Adaptive anisotropic kernels for nonparametric estimation of absolute configurational entropies in high-dimensional configuration spaces

Hensen, Ulf; Grubmüller, Helmut; Lange, Oliver

doi:10.1103/physreve.80.011913

Cited by 22 publications

(35 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further work should also consider alternatives to the KNN algorithm, or extensions to it such as kernel-density estimation. [39,40] Another finding, which is not unexpected, is that for the randomly generated data the k 5 1 estimates are closer to zero than estimates with larger k values but have larger standard deviations. Real-world applications of KNN need to consider the balance of accuracy and precision that is desired.…”

Section: Discussionmentioning

confidence: 91%

“…It is worth noting that the relative entropy for metric Δ 1 also converges to zero in Figure and this suggests that Δ 1 is a good distance metric but requires significantly more sampling than the quaternion metrics to reach the same level of accuracy. Further work should also consider alternatives to the KNN algorithm, or extensions to it such as kernel‐density estimation …”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Comparing distance metrics for rotation using the k ‐nearest neighbors algorithm for entropy estimation

Huggins

2013

J. Comput. Chem.

View full text Add to dashboard Cite

Distance metrics facilitate a number of methods for statistical analysis. For statistical mechanical applications, it is useful to be able to compute the distance between two different orientations of a molecule. However, a number of distance metrics for rotation have been employed, and in this study, we consider different distance metrics and their utility in entropy estimation using the k-nearest neighbors (KNN) algorithm. This approach shows a number of advantages over entropy estimation using a histogram method, and the different approaches are assessed using uniform randomly generated data, biased randomly generated data, and data from a molecular dynamics (MD) simulation of bulk water. The results identify quaternion metrics as superior to a metric based on the Euler angles. However, it is demonstrated that samples from MD simulation must be independent for effective use of the KNN algorithm and this finding impacts any application to time series data.

show abstract

Section: Discussionmentioning

confidence: 91%

Section: Discussionmentioning

confidence: 99%

Comparing distance metrics for rotation using the k ‐nearest neighbors algorithm for entropy estimation

Huggins

2013

J. Comput. Chem.

View full text Add to dashboard Cite

show abstract

“…For Euclidean spaces, this problem was addressed by using anisotropic kernels. 75,76 Although this idea could also be applied in SO(3) n , the correlation of water molecules at standard conditions is weak enough ( Figure 3A) to allow for sufficiently accurate results under the isotropy assumption.…”

Section: Test Distributionsmentioning

confidence: 99%

Computing Spatially Resolved Rotational Hydration Entropies from Atomistic Simulations

Heinz

Grubmüller

2019

J. Chem. Theory Comput.

Self Cite

View full text Add to dashboard Cite

For a first principles understanding of macromolecular processes, a quantitative understanding of the underlying free energy landscape and in particular its entropy contribution is crucial. The stability of biomolecules, such as proteins, is governed by the hydrophobic effect, which arises from competing enthalpic and entropic contributions to the free energy of the solvent shell. While the statistical mechanics of liquids, as well as molecular dynamics simulations have provided much insight, solvation shell entropies remain notoriously difficult to calculate, especially when spatial resolution is required. Here, we present a method that allows for the computation of spatially resolved rotational solvent entropies via a non-parametric k-nearestneighbor density estimator. We validated our method using analytic test distributions and applied it to atomistic simulations of a water box. With an accuracy of better than 9.6 %, the obtained spatial resolution should shed new light on the hydrophobic effect and the thermodynamics of solvation in general.

show abstract

“…47 , non-parametric methods using histogram 48 and k-nearest neighbor (kNN), 28, 49 , hypothetical scanning approach, 50, 51 the adaptive anisotropic kernels and minimum information methods by Grubmuller et al 52, 53 , and so on.…”

Section: 0 Introductionmentioning

confidence: 99%

Develop and Test a Solvent Accessible Surface Area-Based Model in Conformational Entropy Calculations

Wang

Hou²

2012

J. Chem. Inf. Model.

105

107

View full text Add to dashboard Cite

It is of great interest in modern drug design to accurately calculate the free energies of protein-ligand or nucleic acid-ligand binding. MM-PBSA (Molecular Mechanics-Poisson Boltzmann Surface Area) and MM-GBSA (Molecular Mechanics-Generalized Born Surface Area) have gained popularity in this field. For both methods, the conformational entropy, which is usually calculated through normal mode analysis (NMA), is needed to calculate the absolute binding free energies. Unfortunately, NMA is computationally demanding and becomes a bottleneck of the MM-PB/GBSA-NMA methods. In this work, we have developed a fast approach to estimate the conformational entropy based upon solvent accessible surface area calculations. In our approach, the conformational entropy of a molecule, S, can be obtained by summing up the contributions of all atoms, no matter they are buried or exposed. Each atom has two types of surface areas, solvent accessible surface area (SAS) and buried SAS (BSAS). The two types of surface areas are weighted to estimate the contribution of an atom to S. Atoms having the same atom type share the same weight and a general parameter k is applied to balance the contributions of the two types of surface areas. This entropy model was parameterized using a large set of small molecules for which their conformational entropies were calculated at the B3LYP/6-31G* level taking the solvent effect into account. The weighted solvent accessible surface area (WSAS) model was extensively evaluated in three tests. For the convenience, TS, the product of temperature T and conformational entropy S, were calculated in those tests. T was always set to 298.15 K through the text. First of all, good correlations were achieved between WSAS TS and NMA TS for 44 protein or nucleic acid systems sampled with molecular dynamics simulations (10 snapshots were collected for post-entropy calculations): the mean correlation coefficient squares (R2) was 0.56. As to the 20 complexes, the TS changes upon binding, TΔS, were also calculated and the mean R2 was 0.67 between NMA and WSAS. In the second test, TS were calculated for 12 proteins decoy sets (each set has 31 conformations) generated by the Rosetta software package. Again, good correlations were achieved for all decoy sets: the mean, maximum, minimum of R2 were 0.73, 0.89 and 0.55, respectively. Finally, binding free energies were calculated for 6 protein systems (the numbers of inhibitors range from 4 to 18) using four scoring functions. Compared to the measured binding free energies, the mean R2 of the six protein systems were 0.51, 0.47, 0.40 and 0.43 for MM-GBSA-WSAS, MM-GBSA-NMA, MM-PBSA-WSAS and MM-PBSA-NMA, respectively. The mean RMS errors of prediction were 1.19, 1.24, 1.41, 1.29 kcal/mol for the four scoring functions, correspondingly. Therefore, the two scoring functions employing WSAS achieved a comparable prediction performance to that of the scoring functions using NMA. It should be emphasized that no minimization was performed prior to the WSAS calculation in the last test. ...

show abstract

Adaptive anisotropic kernels for nonparametric estimation of absolute configurational entropies in high-dimensional configuration spaces

Cited by 22 publications

References 30 publications

Comparing distance metrics for rotation using the k ‐nearest neighbors algorithm for entropy estimation

Comparing distance metrics for rotation using the k ‐nearest neighbors algorithm for entropy estimation

Computing Spatially Resolved Rotational Hydration Entropies from Atomistic Simulations

Develop and Test a Solvent Accessible Surface Area-Based Model in Conformational Entropy Calculations

Contact Info

Product

Resources

About