SHR and SCR coordinate root patterning and growth early in the cell cycle.

Precise control of cell division is essential for proper patterning and growth during the development of multicellular organisms. Coordination of formative divisions that generate new tissue patterns with proliferative divisions that promote growth is poorly understood. SHORTROOT (SHR) and SCARECROW (SCR) are transcription factors that are required for formative divisions in the stem cell niche of Arabidopsis roots1,2. Here we show that levels of SHR and SCR early in the cell cycle determine the orientation of the division plane, resulting in either formative or proliferative cell division. We used 4D quantitative, long-term and frequent (every 15 min for up to 48 h) light sheet and confocal microscopy to probe the dynamics of SHR and SCR in tandem within single cells of living roots. Directly controlling their dynamics with an SHR induction system enabled us to challenge an existing bistable model3 of the SHR-SCR gene-regulatory network and to identify key features that are essential for rescue of formative divisions in shr mutants. SHR and SCR kinetics do not align with the expected behaviour of a bistable system, and only low transient levels, present early in the cell cycle, are required for formative divisions. These results reveal an uncharacterized mechanism by which developmental regulators directly coordinate patterning and growth.

Brassinosteroid gene regulatory networks at cellular resolution in the Arabidopsis root.

Brassinosteroids are plant steroid hormones that regulate diverse processes, such as cell division and cell elongation, through gene regulatory networks that vary in space and time. By using time series single-cell RNA sequencing to profile brassinosteroid-responsive gene expression specific to different cell types and developmental stages of the Arabidopsis root, we identified the elongating cortex as a site where brassinosteroids trigger a shift from proliferation to elongation associated with increased expression of cell wall-related genes. Our analysis revealed HOMEOBOX FROM ARABIDOPSIS THALIANA 7 (HAT7) and GT-2-LIKE 1 (GTL1) as brassinosteroid-responsive transcription factors that regulate cortex cell elongation. These results establish the cortex as a site of brassinosteroid-mediated growth and unveil a brassinosteroid signaling network regulating the transition from proliferation to elongation, which illuminates aspects of spatiotemporal hormone responses.

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.

Tumor diversity and the trade-off between universal cancer tasks.

Recent advances have enabled powerful methods to sort tumors into prognosis and treatment groups. We are still missing, however, a general theoretical framework to understand the vast diversity of tumor gene expression and mutations. Here we present a framework based on multi-task evolution theory, using the fact that tumors need to perform multiple tasks that contribute to their fitness. We find that trade-offs between tasks constrain tumor gene-expression to a continuum bounded by a polyhedron whose vertices are gene-expression profiles, each specializing in one task. We find five universal cancer tasks across tissue-types: cell-division, biomass and energy, lipogenesis, immune-interaction and invasion and tissue-remodeling. Tumors that specialize in a task are sensitive to drugs that interfere with this task. Driver, but not passenger, mutations tune gene-expression towards specialization in specific tasks. This approach can integrate additional types of molecular data into a framework of tumor diversity grounded in evolutionary theory.

Structure and Interactions between Charged Lipid Membranes in the Presence of Multivalent Ions.

When aqueous salt solutions contain multivalent ions (like Ca2+ or Mg2+), strong correlation effects may lead to ion-bridging, net attraction, and tight-coupling between like-charged interfaces. To examine the effects of surface charge density, temperature, salt type, and salt concentration on the structures of tightly coupled charged interfaces, we have used mixed lipid membranes, containing either saturated or unsaturated tails in the presence of multivalent ions. We discovered that tightly coupled membrane lamellar phases, dominated by attractive interactions, coexisted with weakly coupled lamellar phases, dominated by repulsive interactions. To control the membrane charge density, we mixed lipids with negatively charged headgroups, DLPS and DOPS, with their zwitterionic analogue having the same tails, DLPC and DOPC, respectively. Using solution X-ray scattering we measured the lamellar repeat distance, D, at different ion concentrations, temperatures, and membrane charge densities. The multivalent ions tightly coupled the mixed lipid bilayers whose charged lipid molar fraction was between 0.1 and 1. The repeat distance of the tightly coupled phase was about 4 nm for the DLPS/DLPC mixtures and about 5 nm for the DOPS/DOPC mixtures. In this phase, the repeat distance slightly increased with increasing temperature and decreased with increasing charge density. When the molar fraction of charged lipid was 0.1 or 0.25, a less tightly coupled phase coexisted with the tightly coupled phase. The weakly coupled lamellar phase had significantly larger D values, although they were consistently shorter than the D values in monovalent salt solutions with similar screening lengths.

