Enhanced 3-epi-25-hydroxyvitamin D3 signal leads to overestimation of its concentration and amplifies interference in 25-hydroxyvitamin D LC-MS/MS assays

Background 3-epi-25-hydroxyvitamin D3 (3-epi-25OHD3) interferes in most liquid chromatography-tandem mass spectrometry (LC-MS/MS) assays for 25-hydroxyvitamin D (25OHD). The clinical significance of this is unclear, with concentrations from undetectable to 230 nmol/L reported. Many studies have quantified 3-epi-25OHD3 based on 25OHD3 calibrators or other indirect methods, and we speculated that this contributes to the observed variability in reported 3-epi-25OHD3 concentrations. Methods We compared continuous MS/MS infusions of 3-epi-25OHD3 and 25OHD3 solutions, spiked both analytes into the same serum matrix and analysed patient samples to assess the effect of three different quantitation methods on 3-epi-25OHD3 concentration. Experiments were performed on an LC-MS/MS system using a phenyl column which does not resolve 3-epi-25OHD3, and a modified method utilizing a Zorbax SB-CN column that chromatographically resolves 3-epi-25OHD3 from 25OHD3. Results A greater 3-epi-25OHD3 signal, compared with 25OHD3, was observed during equimolar post-column continuous infusion of analyte solutions, and following analysis of a serum pool spiked with both analytes. 3-epi-25OHD3 signal enhancement was dependent on mobile phase composition. Compared with 3-epi-25OHD3 calibrators, indirect quantitation methods resulted in up to 10 times as many samples having 3-epi-25OHD3 concentrations ≥ 10 nmol/L, and an approximately fourfold increase in the maximum observed 3-epi-25OHD3 concentration to 95 nmol/L. Conclusions Enhanced 3-epi-25OHD3 signal leads to overestimation of its concentrations in the indirect quantitation methods used in many previous studies. The enhanced signal may contribute to greater interference in some 25OHD LC-MS/MS assays than others. We highlight that equimolar responses cannot be assumed in LC-MS/MS systems, even if two molecules are structurally similar

On the convergence of the maximum likelihood estimator for the transition rate under a 2-state symmetric model

Maximum likelihood estimators are used extensively to estimate unknown parameters of stochastic trait evolution models on phylogenetic trees. Although the MLE has been proven to converge to the true value in the independent-sample case, we cannot appeal to this result because trait values of different species are correlated due to shared evolutionary history. In this paper, we consider a $2$-state symmetric model for a single binary trait and investigate the theoretical properties of the MLE for the transition rate in the large-tree limit. Here, the large-tree limit is a theoretical scenario where the number of taxa increases to infinity and we can observe the trait values for all species. Specifically, we prove that the MLE converges to the true value under some regularity conditions. These conditions ensure that the tree shape is not too irregular, and holds for many practical scenarios such as trees with bounded edges, trees generated from the Yule (pure birth) process, and trees generated from the coalescent point process. Our result also provides an upper bound for the distance between the MLE and the true value

Consistency and convergence rate of phylogenetic inference via regularization

It is common in phylogenetics to have some, perhaps partial, information about the overall evolutionary tree of a group of organisms and wish to find an evolutionary tree of a specific gene for those organisms. There may not be enough information in the gene sequences alone to accurately reconstruct the correct "gene tree." Although the gene tree may deviate from the "species tree" due to a variety of genetic processes, in the absence of evidence to the contrary it is parsimonious to assume that they agree. A common statistical approach in these situations is to develop a likelihood penalty to incorporate such additional information. Recent studies using simulation and empirical data suggest that a likelihood penalty quantifying concordance with a species tree can significantly improve the accuracy of gene tree reconstruction compared to using sequence data alone. However, the consistency of such an approach has not yet been established, nor have convergence rates been bounded. Because phylogenetics is a non-standard inference problem, the standard theory does not apply. In this paper, we propose a penalized maximum likelihood estimator for gene tree reconstruction, where the penalty is the square of the Billera-Holmes-Vogtmann geodesic distance from the gene tree to the species tree. We prove that this method is consistent, and derive its convergence rate for estimating the discrete gene tree structure and continuous edge lengths (representing the amount of evolution that has occurred on that branch) simultaneously. We find that the regularized estimator is "adaptive fast converging," meaning that it can reconstruct all edges of length greater than any given threshold from gene sequences of polynomial length. Our method does not require the species tree to be known exactly; in fact, our asymptotic theory holds for any such guide tree.Comment: 34 pages, 5 figures. To appear on The Annals of Statistic

Kinetic Monte Carlo simulation of faceted islands in heteroepitaxy using multi-state lattice model

A solid-on-solid model is generalized to study the formation of Ge pyramid islands bounded by (105) facets on Si(100) substrates in two dimensions. Each atomic column is not only characterized by the local surface height but also by two deformation state variables dictating the local surface tilt and vertical extension. These deformations phenomenologically model surface reconstructions in (105) facets and enable the formation of islands which better resemble faceted pyramids. We demonstrate the model by application to a kinetic limited growth regime. We observe significantly reduced growth rates after faceting and a continuous nucleation of new islands until overcrowding occurs.Comment: 7 pages, 5 figure