A synthetic differentiation circuit in Escherichia coli for suppressing mutant takeover.

Differentiation is crucial for multicellularity. However, it is inherently susceptible to mutant cells that fail to differentiate. These mutants outcompete normal cells by excessive self-renewal. It remains unclear what mechanisms can resist such mutant expansion. Here, we demonstrate a solution by engineering a synthetic differentiation circuit in Escherichia coli that selects against these mutants via a biphasic fitness strategy. The circuit provides tunable production of synthetic analogs of stem, progenitor, and differentiated cells. It resists mutations by coupling differentiation to the production of an essential enzyme, thereby disadvantaging non-differentiating mutants. The circuit selected for and maintained a positive differentiation rate in long-term evolution. Surprisingly, this rate remained constant across vast changes in growth conditions. We found that transit-amplifying cells (fast-growing progenitors) underlie this environmental robustness. Our results provide insight into the stability of differentiation and demonstrate a powerful method for engineering evolutionarily stable multicellular consortia.

Circuit Design Features of a Stable Two-Cell System.

Cell communication within tissues is mediated by multiple paracrine signals including growth factors, which control cell survival and proliferation. Cells and the growth factors they produce and receive constitute a circuit with specific properties that ensure homeostasis. Here, we used computational and experimental approaches to characterize the features of cell circuits based on growth factor exchange between macrophages and fibroblasts, two cell types found in most mammalian tissues. We found that the macrophage-fibroblast cell circuit is stable and robust to perturbations. Analytical screening of all possible two-cell circuit topologies revealed the circuit features sufficient for stability, including environmental constraint and negative-feedback regulation. Moreover, we found that cell-cell contact is essential for the stability of the macrophage-fibroblast circuit. These findings illustrate principles of cell circuit design and provide a quantitative perspective on cell interactions.

Endocrine Autoimmune Disease as a Fragility of Immune Surveillance against Hypersecreting Mutants.

Some endocrine organs are frequent targets of autoimmune attack. Here, we addressed the origin of autoimmune disease from the viewpoint of feedback control. Endocrine tissues maintain mass through feedback loops that balance cell proliferation and removal according to hormone-driven regulatory signals. We hypothesized the existence of a dedicated mechanism that detects and removes mutant cells that missense the signal and therefore hyperproliferate and hypersecrete with potential to disrupt organismal homeostasis. In this mechanism, hypersecreting cells are preferentially eliminated by autoreactive T cells at the cost of a fragility to autoimmune disease. The "autoimmune surveillance of hypersecreting mutants" (ASHM) hypothesis predicts the presence of autoreactive T cells in healthy individuals and the nature of self-antigens as peptides from hormone secretion pathway. It explains why some tissues get prevalent autoimmune disease, whereas others do not and instead show prevalent mutant-expansion disease (e.g., hyperparathyroidism). The ASHM hypothesis is testable, and we discuss experimental follow-up.

Tradeoffs in bacterial physiology determine the efficiency of antibiotic killing.

Antibiotic effectiveness depends on a variety of factors. While many mechanistic details of antibiotic action are known, the connection between death rate and bacterial physiology is poorly understood. A common observation is that death rate in antibiotics rises linearly with growth rate; however, it remains unclear how other factors, such as environmental conditions and whole-cell physiological properties, affect bactericidal activity. To address this, we developed a high-throughput assay to precisely measure antibiotic-mediated death. We found that death rate is linear in growth rate, but the slope depends on environmental conditions. Growth under stress lowers death rate compared to nonstressed environments with similar growth rate. To understand stress's role, we developed a mathematical model of bacterial death based on resource allocation that includes a stress-response sector; we identify this sector using RNA-seq. Our model accurately predicts the minimal inhibitory concentration (MIC) with zero free parameters across a wide range of growth conditions. The model also quantitatively predicts death and MIC when sectors are experimentally modulated using cyclic adenosine monophosphate (cAMP), including protection from death at very low cAMP levels. The present study shows that different conditions with equal growth rate can have different death rates and establishes a quantitative relation between growth, death, and MIC that suggests approaches to improve antibiotic efficacy.

Major depressive disorder and bistability in an HPA-CNS toggle switch.

