Nearest Neighbor Estimates of Entropy

Singh, Harshinder; Misra, Neeraj; Hnizdo, V.; Fedorowicz, Adam; Demchuk, Eugene

doi:10.1080/01966324.2003.10737616

Cited by 158 publications

(229 citation statements)

References 10 publications

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“…We used a nearest neighbor method [61][62][63] to compute the orientational entropy associated with each voxel k, i.e., S ω (r k ), from water simulation data. This provides substantially better convergence properties than a uniform histogram method we initially tried.…”

Section: Orientational Entropymentioning

confidence: 99%

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Nguyen

Young²,

Gilson³

2012

The Journal of Chemical Physics

302

506

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The displacement of perturbed water upon binding is believed to play a critical role in the thermodynamics of biomolecular recognition, but it is nontrivial to unambiguously define and answer questions about this process. We address this issue by introducing grid inhomogeneous solvation theory (GIST), which discretizes the equations of inhomogeneous solvation theory (IST) onto a threedimensional grid situated in the region of interest around a solute molecule or complex. Snapshots from explicit solvent simulations are used to estimate localized solvation entropies, energies, and free energies associated with the grid boxes, or voxels, and properly summing these thermodynamic quantities over voxels yields information about hydration thermodynamics. GIST thus provides a smoothly varying representation of water properties as a function of position, rather than focusing on hydration sites where solvent is present at high density. It therefore accounts for full or partial displacement of water from sites that are highly occupied by water, as well as for partly occupied and water-depleted regions around the solute. GIST can also provide a well-defined estimate of the solvation free energy and therefore enables a rigorous end-states analysis of binding. For example, one may not only use a first GIST calculation to project the thermodynamic consequences of displacing water from the surface of a receptor by a ligand, but also account, in a second GIST calculation, for the thermodynamics of subsequent solvent reorganization around the bound complex. In the present study, a first GIST analysis of the molecular host cucurbit [7]uril is found to yield a rich picture of hydration structure and thermodynamics in and around this miniature receptor. One of the most striking results is the observation of a toroidal region of high water density at the center of the host's nonpolar cavity. Despite its high density, the water in this toroidal region is disfavored energetically and entropically, and hence may contribute to the known ability of this small receptor to bind guest molecules with unusually high affinities. Interestingly, the toroidal region of high water density persists even when all partial charges of the receptor are set to zero. Thus, localized regions of high solvent density can be generated in a binding site without strong, attractive solute-solvent interactions.

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Section: Orientational Entropymentioning

confidence: 99%

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Nguyen

Young²,

Gilson³

2012

The Journal of Chemical Physics

302

506

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“…The simplest way to calculateS G is using a non-parametric entropy estimator [4][5][6]. The idea is to coarse grain the distribution function on the scale of the nearest neighbor distance between the particles.…”

Section: Systems With Long Range Interactionsmentioning

confidence: 99%

Entropy production in systems with long range interactions

Pakter

Levin

2017

J. Stat. Mech.

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On a fine grained scale the Gibbs entropy of an isolated system remains constant throughout its dynamical evolution. This is a consequence of Liouville's theorem for Hamiltonian systems and appears to contradict the second law of thermodynamics. In reality, however, there is no problem since the thermodynamic entropy should be associated with the Boltzmann entropy, which for non-equilibrium systems is different from Gibbs entropy. The Boltzmann entropy accounts for the microstates which are not accessible from a given initial condition, but are compatible with a given macrostate. In a sense the Boltzmann entropy is a coarse grained version of the Gibbs entropy and will not decrease during the dynamical evolution of a macroscopic system. In this paper we will explore the entropy production for systems with long range interactions. Unlike for short range systems, in the thermodynamic limit, the probability density function for these systems decouples into a product of one particle distribution functions and the coarse grained entropy can be calculated explicitly. We find that the characteristic time for the entropy production scales with the number of particles as N α , with α > 0, so that in the thermodynamic limit entropy production takes an infinite amount of time. * pakter@if.ufrgs.br † levin@if.ufrgs.br 2

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“…When the sample points are very close one to each other, small fluctuations in their distances produce high fluctuations of H n . In order to overcome this problem, Singh et al [21] defined an entropy estimator based on the k-th nearest neighbor distances. A kNN estimate of the Kullback-Leibler divergence was obtained by Wang et al in [23].…”

Section: The Nearest Neighbor Methodsmentioning

confidence: 99%

Asymptotically Unbiased Estimator of the Informational Energy with kNN

Caţaron

Andonie

Chueh

2013

INT J COMPUT COMMUN

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Motivated by machine learning applications (e.g., classification, function approximation, feature extraction), in previous work, we have introduced a nonparametric estimator of Onicescu's informational energy. Our method was based on the k-th nearest neighbor distances between the n sample points, where k is a fixed positive integer. In the present contribution, we discuss mathematical properties of this estimator. We show that our estimator is asymptotically unbiased and consistent. We provide further experimental results which illustrate the convergence of the estimator for standard distributions.

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Nearest Neighbor Estimates of Entropy

Cited by 158 publications

References 10 publications

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Grid inhomogeneous solvation theory: Hydration structure and thermodynamics of the miniature receptor cucurbit[7]uril

Entropy production in systems with long range interactions

Asymptotically Unbiased Estimator of the Informational Energy with kNN

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