Evolutionary trade-offs and the structure of polymorphisms.

Populations of organisms show genetic differences called polymorphisms. Understanding the effects of polymorphisms is important for biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under trade-offs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that trade-offs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under trade-offs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species.This article is part of the theme issue 'Self-organization in cell biology'.

Optimal Regulatory Circuit Topologies for Fold-Change Detection.

Evolution repeatedly converges on only a few regulatory circuit designs that achieve a given function. This simplicity helps us understand biological networks. However, why so few circuits are rediscovered by evolution is unclear. We address this question for the case of fold-change detection (FCD): a response to relative changes of input rather than absolute changes. Two types of FCD circuits recur in biological systems-the incoherent feedforward and non-linear integral-feedback loops. We performed an analytical screen of all three-node circuits in a class comprising ∼500,000 topologies. We find that FCD is rare, but still there are hundreds of FCD topologies. The two experimentally observed circuits are among the very few minimal circuits that optimally trade off speed, noise resistance, and response amplitude. This suggests a way to understand why evolution converges on only few topologies for a given function and provides FCD designs for synthetic construction and future discovery.

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.

Inferring biological tasks using Pareto analysis of high-dimensional data.

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.

Linear superposition and prediction of bacterial promoter activity dynamics in complex conditions.

Bacteria often face complex environments. We asked how gene expression in complex conditions relates to expression in simpler conditions. To address this, we obtained accurate promoter activity dynamical measurements on 94 genes in E. coli in environments made up of all possible combinations of four nutrients and stresses. We find that the dynamics across conditions is well described by two principal component curves specific to each promoter. As a result, the promoter activity dynamics in a combination of conditions is a weighted average of the dynamics in each condition alone. The weights tend to sum up to approximately one. This weighted-average property, called linear superposition, allows predicting the promoter activity dynamics in a combination of conditions based on measurements of pairs of conditions. If these findings apply more generally, they can vastly reduce the number of experiments needed to understand how E. coli responds to the combinatorially huge space of possible environments.

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.

Effect of temperature on the interactions between dipolar membranes.

It is well-known that phospholipids in aqueous environment self-assemble into lamellar structures with a repeat distance governed by the interactions between them. Yet, the understanding of these interactions is incomplete. In this paper, we study the effect of temperature on the interlamellar interactions between dipolar membranes. Using solution small-angle X-ray scattering (SAXS), we measured the repeat distance between 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) bilayers at different temperatures and osmotic stresses. We found that when no pressure is applied the lamellar repeat distance, D, decreases and then increases with increasing temperature. As the osmotic stress increases, D decreases with temperature and then increases to a limited extent, until at sufficiently high pressure D decreases with temperature in all the examined range. We then reconstructed experimentally the equation of state and fit it with a modified interaction model that takes into account the temperature dependence of the fluctuation term. Finally, we showed how the thickness of DLPC membranes decreases with temperature.

Entropic attraction condenses like-charged interfaces composed of self-assembled molecules.

Like-charged solid interfaces repel and separate from one another as much as possible. Charged interfaces composed of self-assembled charged-molecules such as lipids or proteins are ubiquitous. The present study shows that although charged lipid-membranes are sufficiently rigid, in order to swell as much as possible, they deviate markedly from the behavior of typical like-charged solids when diluted below a critical concentration (ca. 15 wt %). Unexpectedly, they swell into lamellar structures with spacing that is up to four times shorter than the layers should assume (if filling the entire available space). This process is reversible with respect to changing the lipid concentration. Additionally, the research shows that, although the repulsion between charged interfaces increases with temperature, like-charged membranes, remarkably, condense with increasing temperature. This effect is also shown to be reversible. Our findings hold for a wide range of conditions including varying membrane charge density, bending rigidity, salt concentration, and conditions of typical living systems. We attribute the limited swelling and condensation of the net repulsive interfaces to their self-assembled character. Unlike solids, membranes can rearrange to gain an effective entropic attraction, which increases with temperature and compensates for the work required for condensing the bilayers. Our findings provide new insight into the thermodynamics and self-organization of like-charged interfaces composed of self-assembled molecules such as charged biomaterials and supramolecular assemblies that are widely found in synthetic and natural constructs.

