Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models.

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.

Nonparametric density estimation and optimal bandwidth selection for protein unfolding and unbinding data.

Dynamic force spectroscopy and steered molecular simulations have become powerful tools for analyzing the mechanical properties of proteins, and the strength of protein-protein complexes and aggregates. Probability density functions of the unfolding forces and unfolding times for proteins, and rupture forces and bond lifetimes for protein-protein complexes allow quantification of the forced unfolding and unbinding transitions, and mapping the biomolecular free energy landscape. The inference of the unknown probability distribution functions from the experimental and simulated forced unfolding and unbinding data, as well as the assessment of analytically tractable models of the protein unfolding and unbinding requires the use of a bandwidth. The choice of this quantity is typically subjective as it draws heavily on the investigator's intuition and past experience. We describe several approaches for selecting the "optimal bandwidth" for nonparametric density estimators, such as the traditionally used histogram and the more advanced kernel density estimators. The performance of these methods is tested on unimodal and multimodal skewed, long-tailed distributed data, as typically observed in force spectroscopy experiments and in molecular pulling simulations. The results of these studies can serve as a guideline for selecting the optimal bandwidth to resolve the underlying distributions from the forced unfolding and unbinding data for proteins.

Analyzing forced unfolding of protein tandems by ordered variates, 2: dependent unfolding times.

Statistical analyses of forced unfolding data for protein tandems, i.e., unfolding forces (force-ramp) and unfolding times (force-clamp), used in single-molecule dynamic force spectroscopy rely on the assumption that the unfolding transitions of individual protein domains are independent (uncorrelated) and characterized, respectively, by identically distributed unfolding forces and unfolding times. In our previous work, we showed that in the experimentally accessible piconewton force range, this assumption, which holds at a lower constant force, may break at an elevated force level, i.e., the unfolding transitions may become correlated when force is increased. In this work, we develop much needed statistical tests for assessing the independence of the unobserved forced unfolding times for individual protein domains in the tandem and equality of their parent distributions, which are based solely on the observed ordered unfolding times. The use and performance of these tests are illustrated through the analysis of unfolding times for computer models of protein tandems. The proposed tests can be used in force-clamp atomic force microscopy experiments to obtain accurate information on protein forced unfolding and to probe data on the presence of interdomain interactions. The order statistics-based formalism is extended to cover the analysis of correlated unfolding transitions. The use of order statistics leads naturally to the development of new kinetic models, which describe the probabilities of ordered unfolding transitions rather than the populations of chemical species.

Analyzing forced unfolding of protein tandems by ordered variates, 1: Independent unfolding times.

Most of the mechanically active proteins are organized into tandems of identical repeats, (D)N, or heterogeneous tandems, D1-D2-...-DN. In current atomic force microscopy experiments, conformational transitions of protein tandems can be accessed by employing constant stretching force f (force-clamp) and by analyzing the recorded unfolding times of individual domains. Analysis of unfolding data for homogeneous tandems relies on the assumption that unfolding times are independent and identically distributed, and involves inference of the (parent) probability density of unfolding times from the histogram of the combined unfolding times. This procedure cannot be used to describe tandems characterized by interdomain interactions, or heteregoneous tandems. In this article, we introduce an alternative approach that is based on recognizing that the observed data are ordered, i.e., first, second, third, etc., unfolding times. The approach is exemplified through the analysis of unfolding times for a computer model of the homogeneous and heterogeneous tandems, subjected to constant force. We show that, in the experimentally accessible range of stretching forces, the independent and identically distributed assumption may not hold. Specifically, the uncorrelated unfolding transitions of individual domains at lower force may become correlated (dependent) at elevated force levels. The proposed formalism can be used in atomic force microscopy experiments to infer the unfolding time distributions of individual domains from experimental histograms of ordered unfolding times, and it can be extended to analyzing protein tandems that exhibit interdomain interactions.

Cuticular hydrocarbons of the paper wasp,Polistes fuscatus: A search for recognition pheromones.

The cuticular chemicals of 124 individual wasps (foundresses and workers) from 23 colonies ofPolistes fuscatus were analyzed. The compounds identified, all of which were hydrocarbons, were similar to those of other vespid wasps in that the bulk of the hydrocarbons were 23-33 carbons in chain length. However, the hydrocarbon profile ofP. fuscatus differed from those of its congeners in its proportions of straight-chain alkanes, methylalkanes, and alkenes. Three of the 20 identified hydrocarbons, 13- and 15-MeC31, 11,15- and 13,17-diMeC31, and 13-, 15-, and 17-MeC33, had properties postulated for recognition pheromones: colony specificity, efficacy in assigning wasps to the appropriate colony, heritability, lack of differences between foundresses and workers, and distinctive stereochemistry.