Communication: Regularizing binding energy distributions and thermodynamics of hydration: Theory and application to water modeled with classical and ab initio simulations

Abstract

The high-energy tail of the distribution of solute-solvent interaction energies is poorly characterized for condensed systems, but this tail region is of principal interest in determining the excess free energy of the solute. We introduce external fields centered on the solute to modulate the short-range repulsive interaction between the solute and solvent. This regularizes the binding energy distribution and makes it easy to calculate the free energy of the solute with the field. Together with the work done to apply the field in the presence and absence of the solute, we calculate the excess chemical potential of the solute. We present the formal development of this idea and apply it to study liquid water.

Interfaces of propylene carbonate

“…That contribution thus gauges the free energy cost of finding space for positioning the additional PC molecule in the liquid. More broadly, these formalities follow from the identity 22,27 …”

Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix–Coil Transition and Helix–Helix Assembly in a Deca-Alanine Peptide

“…Our hydration free energies based on their structures are in fair agreement (data not shown), and the agreement becomes excellent with more extensive sampling in the calculation of the van der Waals contribution. 45 Besides these, the regularization approach has been tested in studies on water, 2 ions, 46 short peptides, 11,12 and the protein cytochrome c . 3 Further, the quasichemical framework has also been thoroughly documented.…”

“…Since the solvent interface is pushed away from the solute, the solute–solvent interaction is tempered and the conditional distribution P (ε|ϕ) is better behaved than P (ε). 2,3,11 In practice, we adjust the range λ such that P (ε|ϕ) is Gaussian. With the introduction of the field, we have 2,3,11 $$\beta {\mu }^{\text{ex}}=\underset{\text{local chemistry}}{\underset{true︸}{\text{ln }{x}_0[\varphi ]}}+\underset{\text{long}-\text{range}}{\underset{true︸}{\beta {\mu }^{\text{ex}}[P(\epsilon |\varphi )]}}-\underset{\text{G packing}}{\underset{true︸}{\text{ln }{p}_0[\varphi ]}}$$ where − k B T ln x 0 [ϕ(λ)] is the work done to apply the field in the presence of the solute, − k B T ln p 0 [ϕ(λ)] is the corresponding quantity in the absence of the solute, and βμ ex [ P (ε|ϕ)] is the contribution to the interaction free energy in the presence of the field.…”

“…This soft-cavity packing estimate is always a lower-bound to the hard-cavity estimate and can be easily corrected to give the latter. 2 We do not pursue those corrections here and instead use the soft-cavity packing result as a measure of model hydrophobic effects. (Importantly, distinction between a hard-and soft-repulsive cavity is minimized in the relative balance of chemistry and packing contributions (eqs 1 and 2). )…”

“…1 In proteins the α-helix is a common secondary structural motif and understanding the formation of α-helices occupies a pre-eminent place in efforts to understand protein folding. Using computer simulations and a new approach to free energy calculations, 2,3 we re-examine this classic problem and study two transitions in a model decaalanine peptide. Mirroring the primary-to-secondary and secondary-to-tertiary transitions in protein folding, we study the extended coil-to-helix transition and the pairing of two helices to form a helix dimer, respectively.…”