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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.

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. 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. 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. 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. 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.

Improving the efficiency of root systems should result in crop varieties with better yields, requiring fewer chemical inputs, and that can grow in harsher environments. Little is known about the genetic factors that condition root growth because of roots’ complex shapes, the opacity of soil, and environmental influences. We designed a 3D root imaging and analysis platform and used it to identify regions of the rice genome that control several different aspects of root system growth. The results of this study should inform future efforts to enhance root architecture for agricultural benefit. 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.

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.

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.

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.

Given a distribution ρ on persistence diagrams and observations X 1 , … , X n ∼ i i d ρ we introduce an algorithm in this paper that estimates a Fréchet mean from the set of diagrams X 1 , … , X n . If the underlying measure ρ is a combination of Dirac masses ρ = 1 m ∑ i = 1 m δ Z i then we prove the algorithm converges to a local minimum and a law of large numbers result for a Fréchet mean computed by the algorithm given observations drawn iid from ρ . We illustrate the convergence of an empirical mean computed by the algorithm to a population mean by simulations from Gaussian random fields.

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.

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 Mānoa aims to fill this gap. 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 Mānoa 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.

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this disease and others like it, such as the ability of exposed individuals to recover without becoming infectious, or the possibility that asymptomatic individuals can indeed transmit the disease but at a lesser rate than the symptomatic. In the first part of this paper, we propose two new compartmental epidemiological models and study their equilibria, obtaining an endemic threshold theorem for the first model. In the second part of the paper, we treat the second model as an affine control system with two controls: vaccination and mitigation. We show that this system is static feedback linearizable, presents some simulations, and investigates an optimal control version of the problem. We conclude with some open problems and ideas for future research.