Latent group detection in functional partially linear regression models

In this paper, we propose a functional partially linear regression model with latent group structures to accommodate the heterogeneous relationship between a scalar response and functional covariates. The proposed model is motivated by a salinity tolerance study of barley families, whose main objective is to detect salinity tolerant barley plants. Our model is flexible, allowing for heterogeneous functional coefficients while being efficient by pooling information within a group for estimation. We develop an algorithm in the spirit of the K-means clustering to identify latent groups of the subjects under study. We establish the consistency of the proposed estimator, derive the convergence rate and the asymptotic distribution, and develop inference procedures. We show by simulation studies that the proposed method has higher accuracy for recovering latent groups and for estimating the functional coefficients than existing methods. The analysis of the barley data shows that the proposed method can help identify groups of barley families with different salinity tolerant abilities.     

Variable selection in nonlinear function-on-scalar regression

We develop a new method for variable selection in a nonlinear additive function-on-scalar regression (FOSR) model. Existing methods for variable selection in FOSR have focused on the linear effects of scalar predictors, which can be a restrictive assumption in the presence of multiple continuously measured covariates. We propose a computationally efficient approach for variable selection in existing linear FOSR using functional principal component scores of the functional response and extend this framework to a nonlinear additive function-on-scalar model. The proposed method provides a unified and flexible framework for variable selection in FOSR, allowing nonlinear effects of the covariates. Numerical analysis using simulation study illustrates the advantages of the proposed method over existing variable selection methods in FOSR even when the underlying covariate effects are all linear. The proposed procedure is demonstrated on accelerometer data from the 2003–2004 cohorts of the National Health and Nutrition Examination Survey (NHANES) in understanding the association between diurnal patterns of physical activity and demographic, lifestyle, and health characteristics of the participants.     

Evaluating treatment effects in group sequential multivariate longitudinal studies with covariate adjustment

Jeffries et al. (2018) investigated testing for a treatment difference in the setting of a randomized clinical trial with a single outcome measured longitudinally over a series of common follow-up times while adjusting for covariates. That paper examined the null hypothesis of no difference at any follow-up time versus the alternative of a difference for at least one follow-up time. We extend those results here by considering multivariate outcome measurements, where each individual outcome is examined at common follow-up times. We consider the case where there is interest in first testing for a treatment difference in a global function of the outcomes (e.g., weighted average or sum) with subsequent interest in examining the individual outcomes, should the global function show a treatment difference. Testing is conducted for each follow-up time and may be performed in the setting of a group sequential trial. Testing procedures are developed to determine follow-up times for which a global treatment difference exists and which individual combinations of outcome and follow-up time show evidence of a difference while controlling for multiplicity in outcomes, follow-up, and interim analyses. These approaches are examined in a study evaluating the effects of tissue plasminogen activator on longitudinally obtained stroke severity measurements.     

Multikink quantile regression for longitudinal data with application to progesterone data analysis

Motivated by investigating the relationship between progesterone and the days in a menstrual cycle in a longitudinal study, we propose a multikink quantile regression model for longitudinal data analysis. It relaxes the linearity condition and assumes different regression forms in different regions of the domain of the threshold covariate. In this paper, we first propose a multikink quantile regression for longitudinal data. Two estimation procedures are proposed to estimate the regression coefficients and the kink points locations: one is a computationally efficient profile estimator under the working independence framework while the other one considers the within-subject correlations by using the unbiased generalized estimation equation approach. The selection consistency of the number of kink points and the asymptotic normality of two proposed estimators are established. Second, we construct a rank score test based on partial subgradients for the existence of the kink effect in longitudinal studies. Both the null distribution and the local alternative distribution of the test statistic have been derived. Simulation studies show that the proposed methods have excellent finite sample performance. In the application to the longitudinal progesterone data, we identify two kink points in the progesterone curves over different quantiles and observe that the progesterone level remains stable before the day of ovulation, then increases quickly in 5 to 6 days after ovulation and then changes to stable again or drops slightly.     

Fluorescent in situ hybridization of the telomere repeat sequence in hamster sperm nuclear structures

The flat, hooked-shaped architecture of the hamster sperm nucleus makes this an excellent model for in situ hybridization studies of the three dimensional structure of the genome. We have examined the structure of the telomere repeat sequence (TTAGGG)_n with respect to the various nuclear structures present in hamster spermatozoa, using fluorescent in situ hybridization. In fully condensed, mature sperm nuclei, the telomere sequences appeared as discrete spots of various sizes interspersed throughout the volume of the nuclei. While the pattern of these signals was non-random, it varied significantly in different nuclei. These discrete telomere foci were seen to gradually lengthen into linear, beaded signals as sperm nuclei were decondensed, in vitro, and were not associated with the nuclear annulus. We also examined the relationship of telomeres to the sperm nuclear matrix, a residual nuclear structure that retains the original size and shape of the nucleus. In these structures the DNA extends beyond the perimeter of the nucleus to form a halo around it, representing the arrangement of the chromosomal DNA into loop domains attached at their bases to the nuclear matrix. Telomere signals in these structures were also linear and equal in length to those of the decondensed nuclei, and each signal represented part of a single DNA loop domain. The telomeres were attached at one end to the nuclear matrix and extended into the halo. Sperm nuclear matrices treated with Eco RI retained the telomere signals. These data support sperm DNA packaging models in which DNA is coiled into discrete foci, rather than spread out linearly along the length of the sperm nucleus.     

