Nearest‐neighbor nonparametric method for estimating the configurational entropy of complex molecules

Abstract

A method for estimating the configurational (i.e., non-kinetic) part of the entropy of internal motion in complex molecules is introduced that does not assume any particular parametric form for the underlying probability density function. It is based on the nearest-neighbor (NN) distances of the points of a sample of internal molecular coordinates obtained by a computer simulation of a given molecule. As the method does not make any assumptions about the underlying potential energy function, it accounts fully for any anharmonicity of internal molecular motion. It provides an asymptotically unbiased and consistent estimate of the configurational part of the entropy of the internal degrees of freedom of the molecule. The NN method is illustrated by estimating the configurational entropy of internal rotation of capsaicin and two stereoisomers of tartaric acid, and by providing a much closer upper bound on the configurational entropy of internal rotation of a pentapeptide molecule than that obtained by the standard quasi-harmonic method. As a measure of dependence between any two internal molecular coordinates, a general coefficient of association based on the information-theoretic quantity of mutual information is proposed. Using NN estimates of this measure, statistical clustering procedures can be employed to group the coordinates into clusters of manageable dimensions and characterized by minimal dependence between coordinates belonging to different clusters.

Robustness measure for an adeno-associated viral shell self-assembly is accurately predicted by configuration space atlasing using EASAL

“…To do this, we only take into account the change in interface configurational entropy, Factor (2a) above, when an inter-atomic interaction is removed. Moreover, we use a coarse approximation of the full-blown entropy computation which is a notoriously difficult problem in general with a vast literature [15,34,2,13,14,12,16,11,27,17]. Yet our ranking tallied remarkably well with the mutagenesis results obtained at the Agbandje-Mckenna lab as described in the previous section.…”

“…There is extensive literature for using MC and MD to uniformly sample and thereby compute configurational entropy and free nergy for all types of molecular configuration spaces [15,34,2,13,14,12,16,11,27,17]. There has also been some research on infering the topology of the configuration space [10,31,19] starting from MC and MD samples, and using the topology to guide dimensionality reduction, [33].…”

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

“…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.…”

Modeling Autonomous Supramolecular Assembly

“…There has been a long and distinguished history of configurational entropy and free energy computation methods [18,2,14,15,13,19,12,33,20], many of which use as input the configuration trajectories of Molecular Dynamics or Monte Carlo simulations.…”

“…For both Monte Carlo and Molecular Dynamics, uniform sampling can only be claimed in the limit, or "if run for sufficiently long, or starting from sufficiently many initial configurations." This also causes problems for many entropy computation methods that rely on principal component analyses of the covariance matrices from a trajectory of samples in internal coordinates, followed by a quasiharmonic [2] or nonparametric (such as nearestneighbor-based) [14] estimates. Such methods generally overestimate the volumes of configuration space regions with high geometric or topological complexity, even when hybridized with higher order mutual information [15], and nonlinear kernel methods, such as the Minimally Coupled Subspace approach of [13].…”