A new approach to age-period-cohort analysis using partial least squares regression: the trend in blood pressure in the Glasgow Alumni cohort

Due to a problem of identification, how to estimate the distinct effects of age, time period and cohort has been a controversial issue in the analysis of trends in health outcomes in epidemiology. In this study, we propose a novel approach, partial least squares (PLS) analysis, to separate the effects of age, period, and cohort. Our example for illustration is taken from the Glasgow Alumni cohort. A total of 15,322 students (11,755 men and 3,567 women) received medical screening at the Glasgow University between 1948 and 1968. The aim is to investigate the secular trends in blood pressure over 1925 and 1950 while taking into account the year of examination and age at examination. We excluded students born before 1925 or aged over 25 years at examination and those with missing values in confounders from the analyses, resulting in 12,546 and 12,516 students for analysis of systolic and diastolic blood pressure, respectively. PLS analysis shows that both systolic and diastolic blood pressure increased with students' age, and students born later had on average lower blood pressure (SBP: -0.17 mmHg/per year [95% confidence intervals: -0.19 to -0.15] for men and -0.25 [-0.28 to -0.22] for women; DBP: -0.14 [-0.15 to -0.13] for men; -0.09 [-0.11 to -0.07] for women). PLS also shows a decreasing trend in blood pressure over the examination period. As identification is not a problem for PLS, it provides a flexible modelling strategy for age-period-cohort analysis. More emphasis is then required to clarify the substantive and conceptual issues surrounding the definitions and interpretations of age, period and cohort effects.     

LSimpute: accurate estimation of missing values in microarray data with least squares methods

Microarray experiments generate data sets with information on the expression levels of thousands of genes in a set of biological samples. Unfortunately, such experiments often produce multiple missing expression values, normally due to various experimental problems. As many algorithms for gene expression analysis require a complete data matrix as input, the missing values have to be estimated in order to analyze the available data. Alternatively, genes and arrays can be removed until no missing values remain. However, for genes or arrays with only a small number of missing values, it is desirable to impute those values. For the subsequent analysis to be as informative as possible, it is essential that the estimates for the missing gene expression values are accurate. A small amount of badly estimated missing values in the data might be enough for clustering methods, such as hierachical clustering or K-means clustering, to produce misleading results. Thus, accurate methods for missing value estimation are needed. We present novel methods for estimation of missing values in microarray data sets that are based on the least squares principle, and that utilize correlations between both genes and arrays. For this set of methods, we use the common reference name LSimpute. We compare the estimation accuracy of our methods with the widely used KNNimpute on three complete data matrices from public data sets by randomly knocking out data (labeling as missing). From these tests, we conclude that our LSimpute methods produce estimates that consistently are more accurate than those obtained using KNNimpute. Additionally, we examine a more classic approach to missing value estimation based on expectation maximization (EM). We refer to our EM implementations as EMimpute, and the estimate errors using the EMimpute methods are compared with those our novel methods produce. The results indicate that on average, the estimates from our best performing LSimpute method are at least as accurate as those from the best EMimpute algorithm.     

Expression count: a method for calculating morphological dental trait frequencies by using adjustable weighting coefficients with standard ranked scales

Expression count is the term used for a new method of calculating the frequency of a morphological dental trait in a population sample. This method incorporates into a single value the total trait variation expressed in the sample. It has been designed to increase the information content of small samples of dental remains common with archeological recovery.     

Measurement of hemoglobin in whole blood using a partial least squares regression model with selected second derivative near infrared transmission spectral signals

In this work, we propose a signal selection procedure for determination of hemoglobin (Hb) concentration in whole blood using near infrared (NIR) transmission spectral signals. A dataset of 190 whole blood NIR transmission spectra with reference Hb concentrations was used to evaluate the method. Spectral signals were selected based on the squared correlation coefficient (R(2)) between the signal and the Hb concentration. An improved uninformative variable elimination (UVE) procedure was performed to remove redundant signals from the primary selected signal set. A partial least squares (PLS) regression model was built with the final selected signals and the corresponding Hb concentrations. The results indicate that the proposed method is effective at increasing the predictive power of the NIR-PLS spectral model for determining Hb concentration in whole blood samples.     

