COVID-19 heterogeneity in islands chain environment.

BACKGROUND: It is critical to capture data and modeling from the COVID-19 pandemic to understand as much as possible and prepare for future epidemics and possible pandemics. The Hawaiian Islands provide a unique opportunity to study heterogeneity and demographics in a controlled environment due to the geographically closed borders and mostly uniform pandemic-induced governmental controls and restrictions. OBJECTIVE: The goal of the paper is to quantify the differences and similarities in the spread of COVID-19 among different Hawaiian islands as well as several other archipelago and islands, which could potentially help us better understand the effect of differences in social behavior and various mitigation measures. The approach should be robust with respect to the unavoidable differences in time, as the arrival of the virus and promptness of mitigation measures may vary significantly among the chosen locations. At the same time, the comparison should be able to capture differences in the overall pandemic experience. METHODS: We examine available data on the daily cases, positivity rates, mobility, and employ a compartmentalized model fitted to the daily cases to develop appropriate comparison approaches. In particular, we focus on merge trees for the daily cases, normalized positivity rates, and baseline transmission rates of the models. RESULTS: We observe noticeable differences among different Hawaiian counties and interesting similarities between some Hawaiian counties and other geographic locations. The results suggest that mitigation measures should be more localized, that is, targeting the county level rather than the state level if the counties are reasonably insulated from one another. We also notice that the spread of the disease is very sensitive to unexpected events and certain changes in mitigation measures. CONCLUSIONS: Despite being a part of the same archipelago and having similar protocols for mitigation measures, different Hawaiian counties exhibit quantifiably different dynamics of the spread of the disease. One potential explanation is that not sufficiently targeted mitigation measures are incapable of handling unexpected, localized outbreak events. At a larger-scale view of the general spread of the disease on the Hawaiian island counties, we find very interesting similarities between individual Hawaiian islands and other archipelago and islands.

Synergy among Microbiota and Their Hosts: Leveraging the Hawaiian Archipelago and Local Collaborative Networks To Address Pressing Questions in Microbiome Research.

Despite increasing acknowledgment that microorganisms underpin the healthy functioning of basically all multicellular life, few cross-disciplinary teams address the diversity and function of microbiota across organisms and ecosystems. Our newly formed consortium of junior faculty spanning fields such as ecology and geoscience to mathematics and molecular biology from the University of Hawai'i at Manoa aims to fill this gap. We are united in our mutual interest in advancing a new paradigm for biology that incorporates our modern understanding of the importance of microorganisms. As our first concerted research effort, we will assess the diversity and function of microbes across an entire watershed on the island of Oahu, Hawai'i. Due to its high ecological diversity across tractable areas of land and sea, Hawai'i provides a model system for the study of complex microbial communities and the processes they mediate. Owing to our diverse expertise, we will leverage this study system to advance the field of biology.

3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture.

Identification of genes that control root system architecture in crop plants requires innovations that enable high-throughput and accurate measurements of root system architecture through time. We demonstrate the ability of a semiautomated 3D in vivo imaging and digital phenotyping pipeline to interrogate the quantitative genetic basis of root system growth in a rice biparental mapping population, Bala × Azucena. We phenotyped >1,400 3D root models and >57,000 2D images for a suite of 25 traits that quantified the distribution, shape, extent of exploration, and the intrinsic size of root networks at days 12, 14, and 16 of growth in a gellan gum medium. From these data we identified 89 quantitative trait loci, some of which correspond to those found previously in soil-grown plants, and provide evidence for genetic tradeoffs in root growth allocations, such as between the extent and thoroughness of exploration. We also developed a multivariate method for generating and mapping central root architecture phenotypes and used it to identify five major quantitative trait loci (r(2) = 24-37%), two of which were not identified by our univariate analysis. Our imaging and analytical platform provides a means to identify genes with high potential for improving root traits and agronomic qualities of crops.

GiA Roots: software for the high throughput analysis of plant root system architecture.

BACKGROUND: Characterizing root system architecture (RSA) is essential to understanding the development and function of vascular plants. Identifying RSA-associated genes also represents an underexplored opportunity for crop improvement. Software tools are needed to accelerate the pace at which quantitative traits of RSA are estimated from images of root networks. RESULTS: We have developed GiA Roots (General Image Analysis of Roots), a semi-automated software tool designed specifically for the high-throughput analysis of root system images. GiA Roots includes user-assisted algorithms to distinguish root from background and a fully automated pipeline that extracts dozens of root system phenotypes. Quantitative information on each phenotype, along with intermediate steps for full reproducibility, is returned to the end-user for downstream analysis. GiA Roots has a GUI front end and a command-line interface for interweaving the software into large-scale workflows. GiA Roots can also be extended to estimate novel phenotypes specified by the end-user. CONCLUSIONS: We demonstrate the use of GiA Roots on a set of 2393 images of rice roots representing 12 genotypes from the species Oryza sativa. We validate trait measurements against prior analyses of this image set that demonstrated that RSA traits are likely heritable and associated with genotypic differences. Moreover, we demonstrate that GiA Roots is extensible and an end-user can add functionality so that GiA Roots can estimate novel RSA traits. In summary, we show that the software can function as an efficient tool as part of a workflow to move from large numbers of root images to downstream analysis.

Hierarchical ordering of reticular networks.

The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the "root" of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.

Leaf extraction and analysis framework graphical user interface: segmenting and analyzing the structure of leaf veins and areoles.

