Modeling single cell trajectory using forward-backward stochastic differential equations.

Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings between cells from different time points. However, optimal transport methods have limitations in capturing nonlinear trajectories, as they are static and can only infer linear paths between endpoints. In contrast, stochastic differential equations (SDEs) offer a dynamic and flexible approach that can model non-linear trajectories, including the shape of the path. Nevertheless, existing SDE methods often rely on numerical approximations that can lead to inaccurate inferences, deviating from true trajectories. To address this challenge, we propose a novel approach combining forward-backward stochastic differential equations (FBSDE) with a refined approximation procedure. Our FBSDE model integrates the forward and backward movements of two SDEs in time, aiming to capture the underlying dynamics of single-cell developmental trajectories. Through comprehensive benchmarking on multiple scRNA-seq datasets, we demonstrate the superior performance of FBSDE compared to other methods, highlighting its efficacy in accurately inferring developmental trajectories.

Dietary Lysine Requirements of Older Adults Stratified by Age and Sex.

BACKGROUND: Current recommendation for lysine in older adults, 30 mg/kg/d, is based on young adult data. Evidence suggests that amino acid requirements may differ between young and old adults with both sex and age having an effect in the elderly. OBJECTIVES: This study aimed to define the lysine requirements in healthy older adults using the indicator amino acid oxidation (IAAO) method with L-[1-13C] phenylalanine as the indicator and to compare the derived estimates based on age: 60-69 y and >70 y. METHODS: Fourteen healthy males and 16 healthy females [>60 y, body mass index (BMI) = 26.3 kg/m2] were randomly assigned to receive 3-7 lysine intakes from 10 to 80 mg/kg/d. Subjects were adapted to a standard liquid diet providing 1.0 g/kg/d protein and adequate energy, for 2 d, with indicator oxidation measurements performed on day 3. The rate of release of 13CO2 from the oxidation of L-[1-13C] phenylalanine was measured in breath. A 2-phase linear mixed-effect model, and parametric bootstrap were used to determine mean lysine requirements and the 95% confidence intervals (CIs). The overlap of the 95% CI between the 2 age groups were used to compare the requirement estimates. The null hypothesis was accepted if the interval contained zero. RESULTS: The mean and upper 95% CI of the lysine requirement for females were 32.9 and 40.9 and 46.2 and 53.7 mg/kg/d for those aged 60-69 y and >70 y, respectively. The mean and upper 95% CI of the lysine requirement for the 2 groups of males were not different so was combined to yield a mean and 95% CI of 32.2 and 38.2 mg/kg/d. CONCLUSIONS: To our knowledge, this is the first study to report on the lysine requirement in adults aged >60 y. These results provide a basis from which the adequacy of diets to meet lysine needs of older adults can be assessed. The trial was registered at clinicaltrials.gov as NCT02008955 (https://clinicaltrials.gov/study/NCT02008955).

Age-related effects on the anterior and posterior hippocampal volumes in 6-21 year olds: A model selection approach.

Although recent studies support significant differences in intrinsic structure, function, and connectivity along the longitudinal axis of the hippocampus, few studies have investigated the normative development of this dimension. In addition, factors known to influence hippocampal structure, such as sex or puberty, have yet to be characterized when assessing age-related effects on its subregions. This study addresses this gap by investigating the relationship of the anterior (antHC) and posterior (postHC) hippocampus volumes with age, and how these are moderated by sex or puberty, in structural magnetic resonance imaging scans from 183 typically developing participants aged 6-21 years. Based on previous literature, we first anticipated that non-linear models would best represent the relationship between age and the antHC and postHC volumes. We found that age-related effects are region-specific, such that the antHC volume remains stable with increasing age, while the postHC shows a cubic function characterized by overall volume increase with age but a slower rate during adolescence. Second, we hypothesized that models, which include biological sex or pubertal status would best describe these relationships. Contrary to expectation, models comprising either biological sex or pubertal status did not significantly improve model performance. Further longitudinal research is needed to evaluate their effects on the antHC and postHC development.

Length of Adaptation Has No Effect on the Threonine Requirement Determined in Healthy Young Adult Males Using the Indicator Amino Acid Oxidation Method.

