Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points

Harris, Robert C.; Deng, Nanjie; Levy, Ronald M.; Ishizuka, Ryosuke; Matubayasi, Nobuyuki

doi:10.1002/jcc.24668

Cited by 15 publications

(17 citation statements)

References 83 publications

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“…We have chosen β -cyclodextrin ( β -CD) to be the solute; it is a classic “host” molecule used for modeling molecular recognition 57–62 which we have studied previously. 63–65 Structurally, β -CD is made up of 7 D-glucose molecules linked in a 7-membered ring, which surrounds a central opening to which “guest” molecules can bind. β -CD is frustum shaped with a wider opening at one end lined by 14 secondary alcohols, and a narrower opening at the other end lined by 7 primary alcohols.…”

Section: Model Pdt Calculations For the Solvent Excess Chemical Potenmentioning

confidence: 99%

Relationship between Solvation Thermodynamics from IST and DFT Perspectives

et al. 2017

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Inhomogeneous solvation theory (IST) and classical density functional theory (DFT) each provide a framework for relating distribution functions of solutions to their thermodynamic properties. As reviewed in this work, both IST and DFT can be formulated in a way that use two “end point” simulations, one of the pure solvent and the other of the solution, to determine the solute chemical potential and other thermodynamic properties of the solution and of subvolumes in regions local to the solute containing hydrating waters. In contrast to IST, where expressions for the excess energy and entropy of solution are the object of analysis, in the DFT end point formulation of the problem, the solute–solvent potential of mean force (PMF) plays a central role. The indirect part of the PMF corresponds to the lowest order (1-body) truncation of the IST expression. Because the PMF is a free energy function, powerful numerical methods can be used to estimate it. We show that the DFT expressions for the solute excess chemical potential can be written in a form which is local, involving integrals only over regions proximate to the solute. The DFT end point route to estimating solvation free energies provides an alternative path to that of IST for analyzing solvation effects on molecular recognition and conformational changes in solution, which can lead to new insights. In order to illustrate the kind of information that is contained in the solute–solvent PMF, we have carried out simulations of β-cyclodextrin in water. This solute is a well studied “host” molecule to which “guest” molecules bind; host–guest systems serve as models for molecular recognition. We illustrate the range of values the direct and indirect parts of the solute–solvent PMF can have as a water molecule is brought to the interface of β-cyclodextrin from the bulk; we discuss the “competition” between these two terms, and the role it plays in molecular recognition.

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Section: Model Pdt Calculations For the Solvent Excess Chemical Potenmentioning

confidence: 99%

Relationship between Solvation Thermodynamics from IST and DFT Perspectives

et al. 2017

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“…Because of their small sizes and simpler intermolecular energy landscapes compared to the more complex proteinligand systems, host-guest systems allow for more complete sampling of the phase space and serve as useful model systems for validating and comparing binding free energy models. 21,36,[56][57][58][59] Using host-guest systems as examples, Chang and Gilson et al in an early study elucidated the roles of configurational entropy, preorganization, and induced fit effects in binding and observed strong compensation between the configurational entropy and effective energy. 21 Recently Chang's group reported the binding thermodynamics and kinetics of host-guest systems obtained using direct sampling of the association/dissociation event in microseconds MD and end-point calculations in explicit solvent.…”

Section: Introductionmentioning

confidence: 99%

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

Wickstrom

Gallichio

Chen

et al. 2022

Phys. Chem. Chem. Phys.

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“…When seen in terms of the solute volume, however, the deviation of the solvation free energy Δμ u from its numerically exact value in Table 2 is larger than those in previous studies. 13,58,59 The volumes of the C×2 and C×3 solutes are ∼3 and ∼5 times that of the C×1 (methane-like) solute (note that we adopted the geometric combination rule for LJ σ). Many of the amino acid analogues examined in refs 13 and 58 have more than 3 or 5 non-hydrogen atoms, while the difference between the approximate and exact values is less than 1 kcal/mol.…”

Section: Structural Features Of the Cavity Particlementioning

confidence: 99%

“…13,58 Alanine dipeptide and β-cyclodextrin have even more non-hydrogen atoms (10 and 77, respectively), and the deviation from the exact value was still found to be within 2 and 10 kcal/mol, respectively. 59 This results from a cancellation of errors between the hydrophobic and polar contributions for realistic solutes. As noted in section 5.3, the contribution from the repulsive region of the solute−solvent interaction to Δμ u is overestimated in the endpoints method.…”

Section: Structural Features Of the Cavity Particlementioning

confidence: 99%

Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals

2020

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Endpoints density functional theory (DFT) provides a framework for calculating the excess chemical potential of a solute in solution using solvent distribution functions obtained from both physical endpoints of a hypothetical charging process which transforms the solvent density from that of the pure liquid to the solution state. In this work, the endpoints DFT equations are formulated in terms of the indirect (solvent-mediated) contribution ω(x) to the solute–solvent potential of mean force, and their connections are established with the conventional DFT expressions which are based on the use of direct correlation functions. ω actually corresponds to the free-energy cost to move a cavity particle (a tagged solvent molecule which interacts with the other solvent molecules but not the solute) from the bulk to the configuration x of a solvent molecule relative to the solute and is a suitable variable to describe the solvent effects on the solute–solvent interactions. HNC and PY type approximations are then used to integrate the DFT charging integral involved in the exact expression for the excess chemical potential. With these approximations, molecular simulations are to be performed at the two endpoints of solute insertion: pure solvent without the solute and the solution system with the fully coupled solute–solvent interaction. An endpoints method thus utilizes the ensembles of intermolecular configurations of physical interest, which are often readily accessible with MD simulations given the present computational power. To illustrate properties of the formulation, we perform simulations of model systems consisting of a cavity particle in an aqueous solution containing a spherical hydrophobic solute of three different sizes from which ω(x) and the solute chemical potential can be calculated using endpoints DFT expressions. These are compared with corresponding results obtained using the approximations needed in order to evaluate the endpoints DFT charging integral when cavity particle simulation data is not available. We analyze a new approximation (two-points quadratic HNC) to the DFT charging integral which captures the correct behavior of the cavity distributions at both endpoints of the solute insertion. The behavior of the cavity particle in simple and complex liquids plays an important role in various theoretical treatments of the solute chemical potential. For pure Lennard-Jones fluids, the free energy to bring a cavity particle from the bulk to the center of a fluid particle is negative. However, for solutes of varying size, this is not generally true for Lennard-Jones fluids or the systems studied in this work. We carry out energetic and structural analyses of the cavity particle in aqueous solution with hydrophobic solutes of varying size and discuss the results in the context of the hydrophobic effect.

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Computing conformational free energy differences in explicit solvent: An efficient thermodynamic cycle using an auxiliary potential and a free energy functional constructed from the end points

Cited by 15 publications

References 83 publications

Relationship between Solvation Thermodynamics from IST and DFT Perspectives

Relationship between Solvation Thermodynamics from IST and DFT Perspectives

Developing end-point methods for absolute binding free energy calculation using the Boltzmann-quasiharmonic model

Cavity Particle in Aqueous Solution with a Hydrophobic Solute: Structure, Energetics, and Functionals

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