Interest in the structure and function of physical biological networks has spurred the development of a number of theoretical models that predict optimal network structures across a broad array of taxonomic groups, from mammals to plants. In many cases, direct tests of predicted network structure are impossible given the lack of suitable empirical methods to quantify physical network geometry with sufficient scope and resolution. There is a long history of empirical methods to quantify the network structure of plants, from roots, to xylem networks in shoots and within leaves. However, with few exceptions, current methods emphasize the analysis of portions of, rather than entire networks. Here, we introduce the Leaf Extraction and Analysis Framework Graphical User Interface (LEAF GUI), a user-assisted software tool that facilitates improved empirical understanding of leaf network structure. LEAF GUI takes images of leaves where veins have been enhanced relative to the background, and following a series of interactive thresholding and cleaning steps, returns a suite of statistics and information on the structure of leaf venation networks and areoles. Metrics include the dimensions, position, and connectivity of all network veins, and the dimensions, shape, and position of the areoles they surround. Available for free download, the LEAF GUI software promises to facilitate improved understanding of the adaptive and ecological significance of leaf vein network structure.

Imaging and analysis platform for automatic phenotyping and trait ranking of plant root systems.

The ability to nondestructively image and automatically phenotype complex root systems, like those of rice (Oryza sativa), is fundamental to identifying genes underlying root system architecture (RSA). Although root systems are central to plant fitness, identifying genes responsible for RSA remains an underexplored opportunity for crop improvement. Here we describe a nondestructive imaging and analysis system for automated phenotyping and trait ranking of RSA. Using this system, we image rice roots from 12 genotypes. We automatically estimate RSA traits previously identified as important to plant function. In addition, we expand the suite of features examined for RSA to include traits that more comprehensively describe monocot RSA but that are difficult to measure with traditional methods. Using 16 automatically acquired phenotypic traits for 2,297 images from 118 individuals, we observe (1) wide variation in phenotypes among the genotypes surveyed; and (2) greater intergenotype variance of RSA features than variance within a genotype. RSA trait values are integrated into a computational pipeline that utilizes supervised learning methods to determine which traits best separate two genotypes, and then ranks the traits according to their contribution to each pairwise comparison. This trait-ranking step identifies candidate traits for subsequent quantitative trait loci analysis and demonstrates that depth and average radius are key contributors to differences in rice RSA within our set of genotypes. Our results suggest a strong genetic component underlying rice RSA. This work enables the automatic phenotyping of RSA of individuals within mapping populations, providing an integrative framework for quantitative trait loci analysis of RSA.

Small-scale copy number variation and large-scale changes in gene expression.

The expression dynamics of interacting genes depends, in part, on the structure of regulatory networks. Genetic regulatory networks include an overrepresentation of subgraphs commonly known as network motifs. In this article, we demonstrate that gene copy number is an omnipresent parameter that can dramatically modify the dynamical function of network motifs. We consider positive feedback, bistable feedback, and toggle switch motifs and show that variation in gene copy number, on the order of a single or few copies, can lead to multiple orders of magnitude change in gene expression and, in some cases, switches in deterministic control. Further, small changes in gene copy number for a 3-gene motif with successive inhibition (the "repressilator") can lead to a qualitative switch in system behavior among oscillatory and equilibrium dynamics. In all cases, the qualitative change in expression is due to the nonlinear nature of transcriptional feedback in which duplicated motifs interact via common pools of transcription factors. We are able to implicitly determine the critical values of copy number which lead to qualitative shifts in system behavior. In some cases, we are able to solve for the sufficient condition for the existence of a bifurcation in terms of kinetic rates of transcription, translation, binding, and degradation. We discuss the relevance of our findings to ongoing efforts to link copy number variation with cell fate determination by viruses, dynamics of synthetic gene circuits, and constraints on evolutionary adaptation.

Comparison of pattern detection methods in microarray time series of the segmentation clock.

While genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis. A method related to Fourier analysis, the Lomb-Scargle periodogram, was used to detect periodic profiles in the dataset, leading to the identification of a novel set of cyclic genes associated with the segmentation clock. Here, we applied to the same microarray time series dataset four distinct mathematical methods to identify significant patterns in gene expression profiles. These methods are called: Phase consistency, Address reduction, Cyclohedron test and Stable persistence, and are based on different conceptual frameworks that are either hypothesis- or data-driven. Some of the methods, unlike Fourier transforms, are not dependent on the assumption of periodicity of the pattern of interest. Remarkably, these methods identified blindly the expression profiles of known cyclic genes as the most significant patterns in the dataset. Many candidate genes predicted by more than one approach appeared to be true positive cyclic genes and will be of particular interest for future research. In addition, these methods predicted novel candidate cyclic genes that were consistent with previous biological knowledge and experimental validation in mouse embryos. Our results demonstrate the utility of these novel pattern detection strategies, notably for detection of periodic profiles, and suggest that combining several distinct mathematical approaches to analyze microarray datasets is a valuable strategy for identifying genes that exhibit novel, interesting transcriptional patterns.

Collective decision making in bacterial viruses.

For many bacterial viruses, the choice of whether to kill host cells or enter a latent state depends on the multiplicity of coinfection. Here, we present a mathematical theory of how bacterial viruses can make collective decisions concerning the fate of infected cells. We base our theory on mechanistic models of gene regulatory dynamics. Unlike most previous work, we treat the copy number of viral genes as variable. Increasing the viral copy number increases the rate of transcription of viral mRNAs. When viral regulation of cell fate includes nonlinear feedback loops, very small changes in transcriptional rates can lead to dramatic changes in steady-state gene expression. Hence, we prove that deterministic decisions can be reached, e.g., lysis or latency, depending on the cellular multiplicity of infection within a broad class of gene regulatory models of viral decision-making. Comparisons of a parameterized version of the model with molecular studies of the decision structure in the temperate bacteriophage lambda are consistent with our conclusions. Because the model is general, it suggests that bacterial viruses can respond adaptively to changes in population dynamics, and that features of collective decision-making in viruses are evolvable life history traits.