Chasing long-range evolutionary couplings in the AlphaFold era

Coevolution between protein residues is normally interpreted as direct contact. However, the evolutionary record of a protein sequence contains rich information that may include long-range functional couplings, couplings that report on homo-oligomeric states or even conformational changes. Due to the complexity of the sequence space and the lack of structural information on various members of a protein family, it has been difficult to effectively mine the additional information encoded in a multiple sequence alignment (MSA). Here, taking advantage of the recent release of the AlphaFold (AF) database we attempt to identify coevolutionary couplings that cannot be explained simply by spatial proximity. We propose a simple computational method that performs direct coupling analysis on a MSA and searches for couplings that are not satisfied in any of the AF models of members of the identified protein family. Application of this method on 2012 protein families suggests that ~12% of the total identified coevolving residue pairs are spatially distant and more likely to be disordered than their contacting counterparts. We expect that this analysis will help improve the quality of coevolutionary distance restraints used for structure determination and will be useful in identifying potentially functional/allosteric cross-talk between distant residues.     

Dynamic genome-scale modeling of Saccharomyces cerevisiae unravels mechanisms for ester formation during alcoholic fermentation

Fermentation employing Saccharomyces cerevisiae has produced alcoholic beverages and bread for millennia. More recently, S. cerevisiae has been used to manufacture specific metabolites for the food, pharmaceutical, and cosmetic industries. Among the most important of these metabolites are compounds associated with desirable aromas and flavors, including higher alcohols and esters. Although the physiology of yeast has been well-studied, its metabolic modulation leading to aroma production in relevant industrial scenarios such as winemaking is still unclear. Here we ask what are the underlying metabolic mechanisms that explain the conserved and varying behavior of different yeasts regarding aroma formation under enological conditions? We employed dynamic flux balance analysis (dFBA) to answer this key question using the latest genome-scale metabolic model (GEM) of S. cerevisiae. The model revealed several conserved mechanisms among wine yeasts, for example, acetate ester formation is dependent on intracellular metabolic acetyl-CoA/CoA levels, and the formation of ethyl esters facilitates the removal of toxic fatty acids from cells using CoA. Species-specific mechanisms were also found, such as a preference for the shikimate pathway leading to more 2-phenylethanol production in the Opale strain as well as strain behavior varying notably during the carbohydrate accumulation phase and carbohydrate accumulation inducing redox restrictions during a later cell growth phase for strain Uvaferm. In conclusion, our new metabolic model of yeast under enological conditions revealed key metabolic mechanisms in wine yeasts, which will aid future research strategies to optimize their behavior in industrial settings.     

Functional data analysis with covariate-dependent mean and covariance structures

Functional data analysis has emerged as a powerful tool in response to the ever-increasing resources and efforts devoted to collecting information about response curves or anything that varies over a continuum. However, limited progress has been made with regard to linking the covariance structures of response curves to external covariates, as most functional models assume a common covariance structure. We propose a new functional regression model with covariate-dependent mean and covariance structures. Particularly, by allowing variances of random scores to be covariate-dependent, we identify eigenfunctions for each individual from the set of eigenfunctions that govern the variation patterns across all individuals, resulting in high interpretability and prediction power. We further propose a new penalized quasi-likelihood procedure that combines regularization and B-spline smoothing for model selection and estimation and establish the convergence rate and asymptotic normality of the proposed estimators. The utility of the developed method is demonstrated via simulations, as well as an analysis of the Avon Longitudinal Study of Parents and Children concerning parental effects on the growth curves of their offspring, which yields biologically interesting results.     

Genetic inference of orchid population dynamics on different-aged lava flows in Costa Rica

Colonization is a fundamental ecological process that is important for the persistence of species, particularly when a changing environment necessitates range shifts. Vacant habitats available for colonization often arise from landscape disturbance. Colonization and population expansion processes can be inferred by examining the levels and spatial distribution of genetic variation of plant populations with known disturbance histories. Samples (N = 690) of the terrestrial orchid, Epidendrum radicans, were collected from five lava flow sites on the slopes of Volcán Arenal in Costa Rica that last experienced major eruptions in 1968 and 1992. Individuals were also sampled (N = 188) from four regional populations. Samples were characterized using 15 nuclear genetic markers and analyzed using population genetics statistics. Genetic diversity within sites was moderate (H_e = 0.092–0.192). Contrary to expectation, diversity tended to be lower on the older lava flows (0.131 vs. 0.172) which may reflect their more sheltered topography that restricted pollen/seed immigration, and/or greater intra- and interspecific competition. Genetic diversity measures indicate that the lava flows were colonized by numerous individuals that likely originated from multiple sources while spatial genetic structure (SGS) statistics indicate that most recruitment in the study sites subsequent to colonization resulted from in situ reproduction and localized seed deposition. Younger sites had significantly greater SGS over larger distances which reflects fewer reproductive events, and less spatial and temporal overlap of seed shadows relative to the older sites. Clones were also generally smaller on the younger sites (≤3 m vs. ≤8 m).