Major depressive disorder (MDD) is the most common psychiatric disorder. It has a complex and heterogeneous etiology. Most treatments take weeks to show effects and work well only for a fraction of the patients. Thus, new concepts are needed to understand MDD and its dynamics. One of the strong correlates of MDD is increased activity and dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis which produces the stress hormone cortisol. Existing mathematical models of the HPA axis describe its operation on the scale of hours, and thus are unable to explore the dynamic on the scale of weeks that characterizes many aspects of MDD. Here, we propose a mathematical model of MDD on the scale of weeks, a timescale provided by the growth of the HPA hormone glands under control of HPA hormones. We add to this the mutual inhibition of the HPA axis and the hippocampus and other regions of the central nervous system (CNS) that forms a toggle switch. The model shows bistability between euthymic and depressed states, with a slow timescale of weeks in its dynamics. It explains why prolonged but not acute stress can trigger a self-sustaining depressive episode that persists even after the stress is removed. The model explains the weeks timescale for drugs to take effect, as well as the dysregulation of the HPA axis in MDD, based on gland mass changes. This understanding of MDD dynamics may help to guide strategies for treatment.

Hormone seasonality in medical records suggests circannual endocrine circuits.

Hormones control the major biological functions of stress response, growth, metabolism, and reproduction. In animals, these hormones show pronounced seasonality, with different set-points for different seasons. In humans, the seasonality of these hormones remains unclear, due to a lack of datasets large enough to discern common patterns and cover all hormones. Here, we analyze an Israeli health record on 46 million person-years, including millions of hormone blood tests. We find clear seasonal patterns: The effector hormones peak in winter-spring, whereas most of their upstream regulating pituitary hormones peak only months later, in summer. This delay of months is unexpected because known delays in the hormone circuits last hours. We explain the precise delays and amplitudes by proposing and testing a mechanism for the circannual clock: The gland masses grow with a timescale of months due to trophic effects of the hormones, generating a feedback circuit with a natural frequency of about a year that can entrain to the seasons. Thus, humans may show coordinated seasonal set-points with a winter-spring peak in the growth, stress, metabolism, and reproduction axes.

Controls for Phylogeny and Robust Analysis in Pareto Task Inference.

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 T, Iwasaki W. 2021. The flipping t-ratio test: phylogenetically informed assessment of the Pareto theory for phenotypic evolution. Methods Ecol Evol. 12(4):696-706) or hypothetical p-hacking and population-structure concerns (Sun M, Zhang J. 2021. Rampant false detection of adaptive phenotypic optimization by ParTI-based Pareto front inference. Mol Biol Evol. 38(4):1653-1664). 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 the robustness of preprocessing choices. We also provide new methods to control for population structure and detail the experimental tests of ParTI in systems ranging from ammonites to cancer gene expression. The methods presented here may help to improve future ParTI studies.

Dynamics of thyroid diseases and thyroid-axis gland masses.

Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid-stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life-years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto's thyroiditis and Graves' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.

Endocytosis as a stabilizing mechanism for tissue homeostasis.

Cells in tissues communicate by secreted growth factors (GF) and other signals. An important function of cell circuits is tissue homeostasis: maintaining proper balance between the amounts of different cell types. Homeostasis requires negative feedback on the GFs, to avoid a runaway situation in which cells stimulate each other and grow without control. Feedback can be obtained in at least two ways: endocytosis in which a cell removes its cognate GF by internalization and cross-inhibition in which a GF down-regulates the production of another GF. Here we ask whether there are design principles for cell circuits to achieve tissue homeostasis. We develop an analytically solvable framework for circuits with multiple cell types and find that feedback by endocytosis is far more robust to parameter variation and has faster responses than cross-inhibition. Endocytosis, which is found ubiquitously across tissues, can even provide homeostasis to three and four communicating cell types. These design principles form a conceptual basis for how tissues maintain a healthy balance of cell types and how balance may be disrupted in diseases such as degeneration and fibrosis.

Prediction of drug cocktail effects when the number of measurements is limited.

