibria of chemical reactions, while absolute free energies have little physical meaning. However finding the relative free energy between two macrostates by subtraction of their absolute free energies is a valuable strategy in certain important cases. We present calculations of absolute free energies of biomolecules, using a combination of the well-known Einstein Molecule method (for treating the solute) with a conceptually related method of recent genesis for computing free energies of liquids (to treat the solvent and counterions). The approach is based on thermodynamic integration from a detailed atomistic model to one which is simplified but analytically solvable, thereby giving the absolute free energy as that of the tractable model plus a correction term found numerically. An example calculation giving the free energy with respect to salt concentration for the B- and Z-isomers of all-atom duplex DNA in explicit solvent and counterions is presented. The coexistence salt concentration is found with unprecedented accuracy.