arXiv subjects

Boris I. Shraiman

Publications and source records attributed to Boris I. Shraiman.

At least 19 recordsLinked to original sources

arXiv2026

Tissue shape from cell-scale active tensions

Connecting cell behavior to tissue shape and mechanics is a key challenge in the physics of morphogenesis. Cytoskeletal turnover precludes a fixed reference state, and tensions are actively generated independently of strain; so conventional elasticity theory is not applicable. Here, we study epithelia governed by quasi-static force balance between intracellular pressure and internal, active tensions. This makes the tissue a distributed hydrostatic skeleton. Our theory starts from a set of prescribed active tensions. It treats cell interfaces as force dipoles whose embedding in physical space - the physical cell configuration - is constrained by force balance. To solve this constraint problem geometrically, we represent the tensions as a triangulation dual to the cell tiling. This allows us to use (and extend) the mathematics of discrete conformal geometry to link tensions to cell and tissue shape. Adiabatic changes of tensions cause changes in the physical configuration. Thus, rather than fluidizing, tissues can deform - or "morph" - while resisting external forces like a solid. This constitutes a form of emergent elasticity, mediated by two geometric soft modes. Importantly, tissue-scale stress depends on cell shape, but is independent of microscopic tension anisotropy, with consequences for experimental stress measurements and modeling mechanosensitive feedback loops. Discrete conformal geometry also allows us to analyze how cellular tension dynamics drive cell rearrangement, required for large plastic deformation. The unified description of emergent elasticity of epithelial tissues and their plastic morphing, driven by adiabatic tension dynamics and cell rearrangement, provides a foundation to better understand the role of mechanics in morphogenesis. Furthermore, we highlight connections to the mechanics of other amorphous materials, such as granular media.

cond-mat.soft↗

arXiv2026

Emergent Elasticity and Quasiconformal Flow in Active Solids

A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on deformation relative to a reference. A different approach is needed to describe how cells sculpt tissues through local active forces. We develop a theory of two-dimensional continuum mechanics where the active stress configuration, rather than a reference shape, is the fundamental input. Motivated by the Active Tension Network model for epithelia, we encode motor-driven forces between cells in a Riemannian tension metric. We derive a stress-metric relation for the macroscopic stress that results from embedding the tension manifold into physical space (defining cell positions). Despite the absence of constitutive laws, a stress-free reference state and an effective stress-strain relation arise from the tension metric, making the system an effectively elastic active solid. Moving from statics to dynamics, our framework describes how an active solid can morph its shape through adiabatic dynamics of active stress. To capture large, plastic deformations through cell rearrangement, we introduce a second metric that geometrizes the cell network topology. Topological rearrangement appears as a continuous reparametrization of the tension manifold. This mathematical framework, based on Riemannian geometry, isothermal coordinates, and quasi-conformal flows, quantitatively predicts how local contractile activity determines large-scale shape and provides a principled continuum description of active plasticity. A companion paper validates the continuum analysis through coarse-graining of discrete cell networks. Our theory identifies a geometric origin of emergent elasticity and plasticity in living matter and, more broadly, in active and granular materials.

cond-mat.soft↗

arXiv2024

A Geometric Tension Dynamics Model of Epithelial Convergent Extension

Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer under actively generated internal tension. To resolve this apparent paradox, we formulate a model in which tissue flow in the tension-dominated regime occurs through adiabatic remodeling of force balance in the network of adherens junctions. We propose that the slow dynamics within the manifold of force-balanced configurations is driven by positive feedback on myosin-generated cytoskeletal tension. Shifting force balance within a tension network causes active cell rearrangements (T1 transitions) resulting in net tissue deformation oriented by initial tension anisotropy. Strikingly, we find that the total extent of tissue deformation depends on the initial cellular packing order. T1s degrade this order so that tissue flow is self-limiting. We explain these findings by showing that coordination of T1s depends on coherence in local tension configurations, quantified by a geometric order parameter in tension space. Our model reproduces the salient tissue- and cell-scale features of germ band elongation during Drosophila gastrulation, in particular the slowdown of tissue flow after approximately twofold longation concomitant with a loss of order in tension configurations. This suggests local cell geometry contains morphogenetic information and yields experimentally testable predictions. Defining biologically controlled active tension dynamics on the manifold of force-balanced states may provide a general approach to the description of morphogenetic flow.

