Addressing erroneous scale assumptions in microbe and gene set enrichment analysis.

By applying Differential Set Analysis (DSA) to sequence count data, researchers can determine whether groups of microbes or genes are differentially enriched. Yet sequence count data suffer from a scale limitation: these data lack information about the scale (i.e., size) of the biological system under study, leading some authors to call these data compositional (i.e., proportional). In this article, we show that commonly used DSA methods that rely on normalization make strong, implicit assumptions about the unmeasured system scale. We show that even small errors in these scale assumptions can lead to positive predictive values as low as 9%. To address this problem, we take three novel approaches. First, we introduce a sensitivity analysis framework to identify when modeling results are robust to such errors and when they are suspect. Unlike standard benchmarking studies, this framework does not require ground-truth knowledge and can therefore be applied to both simulated and real data. Second, we introduce a statistical test that provably controls Type-I error at a nominal rate despite errors in scale assumptions. Finally, we discuss how the impact of scale limitations depends on a researcher's scientific goals and provide tools that researchers can use to evaluate whether their goals are at risk from erroneous scale assumptions. Overall, the goal of this article is to catalyze future research into the impact of scale limitations in analyses of sequence count data; to illustrate that scale limitations can lead to inferential errors in practice; yet to also show that rigorous and reproducible scale reliant inference is possible if done carefully.

Measuring and mitigating PCR bias in microbiota datasets.

PCR amplification plays an integral role in the measurement of mixed microbial communities via high-throughput DNA sequencing of the 16S ribosomal RNA (rRNA) gene. Yet PCR is also known to introduce multiple forms of bias in 16S rRNA studies. Here we present a paired modeling and experimental approach to characterize and mitigate PCR NPM-bias (PCR bias from non-primer-mismatch sources) in microbiota surveys. We use experimental data from mock bacterial communities to validate our approach and human gut microbiota samples to characterize PCR NPM-bias under real-world conditions. Our results suggest that PCR NPM-bias can skew estimates of microbial relative abundances by a factor of 4 or more, but that this bias can be mitigated using log-ratio linear models.

Modeling the temporal dynamics of the gut microbial community in adults and infants.

Given the highly dynamic and complex nature of the human gut microbial community, the ability to identify and predict time-dependent compositional patterns of microbes is crucial to our understanding of the structure and functions of this ecosystem. One factor that could affect such time-dependent patterns is microbial interactions, wherein community composition at a given time point affects the microbial composition at a later time point. However, the field has not yet settled on the degree of this effect. Specifically, it has been recently suggested that only a minority of taxa depend on the microbial composition in earlier times. To address the issue of identifying and predicting temporal microbial patterns we developed a new model, MTV-LMM (Microbial Temporal Variability Linear Mixed Model), a linear mixed model for the prediction of microbial community temporal dynamics. MTV-LMM can identify time-dependent microbes (i.e., microbes whose abundance can be predicted based on the previous microbial composition) in longitudinal studies, which can then be used to analyze the trajectory of the microbiome over time. We evaluated the performance of MTV-LMM on real and synthetic time series datasets, and found that MTV-LMM outperforms commonly used methods for microbiome time series modeling. Particularly, we demonstrate that the effect of the microbial composition in previous time points on the abundance of taxa at later time points is underestimated by a factor of at least 10 when applying previous approaches. Using MTV-LMM, we demonstrate that a considerable portion of the human gut microbiome, both in infants and adults, has a significant time-dependent component that can be predicted based on microbiome composition in earlier time points. This suggests that microbiome composition at a given time point is a major factor in defining future microbiome composition and that this phenomenon is considerably more common than previously reported for the human gut microbiome.

Human Gut Microbiota Predicts Susceptibility to Vibrio cholerae Infection.

Background: Cholera is a public health problem worldwide, and the risk factors for infection are only partially understood. Methods: We prospectively studied household contacts of patients with cholera to compare those who were infected to those who were not. We constructed predictive machine learning models of susceptibility, using baseline gut microbiota data. We identified bacterial taxa associated with susceptibility to Vibrio cholerae infection and tested these taxa for interactions with V. cholerae in vitro. Results: We found that machine learning models based on gut microbiota, as well as models based on known clinical and epidemiological risk factors, predicted V. cholerae infection. A predictive gut microbiota of roughly 100 bacterial taxa discriminated between contacts who developed infection and those who did not. Susceptibility to cholera was associated with depleted levels of microbes from the phylum Bacteroidetes. By contrast, a microbe associated with cholera by our modeling framework, Paracoccus aminovorans, promoted the in vitro growth of V. cholerae. Gut microbiota structure, clinical outcome, and age were also linked. Conclusion: These findings support the hypothesis that abnormal gut microbial communities are a host factor related to V. cholerae susceptibility.

