Functional data analysis for computational biology

Understanding spatiotemporal patterns of COVID-19 incidence in Portugal: A functional data analysis from August 2020 to March 2022

During the SARS-CoV-2 pandemic, governments and public health authorities collected massive amounts of data on daily confirmed positive cases and incidence rates. These data sets provide relevant information to develop a scientific understanding of the pandemic's spatiotemporal dynamics. At the same time, there is a lack of comprehensive approaches to describe and classify patterns underlying the dynamics of COVID-19 incidence across regions over time. This seriously constrains the potential benefits for public health authorities to understand spatiotemporal patterns of disease incidence that would allow for better risk communication strategies and improved assessment of mitigation policies efficacy. Within this context, we propose an exploratory statistical tool that combines functional data analysis with unsupervised learning algorithms to extract meaningful information about the main spatiotemporal patterns underlying COVID-19 incidence on mainland Portugal. We focus on the timeframe spanning from August 2020 to March 2022, considering data at the municipality level. First, we describe the temporal evolution of confirmed daily COVID-19 cases by municipality as a function of time, and outline the main temporal patterns of variability using a functional principal component analysis. Then, municipalities are classified according to their spatiotemporal similarities through hierarchical clustering adapted to spatially correlated functional data. Our findings reveal disparities in disease dynamics between northern and coastal municipalities versus those in the southern and hinterland. We also distinguish effects occurring during the 2020-2021 period from those in the 2021-2022 autumn-winter seasons. The results provide proof-of-concept that the proposed approach can be used to detect the main spatiotemporal patterns of disease incidence. The novel approach expands and enhances existing exploratory tools for spatiotemporal analysis of public health data.

Visualization of the landscape of the read alignment shape of ATAC-seq data using Hellinger distance metric

Assay for Transposase-Accessible Chromatin using high-throughput sequencing (ATAC-seq) is the popular technique using next-generation sequencing to measure chromatin accessibility and identify open chromatin regions. While read alignment shape information of next-generation sequencing data with intensity information has been used in various bioinformatics methods, few studies have focused on pure shape information alone. In this study, we investigated what types of ATAC-seq read alignment shapes are observed for the promoter region and whether the pure shape information was related or unrelated to other gene features. We introduced a novel concept and pipeline for handling the pure shape information of NGS data as probability distributions and quantifying their dissimilarities by information theory. Based on this concept, we demonstrate that the pure shape information of ATAC-seq data is correlated with chromatin openness and some gene characteristics. On the other hand, it is suggested that the pure information of ATAC-seq read alignment shape is unlikely to contain additional information to explain differences in RNA expression. Our study suggests that viewing the read alignment shape of NGS data as probability distributions enables us to capture the characteristics of the genome-wide landscape of such data in a non-parametric manner.

Epigenetic and transcriptional regulations prime cell fate before division during human pluripotent stem cell differentiation

Stem cells undergo cellular division during their differentiation to produce daughter cells with a new cellular identity. However, the epigenetic events and molecular mechanisms occurring between consecutive cell divisions have been insufficiently studied due to technical limitations. Here, using the FUCCI reporter we developed a cell-cycle synchronised human pluripotent stem cell (hPSC) differentiation system for uncovering epigenome and transcriptome dynamics during the first two divisions leading to definitive endoderm. We observed that transcription of key differentiation markers occurs before cell division, while chromatin accessibility analyses revealed the early inhibition of alternative cell fates. We found that Activator protein-1 members controlled by p38/MAPK signalling are necessary for inducing endoderm while blocking cell fate shifting toward mesoderm, and that enhancers are rapidly established and decommissioned between different cell divisions. Our study has practical biomedical utility for producing hPSC-derived patient-specific cell types since p38/MAPK induction increased the differentiation efficiency of insulin-producing pancreatic beta-cells.

Constructing a polygenic risk score for childhood obesity using functional data analysis

Obesity is a highly heritable condition that affects increasing numbers of adults and, concerningly, of children. However, only a small fraction of its heritability has been attributed to specific genetic variants. These variants are traditionally ascertained from genome-wide association studies (GWAS), which utilize samples with tens or hundreds of thousands of individuals for whom a single summary measurement (e.g., BMI) is collected. An alternative approach is to focus on a smaller, more deeply characterized sample in conjunction with advanced statistical models that leverage longitudinal phenotypes. Novel functional data analysis (FDA) techniques are used to capitalize on longitudinal growth information from a cohort of children between birth and three years of age. In an ultra-high dimensional setting, hundreds of thousands of single nucleotide polymorphisms (SNPs) are screened, and selected SNPs are used to construct two polygenic risk scores (PRS) for childhood obesity using a weighting approach that incorporates the dynamic and joint nature of SNP effects. These scores are significantly higher in children with (vs. without) rapid infant weight gain-a predictor of obesity later in life. Using two independent cohorts, it is shown that the genetic variants identified in very young children are also informative in older children and in adults, consistent with early childhood obesity being predictive of obesity later in life. In contrast, PRSs based on SNPs identified by adult obesity GWAS are not predictive of weight gain in the cohort of young children. This provides an example of a successful application of FDA to GWAS. This application is complemented with simulations establishing that a deeply characterized sample can be just as, if not more, effective than a comparable study with a cross-sectional response. Overall, it is demonstrated that a deep, statistically sophisticated characterization of a longitudinal phenotype can provide increased statistical power to studies with relatively small sample sizes; and shows how FDA approaches can be used as an alternative to the traditional GWAS.