BACKGROUND: The indicator amino acid oxidation (IAAO) method is minimally invasive; therefore, it is applicable to study the amino acid (AA) requirements of individuals in various age groups. However, the accuracy of this method has been criticized because of the 8 h (1 d) protocol, which has been suggested to be too short an adaptation time for estimating AA requirements. OBJECTIVES: The IAAO method was used to determine whether 3 or 7 d of adaptation to each threonine intake alters the threonine requirement in adult men compared to 1 d of adaptation. METHODS: Eleven healthy adult men (19-35 y, body mass index (BMI) 23.4 in kg⋅m-2) were studied at 6 threonine intakes; each intake was studied over a 9 d period. Following 2 d of pre-adaptation to adequate protein intake (1.0 g·kg-1⋅d-1), subjects received experimental diets containing the randomly assigned test threonine intake (5, 10, 15, 20, 25, or 35 mg·kg-1·d-1) for 7 d. IAAO studies were performed on days 1, 3, and 7 of adaptation to the experimental diet. The rate of release of 13CO2 from the oxidation of L-[1-13C]phenylalanine (F13CO2) was measured, and the threonine requirement was determined by applying mixed-effect change-point regression to the F13CO2 data in R version 4.0.5. The 95% confidence interval (CI) was calculated using parametric bootstrap, and the requirement estimates on days 1, 3, and 7 were compared using analysis of variance (ANOVA). RESULTS: The mean threonine requirements (upper, lower 95% CI) for days 1, 3, and 7 were 10.5 (5.7, 15.9), 10.6 (7.5, 13.7), and 12.1 (9.2, 15.0 mg·kg-1·d-1), respectively; and these requirements were not statistically different (P = 0.213). CONCLUSIONS: We demonstrated that the short, 8 h IAAO protocol results in a threonine requirement that is not statistically different from that obtained on days 3 or 7 of adaptation in healthy adult males. This trial was registered at www. CLINICALTRIALS: gov as NCT04585087.

Ultra-high dimensional variable selection for doubly robust causal inference.

Causal inference has been increasingly reliant on observational studies with rich covariate information. To build tractable causal procedures, such as the doubly robust estimators, it is imperative to first extract important features from high or even ultra-high dimensional data. In this paper, we propose causal ball screening for confounder selection from modern ultra-high dimensional data sets. Unlike the familiar task of variable selection for prediction modeling, our confounder selection procedure aims to control for confounding while improving efficiency in the resulting causal effect estimate. Previous empirical and theoretical studies suggest excluding causes of the treatment that are not confounders. Motivated by these results, our goal is to keep all the predictors of the outcome in both the propensity score and outcome regression models. A distinctive feature of our proposal is that we use an outcome model-free procedure for propensity score model selection, thereby maintaining double robustness in the resulting causal effect estimator. Our theoretical analyses show that the proposed procedure enjoys a number of properties, including model selection consistency and pointwise normality. Synthetic and real data analysis show that our proposal performs favorably with existing methods in a range of realistic settings. Data used in preparation of this paper were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

Body Composition and Physical Activity in Pediatric Intestinal Failure On and Off Parenteral Nutrition.

OBJECTIVES: Data on the relationship between body composition (BC) and physical activity (PA) in children with intestinal failure (IF) are lacking. The objectives were to collect data on PA and BC in children with IF, both parenterally and enterally fed, and to assess the relationship between PA and BC. METHODS: Cross-sectional study in children 5-18 years with IF including those receiving parenteral nutrition (PN) and those fully enterally fed. PA levels were measured using accelerometry. BC was measured by dual-energy X-ray absorptiometry. Data were compared to age- and sex-matched population norms using t tests. Regression analysis assessed the relationship between BC and PA. RESULTS: Fifty-eight children with IF (38 males), mean (SD) age of 10.0 (3.5) years, 20 dependent on PN were included. Patients with IF had significantly fewer steps per day ( P ≤ 0.001) compared with literature controls, with a mean (SD) of 7,972 (3,008) and 11,749 (1,106), respectively. There were no significant differences between patients receiving PN and those enterally fed, but both groups were significantly less active than literature controls ( P < 0.001). Patients with IF had higher fat mass and lower fat-free mass compared to literature controls ( P = 0.008). PA had a significant effect on BC ( r2 = 0.32, P < 0.001). CONCLUSIONS: Children with IF, those receiving PN and those fully enterally fed, are at risk of decreased PA and altered BC. PA should be part of ongoing rehabilitation and management to optimize outcomes.