Delaunay triangulation with partial least squares projection to latent structures: a model for G-protein coupled receptors classification and fast structure recognition

As an important transmembrane protein family in eukaryon, G-protein coupled receptors (GPCRs) play a significant role in cellular signal transduction and are important targets for drug design. However, it is very difficult to resolve their tertiary structure by X-ray crystallography. In this study, we have developed a Delaunay model, which constructs a series of simplexes with latent variables to classify the families of GPCRs and projects unknown sequences to principle component space (PC-space) to predict their topology. Computational results show that, for the classification of GPCRs, the method achieves the accuracy of 91.0 and 87.6% for Class A, more than 80% for the other three classes in differentiating GPCRs from non-GPCRs and 70% for discriminating between four major classes of GPCR, respectively. When recognizing the structure of GPCRs, all the N-terminals of sequences can be determined correctly. The maximum accuracy of predicting transmembrane segments is achieved in the 7th transmembrane segment of Rhodopsin, which is 99.4%, and the average error is 2.1 amino acids, which is the lowest in all of the segments prediction. This method could provide structural information of a novel GPCR as a tool for experiments and other algorithms of structure prediction of GPCRs. Academic users should send their request for the MATLAB program for classifying GPCRs and predicting the topology of them at liml@scu.edu.cn .     

A note on the conditional approach to interval estimation in the calibration problem.

In the calibration problem, the need to construct a confidence interval to estimate the unknown chi 0 arises when the null hypothesis of zero slope is rejected. Otherwise, the resulting confidence interval will be infinite to reflect the fact that the slope of the regression line may be zero. Under the condition of rejecting the hypothesis of zero slope, we study the properties of the conditional coverage rate of the calibration confidence interval. The conditional coverage rate (P1) is a function of the slope, distance between chi 0 and the mean of the trailing sample means, the sum of squares of chi, and n. When the true slope is close to 0 and chi 0 is away from means, P1 can go down to 0. On the other hand, as the power of testing zero slope reaches 1, with or without chi 0 close to means, P1 will tend to the desired nominal coverage rate. In summary, one should choose a reasonably small alpha in testing zero slope to avoid constructing a confidence interval for chi 0 when the true slope is 0. In addition, it is desirable to have high power in testing zero slope so that the resulting confidence interval will maintain the desired coverage rate when using the conditional approach in the calibration problem.     

A problem with using derivatives to explain the matching law

Herrnstein (1979) recently claimed that the matching law could be derived from an ordinary differential equation. He failed, however, to analyze the dynamic properties of his proposed equation. I show that it implies behavior cannot stabilize in accordance with the matching law. Consequently, Herrnstein's equation cannot explain why matching behavior has been widely observed.     

Correction to: Normalization and weighting: the open challenge in LCA

The International Journal of Life Cycle Assessment - The online version of the original article can be found at https://doi.org/10.1007/s11367-020-01790-0     

Assessing calibration uncertainty in molecular dating: the assignment of fossils to alternative calibration points