Beyond Normalization: Incorporating Scale Uncertainty in Microbiome and Gene Expression Analysis.

Though statistical normalizations are often used in differential abundance or differential expression analysis to address sample-to-sample variation in sequencing depth, we offer a better alternative. These normalizations often make strong, implicit assumptions about the scale of biological systems (e.g., microbial load). Thus, analyses are susceptible to even slight errors in these assumptions, leading to elevated rates of false positives and false negatives. We introduce scale models as a generalization of normalizations so researchers can model potential errors in assumptions about scale. By incorporating scale models into the popular ALDEx2 software, we enhance the reproducibility of analyses while often drastically decreasing false positive and false negative rates. We design scale models that are guaranteed to reduce false positives compared to equivalent normalizations. At least in the context of ALDEx2, we recommend using scale models over normalizations in all practical situations.

From Pre-test and Post-test Probabilities to Medical Decision Making.

Background: A central goal of modern evidence-based medicine is the development of simple and easy to use tools that help clinicians integrate quantitative information into medical decision-making. The Bayesian Pre-test/Post-test Probability (BPP) framework is arguably the most well known of such tools and provides a formal approach to quantify diagnostic uncertainty given the result of a medical test or the presence of a clinical sign. Yet, clinical decision-making goes beyond quantifying diagnostic uncertainty and requires that that uncertainty be balanced against the various costs and benefits associated with each possible decision. Despite increasing attention in recent years, simple and flexible approaches to quantitative clinical decision-making have remained elusive. Methods: We extend the BPP framework using concepts of Bayesian Decision Theory. By integrating cost, we can expand the BPP framework to allow for clinical decision-making. Results: We develop a simple quantitative framework for binary clinical decisions (e.g., action/inaction, treat/no-treat, test/no-test). Let p be the pre-test or post-test probability that a patient has disease. We show that r*=(1-p)/p represents a critical value called a decision boundary. In terms of the relative cost of under- to over-acting, r* represents the critical value at which action and inaction are equally optimal. We demonstrate how this decision boundary can be used at the bedside through case studies and as a research tool through a reanalysis of a recent study which found widespread misestimation of pre-test and post-test probabilities among clinicians. Conclusions: Our approach is so simple that it should be thought of as a core, yet previously overlooked, part of the BPP framework. Unlike prior approaches to quantitative clinical decision-making, our approach requires little more than a hand-held calculator, is applicable in almost any setting where the BPP framework can be used, and excels in situations where the costs and benefits associated with a particular decision are patient-specific and difficult to quantify.

Changes in the type 2 diabetes gut mycobiome associate with metformin treatment across populations.

The human gut teems with a diverse ecosystem of microbes, yet non-bacterial portions of that community are overlooked in studies of metabolic diseases firmly linked to gut bacteria. Type 2 diabetes mellitus (T2D) is associated with compositional shifts in the gut bacterial microbiome and the mycobiome, the fungal portion of the microbiome. However, whether T2D and/or metformin treatment underpins fungal community changes is unresolved. To differentiate these effects, we curated a gut mycobiome cohort spanning 1,000 human samples across five countries and validated our findings in a murine experimental model. We use Bayesian multinomial logistic normal models to show that T2D and metformin both associate with shifts in the relative abundance of distinct gut fungi. T2D is associated with shifts in the Saccharomycetes and Sordariomycetes fungal classes, while the genera Fusarium and Tetrapisipora most consistently associate with metformin treatment. We confirmed the impact of metformin on individual gut fungi by administering metformin to healthy mice. Thus, metformin and T2D account for subtle, but significant and distinct variation in the gut mycobiome across human populations. This work highlights for the first time that metformin can confound associations of gut fungi with T2D and warrants the need to consider pharmaceutical interventions in investigations of linkages between metabolic diseases and gut microbial inhabitants. IMPORTANCE: This is the largest to-date multi-country cohort characterizing the human gut mycobiome, and the first to investigate potential perturbations in gut fungi from oral pharmaceutical treatment. We demonstrate the reproducible effects of metformin treatment on the human and murine gut mycobiome and highlight a need to consider metformin as a confounding factor in investigations between type 2 diabetes mellitus and the gut microbial ecosystem.