Bioavailable Lysine Assessed Using the Indicator Amino Acid Oxidation Method in Healthy Young Males is High when Sorghum is Cooked by a Moist Cooking Method.

BACKGROUND: Sorghum is the fifth most consumed cereal grain but limiting in the indispensable amino acid lysine. Complementing sorghum with lentils can improve the quality of sorghum-based diets. However, knowledge of lysine bioavailability in sorghum is lacking. OBJECTIVES: The study objectives were to determine the bioavailability of lysine in sorghum and to assess the effect of complementation of sorghum and lentils in a mixed-meal format. METHODS: We studied 5 healthy young men (≤30 years; BMI <25 kg/m2) in a repeated-measure design using the indicator amino acid oxidation (IAAO) method, with L-[1-13C] phenylalanine as the indicator. Each subject participated in 8 determinations in random order. On the reference diet, subjects received 4 amounts of L-lysine (5, 8, 12, and 15 mg. kg-1 . d-1) from a crystalline amino acid mixture patterned after egg protein. On the test diet, they received 3 levels of lysine (8.2, 12.5, and 15.7 mg. kg-1 . d-1) from sorghum, and on the complementation diet they received 1 level of lysine from a mixed meal of sorghum and lentils. The bioavailability of lysine in sorghum was estimated by comparing the IAAO response to the test diet with the IAAO response to the reference diet using the slope-ratio method. Effectiveness of complementation was assessed by comparing the IAAO response to the mixed meal to the IAAO response to the test protein. RESULTS: The bioavailability of lysine from sorghum was 94%. Upon complementation with lentils, there was a decline in the oxidation of L-[1-13C] phenylalanine by 19% (P < 0.0495), reflecting an improvement in available lysine in the mixed meal due to increased lysine intake. CONCLUSIONS: Although the bioavailability of lysine in sorghum is high, its lysine content is limiting. Complementation with lentils in a 1:1 ratio is recommended to achieve the lysine requirement for adult men consuming a sorghum-based diet. This trial was registered at clinicaltrials.gov as NCT03411005.

Nonparametric matrix response regression with application to brain imaging data analysis.

With the rapid growth of neuroimaging technologies, a great effort has been dedicated recently to investigate the dynamic changes in brain activity. Examples include time course calcium imaging and dynamic brain functional connectivity. In this paper, we propose a novel nonparametric matrix response regression model to characterize the nonlinear association between 2D image outcomes and predictors such as time and patient information. Our estimation procedure can be formulated as a nuclear norm regularization problem, which can capture the underlying low-rank structure of the dynamic 2D images. We present a computationally efficient algorithm, derive the asymptotic theory, and show that the method outperforms other existing approaches in simulations. We then apply the proposed method to a calcium imaging study for estimating the change of fluorescent intensities of neurons, and an electroencephalography study for a comparison in the dynamic connectivity covariance matrices between alcoholic and control individuals. For both studies, the method leads to a substantial improvement in prediction error.

Analysis of fluorescence simulation and experiments for sea surface oil film based on LIF.

In order to effectively analyze the fluorescence distribution of sea surface oil film detected by laser-induced fluorescence (LIF), a novel, to the best of our knowledge, simulation model of the oil film fluorescence was established based on the Monte Carlo method. Using this simulation model, the fluorescence distribution of oil film with different thickness in emission direction and spatial distribution were analyzed. Based on the fluorescence mechanism model of oil film detected by LIF, a criterion for the LIF system calibration, i.e., the fluorescence intensity ratio between oil film and clean seawater (FIR) using the fluorescence collected from clean seawater as a reference was proposed. The validity of the fluorescence simulation model was verified by using the FIR results of theory and simulation. The fluorescence spectra of oil films with different thickness and FIR parameters of corresponding thickness were obtained by experiments. By analyzing the fluorescence spectra of different oil products and oil film thickness, the fluorescence influencing factors of oil film detected by LIF were obtained. The results show that the fluorescence coverage area increases gradually with the increase of oil film thickness. When the incident light is in the same direction as the fluorescence receiving direction, the obtained fluorescence intensity is larger. Moreover, the FIR used as the calibration criterion of the LIF monitoring system can effectively characterize the thickness of oil film on the sea surface for LIF to detect sea surface oil film in real applications.