Cocktails of drugs can be more effective than single drugs, because they can potentially work at lower doses and avoid resistance. However, it is impossible to test all drug cocktails drawn from a large set of drugs because of the huge number of combinations. To overcome this combinatorial explosion problem, one can sample a relatively small number of combinations and use a model to predict the rest. Recently, Zimmer and Katzir et al. presented a model that accurately predicted the effects of cocktails at all doses based on measuring pairs of drugs. This model requires measuring each pair at several different doses and uses interpolation to reduce experimental noise. However, often, it is not possible to measure each pair at multiple doses (for example, in scarce patient-derived tumor material or in large screens). Here, we ask whether measurements at only a single dose can also predict high-order drug cocktails. To address this, we present a fully factorial experimental dataset on all drug cocktails built of 6 chemotherapy drugs on 2 cancer cell lines. We develop a formula that uses only pair measurements at a single dose to predict much of the variation up to 6-drug cocktails in the present data, outperforming commonly used Bliss independence and regression approaches. This model, called the pairs model, is an extension of the Bliss independence model to pairs: For M drugs, it equals the product of all pair effects to the power 1/(M-1). The pairs model also shows good agreement with previously published data on antibiotic triplets and quadruplets. The present model can only predict combinations at the same doses in which the pairs were measured and is not able to predict effects at other doses. This study indicates that pair-based approaches might be able to usefully predict and prioritize high-order combinations, even in large screens or when material for testing is limited.

Noise-precision tradeoff in predicting combinations of mutations and drugs.

Many biological problems involve the response to multiple perturbations. Examples include response to combinations of many drugs, and the effects of combinations of many mutations. Such problems have an exponentially large space of combinations, which makes it infeasible to cover the entire space experimentally. To overcome this problem, several formulae that predict the effect of drug combinations or fitness landscape values have been proposed. These formulae use the effects of single perturbations and pairs of perturbations to predict triplets and higher order combinations. Interestingly, different formulae perform best on different datasets. Here we use Pareto optimality theory to quantitatively explain why no formula is optimal for all datasets, due to an inherent bias-variance (noise-precision) tradeoff. We calculate the Pareto front of log-linear formulae and find that the optimal formula depends on properties of the dataset: the typical interaction strength and the experimental noise. This study provides an approach to choose a suitable prediction formula for a given dataset, in order to best overcome the combinatorial explosion problem.

Dynamic zonation of liver polyploidy.

The liver is a polyploid organ, consisting of hepatocytes with one or two nuclei each containing 2, 4, 8 or more haploid chromosome sets. The dynamic changes in the spatial distributions of polyploid classes across the liver lobule, its repeating anatomical unit, have not been characterized. Identifying these spatial patterns is important for understanding liver homeostatic and regenerative turnover, as well as potential division of labor among ploidy classes. Here, we use single molecule-based tissue imaging to reconstruct the spatial zonation profiles of liver polyploid classes in mice of different ages. We find that liver polyploidy proceeds in spatial waves, advancing more rapidly in the mid-lobule zone compared to the periportal and perivenous zones. We also measure the spatial zonation profiles of S-phase entry at different ages and identify more rapid S-phase entry in the mid-lobule zone at older ages. Our findings reveal fundamental features of liver spatial heterogeneity and highlight their dynamic changes during development and aging.

Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy.

Latency and ongoing replication have both been proposed to explain the drug-insensitive human immunodeficiency virus (HIV) reservoir maintained during antiretroviral therapy. Here we explore a novel mechanism for ongoing HIV replication in the face of antiretroviral drugs. We propose a model whereby multiple infections per cell lead to reduced sensitivity to drugs without requiring drug-resistant mutations, and experimentally validate the model using multiple infections per cell by cell-free HIV in the presence of the drug tenofovir. We then examine the drug sensitivity of cell-to-cell spread of HIV, a mode of HIV transmission that can lead to multiple infection events per target cell. Infections originating from cell-free virus decrease strongly in the presence of antiretrovirals tenofovir and efavirenz whereas infections involving cell-to-cell spread are markedly less sensitive to the drugs. The reduction in sensitivity is sufficient to keep multiple rounds of infection from terminating in the presence of drugs. We examine replication from cell-to-cell spread in the presence of clinical drug concentrations using a stochastic infection model and find that replication is intermittent, without substantial accumulation of mutations. If cell-to-cell spread has the same properties in vivo, it may have adverse consequences for the immune system, lead to therapy failure in individuals with risk factors, and potentially contribute to viral persistence and hence be a barrier to curing HIV infection.

Mapping differentiation under mixed culture conditions reveals a tunable continuum of T cell fates.