physics.bio-ph↗

arXiv2023

A "morphogenetic action" principle for 3D shape formation by the growth of thin sheets

How does growth encode form in developing organisms? Many different spatiotemporal growth profiles may sculpt tissues into the same target 3D shapes, but only specific growth patterns are observed in animal and plant development. In particular, growth profiles may differ in their degree of spatial variation and growth anisotropy, however, the criteria that distinguish observed patterns of growth from other possible alternatives are not understood. Here we exploit the mathematical formalism of quasiconformal transformations to formulate the problem of "growth pattern selection" quantitatively in the context of 3D shape formation by growing 2D epithelial sheets. We propose that nature settles on growth patterns that are the 'simplest' in a certain way. Specifically, we demonstrate that growth pattern selection can be formulated as an optimization problem and solved for the trajectories that minimize spatiotemporal variation in areal growth rates and deformation anisotropy. The result is a complete prediction for the growth of the surface, including not only a set of intermediate shapes, but also a prediction for cell displacement along those surfaces in the process of growth. Optimization of growth trajectories for both idealized surfaces and those observed in nature show that relative growth rates can be uniformized at the cost of introducing anisotropy. Minimizing the variation of programmed growth rates can therefore be viewed as a generic mechanism for growth pattern selection and may help to understand the prevalence of anisotropy in developmental programs.

cond-mat.soft↗

arXiv2021

Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.

cond-mat.soft↗

arXiv2020

Multi-defect Dynamics in Active Nematics

Recent experiments and numerical studies have drawn attention to the dynamics of active nematics. Two-dimensional active nematics flow spontaneously and exhibit spatiotemporal chaotic flows with proliferation of topological defects in the nematic texture. It has been proposed that the dynamics of active nematics can be understood in terms of the dynamics of interacting defects, propelled by active stress. Previous work has derived effective equations of motion for individual defects as quasi-particles moving in the mean field generated by other defects, but an effective theory governing multi-defect dynamics has remained out of reach. In this paper, we examine the dynamics of 2D active nematics in the limit of strong order and overdamped compressible flow. The activity-induced defect dynamics is formulated as a perturbation of the manifold of quasi-static nematic textures explicitly parameterized by defect positions. This makes it possible to derive a set of coupled ordinary differential equations governing defect (and therefore texture) dynamics. Interestingly, because of the non-orthogonality of textures associated with individual defects, their motion is coupled through a position dependent ``collective mobility" matrix. In addition to the familiar active self-propulsion of the $+1/2$ defect, we obtain new collective effects of activity that can be interpreted in terms of non-central and non-reciprocal interactions between defects.

cond-mat.soft↗

arXiv2018

Geometry of epithelial cells provides a robust method for image based inference of stress within tissues

Cellular mechanics plays an important role in epithelial morphogenesis, a process wherein cells reshape and rearrange to produce tissue-scale deformations. However, the study of tissue-scale mechanics is impaired by the difficulty of direct measurement of stress in-vivo. Alternative, image-based inference schemes aim to estimate stress from snapshots of cellular geometry but are challenged by sensitivity to fluctuations and measurement noise as well as the dependence on boundary conditions. Here we overcome these difficulties by introducing a new variational approach - the Geometrical Variation Method (GVM) - which exploits the fundamental duality between stress and cellular geometry that exists in the state of mechanical equilibrium of discrete mechanical networks that approximate cellular tissues. In the Geometrical Variation Method, the two dimensional apical geometry of an epithelial tissue is approximated by a 2D tiling with Circular Arc Polygons (CAP) in which the arcs represent intercellular interfaces defined by the balance of local line tension and pressure differentials between adjacent cells. We take advantage of local constraints that mechanical equilibrium imposes on CAP geometry to define a variational procedure that extracts the best fitting equilibrium configuration from images of epithelial monolayers. The GVM-based stress inference algorithm has been validated by the comparison of the predicted cellular and mesoscopic scale stress and measured myosin II patterns in the epithelial tissue during Drosophila embryogenesis. GVM prediction of mesoscopic stress tensor correlates at the 80% level with the measured myosin distribution and reveals that most of the myosin II activity is involved in a static internal force balance within the epithelial layer. Lastly, this study provides a practical method for non-destructive estimation of stress in live epithelial tissues.