Effect of temperature on the structure of charged membranes.

Interactions between charged and neutral self-assembled phospholipid membranes are well understood and take into account temperature dependence. Yet, the manner in which the structure of the membrane is affected by temperature was hardly studied. Here we study the effect of temperature on the thickness, area per lipid, and volume per lipid of charged membranes. Two types of membranes were studied: membranes composed of charged lipids and dipolar (neutral) membranes that adsorbed divalent cations and became charged. Small-angle X-ray scattering data demonstrate that the thickness of charged membranes decreases with temperature. Wide-angle X-ray scattering data show that the area per headgroup increases with temperature. Intrinsically charged membranes linearly thin with temperature, whereas neutral membranes that adsorb divalent ions and become charged show an exponential decrease of their thickness. The data indicate that, on average, the tails shorten as the temperature rises. We attribute this behavior to higher lipid tail entropy and to the weaker electrostatic screening of the charged headgroups, by their counterions, at elevated temperatures. The latter effect leads to stronger electrostatic repulsion between the charged headgroups that increases the area per headgroup and decreases the bilayer thickness.

The structure of ions and zwitterionic lipids regulates the charge of dipolar membranes.

In pure water, zwitterionic lipids form lamellar phases with an equilibrium water gap on the order of 2 to 3 nm as a result of the dominating van der Waals attraction between dipolar bilayers. Monovalent ions can swell those neutral lamellae by a small amount. Divalent ions can adsorb onto dipolar membranes and charge them. Using solution X-ray scattering, we studied how the structure of ions and zwitterionic lipids regulates the charge of dipolar membranes. We found that unlike monovalent ions that weakly interact with all of the examined dipolar membranes, divalent and trivalent ions adsorb onto membranes containing lipids with saturated tails, with an association constant on the order of ∼10 M(-1). One double bond in the lipid tail is sufficient to prevent divalent ion adsorption. We suggest that this behavior is due to the relatively loose packing of lipids with unsaturated tails that increases the area per lipid headgroup, enabling their free rotation. Divalent ion adsorption links two lipids and limits their free rotation. The ion-dipole interaction gained by the adsorption of the ions onto unsaturated membranes is insufficient to compensate for the loss of headgroup free-rotational entropy. The ion-dipole interaction is stronger for cations with a higher valence. Nevertheless, polyamines behave as monovalent ions near dipolar interfaces in the sense that they interact weakly with the membrane surface, whereas in the bulk their behavior is similar to that of multivalent cations. Advanced data analysis and comparison with theory provide insight into the structure and interactions between ion-induced regulated charged interfaces. This study models biologically relevant interactions between cell membranes and various ions and the manner in which the lipid structure governs those interactions. The ability to monitor these interactions creates a tool for probing systems that are more complex and forms the basis for controlling the interactions between dipolar membranes and charged proteins or biopolymers for encapsulation and delivery applications.

Solution X-ray scattering form factors of supramolecular self-assembled structures.

In this paper, the analysis of several involved models, relevant for evaluating solution X-ray scattering form factors of supramolecular self-assembled structures, is presented. Different geometrical models are discussed, and the scattering form factors of several layers of those shapes are evaluated. The thickness and the electron density of each layer are parameters in those models. The models include Gaussian electron density profiles and/or uniform electron density profiles at each layer. Various forms of cuboid, layered, spherical, cylindrical, and helical structures are carefully treated. The orientation-averaged scattering intensities of those form factors are calculated. Similar classes of form factors are examined and compared, and their fit to scattering data of lipid bilayers, capsids of the Simian virus 40 virus-like particle and microtubule is discussed. A more detailed model of discrete helices composed of uniform spheres was derived and compared to solution X-ray scattering data of microtubules. Our analyses show that when high-resolution data are available the more detailed models with Gaussian electron density profiles or helical structures composed of spheres should be used to better capture all the elements in the scattering curves. The models presented in this paper may also be applied, with minor corrections, for the analysis of solution neutron scattering data.