Sample-Size Determination Methodologies for Machine Learning in Medical Imaging Research: A Systematic Review.

PURPOSE: The required training sample size for a particular machine learning (ML) model applied to medical imaging data is often unknown. The purpose of this study was to provide a descriptive review of current sample-size determination methodologies in ML applied to medical imaging and to propose recommendations for future work in the field. METHODS: We conducted a systematic literature search of articles using Medline and Embase with keywords including "machine learning," "image," and "sample size." The search included articles published between 1946 and 2018. Data regarding the ML task, sample size, and train-test pipeline were collected. RESULTS: A total of 167 articles were identified, of which 22 were included for qualitative analysis. There were only 4 studies that discussed sample-size determination methodologies, and 18 that tested the effect of sample size on model performance as part of an exploratory analysis. The observed methods could be categorized as pre hoc model-based approaches, which relied on features of the algorithm, or post hoc curve-fitting approaches requiring empirical testing to model and extrapolate algorithm performance as a function of sample size. Between studies, we observed great variability in performance testing procedures used for curve-fitting, model assessment methods, and reporting of confidence in sample sizes. CONCLUSIONS: Our study highlights the scarcity of research in training set size determination methodologies applied to ML in medical imaging, emphasizes the need to standardize current reporting practices, and guides future work in development and streamlining of pre hoc and post hoc sample size approaches.

FLCRM: Functional linear cox regression model.

We consider a functional linear Cox regression model for characterizing the association between time-to-event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high-dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time-to-event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high-dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer's disease. Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu).

FGWAS: Functional genome wide association analysis.

Functional phenotypes (e.g., subcortical surface representation), which commonly arise in imaging genetic studies, have been used to detect putative genes for complexly inherited neuropsychiatric and neurodegenerative disorders. However, existing statistical methods largely ignore the functional features (e.g., functional smoothness and correlation). The aim of this paper is to develop a functional genome-wide association analysis (FGWAS) framework to efficiently carry out whole-genome analyses of functional phenotypes. FGWAS consists of three components: a multivariate varying coefficient model, a global sure independence screening procedure, and a test procedure. Compared with the standard multivariate regression model, the multivariate varying coefficient model explicitly models the functional features of functional phenotypes through the integration of smooth coefficient functions and functional principal component analysis. Statistically, compared with existing methods for genome-wide association studies (GWAS), FGWAS can substantially boost the detection power for discovering important genetic variants influencing brain structure and function. Simulation studies show that FGWAS outperforms existing GWAS methods for searching sparse signals in an extremely large search space, while controlling for the family-wise error rate. We have successfully applied FGWAS to large-scale analysis of data from the Alzheimer's Disease Neuroimaging Initiative for 708 subjects, 30,000 vertices on the left and right hippocampal surfaces, and 501,584 SNPs.

Testing and estimation in marker-set association study using semiparametric quantile regression kernel machine.

We consider quantile regression for partially linear models where an outcome of interest is related to covariates and a marker set (e.g., gene or pathway). The covariate effects are modeled parametrically and the marker set effect of multiple loci is modeled using kernel machine. We propose an efficient algorithm to solve the corresponding optimization problem for estimating the effects of covariates and also introduce a powerful test for detecting the overall effect of the marker set. Our test is motivated by traditional score test, and borrows the idea of permutation test. Our estimation and testing procedures are evaluated numerically and applied to assess genetic association of change in fasting homocysteine level using the Vitamin Intervention for Stroke Prevention Trial data.

The role of endogenous IFN-ß in the regulation of Th17 responses in patients with relapsing-remitting multiple sclerosis.