q-bio.CB↗

arXiv2017

Active Tension Network model reveals an exotic mechanical state realized in epithelial tissues

It is now widely recognized that mechanical interactions between cells play a crucial role in epithelial morphogenesis, yet understanding the mechanisms through which stress and deformation affect cell behavior remains an open problem due to the complexity inherent in the mechanical behavior of cells and the difficulty of direct measurement of forces within tissues. Theoretical models can help by focusing experimental studies and by providing the framework for interpreting measurements. To that end, "vertex models" have introduced an approximation of epithelial cell mechanics based on a polygonal tiling representation of planar tissue. Here we formulate and analyze an Active Tension Network (ATN) model, which is based on the same polygonal representation of epithelial tissue geometry, but in addition i) assumes that mechanical balance is dominated by cortical tension and ii) introduces tension dependent local remodeling of the cortex, representing the active nature of cytoskeletal mechanics. The tension-dominance assumption has immediate implications for the geometry of cells, which we demonstrate to hold in certain types of Drosophila epithelial tissues. We demonstrate that stationary configurations of an ATN form a manifold with one degree of freedom per cell, corresponding to "isogonal" - i.e. angle preserving - deformations of cells, which dominate the dynamic response to perturbations. We show that isogonal modes account for approximately 90% of experimentally observed deformation of cells during the process of ventral furrow formation in Drosophila. Other interesting properties of our model include the exponential screening of mechanical stress and a negative Poisson ratio response to external uniaxial stress. We also provide a new approach to the problem of inferring local cortical tensions from the observed geometry of epithelial cells in a tissue

q-bio.TO↗

arXiv2016

Leaf growth is conformal

Growth pattern dynamics lie at the heart of morphogenesis. Here, we investigate the growth of plant leaves. We compute the conformal transformation that maps the contour of a leaf at a given stage onto the contour of the same leaf at a later stage. Based on the mapping we predict the local displacement field in the leaf blade and find it to agree with the experimentally measured displacement field to 92%. This approach is applicable to any two-dimensional system with locally isotropic growth, enabling the deduction of the whole growth field just from observation of the tissue contour.

q-bio.TO↗

arXiv2015

Prediction, dynamics, and visualization of antigenic phenotypes of seasonal influenza viruses

Human seasonal influenza viruses evolve rapidly, enabling the virus population to evade immunity and re-infect previously infected individuals. Antigenic properties are largely determined by the surface glycoprotein hemagglutinin (HA) and amino acid substitutions at exposed epitope sites in HA mediate loss of recognition by antibodies. Here, we show that antigenic differences measured through serological assay data are well described by a sum of antigenic changes along the path connecting viruses in a phylogenetic tree. This mapping onto the tree allows prediction of antigenicity from HA sequence data alone. The mapping can further be used to make predictions about the makeup of the future seasonal influenza virus population, and we compare predictions between models with serological and sequence data. To make timely model output readily available, we developed a web browser based application that visualizes antigenic data on a continuously updated phylogeny.

q-bio.PE↗

arXiv2015

Inferring Epigenetic Dynamics from Kin Correlations

Populations of isogenic embryonic stem cells or clonal bacteria often exhibit extensive phenotypic heterogeneity which arises from stochastic intrinsic dynamics of cells. The internal state of the cell can be transmitted epigenetically in cell division, leading to correlations in the phenotypic states of cells related by descent. Therefore, a phenotypic snapshot of a collection of cells with known genealogical structure, contains information on phenotypic dynamics. Here we use a model of phenotypic dynamics on a genealogical tree to define an inference method which allows to extract an approximate probabilistic description of phenotypic dynamics based on measured correlations as a function of the degree of kinship. The approach is tested and validated on the example of Pyoverdine dynamics in P. aeruginosa colonies. Interestingly, we find that correlations among pairs and triples of distant relatives have a simple but non-trivial structure indicating that observed phenotypic dynamics on the genealogical tree is approximately conformal - a symmetry characteristic of critical behavior in physical systems. Proposed inference method is sufficiently general to be applied in any system where lineage information is available.

