Application of empirical design methodologies to the study of the influence of reaction conditions and N-alpha-protecting group structure on the enzymatic X-Phe-Leu-NH(2) dipeptide synthesis in buffer/dimethylformamide solvents systems

The influence of five different N-terminal protecting groups (For, Ac, Boc, Z, and Fmoc) and reaction conditions (temperature and dimethylformamide content) on the alpha-chymotrypsin-catalyzed synthesis of the dipeptide derivative X-Phe-Leu-NH(2) was studied. Groups such as For, Ac, Boc, and Z always rendered good peptide yields (82% to 85%) at low reaction temperatures and DMF concentrations, which depended on the N-alpha protection choice. Boc and Z were the most reactive N-alpha groups and, in addition, the most suitable for peptide synthesis. On the other hand, the use of empirical design methodologies allowed, with minimal experimentation and by multiple regression, to deduce an equation, which correlates the logarithm of the first order kinetic constant (log k') with reaction temperature, DMF concentration, and hydrophobicity (log P values) of the different protecting groups. The predictive value of the equation was tested by comparing the performance of another protective group, such as Aloc, with the performance predicted by said equation. Experimental and calculated k' values were found to be in good agreement.     

Solvent effects on biocatalysis in organic systems: equilibrium position and rates of lipase catalyzed esterification

Porcine pancreatic lipase immobilized on celite particles has been employed as a catalyst for the esterification of dodecanol and decanoic acid in a predominantly organic system. Solvent influence on the equilibrium position and on the catalyst activity has been studied using 20 solvents, including aliphatic and aromatic hydrocarbons, ethers, ketones, nitro- and halogenated hydrocarbons, and esters. The equilibrium constant for esterification correlates well with the solubility of water in the organic solvent, which in turn shows a good relationship with a function of Guttman's donor number and the electron pair acceptance index number of the solvent. This may be rationalized in terms of the requirements for solvation of water and of the reactants. The catalyst activity, measured as the initial rate of the esterification reaction, is best correlated as a function of both n-octanol-water partition coefficient (log P) and either the electron pair acceptance index or the polarizability.     

Prediction analysis for microbiome sequencing data

One goal of human microbiome studies is to relate host traits with human microbiome compositions. The analysis of microbial community sequencing data presents great statistical challenges, especially when the samples have different library sizes and the data are overdispersed with many zeros. To address these challenges, we introduce a new statistical framework, called predictive analysis in metagenomics via inverse regression (PAMIR), to analyze microbiome sequencing data. Within this framework, an inverse regression model is developed for overdispersed microbiota counts given the trait, and then a prediction rule is constructed by taking advantage of the dimension‐reduction structure in the model. An efficient Monte Carlo expectation‐maximization algorithm is proposed for maximum likelihood estimation. The method is further generalized to accommodate other types of covariates. We demonstrate the advantages of PAMIR through simulations and two real data examples.     

A mixture model for occupational exposure mean testing with a limit of detection

Information from detectable exposure measurements randomly sampled from a left-truncated log-normal distribution may be used to evaluate the distribution of nondetectable values that fall below an analytic limit of detection. If the proportion of nondetects is larger than expected under log normality, alternative models to account for these unobserved data should be considered. We discuss one such model that incorporates a mixture of true zero exposures and a log-normal distribution with possible left censoring, previously considered in a different context by Moulton and Halsey (1995, Biometrics 51, 1570-1578). A particular relationship is demonstrated between maximum likelihood parameter estimates based on this mixture model and those assuming either left-truncated or left-censored data. These results emphasize the need for caution when choosing a model to fit data involving nondetectable values. A one-sided likelihood ratio test for comparing mean exposure under the mixture model to an occupational exposure limit is then developed and evaluated via simulations. An example demonstrates the potential impact of specifying an incorrect model for the nondetectable values.     

Estimating protein-ligand binding free energy: atomic solvation parameters for partition coefficient and solvation free energy calculation

Solvation energy calculation is one of the main difficulties for the estimation of protein-ligand binding free energy and the correct scoring in docking studies. We have developed a new solvation energy estimation method for protein-ligand binding based on atomic solvation parameter (ASP), which has been shown to improve the power of protein-ligand binding free energy predictions. The ASP set, designed to handle both proteins and organic compounds and derived from experimental n-octanol/water partition coefficient (log P) data, contains 100 atom types (united model that treats hydrogen atoms implicitly) or 119 atom types (all-atom model that treats hydrogen atoms explicitly). By using this unified ASP set, an algorithm was developed for solvation energy calculation and was further integrated into a score function for predicting protein-ligand binding affinity. The score function reproduced the absolute binding free energies of a test set of 50 protein-ligand complexes with a standard error of 8.31 kJ/mol. As a byproduct, a conformation-dependent log P calculation algorithm named ASPLOGP was also implemented. The predictive results of ASPLOGP for a test set of 138 compounds were r = 0.968, s = 0.344 for the all-atom model and r = 0.962, s = 0.367 for the united model, which were better than previous conformation-dependent approaches and comparable to fragmental and atom-based methods. ASPLOGP also gave good predictive results for small peptides. The score function based on the ASP model can be applied widely in protein-ligand interaction studies and structure-based drug design.     

Statistical estimators of frontal sinus cross section ontogeny from very noisy data

Cross-sectional areas of human frontal sinuses in the occipitofrontal projection are a good surrogate for frontal sinus volumes. This study looks at these areas in a dataset of some 200 children and 100 adults of both sexes. As measured by planimetry of roentgenograms, the areas are extremely variable ("noisy" in a statistical sense). In fact, they appear to be distributed log-normally with quite high variance. The mean of the distribution is evidently a function of age and the variances differ by sex. After logarithmic transformation, the data are adequately fitted by one sigmoid curve for each sex. Our discussion highlights implications of this finding for the biological aspects of frontal sinuses and methodological issues in ontogenetic analysis of data so noisy.     

Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant

The relationship between spatial density and size of plants is an important topic in plant ecology. The self‐thinning rule suggests a ?3/2 power between average biomass and density or a ?1/2 power between stand yield and density. However, the self‐thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log‐linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self‐thinning rule to improve light interception.