Cell differentiation is typically directed by external signals that drive opposing regulatory pathways. Studying differentiation under polarizing conditions, with only one input signal provided, is limited in its ability to resolve the logic of interactions between opposing pathways. Dissection of this logic can be facilitated by mapping the system's response to mixtures of input signals, which are expected to occur in vivo, where cells are simultaneously exposed to various signals with potentially opposing effects. Here, we systematically map the response of naïve T cells to mixtures of signals driving differentiation into the Th1 and Th2 lineages. We characterize cell state at the single cell level by measuring levels of the two lineage-specific transcription factors (T-bet and GATA3) and two lineage characteristic cytokines (IFN-γ and IL-4) that are driven by these transcription regulators. We find a continuum of mixed phenotypes in which individual cells co-express the two lineage-specific master regulators at levels that gradually depend on levels of the two input signals. Using mathematical modeling we show that such tunable mixed phenotype arises if autoregulatory positive feedback loops in the gene network regulating this process are gradual and dominant over cross-pathway inhibition. We also find that expression of the lineage-specific cytokines follows two independent stochastic processes that are biased by expression levels of the master regulators. Thus, cytokine expression is highly heterogeneous under mixed conditions, with subpopulations of cells expressing only IFN-γ, only IL-4, both cytokines, or neither. The fraction of cells in each of these subpopulations changes gradually with input conditions, reproducing the continuous internal state at the cell population level. These results suggest a differentiation scheme in which cells reflect uncertainty through a continuously tuneable mixed phenotype combined with a biased stochastic decision rather than a binary phenotype with a deterministic decision.

The Mass-Longevity Triangle: Pareto Optimality and the Geometry of Life-History Trait Space.

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.

Geometry of the Gene Expression Space of Individual Cells.

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.

Logarithmic and power law input-output relations in sensory systems with fold-change detection.

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.

Cell lineage analysis of the mammalian female germline.

Fundamental aspects of embryonic and post-natal development, including maintenance of the mammalian female germline, are largely unknown. Here we employ a retrospective, phylogenetic-based method for reconstructing cell lineage trees utilizing somatic mutations accumulated in microsatellites, to study female germline dynamics in mice. Reconstructed cell lineage trees can be used to estimate lineage relationships between different cell types, as well as cell depth (number of cell divisions since the zygote). We show that, in the reconstructed mouse cell lineage trees, oocytes form clusters that are separate from hematopoietic and mesenchymal stem cells, both in young and old mice, indicating that these populations belong to distinct lineages. Furthermore, while cumulus cells sampled from different ovarian follicles are distinctly clustered on the reconstructed trees, oocytes from the left and right ovaries are not, suggesting a mixing of their progenitor pools. We also observed an increase in oocyte depth with mouse age, which can be explained either by depth-guided selection of oocytes for ovulation or by post-natal renewal. Overall, our study sheds light on substantial novel aspects of female germline preservation and development.

Evolutionary tradeoffs between economy and effectiveness in biological homeostasis systems.

Biological regulatory systems face a fundamental tradeoff: they must be effective but at the same time also economical. For example, regulatory systems that are designed to repair damage must be effective in reducing damage, but economical in not making too many repair proteins because making excessive proteins carries a fitness cost to the cell, called protein burden. In order to see how biological systems compromise between the two tasks of effectiveness and economy, we applied an approach from economics and engineering called Pareto optimality. This approach allows calculating the best-compromise systems that optimally combine the two tasks. We used a simple and general model for regulation, known as integral feedback, and showed that best-compromise systems have particular combinations of biochemical parameters that control the response rate and basal level. We find that the optimal systems fall on a curve in parameter space. Due to this feature, even if one is able to measure only a small fraction of the system's parameters, one can infer the rest. We applied this approach to estimate parameters in three biological systems: response to heat shock and response to DNA damage in bacteria, and calcium homeostasis in mammals.

Longitudinal hair cortisol in bipolar disorder and a mechanism based on HPA dynamics.

Bipolar disorder (BD) is marked by fluctuating mood states over months to years, often with elevated cortisol levels. Elevated cortisol can also trigger mood episodes. Here, we combine longitudinal hair cortisol and mood measurements with mathematical modeling to provide a potential mechanistic link between cortisol and mood timescales in BD. Using 12 cm hair samples, representing a year of growth, we found enhanced year-scale cortisol fluctuations whose amplitude averaged 4-fold higher in BD (n = 26) participants than controls (n = 59). The proximal 2 cm of hair correlated with recent mood scores. Depression (n = 266) and mania (n = 273) scores from a longitudinal study of BD showed similar frequency spectra. These results suggest a mechanism for BD in which high emotional reactivity excites the slow timescales in the hypothalamic-pituitary-adrenal (HPA) axis to generate elevated months-scale cortisol fluctuations, triggering cortisol-induced mood episodes.