IFN-ß has been used as a first-line therapy for relapsing-remitting multiple sclerosis (RRMS). Because only a few studies have addressed the role of endogenous IFN-ß in the pathogenesis of the disease, our objective was to characterize its role in the transcriptional regulation of pathogenic Th17 cytokines in patients with RRMS. In vitro studies have demonstrated that IFN-ß inhibits IL-17A, IL-17F, IL-21, IL-22, and IFN-γ secretion in CD4(+) lymphocytes through the induction of suppressor of cytokine secretion 1 and suppressor of cytokine secretion 3. We found that patients with RRMS have increased serum and cerebrospinal fluid Th17 (IL-17A and IL-17F) cytokine levels in comparison with the control subjects, suggesting that deficient endogenous IFN-ß secretion or signaling can contribute to the dysregulation of those pathogenic cytokines in CD4(+) cells. We identified that the endogenous IFN-ß from serum of RRMS patients induced a significantly lower IFN-inducible gene expression in comparison with healthy controls. In addition, in vitro studies have revealed deficient endogenous and exogenous IFN-ß signaling in the CD4(+) cells derived from patients with MS. Interestingly, upon inhibition of the endogenous IFN-ß signaling by silencing IFN regulatory factor (IRF) 7 gene expression, the resting CD4(+) T cells secreted significantly higher level of IL-17A, IL-17F, IL-21, IL-22, and IL-9, suggesting that endogenous IFN-ß suppresses the secretion of these pathogenic cytokines. In vivo recombinant IFN-ß-1a treatment induced IFNAR1 and its downstream signaling molecules' gene expression, suggesting that treatment reconstitutes a deficient endogenous IFN-ß regulation of the CD4(+) T cells' pathogenic cytokine production in patients with MS.

Crowdsourced estimation of cognitive decline and resilience in Alzheimer's disease.

Identifying accurate biomarkers of cognitive decline is essential for advancing early diagnosis and prevention therapies in Alzheimer's disease. The Alzheimer's disease DREAM Challenge was designed as a computational crowdsourced project to benchmark the current state-of-the-art in predicting cognitive outcomes in Alzheimer's disease based on high dimensional, publicly available genetic and structural imaging data. This meta-analysis failed to identify a meaningful predictor developed from either data modality, suggesting that alternate approaches should be considered for prediction of cognitive performance.

Classical Testing in Functional Linear Models.

We extend four tests common in classical regression - Wald, score, likelihood ratio and F tests - to functional linear regression, for testing the null hypothesis, that there is no association between a scalar response and a functional covariate. Using functional principal component analysis, we re-express the functional linear model as a standard linear model, where the effect of the functional covariate can be approximated by a finite linear combination of the functional principal component scores. In this setting, we consider application of the four traditional tests. The proposed testing procedures are investigated theoretically for densely observed functional covariates when the number of principal components diverges. Using the theoretical distribution of the tests under the alternative hypothesis, we develop a procedure for sample size calculation in the context of functional linear regression. The four tests are further compared numerically for both densely and sparsely observed noisy functional data in simulation experiments and using two real data applications.

Domain selection for the varying coefficient model via local polynomial regression.

In this article, we consider the varying coefficient model, which allows the relationship between the predictors and response to vary across the domain of interest, such as time. In applications, it is possible that certain predictors only affect the response in particular regions and not everywhere. This corresponds to identifying the domain where the varying coefficient is nonzero. Towards this goal, local polynomial smoothing and penalized regression are incorporated into one framework. Asymptotic properties of our penalized estimators are provided. Specifically, the estimators enjoy the oracle properties in the sense that they have the same bias and asymptotic variance as the local polynomial estimators as if the sparsity is known as a priori. The choice of appropriate bandwidth and computational algorithms are discussed. The proposed method is examined via simulations and a real data example.

Protein intake affects erythrocyte glutathione synthesis in young healthy adults in a repeated-measures trial.

