Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid

Torrie, G. M.; Valleau, J. P.

doi:10.1016/0009-2614(74)80109-0

Cited by 1,261 publications

(978 citation statements)

References 8 publications

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“…35 For that purpose, a hexadecane/water simulation system box was taken from previous research, 36 which contained 80 n-hexadecane and 1104 TIP4P water molecules 37 ( Figure 1A). The system was equilibrated for 5 ns and simulated for another 15 ns under equilibrium conditions.…”

Section: ■ Methodsmentioning

confidence: 99%

Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Hub

Groot

Grubmüller

et al. 2014

J. Chem. Theory Comput.

201

218

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Ewald summation, which has become the de facto standard for computing electrostatic interactions in biomolecular simulations, formally requires that the simulation box is neutral. For non-neutral systems, the Ewald algorithm implicitly introduces a uniform background charge distribution that effectively neutralizes the simulation box. Because a uniform distribution of counter charges typically deviates from the spatial distribution of counterions in real systems, artifacts may arise, in particular in systems with an inhomogeneous dielectric constant. Here, we derive an analytical expression for the effect of using an implicit background charge instead of explicit counterions, on the chemical potential of ions in heterogeneous systems, which (i) provides a quantitative criterium for deciding if the background charge offers an acceptable trade-off between artifacts arising from sampling problems and artifacts arising from the homogeneous background charge distribution, and (ii) can be used to correct this artifact in certain cases. Our model quantifies the artifact in terms of the dif ference in charge density between the non-neutral system with a uniform neutralizing background charge and the real neutral system with a physically correct distribution of explicit counterions. We show that for inhomogeneous systems, such as proteins and membranes in water, the artifact manifests itself by an overstabilization of ions inside the lower dielectric by tens to even hundreds kilojoules per mole. We have tested the accuracy of our model in molecular dynamics simulations and found that the error in the calculated free energy for moving a test charge from water into hexadecane, at different net charges of the system and different simulation box sizes, is correctly predicted by the model. The calculations further confirm that the incorrect distribution of counter charges in the simulation box is solely responsible for the errors in the PMFs. ■ INTRODUCTIONMolecular dynamics (MD) simulations have come of age. Since the first applications of MD on protein systems more than three decades ago, 1,2 advances in computer power, algorithmic developments, and improvements in the accuracy of the applied interaction functions have established MD as an important predictive technique to study dynamic processes at atomic resolution. 3,4 An important improvement in accuracy is achieved by the use of lattice summation methods for the evaluation of the Coulombic interactions in simulation boxes subject to periodic boundary conditions. In such approaches, the Coulomb interactions between all pairs of charged particles are accounted for, including interactions between the charges in the central box and their periodic images,where we used Gaussian units, as in the remainder of this article. Here, N is the number of charged particles in the central simulation box, n = (n x , n y , n z ) is the box index vector. The prime indicates that if i = j the term n = 0 should be omitted. The distance r ij,n is the real distance between the charg...

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Section: ■ Methodsmentioning

confidence: 99%

Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Hub

Groot

Grubmüller

et al. 2014

J. Chem. Theory Comput.

201

218

View full text Add to dashboard Cite

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“…To estimate c we have used Turnbull's empirical rule that the surface free energy is proportional to the latent heat of melting [16]. The height of the free-energy barrier was computed with molecular dynamics, using the umbrella sampling scheme [17,18]. In this scheme we compute the free energy of a nucleus as a function of its size.…”

Section: Methodsmentioning

confidence: 99%

Enhanced protein crystallization around the metastable critical point

Wolde

Frenkel

1999

Theoretical Chemistry Accounts: Theory, Computation, and Modeli

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Abstract. We report on a computer-simulation study of homogeneous crystal nucleation in a model for globular proteins. We ®nd that the presence of a metastable vapour-liquid critical point drastically changes the pathway for the formation of a critical nucleus. But what is more important, the large density¯uctuations near the critical point also lowers the free-energy barrier to nucleation and hence increases the nucleation rate. As the location of the vapour-liquid critical point can be controlled by changing the solvent conditions, our simulation results suggest a guided approach to protein crystallization.

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“…The common analysis is based on projecting MD (MC) trajectories onto a small number of coordinates using principal component analysis or calculating the populations along one or two physically significant reaction coordinates. 23,24 Differences, ∆F mn , are commonly calculated by thermodynamic integration (TI) over physical quantities such as the energy, temperature, and the specific heat 25,26 as well as nonphysical parameters [13][14][15][16][17][18][19][27][28][29][30][31][32][33][34] (free energy perturbation methods and umbrella and histogram analysis methods [35][36][37] are also included in this category, see ref 19 and references cited therein). This is a robust and highly versatile approach, which is used successfully for calculating the difference in the free energy of binding of two ligands to the active site of an enzyme.…”

Section: I1 the Role Of Free Energy In Structural Biologymentioning

confidence: 99%

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy

Cheluvaraja

Meirovitch

2007

J. Chem. Theory Comput.

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Abstract:The hypothetical scanning molecular dynamics (HSMD) method is a relatively new technique for calculating the absolute entropy, S, and free energy, F, from a given sample generated by any simulation procedure. Thus, each sample conformation, i, is reconstructed by calculating transition probabilities that their product leads to the probability of i, hence to the entropy. HSMD is an exact method where all interactions are considered, and the only approximation is due to insufficient sampling. In previous studies HSMD (and HS Monte Carlo -HSMC) has been applied very successfully to liquid argon, TIP3P water, self-avoiding walks, and peptides in a R-helix, extended, and hairpin microstates. In this paper HSMD is developed further as applied to the flexible 7-residue surface loop, 304-310 (Gly-His-Gly-Ala-Gly-GlySer) of the enzyme porcine pancreatic R-amylase. We are mainly interested in entropy and free energy differences ∆S ) S free -S bound (and ∆F)F free -F bound ) between the free and bound microstates of the loop, which are obtained from two separate MD samples of these microstates without the need to carry out thermodynamic integration. As for peptides, we find that relatively large systematic errors in S free and S bound (and F free and F bound ) are cancelled in ∆S (∆F) which is thus obtained efficiently with high accuracy, i.e., with a statistical error of 0.1-0.2 kcal/mol (T)300 K) using the AMBER force field and AMBER with the implicit solvation GB/SA. We provide theoretical arguments in support of this cancellation, discuss in detail the problems involved in the computational definition of a microstate in conformational space, suggest potential ways for enhancing efficiency further, and describe the next development where explicit water will replace implicit solvation.

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Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid

Cited by 1,261 publications

References 8 publications

Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Enhanced protein crystallization around the metastable critical point

Stability of the Free and Bound Microstates of a Mobile Loop of α-Amylase Obtained from the Absolute Entropy and Free Energy

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