q-bio.PE↗

arXiv2014

Predicting evolution from the shape of genealogical trees

Given a sample of genome sequences from an asexual population, can one predict its evolutionary future? Here we demonstrate that the branching patterns of reconstructed genealogical trees contains information about the relative fitness of the sampled sequences and that this information can be used to predict successful strains. Our approach is based on the assumption that evolution proceeds by accumulation of small effect mutations, does not require species specific input and can be applied to any asexual population under persistent selection pressure. We demonstrate its performance using historical data on seasonal influenza A/H3N2 virus. We predict the progenitor lineage of the upcoming influenza season with near optimal performance in 30% of cases and make informative predictions in 16 out of 19 years. Beyond providing a tool for prediction, our ability to make informative predictions implies persistent fitness variation among circulating influenza A/H3N2 viruses.

q-bio.PE↗

arXiv2013

Coalescence, genetic diversity in sexual populations under selection

In sexual populations, selection operates neither on the whole genome, which is repeatedly taken apart and reassembled by recombination, nor on individual alleles that are tightly linked to the chromosomal neighborhood. The resulting interference between linked alleles reduces the efficiency of selection and distorts patterns of genetic diversity. Inference of evolutionary history from diversity shaped by linked selection requires an understanding of these patterns. Here, we present a simple but powerful scaling analysis identifying the unit of selection as the genomic "linkage block" with a characteristic length determined in a self-consistent manner by the condition that the rate of recombination within the block is comparable to the fitness differences between different alleles of the block. We find that an asexual model with the strength of selection tuned to that of the linkage block provides an excellent description of genetic diversity and the site frequency spectra when compared to computer simulations. This linkage block approximation is accurate for the entire spectrum of strength of selection and is particularly powerful in scenarios with many weakly selected loci. The latter limit allows us to characterize coalescence, genetic diversity, and the speed of adaptation in the infinitesimal model of quantitative genetics.

q-bio.PE↗

arXiv2012

Emergence of clones in sexual populations

In sexual population, recombination reshuffles genetic variation and produces novel combinations of existing alleles, while selection amplifies the fittest genotypes in the population. If recombination is more rapid than selection, populations consist of a diverse mixture of many genotypes, as is observed in many populations. In the opposite regime, which is realized for example in the facultatively sexual populations that outcross in only a fraction of reproductive cycles, selection can amplify individual genotypes into large clones. Such clones emerge when the fitness advantage of some of the genotypes is large enough that they grow to a significant fraction of the population despite being broken down by recombination. The occurrence of this "clonal condensation" depends, in addition to the outcrossing rate, on the heritability of fitness. Clonal condensation leads to a strong genetic heterogeneity of the population which is not adequately described by traditional population genetics measures, such as Linkage Disequilibrium. Here we point out the similarity between clonal condensation and the freezing transition in the Random Energy Model of spin glasses. Guided by this analogy we explicitly calculate the probability, Y, that two individuals are genetically identical as a function of the key parameters of the model. While Y is the analog of the spin-glass order parameter, it is also closely related to rate of coalescence in population genetics: Two individuals that are part of the same clone have a recent common ancestor.

q-bio.PE↗

arXiv2012

Fluctuations of fitness distributions and the rate of Muller's ratchet

The accumulation of deleterious mutations is driven by rare fluctuations which lead to the loss of all mutation free individuals, a process known as Muller's ratchet. Even though Muller's ratchet is a paradigmatic process in population genetics, a quantitative understanding of its rate is still lacking. The difficulty lies in the nontrivial nature of fluctuations in the fitness distribution which control the rate of extinction of the fittest genotype. We address this problem using the simple but classic model of mutation selection balance with deleterious mutations all having the same effect on fitness. We show analytically how fluctuations among the fittest individuals propagate to individuals of lower fitness and have a dramatically amplified effects on the bulk of the population at a later time. If a reduction in the size of the fittest class reduces the mean fitness only after a delay, selection opposing this reduction is also delayed. This delayed restoring force speeds up Muller's ratchet. We show how the delayed response can be accounted for using a path integral formulation of the stochastic dynamics and provide an expression for the rate of the ratchet that is accurate across a broad range of parameters.