Race, employment, and the pandemic: An exploration of covariate explanations of COVID-19 case fatality rate variance.

We derive a simple asymptotic approximation for the long-run case fatality rate of COVID-19 (alpha and delta variants) and show that these estimations are highly correlated to the interaction between US State median age and projected US unemployment rate (Adj. r2 = 60%). We contrast this to the high level of correlation between point (instantaneous) estimates of per state case fatality rates and the interaction of median age, population density and current unemployment rates (Adj. r2 = 50.2%). To determine whether this is caused by a "race effect," we then analyze unemployment, race, median age and population density across US states and show that adding the interaction of African American population and unemployment explains 53.5% of the variance in COVID case fatality rates for the alpha and delta variants when considering instantaneous case fatality rate. Interestingly, when the asymptotic case fatality rate is used, the dependence on the African American population disappears, which is consistent with the fact that in the long-run COVID does not discriminate on race, but may discriminate on access to medical care which is highly correlated to employment in the US. The results provide further evidence of the impact inequality can have on case fatality rates in COVID-19 and the impact complex social, health and economic factors can have on patient survival.

Changes in the Type 2 diabetes gut mycobiome associate with metformin treatment across populations.

The human gut teems with a diverse ecosystem of microbes, yet non-bacterial portions of that community are overlooked in studies of metabolic diseases firmly linked to gut bacteria. Type 2 diabetes mellitus (T2D) associates with compositional shifts in the gut bacterial microbiome and fungal mycobiome, but whether T2D and/or pharmaceutical treatments underpin the community change is unresolved. To differentiate these effects, we curated a gut mycobiome cohort to-date spanning 1,000 human samples across 5 countries and a murine experimental model. We use Bayesian multinomial logistic normal models to show that metformin and T2D both associate with shifts in the relative abundance of distinct gut fungi. T2D associates with shifts in the Saccharomycetes and Sordariomycetes fungal classes, while the genera Fusarium and Tetrapisipora most consistently associate with metformin treatment. We confirmed the impact of metformin on individual gut fungi by administering metformin to healthy mice. Thus, metformin and T2D account for subtle, but significant and distinct variation in the gut mycobiome across human populations. This work highlights for the first time that oral pharmaceuticals can confound associations of gut fungi with T2D and warrants the need to consider pharmaceutical interventions in investigations of linkages between metabolic diseases and gut microbial inhabitants.

Quantitative Geometric Modeling of Blood Cells from X-ray Histotomograms of Whole Zebrafish Larvae.

Tissue phenotyping is foundational to understanding and assessing the cellular aspects of disease in organismal context and an important adjunct to molecular studies in the dissection of gene function, chemical effects, and disease. As a first step toward computational tissue phenotyping, we explore the potential of cellular phenotyping from 3-Dimensional (3D), 0.74 µm isotropic voxel resolution, whole zebrafish larval images derived from X-ray histotomography, a form of micro-CT customized for histopathology. As proof of principle towards computational tissue phenotyping of cells, we created a semi-automated mechanism for the segmentation of blood cells in the vascular spaces of zebrafish larvae, followed by modeling and extraction of quantitative geometric parameters. Manually segmented cells were used to train a random forest classifier for blood cells, enabling the use of a generalized cellular segmentation algorithm for the accurate segmentation of blood cells. These models were used to create an automated data segmentation and analysis pipeline to guide the steps in a 3D workflow including blood cell region prediction, cell boundary extraction, and statistical characterization of 3D geometric and cytological features. We were able to distinguish blood cells at two stages in development (4- and 5-days-post-fertilization) and wild-type vs. polA2 huli hutu ( hht ) mutants. The application of geometric modeling across cell types to and across organisms and sample types may comprise a valuable foundation for computational phenotyping that is more open, informative, rapid, objective, and reproducible.

Ancient dental calculus reveals oral microbiome shifts associated with lifestyle and disease in Great Britain.

