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Efficient calculation of molecular configurational entropies using an information theoretic approximation.

ABSTRACT: Accurate computation of free energy changes upon molecular binding remains a challenging problem, and changes in configurational entropy are especially difficult due to the potentially large numbers of local minima, anharmonicity, and high-order coupling among degrees of freedom. Here we propose a new method to compute molecular entropies based on the maximum information spanning tree (MIST) approximation that we have previously developed. Estimates of high-order couplings using only low-order terms provide excellent convergence properties, and the theory is also guaranteed to bound the entropy. The theory is presented together with applications to the calculation of the entropies of a variety of small molecules and the binding entropy change for a series of HIV protease inhibitors. The MIST framework developed here is demonstrated to compare favorably with results computed using the related mutual information expansion (MIE) approach, and an analysis of similarities between the methods is presented.

SUBMITTER: King BM

PROVIDER: S-EPMC3465721 | biostudies-literature | 2012 Mar

REPOSITORIES: biostudies-literature

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Efficient calculation of molecular configurational entropies using an information theoretic approximation.

King Bracken M BM Silver Nathaniel W NW Tidor Bruce B

The journal of physical chemistry. B 20120222 9

Accurate computation of free energy changes upon molecular binding remains a challenging problem, and changes in configurational entropy are especially difficult due to the potentially large numbers of local minima, anharmonicity, and high-order coupling among degrees of freedom. Here we propose a new method to compute molecular entropies based on the maximum information spanning tree (MIST) approximation that we have previously developed. Estimates of high-order couplings using only low-order t ...[more]

PMID: 22229789

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Project description:Entropy and the second law of thermodynamics are fundamental concepts that underlie all natural processes and patterns. Recent research has shown how the entropy of a landscape mosaic can be calculated using the Boltzmann equation, with the entropy of a lattice mosaic equal to the logarithm of the number of ways a lattice with a given dimensionality and number of classes can be arranged to produce the same total amount of edge between cells of different classes. However, that work seemed to also suggest that the feasibility of applying this method to real landscapes was limited due to intractably large numbers of possible arrangements of raster cells in large landscapes. Here I extend that work by showing that: (1) the proportion of arrangements rather than the number with a given amount of edge length provides a means to calculate unbiased relative configurational entropy, obviating the need to compute all possible configurations of a landscape lattice; (2) the edge lengths of randomized landscape mosaics are normally distributed, following the central limit theorem; and (3) given this normal distribution it is possible to fit parametric probability density functions to estimate the expected proportion of randomized configurations that have any given edge length, enabling the calculation of configurational entropy on any landscape regardless of size or number of classes. I evaluate the boundary limits (4) for this normal approximation for small landscapes with a small proportion of a minority class and show it holds under all realistic landscape conditions. I further (5) demonstrate that this relationship holds for a sample of real landscapes that vary in size, patch richness, and evenness of area in each cover type, and (6) I show that the mean and standard deviation of the normally distributed edge lengths can be predicted nearly perfectly as a function of the size, patch richness and diversity of a landscape. Finally, (7) I show that the configurational entropy of a landscape is highly related to the dimensionality of the landscape, the number of cover classes, the evenness of landscape composition across classes, and landscape heterogeneity. These advances provide a means for researchers to directly estimate the frequency distribution of all possible macrostates of any observed landscape, and then directly calculate the relative configurational entropy of the observed macrostate, and to understand the ecological meaning of different amounts of configurational entropy. These advances enable scientists to take configurational entropy from a concept to an applied tool to measure and compare the disorder of real landscapes with an objective and unbiased measure based on entropy and the second law.

Dataset Information

Efficient calculation of molecular configurational entropies using an information theoretic approximation.

Publications

Efficient calculation of molecular configurational entropies using an information theoretic approximation.

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