q-bio.PE↗

arXiv2011

Mechanical Stress Inference for Two Dimensional Cell Arrays

Many morphogenetic processes involve mechanical rearrangement of epithelial tissues that is driven by precisely regulated cytoskeletal forces and cell adhesion. The mechanical state of the cell and intercellular adhesion are not only the targets of regulation, but are themselves likely signals that coordinate developmental process. Yet, because it is difficult to directly measure mechanical stress {\it in vivo} on sub-cellular scale, little is understood about the role of mechanics of development. Here we present an alternative approach which takes advantage of the recent progress in live imaging of morphogenetic processes and uses computational analysis of high resolution images of epithelial tissues to infer relative magnitude of forces acting within and between cells. We model intracellular stress in terms of bulk pressure and interfacial tension, allowing these parameters to vary from cell to cell and from interface to interface. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. Here we present the mathematical formulation of the proposed Mechanical Inverse method and apply it to the analysis of epithelial cell layers observed at the onset of ventral furrow formation in the {\it Drosophila} embryo and in the process of hair-cell determination in the avian cochlea. The analysis reveals mechanical anisotropy in the former process and mechanical heterogeneity, correlated with cell differentiation, in the latter process. The method opens a way for quantitative and detailed experimental tests of models of cell and tissue mechanics.

q-bio.CB↗

arXiv2011

Collective and single cell behavior in epithelial contact inhibition

Control of cell proliferation is a fundamental aspect of tissue physiology central to morphogenesis, wound healing and cancer. Although many of the molecular genetic factors are now known, the system level regulation of growth is still poorly understood. A simple form of inhibition of cell proliferation is encountered in vitro in normally differentiating epithelial cell cultures and is known as "contact inhibition". The study presented here provides a quantitative characterization of contact inhibition dynamics on tissue-wide and single cell levels. Using long-term tracking of cultured MDCK cells we demonstrate that inhibition of cell division in a confluent monolayer follows inhibition of cell motility and sets in when mechanical constraint on local expansion causes divisions to reduce cell area. We quantify cell motility and cell cycle statistics in the low density confluent regime and their change across the transition to epithelial morphology which occurs with increasing cell density. We then study the dynamics of cell area distribution arising through reductive division, determine the average mitotic rate as a function of cell size and demonstrate that complete arrest of mitosis occurs when cell area falls below a critical value. We also present a simple computational model of growth mechanics which captures all aspects of the observed behavior. Our measurements and analysis show that contact inhibition is a consequence of mechanical interaction and constraint rather than interfacial contact alone, and define quantitative phenotypes that can guide future studies of molecular mechanisms underlying contact inhibition.

q-bio.TO↗

arXiv2011

Rare beneficial mutations can halt Muller's ratchet

The vast majority of mutations are deleterious, and are eliminated by purifying selection. Yet in finite asexual populations, purifying selection cannot completely prevent the accumulation of deleterious mutations due to Muller's ratchet: once lost by stochastic drift, the most-fit class of genotypes is lost forever. If deleterious mutations are weakly selected, Muller's ratchet turns into a mutational "meltdown" leading to a rapid degradation of population fitness. Evidently, the long term stability of an asexual population requires an influx of beneficial mutations that continuously compensate for the accumulation of the weakly deleterious ones. Here we propose that the stable evolutionary state of a population in a static environment is a dynamic mutation-selection balance, where accumulation of deleterious mutations is on average offset by the influx of beneficial mutations. We argue that this state exists for any population size N and mutation rate $U$. Assuming that beneficial and deleterious mutations have the same fitness effect s, we calculate the fraction of beneficial mutations, ε, that maintains the balanced state. We find that a surprisingly low εsuffices to maintain stability, even in small populations in the face of high mutation rates and weak selection. This may explain the maintenance of mitochondria and other asexual genomes, and has implications for the expected statistics of genetic diversity in these populations.

q-bio.PE↗