The prevalence of chronic, non-communicable diseases has risen sharply in recent decades, especially in industrialized countries. While several studies implicate the microbiome in this trend, few have examined the evolutionary history of industrialized microbiomes. Here we sampled 235 ancient dental calculus samples from individuals living in Great Britain (∼2200 BCE to 1853 CE), including 127 well-contextualized London adults. We reconstructed their microbial history spanning the transition to industrialization. After controlling for oral geography and technical biases, we identified multiple oral microbial communities that coexisted in Britain for millennia, including a community associated with Methanobrevibacter, an anaerobic Archaea not commonly prevalent in the oral microbiome of modern industrialized societies. Calculus analysis suggests that oral hygiene contributed to oral microbiome composition, while microbial functions reflected past differences in diet, specifically in dairy and carbohydrate consumption. In London samples, Methanobrevibacter-associated microbial communities are linked with skeletal markers of systemic diseases (for example, periostitis and joint pathologies), and their disappearance is consistent with temporal shifts, including the arrival of the Second Plague Pandemic. This suggests pre-industrialized microbiomes were more diverse than previously recognized, enhancing our understanding of chronic, non-communicable disease origins in industrialized populations.

Phosphorylation barcodes direct biased chemokine signaling at CXCR3.

G protein-coupled receptor (GPCR) biased agonism, the activation of some signaling pathways over others, is thought to largely be due to differential receptor phosphorylation, or "phosphorylation barcodes." At chemokine receptors, ligands act as "biased agonists" with complex signaling profiles, which contributes to the limited success in pharmacologically targeting these receptors. Here, mass spectrometry-based global phosphoproteomics revealed that CXCR3 chemokines generate different phosphorylation barcodes associated with differential transducer activation. Chemokine stimulation resulted in distinct changes throughout the kinome in global phosphoproteomic studies. Mutation of CXCR3 phosphosites altered ß-arrestin conformation in cellular assays and was confirmed by molecular dynamics simulations. T cells expressing phosphorylation-deficient CXCR3 mutants resulted in agonist- and receptor-specific chemotactic profiles. Our results demonstrate that CXCR3 chemokines are non-redundant and act as biased agonists through differential encoding of phosphorylation barcodes and lead to distinct physiological processes.

Phosphorylation barcodes direct biased chemokine signaling at CXCR3.

G protein-coupled receptor (GPCR)-biased agonism, selective activation of certain signaling pathways relative to others, is thought to be directed by differential GPCR phosphorylation "barcodes." At chemokine receptors, endogenous chemokines can act as "biased agonists", which may contribute to the limited success when pharmacologically targeting these receptors. Here, mass spectrometry-based global phosphoproteomics revealed that CXCR3 chemokines generate different phosphorylation barcodes associated with differential transducer activation. Chemokine stimulation resulted in distinct changes throughout the kinome in global phosphoproteomics studies. Mutation of CXCR3 phosphosites altered ß-arrestin 2 conformation in cellular assays and was consistent with conformational changes observed in molecular dynamics simulations. T cells expressing phosphorylation-deficient CXCR3 mutants resulted in agonist- and receptor-specific chemotactic profiles. Our results demonstrate that CXCR3 chemokines are non-redundant and act as biased agonists through differential encoding of phosphorylation barcodes, leading to distinct physiological processes.

Metformin modulates the gut microbiome in broiler breeder hens.