Although recent methodological advances have allowed the incorporation of rate variation in molecular dating analyses, the calibration procedure, performed mainly through fossils, remains resistant to improvements. One source of uncertainty pertains to the assignment of fossils to specific nodes in a phylogeny, especially when alternative possibilities exist that can be equally justified on morphological grounds. Here we expand on a recently developed fossil cross-validation method to evaluate whether alternative nodal assignments of multiple fossils produce calibration sets that differ in their internal consistency. We use an enlarged Crypteroniaceae-centered phylogeny of Myrtales, six fossils, and 72 combinations of calibration points, termed calibration sets, to identify (i) the fossil assignments that produce the most internally consistent calibration sets and (ii) the mean ages, derived from these calibration sets, for the split of the Southeast Asian Crypteroniaceae from their West Gondwanan sister clade (node X). We found that a correlation exists between s values, devised to measure the consistency among the calibration points of a calibration set (Near and Sanderson, 2004), and nodal distances among calibration points. By ranking all sets according to the percent deviation of s from the regression line with nodal distance, we identified the sets with the highest level of corrected calibration-set consistency. These sets generated lower standard deviations associated with the ages of node X than sets characterized by lower corrected consistency. The three calibration sets with the highest corrected consistencies produced mean age estimates for node X of 79.70, 79.14, and 78.15 My. These timeframes are most compatible with the hypothesis that the Crypteroniaceae stem lineage dispersed from Africa to the Deccan plate as it drifted northward during the Late Cretaceous.     

Towards the in silico identification of class II restricted T-cell epitopes: a partial least squares iterative self-consistent algorithm for affinity prediction

MOTIVATION: The immunogenicity of peptides depends on their ability to bind to MHC molecules. MHC binding affinity prediction methods can save significant amounts of experimental work. The class II MHC binding site is open at both ends, making epitope prediction difficult because of the multiple binding ability of long peptides. RESULTS: An iterative self-consistent partial least squares (PLS)-based additive method was applied to a set of 66 peptides no longer than 16 amino acids, binding to DRB1*0401. A regression equation containing the quantitative contributions of the amino acids at each of the nine positions was generated. Its predictability was tested using two external test sets which gave r(pred) = 0.593 and r(pred) = 0.655, respectively. Furthermore, it was benchmarked using 25 known T-cell epitopes restricted by DRB1*0401 and we compared our results with four other online predictive methods. The additive method showed the best result finding 24 of the 25 T-cell epitopes. AVAILABILITY: Peptides used in the study are available from http://www.jenner.ac.uk/JenPep. The PLS method is available commercially in the SYBYL molecular modelling software package. The final model for affinity prediction of peptides binding to DRB1*0401 molecule is available at http://www.jenner.ac.uk/MHCPred. Models developed for DRB1*0101 and DRB1*0701 also are available in MHCPred.     

Beyond binding: using phage display to select for structure, folding and enzymatic activity in proteins.

Phage display of a wide range of polypeptides has been increasingly used to identify novel molecules with useful binding properties for research, medical and industrial applications. Recent developments include methods for the selection of stabilized variants of a protein, the selection of regulatable enzymes and promising strategies for the selection and evolution of protein catalysts.     

Engineering of restriction endonucleases: using methylation activity of the bifunctional endonuclease Eco57I to select the mutant with a novel sequence specificity

Type II restriction endonucleases (REs) are widely used tools in molecular biology, biotechnology and diagnostics. Efforts to generate new specificities by structure-guided design and random mutagenesis have been unsuccessful so far. We have developed a new procedure called the methylation activity-based selection (MABS) for generating REs with a new specificity. MABS uses a unique property of bifunctional type II REs to methylate DNA targets they recognize. The procedure includes three steps: (1) conversion of a bifunctional RE into a monofunctional DNA-modifying enzyme by cleavage center disruption; (2) mutagenesis and selection of mutants with altered DNA modification specificity based on their ability to protect predetermined DNA targets; (3) reconstitution of the cleavage center's wild-type structure. The efficiency of the MABS technique was demonstrated by altering the sequence specificity of the bifunctional RE Eco57I from 5'-CTGAAG to 5'-CTGRAG, and thus generating the mutant restriction endonuclease (and DNA methyltransferase) of a specificity not known before. This study provides evidence that MABS is a promising technique for generation of REs with new specificities.     

