Adam Fedorowicz

Nearest Neighbor Estimates of Entropy

SYNOPTIC ABSTRACT Motivated by the problems in molecular sciences, we introduce new nonparametric estimators of entropy which are based on the kth nearest neighbor distances between the n sample points, where k (< n – 1) is a fixed positive integer. These provide competing estimators to an estimator proposed by Kozachenko and Leonenko (1987), which is based on the first nearest neighbor distances of the sample points. These estimators are helpful in the evaluation of entropies of random vectors. We establish the asymptotic unbiasedness and consistency of the proposed estimators. For some standard distributions, we also investigate their performance for finite sample sizes using Monte Carlo simulations. The proposed estimators are applied to estimate the entropy of internal rotation in the methanol molecule, which can be characterized by a one-dimensional random vector, and of diethyl ether, which is described by a four-dimensional random vector.

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

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.

Application of the random forest method in studies of local lymph node assay based skin sensitization data

The random forest and classification tree modeling methods are used to build predictive models of the skin sensitization activity of a chemical. A new two-stage backward elimination algorithm for descriptor selection in the random forest method is introduced. The predictive performance of the random forest model was maximized by tuning voting thresholds to reflect the unbalanced size of classification groups in available data. Our results show that random forest with a proposed backward elimination procedure outperforms a single classification tree and the standard random forest method in predicting Local Lymph Node Assay based skin sensitization activity. The proximity measure obtained from the random forest is a natural similarity measure that can be used for clustering of chemicals. Based on this measure, the clustering analysis partitioned the chemicals into several groups sharing similar molecular patterns. The improved random forest method demonstrates the potential for future QSAR studies based on a large number of descriptors or when the number of available data points is limited.

Correlation as a determinant of configurational entropy in supramolecular and protein systems.

For biomolecules in solution, changes in configurational entropy are thought to contribute substantially to the free energies of processes like binding and conformational change. In principle, the configurational entropy can be strongly affected by pairwise and higher-order correlations among conformational degrees of freedom. However, the literature offers mixed perspectives regarding the contributions that changes in correlations make to changes in configurational entropy for such processes. Here we take advantage of powerful techniques for simulation and entropy analysis to carry out rigorous in silico studies of correlation in binding and conformational changes. In particular, we apply information-theoretic expansions of the configurational entropy to well-sampled molecular dynamics simulations of a model host–guest system and the protein bovine pancreatic trypsin inhibitor. The results bear on the interpretation of NMR data, as they indicate that changes in correlation are important determinants of entropy changes for biologically relevant processes and that changes in correlation may either balance or reinforce changes in first-order entropy. The results also highlight the importance of main-chain torsions as contributors to changes in protein configurational entropy. As simulation techniques grow in power, the mathematical techniques used here will offer new opportunities to answer challenging questions about complex molecular systems.

Estimation of the absolute internal-rotation entropy of molecules with two torsional degrees of freedom from stochastic simulations.

A method of statistical estimation is applied to the problem of evaluating the absolute entropy of internal rotation in a molecule with two torsional degrees of freedom. The configurational part of the entropy is obtained as that of the joint probability density of an arbitrary form represented by a two‐dimensional Fourier series, the coefficients of which are statistically estimated using a sample of the torsional angles of the molecule obtained by a stochastic simulation. The internal rotors in the molecule are assumed to be attached to a common frame, and their reduced moments of inertia are initially calculated as functions of the two torsional angles, but averaged over all the remaining internal degrees of freedom using the stochastic‐simulation sample of the atomic configurations of the molecule. The torsional‐angle dependence of the reduced moments of inertia can be also averaged out, and the absolute internal‐rotation entropy of the molecule is obtained in a good approximation as the sum of the configurational entropy and a kinetic contribution fully determined by the averaged reduced moments of inertia. The method is illustrated using Monte Carlo simulations of isomers of stilbene and halogenated derivatives of propane. The two torsional angles in cis‐stilbene are found to be much more strongly correlated than those in trans‐stilbene, while the degree of the angular correlation in propane increases strongly on substitution of hydrogen atoms with chlorine.

Statistical thermodynamics of internal rotation in a hindering potential of mean force obtained from computer simulations.