Broiler breeder hens, the parent stock of commercial broiler chickens, are genetically selected for rapid growth. Due to a longer production period and the focus of genetic selection on superior carcass traits in their progeny, these hens have the propensity to gain excess adipose tissue and exhibit severe ovarian dysfunction, a phenotype that is similar to human polycystic ovary syndrome (PCOS). Metformin is an antihyperglycemic drug approved for type 2 diabetes that is prescribed off-label for PCOS with benefits on metabolic and reproductive health. An additional effect of metformin treatments in humans is modulation of gut microbiome composition, hypothesized to benefit glucose sensitivity and systemic inflammation. The effects of dietary metformin supplementation in broiler breeder hens have not been investigated, thus we hypothesized that dietary metformin supplementation would alter the gut microbiome of broiler breeder hens. Broiler breeder hens were supplemented with metformin at four different levels (0, 25, 50, and 75 mg/kg body weight) from 25 to 65 weeks of age, and a subset of hens (n = 8-10 per treatment group) was randomly selected to undergo longitudinal microbiome profiling with 16S rRNA sequencing. Metformin impacted the microbial community composition in 75 mg/kg metformin compared to controls (adjusted PERMANOVA p = 0.0006) and an additional dose-dependent difference was observed between 25 mg/kg and 75 mg/kg (adjusted PERMANOVA p = 0.001) and between 50 mg/kg and 75 mg/kg (adjusted PERMANOVA p = 0.001) but not between 25 mg/kg and 50 mg/kg (adjusted PERMANOVA p = 0.863). There were few differences in the microbiome attributed to hen age, and metformin supplementation did not alter alpha diversity. Bacteria that were identified as differentially relatively abundant between 75 mg/kg metformin treatment and the control, and between metformin doses, included Ruminococcus and members of the Clostridia family that have been previously identified in human trials of PCOS. These results demonstrate that metformin impacts the microbiome of broiler breeder hens in a dose-dependent manner and several findings were consistent with PCOS in humans and with metformin treatment in type 2 diabetes. Metformin supplementation is a potentially promising option to improve gut health and reproductive efficiency in broiler breeder hens.

Decoding the olfactory map through targeted transcriptomics links murine olfactory receptors to glomeruli.

Sensory processing in olfactory systems is organized across olfactory bulb glomeruli, wherein axons of peripheral sensory neurons expressing the same olfactory receptor co-terminate to transmit receptor-specific activity to central neurons. Understanding how receptors map to glomeruli is therefore critical to understanding olfaction. High-throughput spatial transcriptomics is a rapidly advancing field, but low-abundance olfactory receptor expression within glomeruli has previously precluded high-throughput mapping of receptors to glomeruli in the mouse. Here we combined sequential sectioning along the anteroposterior, dorsoventral, and mediolateral axes with target capture enrichment sequencing to overcome low-abundance target expression. This strategy allowed us to spatially map 86% of olfactory receptors across the olfactory bulb and uncover a relationship between OR sequence and glomerular position.

Microbiota responses to different prebiotics are conserved within individuals and associated with habitual fiber intake.

BACKGROUND: Short-chain fatty acids (SCFAs) derived from gut bacteria are associated with protective roles in diseases ranging from obesity to colorectal cancers. Intake of microbially accessible dietary fibers (prebiotics) lead to varying effects on SCFA production in human studies, and gut microbial responses to nutritional interventions vary by individual. It is therefore possible that prebiotic therapies will require customizing to individuals. RESULTS: Here, we explored prebiotic personalization by conducting a three-way crossover study of three prebiotic treatments in healthy adults. We found that within individuals, metabolic responses were correlated across the three prebiotics. Individual identity, rather than prebiotic choice, was also the major determinant of SCFA response. Across individuals, prebiotic response was inversely related to basal fecal SCFA concentration, which, in turn, was associated with habitual fiber intake. Experimental measures of gut microbial SCFA production for each participant also negatively correlated with fiber consumption, supporting a model in which individuals' gut microbiota are limited in their overall capacity to produce fecal SCFAs from fiber. CONCLUSIONS: Our findings support developing personalized prebiotic regimens that focus on selecting individuals who stand to benefit, and that such individuals are likely to be deficient in fiber intake. Video Abstract.

DNA Extraction and Host Depletion Methods Significantly Impact and Potentially Bias Bacterial Detection in a Biological Fluid.