Enhanced sampling of the molecular potential energy surface using mutually orthogonal latin squares: application to peptide structures

The computational identification of the optimal three-dimensional fold of even a small peptide chain from its sequence, without reference to other known structures, is a complex problem. There have been several attempts at solving this by sampling the potential energy surface of the molecule in a systematic manner. Here we present a new method to carry out the sampling, and to identify low energy conformers of the molecule. The method uses mutually orthogonal Latin squares to select (of the order of) n(2) points from the multidimensional conformation space of size m(n), where n is the number of dimensions (i.e., the number of conformational variables), and m specifies the fineness of the search grid. The sampling is accomplished by first calculating the value of the potential energy function at each one of the selected points. This is followed by analysis of these values of the potential energy to obtain the optimal value for each of the n-variables separately. We show that the set of the n-optimal values obtained in this manner specifies a low energy conformation of the molecule. Repeated application of the method identifies other low energy structures. The computational complexity of this algorithm scales as the fourth power of the size of the molecule. We applied this method to several small peptides, such as the neuropeptide enkephalin, and could identify a set of low energy conformations for each. Many of the structures identified by this method have also been previously identified and characterized by experiment and theory. We also compared the best structures obtained for the tripeptide (Ala)(3) by the present method, with those obtained by an exhaustive grid search, and showed that the algorithm is successful in identifying all the low energy conformers of this molecule.     

Resistance to barley scald (Rhynchosporium secalis) in the Ethiopian donor lines 'Steudelli' and 'Jet', analyzed by partial least squares regression and interval mapping

The resistance of barley (Hordeum vulgare L.) to Rhynchosporium secalis (scald) has been investigated in two crosses between the susceptible cv. 'Ingrid' and two resistant Ethiopian landraces, 'Steudelli' and 'Jet'. Doubled haploids were inoculated in replicated tests using two isolates of R. secalis, '4004' and 'WRS1872'. Expression of resistance differed widely between replicated tests. AFLP, SSR and RFLP markers were used to develop chromosome maps. Results have been analysed using partial least squares regression (PLSR) and interval mapping. In PLSR the major covariance structures or 'latent variables' between X (markers) and Y (isolates, tests) are modelled as principal components and their optimal number determined by cross-validation. In 'Steudelli' two QTL were detected, one on each of chromosomes 3H and 7H, in 4 out of 5 tests, while in 'Jet' only one (different) allele at the 3H locus was found. The validated R(2) varied between 11.0% and 64.9% in the replicated tests with '4004'.With isolate 'WRS1872' the 7H locus and another 3H locus were detected. By interval mapping the QTL detected were less stable and generally gave lower R(2) values than PLSR. PLSR does not depend on maps, but interval mapping based on values predicted by PLSR had R(2) around 90%. It is suggested that PLSR may be a useful tool in QTL analysis.     

Levels of Ly-49 receptor expression are determined by the frequency of interactions with MHC ligands: evidence against receptor calibration to a "useful" level.

Ly-49 receptor expression was studied in NK cells that developed in fully MHC-mismatched mixed bone marrow chimeras, in which host and donor MHC ligands were expressed solely on various proportions of hemopoietic cells or on both hemopoietic and nonhemopoietic cells. When hemopoietic cells were the only source of MHC ligand, a strong correlation between the level of down-regulation of Ly-49A, Ly-49C, and Ly-49G2 and the number of hemopoietic cells expressing their MHC ligands was observed on both donor and host NK cells. In some animals with low levels of donor hemopoietic chimerism, NK cells of donor origin expressed Ly-49 receptors at higher levels than was observed in normal mice of the same strain. This unexpected observation is inconsistent with the receptor calibration theory, which states that expression of Ly-49 inhibitory receptors is calibrated to an optimal level to maintain an NK cell repertoire that is sensitive to perturbations in normal class I ligand expression. Our data suggest a model in which Ly-49 receptors down-modulate in accordance with the frequency of their interactions with ligand-bearing cells, rather than a model in which these receptors calibrate to a specific "useful" level in response to ligands present in their environment.