A method of statistical estimation is applied to the problem of one‐dimensional internal rotation in a hindering potential of mean force. The hindering potential, which may have a completely general shape, is expanded in a Fourier series, the coefficients of which are estimated by fitting an appropriate statistical–mechanical distribution to the random variable of internal rotation angle. The function of reduced moment of inertia of an internal rotation is averaged over the thermodynamic ensemble of atomic configurations of the molecule obtained in stochastic simulations. When quantum effects are not important, an accurate estimate of the absolute internal rotation entropy of a molecule with a single rotatable bond is obtained. When there is more than one rotatable bond, the “marginal” statistical–mechanical properties corresponding to a given internal rotational degree of freedom are educed. The method is illustrated using Monte Carlo simulations of two public health relevant halocarbon molecules, each having a single internal‐rotation degree of freedom, and a molecular dynamics simulation of an immunologically relevant polypeptide, in which several dihedral angles are analyzed.

Evaluation of irritancy and sensitization potential of metalworking fluid mixtures and components.

There are approximately 1.2 million workers exposed to metalworking fluids (MWF), which are used to reduce the heat and friction associated with industrial machining and grinding operations. Irritancy and sensitization potential of 9 National Toxicology Program (NTP) nominated MWFs (TRIM 229, TRIM VX, TRIM SC210, CIMTECH 310, CIMPERIAL 1070, CIMSTAR 3800, SYNTILO 1023, SUPEREDGE 6768, and CLEAREDGE 6584) were examined in a combined local lymph node assay (LLNA). BALB/c mice were dermally exposed to each MWF at concentrations up to 50%. Significant irritation was observed after dermal exposure to all MWFs except CIMTECH 310 and SYNTILO 1023. Of the 9 MWFs, 6 induced greater than a 3-fold increase in lymphocyte proliferation and 7 tested positive in the irritancy assay. TRIM VX yielded the lowest EC3 value (6.9%) with respect to lymphocyte proliferation. Chemical components of TRIM VX identified using HPLC were screened for sensitization potential using structural activity relationship (SAR) modeling and the LLNA. TOPKAT predicted triethanolamine (TEA) as a sensitizer while Derek for Windows predicted only 4-chloro-3-methylphenol (CMP) to be positive for sensitization. When tested in the LLNA only CMP (EC3 = 11.6%) and oleic acid (OA) (EC3 = 29.7%) were identified as sensitizers. Exposure to all tested TRIM VX components resulted in statistically significant irritation. An additive proliferative response was observed when mixtures of the two identified sensitizing TRIM VX components, OA and CMP, were tested in the LLNA. This is one explanation of why the EC3 value of TRIM VX, with respect to lymphocyte proliferation, is lower than those assigned to its sensitizing components.

Identification of Phenolic Dermal Sensitizers in a Wound Closure Tape

A latex-allergic patient presented with a severe local reaction to a non-latex wound closure bandage following surgery. Extracts of the bandage were analyzed by gas chromatograph-electron impact-mass spectrometry (GC EI-MS) in the total ion monitoring mode. Components were identified by their ion mass fingerprint and elution time as a corresponding standard from the GC column. The chemicals identified were 4,4′-thiobis-(6-tert-butyl-m-cresol) (TBBC), 6-tert-Butyl-m-cresol (BC), 2,4-di-tert-butylphenol (BP) and erucamide (EA). Sensitization potential of these chemicals was evaluated using two quantitative structure-activity relationship (QSAR) programs. The phenol 2,6-di-tert-butyl-4-(hydroxymethyl)phenol (BHP) was also included in the test series. It was initially thought to be present in the bandage but detectable levels could not be confirmed. The potential for TBBC to induce a sensitization response was predicted by both Derek for Windows and TOPKAT 6.2. The potential for BC and BP to induce a sensitization response was predicted by Derek for Windows, but not TOPKAT. BHP and EA were not predicted to be sensitizers by either QSAR program. Local lymph node assay (LLNA) analysis of the chemicals identified TBBC, BP, and BC as potential sensitizers with EC3 values between 0.2 and 4.5%. None of the animals exhibited body weight loss or skin irritation at the concentrations tested. In agreement with the toxicological modeling, BHP did not induce a sensitization response in the LLNA. Following a positive LLNA response, TBBC, BP, and BC were further characterized by phenotypic analysis of the draining lymph nodes. A positive LLNA result coupled with a lack of increase in B220+IgE+ cell and serum IgE characterize these chemicals as Type IV sensitizers. These studies used a multidisciplinary approach combining clinical observation, GC-EI-MS for chemical identification, QSAR modeling of chemicals prior to animal testing, and the LLNA for determination of the sensitization potential of chemicals in a manufactured product.