Untargeted sequencing of nucleic acids present in food can inform the detection of food safety and origin, as well as product tampering and mislabeling issues. The application of such technologies to food analysis may reveal valuable insights that are simply unobtainable by targeted testing, leading to the efforts of applying such technologies in the food industry. However, before these approaches can be applied, it is imperative to verify that the most appropriate methods are used at every step of the process: gathering of primary material, laboratory methods, data analysis, and interpretation. The focus of this study is on gathering the primary material, in this case, DNA. We used bovine milk as a model to (i) evaluate commercially available kits for their ability to extract nucleic acids from inoculated bovine milk, (ii) evaluate host DNA depletion methods for use with milk, and (iii) develop and evaluate a selective lysis-propidium monoazide (PMA)-based protocol for host DNA depletion in milk. Our results suggest that magnetically based nucleic acid extraction methods are best for nucleic acid isolation of bovine milk. Removal of host DNA remains a challenge for untargeted sequencing of milk, highlighting the finding that the individual matrix characteristics should always be considered in food testing. Some reported methods introduce bias against specific types of microbes, which may be particularly problematic in food safety, where the detection of Gram-negative pathogens and hygiene indicators is essential. Continuous efforts are needed to develop and validate new approaches for untargeted metagenomics in samples with large amounts of DNA from a single host. IMPORTANCE Tracking the bacterial communities present in our food has the potential to inform food safety and product origin. To do so, the entire genetic material present in a sample is extracted using chemical methods or commercially available kits and sequenced using next-generation platforms to provide a snapshot of the microbial composition. Because the genetic material of higher organisms present in food (e.g., cow in milk or beef, wheat in flour) is around 1,000 times larger than the bacterial content, challenges exist in gathering the information of interest. Additionally, specific bacterial characteristics can make them easier or harder to detect, adding another layer of complexity to this issue. In this study, we demonstrate the impact of using different methods for the ability to detect specific bacteria and highlight the need to ensure that the most appropriate methods are being used for each particular sample.

Estimated transmissibility and impact of SARS-CoV-2 lineage B.1.1.7 in England.

A severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variant, VOC 202012/01 (lineage B.1.1.7), emerged in southeast England in September 2020 and is rapidly spreading toward fixation. Using a variety of statistical and dynamic modeling approaches, we estimate that this variant has a 43 to 90% (range of 95% credible intervals, 38 to 130%) higher reproduction number than preexisting variants. A fitted two-strain dynamic transmission model shows that VOC 202012/01 will lead to large resurgences of COVID-19 cases. Without stringent control measures, including limited closure of educational institutions and a greatly accelerated vaccine rollout, COVID-19 hospitalizations and deaths across England in the first 6 months of 2021 were projected to exceed those in 2020. VOC 202012/01 has spread globally and exhibits a similar transmission increase (59 to 74%) in Denmark, Switzerland, and the United States.

Using influenza surveillance networks to estimate state-specific prevalence of SARS-CoV-2 in the United States.

Detection of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections to date has relied heavily on reverse transcription polymerase chain reaction testing. However, limited test availability, high false-negative rates, and the existence of asymptomatic or subclinical infections have resulted in an undercounting of the true prevalence of SARS-CoV-2. Here, we show how influenza-like illness (ILI) outpatient surveillance data can be used to estimate the prevalence of SARS-CoV-2. We found a surge of non-influenza ILI above the seasonal average in March 2020 and showed that this surge correlated with coronavirus disease 2019 (COVID-19) case counts across states. If one-third of patients infected with SARS-CoV-2 in the United States sought care, this ILI surge would have corresponded to more than 8.7 million new SARS-CoV-2 infections across the United States during the 3-week period from 8 to 28 March 2020. Combining excess ILI counts with the date of onset of community transmission in the United States, we also show that the early epidemic in the United States was unlikely to have been doubling slower than every 4 days. Together, these results suggest a conceptual model for the COVID-19 epidemic in the United States characterized by rapid spread across the United States with more than 80% infected individuals remaining undetected. We emphasize the importance of testing these findings with seroprevalence data and discuss the broader potential to use syndromic surveillance for early detection and understanding of emerging infectious diseases.

Naught all zeros in sequence count data are the same.

Genomic studies feature multivariate count data from high-throughput DNA sequencing experiments, which often contain many zero values. These zeros can cause artifacts for statistical analyses and multiple modeling approaches have been developed in response. Here, we apply different zero-handling models to gene-expression and microbiome datasets and show models can disagree substantially in terms of identifying the most differentially expressed sequences. Next, to rationally examine how different zero handling models behave, we developed a conceptual framework outlining four types of processes that may give rise to zero values in sequence count data. Last, we performed simulations to test how zero handling models behave in the presence of these different zero generating processes. Our simulations showed that simple count models are sufficient across multiple processes, even when the true underlying process is unknown. On the other hand, a common zero handling technique known as "zero-inflation" was only suitable under a zero generating process associated with an unlikely set of biological and experimental conditions. In concert, our work here suggests several specific guidelines for developing and choosing state-of-the-art models for analyzing sparse sequence count data.