We present the Pareto task inference method (ParTI; http://www.weizmann.ac.il/mcb/UriAlon/download/ParTI) for inferring biological tasks from high-dimensional biological data. Data are described as a polytope, and features maximally enriched closest to the vertices (or archetypes) allow identification of the tasks the vertices represent. We demonstrate that human breast tumors and mouse tissues are well described by tetrahedrons in gene expression space, with specific tumor types and biological functions enriched at each of the vertices, suggesting four key tasks.

Organisms adjust their gene expression to improve fitness in diverse environments. But finding the optimal expression in each environment presents a challenge. We ask how good cells are at finding such optima by studying the control of carbon catabolism genes in Escherichia coli. Bacteria show a growth law: growth rate on different carbon sources declines linearly with the steady-state expression of carbon catabolic genes. We experimentally modulate gene expression to ask if this growth law always maximizes growth rate, as has been suggested by theory. We find that the growth law is optimal in many conditions, including a range of perturbations to lactose uptake, but provides sub-optimal growth on several other carbon sources. Combining theory and experiment, we genetically re-engineer E. coli to make sub-optimal conditions into optimal ones and vice versa. We conclude that the carbon growth law is not always optimal, but represents a practical heuristic that often works but sometimes fails.

In C. elegans, small RNAs enable transmission of epigenetic responses across multiple generations. While RNAi inheritance mechanisms that enable "memorization" of ancestral responses are being elucidated, the mechanisms that determine the duration of inherited silencing and the ability to forget the inherited epigenetic effects are not known. We now show that exposure to dsRNA activates a feedback loop whereby gene-specific RNAi responses dictate the transgenerational duration of RNAi responses mounted against unrelated genes, elicited separately in previous generations. RNA-sequencing analysis reveals that, aside from silencing of genes with complementary sequences, dsRNA-induced RNAi affects the production of heritable endogenous small RNAs, which regulate the expression of RNAi factors. Manipulating genes in this feedback pathway changes the duration of heritable silencing. Such active control of transgenerational effects could be adaptive, since ancestral responses would be detrimental if the environments of the progeny and the ancestors were different.

Many countries have applied lockdown that helped suppress COVID-19, but with devastating economic consequences. Here we propose exit strategies from lockdown that provide sustainable, albeit reduced, economic activity. We use mathematical models to show that a cyclic schedule of 4-day work and 10-day lockdown, or similar variants, can, in certain conditions, suppress the epidemic while providing part-time employment. The cycle reduces the reproduction number R by a combination of reduced exposure time and an anti-phasing effect in which those infected during work days reach peak infectiousness during lockdown days. The number of work days can be adapted in response to observations. Throughout, full epidemiological measures need to continue including hygiene, physical distancing, compartmentalization and extensive testing and contact tracing. We do not call for immediate adoption of this policy, but rather to consider it as a conceptual framework, which, when combined with other interventions to control the epidemic, can offer the beginnings of predictability to many economic sectors.Current non-pharmaceutical interventions (NPI) to suppress COVID-19 use testing, contact tracing, physical distancing, mask use, identification of regional outbreaks, compartmentalization down to the neighborhood and company level, and population-level quarantine at home known as lockdown ( 1 -4 ) . The aim is to flatten the infection curve and prevent overload of the medical system until a vaccine becomes available.Lockdown is currently in place in many countries. It has a large economic and social cost, including unemployment on a massive scale. Once a lockdown has reduced the number of critical cases to a desired goal, a decision must be reached on how to exit it responsibly. The main concern is the risk of resurgence of the epidemic. One strategy proposes reinstating lockdown when a threshold number of critical cases is exceeded in a resurgence, and stopping lockdown again once cases drop below a low threshold ( 2 , 5 ) ( Fig 1A,S1). While such an "adaptive triggering" strategy can prevent healthcare services from becoming overloaded, it leads to economic uncertainty and continues to accumulate cases with each resurgence.

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.

When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypes—phenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.

Understanding the tradeoffs faced by organisms is a major goal of evolutionary biology. One of the main approaches for identifying these tradeoffs is Pareto task inference (ParTI). Two recent papers claim that results obtained in ParTI studies are spurious due to phylogenetic dependence (Mikami and Iwasaki, 2021) or hypothetical p-hacking and population-structure concerns (Sun and Zhang, 2020). Here we show that these claims are baseless. We present a new method to control for phylogenetic dependence, called SibSwap, and show that published ParTI inference is robust to phylogenetic dependence. We show how researchers avoided p-hacking by testing for robustness of preprocessing choices. We also provide new methods to control for population structure and detail the extensive experimental tests of ParTI in systems ranging from ammonites to cancer gene expression. The methods presented here may help to improve future ParTI studies.

Longitudinal multi-omics measurements are highly valuable in studying heterogeneity in health and disease phenotypes. For thousands of people, we have collected longitudinal multi-omics data. To analyze, interpret and visualize this extremely high-dimensional data, we use the Pareto Task Inference (ParTI) method. We find that the clinical labs data fall within a tetrahedron. We then use all other data types to characterize the four archetypes. We find that the tetrahedron comprises three wellness states, defining a wellness triangular plane, and one aberrant health state that captures aspects of commonality in movement away from wellness. We reveal the tradeoffs that shape the data and their hierarchy, and use longitudinal data to observe individual trajectories. We then demonstrate how the movement on the tetrahedron can be used for detecting unexpected trajectories, which might indicate transitions from health to disease and reveal abnormal conditions, even when all individual blood measurements are in the norm.