BACKGROUND: In 2005, the Institute of Medicine advised using methods other than nitrogen balance (NB) for determining protein requirements. Since then, protein requirements using indicator amino acid oxidation (IAAO) have been published and are higher than NB. Glutathione (GSH), a tripeptide of cysteine, glutamate, and glycine, is a principal antioxidant that can be used as a functional indicator of protein adequacy. OBJECTIVES: The aim of this study was to measure changes in erythrocyte GSH kinetics [fractional synthesis rate (FSR) and absolute synthesis rate (ASR)] in healthy adults following a range of protein intakes at and above the current recommendations. METHODS: Sixteen healthy adults [8 males and 8 females, aged 25.6 ± 0.9 y (mean ± SEM)] were studied at 4 of 6 protein intakes ranging from 0.6 to 1.5 g⋅kg-1⋅d-1. Erythrocyte GSH kinetics were assessed during a 7-h infusion of [U-13C2-15N]glycine following 2 d of adaptation to each protein intake. Blood and urine tests were performed to measure oxidative stress markers, plasma homocysteine, triglycerides, plasma amino acid concentrations, 5-L-oxoproline (5-OP), and urinary sulfate. The protein intake that maximized GSH synthesis was determined using mixed-effect change-point regression in R. Primary and secondary outcomes were analyzed using linear mixed-effects and repeated-measures analysis of variance with Tukey's post hoc test. RESULTS: The protein intake that maximized GSH FSR at 78%⋅d-1 was 1.0 g⋅kg-1⋅d-1 (95% confidence interval: 0.63, 1.39). GSH ASR was significantly lower at 0.6 and 0.8 g⋅kg-1⋅d-1 than at 1.5 g⋅kg-1⋅d-1 (2.03 and 2.17, respectively, compared with 3.71 mmol⋅L-1⋅d-1). Increasing the protein intake led to increased urinary sulfate but did not affect erythrocyte GSH concentration, plasma oxidative stress markers, triglycerides, homocysteine, or 5-OP. CONCLUSIONS: A protein intake of 1.0 g⋅kg-1⋅d-1 maximized GSH synthesis, which is in agreement with earlier IAAO-derived protein requirements of 0.93 to 1.2 g⋅kg-1⋅d-1. These findings suggest that recommendations based on NB (0.66 g⋅kg-1⋅d-1) may underestimate protein needs for adequate health. This trial was registered at clinicaltrials.gov as NCT02971046.

Protein intake affects erythrocyte glutathione synthesis in healthy adults aged ≥60 years in a repeated-measures trial.

BACKGROUND: Protein recommendations for older adults are based on nitrogen balance data from young adults. Physiological studies using the indicator amino acid oxidation method suggest they need 30% to 50% more protein than current recommendations. We herein present glutathione (GSH) as a physiological estimate of protein adequacy in older adults. OBJECTIVES: The objective was to measure GSH kinetics in response to varying protein intakes in a repeated-measures design in healthy adults aged ≥60 y using the precursor-product method. METHODS: Sixteen healthy older adults (n = 8 male and n = 8 female; body mass index ≤30 kg/m2) were studied. Each received 4 of 6 protein intakes in random order (0.66, 0.8, 0.9, 1.1, 1.3 and 1.5 g⋅kg-1⋅d-1). At each intake level, participants underwent isotope infusion studies of 7 h duration following a 3-d adaptation to the test level of protein. On the fourth day, GSH fractional (FSR) and absolute synthesis (ASR) rates were quantified by measuring the incorporation of U-[13C2-15N]glycine into GSH at isotopic steady state. A mixed-effect change-point regression model was used to determine a breakpoint in FSR and ASR. Secondary outcomes included plasma concentrations of oxidative stress markers, homocysteine, 5-L-oxoproline (5-OP), and urinary sulfate. The effect of secondary outcomes on GSH kinetics was analyzed using a joint linear mixed-effect model and Tukey's post hoc test. RESULTS: A protein intake of 1.08 g⋅kg-1⋅d-1 (95% confidence interval [CI]: 0.83, 1.32; Rm2 = 0.207; Rc2 = 0.671; P < 0.001) maximized GSH FSR. There was no effect of protein intake on concentrations of erythrocyte GSH, plasma homocysteine, oxidative stress markers, or 5-OP (P > 0.05). Protein intake had a positive effect on urinary sulfate excretion (P < 0.0001). CONCLUSION: A protein intake of 1.08 g⋅kg-1⋅d-1 from a high-quality protein maximized GSH synthesis in adults ≥60 y. This lends support to data suggesting a requirement higher than the current recommendation. This study was registered at clinicaltrials.gov as NCT02971046.