Integration of Count Difference and Curve Similarity in Negative Regulatory Element Detection

Negative regulatory elements (NREs) down-regulate gene expression by inhibiting the activities of promoters or enhancers. The repressing activity of NREs can be measured globally by massively parallel reporter assays (MPRAs). However, most existing algorithms are designed for the statistical detection of positively enriched signals in MPRA datasets. To identify reduced signals in MPRA experiments, we designed a NRE identification program, fast-NR, by integrating the count and graphic features of sequenced reads to detect NREs using datasets generated by experiments of self-transcribing active regulatory region sequencing (STARR-seq). Fast-NR identified hundreds of silencers in human K562 cells that can be validated by independent methods.

Functional data analysis characterizes the shapes of the first COVID-19 epidemic wave in Italy

We investigate patterns of COVID-19 mortality across 20 Italian regions and their association with mobility, positivity, and socio-demographic, infrastructural and environmental covariates. Notwithstanding limitations in accuracy and resolution of the data available from public sources, we pinpoint significant trends exploiting information in curves and shapes with Functional Data Analysis techniques. These depict two starkly different epidemics; an "exponential" one unfolding in Lombardia and the worst hit areas of the north, and a milder, "flat(tened)" one in the rest of the country-including Veneto, where cases appeared concurrently with Lombardia but aggressive testing was implemented early on. We find that mobility and positivity can predict COVID-19 mortality, also when controlling for relevant covariates. Among the latter, primary care appears to mitigate mortality, and contacts in hospitals, schools and workplaces to aggravate it. The techniques we describe could capture additional and potentially sharper signals if applied to richer data.

Human L1 Transposition Dynamics Unraveled with Functional Data Analysis

Long INterspersed Elements-1 (L1s) constitute >17% of the human genome and still actively transpose in it. Characterizing L1 transposition across the genome is critical for understanding genome evolution and somatic mutations. However, to date, L1 insertion and fixation patterns have not been studied comprehensively. To fill this gap, we investigated three genome-wide data sets of L1s that integrated at different evolutionary times: 17,037 de novo L1s (from an L1 insertion cell-line experiment conducted in-house), and 1,212 polymorphic and 1,205 human-specific L1s (from public databases). We characterized 49 genomic features-proxying chromatin accessibility, transcriptional activity, replication, recombination, etc.-in the ±50 kb flanks of these elements. These features were contrasted between the three L1 data sets and L1-free regions using state-of-the-art Functional Data Analysis statistical methods, which treat high-resolution data as mathematical functions. Our results indicate that de novo, polymorphic, and human-specific L1s are surrounded by different genomic features acting at specific locations and scales. This led to an integrative model of L1 transposition, according to which L1s preferentially integrate into open-chromatin regions enriched in non-B DNA motifs, whereas they are fixed in regions largely free of purifying selection-depleted of genes and noncoding most conserved elements. Intriguingly, our results suggest that L1 insertions modify local genomic landscape by extending CpG methylation and increasing mononucleotide microsatellite density. Altogether, our findings substantially facilitate understanding of L1 integration and fixation preferences, pave the way for uncovering their role in aging and cancer, and inform their use as mutagenesis tools in genetic studies.

Non-B DNA: a major contributor to small- and large-scale variation in nucleotide substitution frequencies across the genome

Approximately 13% of the human genome can fold into non-canonical (non-B) DNA structures (e.g. G-quadruplexes, Z-DNA, etc.), which have been implicated in vital cellular processes. Non-B DNA also hinders replication, increasing errors and facilitating mutagenesis, yet its contribution to genome-wide variation in mutation rates remains unexplored. Here, we conducted a comprehensive analysis of nucleotide substitution frequencies at non-B DNA loci within noncoding, non-repetitive genome regions, their ±2 kb flanking regions, and 1-Megabase windows, using human-orangutan divergence and human single-nucleotide polymorphisms. Functional data analysis at single-base resolution demonstrated that substitution frequencies are usually elevated at non-B DNA, with patterns specific to each non-B DNA type. Mirror, direct and inverted repeats have higher substitution frequencies in spacers than in repeat arms, whereas G-quadruplexes, particularly stable ones, have higher substitution frequencies in loops than in stems. Several non-B DNA types also affect substitution frequencies in their flanking regions. Finally, non-B DNA explains more variation than any other predictor in multiple regression models for diversity or divergence at 1-Megabase scale. Thus, non-B DNA substantially contributes to variation in substitution frequencies at small and large scales. Our results highlight the role of non-B DNA in germline mutagenesis with implications to evolution and genetic diseases.

Learning the properties of adaptive regions with functional data analysis

Identifying regions of positive selection in genomic data remains a challenge in population genetics. Most current approaches rely on comparing values of summary statistics calculated in windows. We present an approach termed SURFDAWave, which translates measures of genetic diversity calculated in genomic windows to functional data. By transforming our discrete data points to be outputs of continuous functions defined over genomic space, we are able to learn the features of these functions that signify selection. This enables us to confidently identify complex modes of natural selection, including adaptive introgression. We are also able to predict important selection parameters that are responsible for shaping the inferred selection events. By applying our model to human population-genomic data, we recapitulate previously identified regions of selective sweeps, such as OCA2 in Europeans, and predict that its beneficial mutation reached a frequency of 0.02 before it swept 1,802 generations ago, a time when humans were relatively new to Europe. In addition, we identify BNC2 in Europeans as a target of adaptive introgression, and predict that it harbors a beneficial mutation that arose in an archaic human population that split from modern humans within the hypothesized modern human-Neanderthal divergence range.