arXiv subjects

Marko Popović

Publications and source records attributed to Marko Popović.

At least 19 recordsLinked to original sources

arXiv2026

Signature of mechanically induced cell extrusions in cell size distribution

How a growing tissue organizes its own homeostatic state is a central question in the physics of living matter. We show that when a growing epithelial sheet counteracts increasing cell density by mechanically squeezing cells out of its plane, a homeostatic in-plane pressure emerges as a generalization of a yield stress. We find that in the quasistatic growth limit the homeostatic state is marginally stable, with a pseudogap in the distribution of local distances to the extrusion threshold pressure. Because such mechanically induced extrusions arise from an instability of individual cells, the pseudogap is imprinted in the distribution of cell areas. This provides an image-based way to test for presence of mechanically induced extrusions and we identify this signature in the developing wing epithelium of \textit{D.~melanogaster}. We expect the same principles to apply to confined three-dimensional tissues.

physics.bio-ph↗

arXiv2026

Cell size heterogeneity controls crystallization of the developing fruit fly wing

A fundamental question in biology is to understand how patterns and shapes emerge from the collective interplay of large numbers of cells. Cells forming two-dimensional epithelial tissues behave as active materials that undergo remodeling and spontaneous shape changes. Focusing on the fly wing as a model system, we find that the cellular packing in the wing epithelium transitions from a disordered packing to an ordered, crystalline packing. While previous studies propose a role of tissue shear flow in establishing the ordered cell packing in the fly wing, we reveal a role of cell size heterogeneity. Indeed, we find that even if tissue shear have been inhibited, cell packings in the fruit fly wing epithelium transition from disordered to an ordered packing. We propose that the transition is controlled by the cell size heterogeneity, which is quantified by the cell size polydispersity. To explore the role of cell size polydispersity in controlling cellular packings, we implement polydispersity in a vertex model of epithelial tissues. Through numerical simulations of this model, we show that there is a critical value of cell size polydispersity above which cellular packings are disordered and below which they form a crystalline packing. By analyzing experimental data, we find that cell size polydispersity decreases during fly wing development. The observed dynamics of tissue crystallisation is consistent with the slow ordering kinetics we observe in the vertex model. Therefore, although tissue shear does not control the transition, it significantly enhances the rate of tissue-scale ordering by facilitating alignment of locally ordered crystallites. Our results identify cell size heterogeneity as a control parameter, in both the vertex model and the fruit fly wing epithelium, controlling the transition between ordered and disordered cellular packings.

physics.bio-ph↗

arXiv2026

Cell divisions suppress dynamical correlations in solid tissues

Developing tissues often maintain mechanical coherence while continuously remodeling through cellular processes such as cell divisions and rearrangements. In this way, they are an example of amorphous solids. In passive amorphous solids, local rearrangements can trigger one another through long-ranged elastic interactions, leading to system-spanning avalanches near yielding. Whether similar collective dynamics should be expected in living tissues is unclear, because cell divisions generate stress and remodeling events independently of local mechanical stability. Here, we address this question using a two-dimensional elastoplastic model in which cell divisions are treated as active plastic events. We find that while cell divisions fluidize the tissue below the passive yield stress, but preserve the marginal stability in the quasistatic limit. However, they also strongly suppress the system-spanning avalanches of cell rearrangements, in constrast with the expected behavior in passive amorphous solids. Finally, we show that the avalanche supression originates from the energy balance in the system. Namely, the energy injected by cell divisions allows for shear flow below the yield stress, but also provides a finite budget for rearrangements. These results suggest that proliferating tissues display the structural hallmarks of marginal amorphous solids while exhibiting much shorter-ranged correlations in dynamics, compared to passive amorphous solids.

cond-mat.soft↗

arXiv2026

Cell proliferation maintains cell area polydispersity in the growing fruit fly wing epithelium

Developing epithelial tissues coordinate cell proliferation and mechanical forces to achieve proper size and shape. As epithelial cells tightly adhere together to form the confluent tissue, the distribution of cell areas significantly influences possible patterns of cellular packing and thereby also the mechanics of the epithelium. Therefore, it is important to understand the origin of cell area heterogeneity in developing tissues and, if possible, how to control it. Previous models of cell growth and division have been successful in accounting for experimentally observed area distributions in cultured cells and bacterial colonies, but developing tissues present additional complexity due to self-organized patterns of mechanical stresses that guide morphogenesis. Here, we address this challenge focusing on the D. melanogaster wing disc epithelium. We consider a simple model that couples cell cycle dynamics to tissue mechanics. From time-lapse imaging of the cellular network, we extract all model parameters - cell growth rates, division rates, and mechanical fluctuations - revealing that they all depend on cell size. With these independently measured parameters, our model quantitatively reproduces the observed cell area distribution without any fitting parameters and further predicts tissue pressure gradients, in quantitative agreement with previously published data. Importantly, we find that cell proliferation accounts for 85% of cell area variance, establishing it as the dominant source of packing disorder that influences tissue mechanics and organization.

physics.bio-ph↗

arXiv2025

Cell divisions imprint long lasting elastic strain fields in epithelial tissues

A hallmark of biological tissues, viewed as complex cellular materials, is the active generation of mechanical stresses by cellular processes, such as cell divisions. Each cellular event generates a force dipole that deforms the surrounding tissue. Therefore, a quantitative description of these force dipoles, and their consequences on tissue mechanics, is one of the central problems in understanding the overall tissue mechanics. In this work we analyze previously published experimental data on fruit fly \textit{D. melanogaster} wing epithelia to quantitatively describe the deformation fields induced by a cell-scale force dipole. We find that the measured deformation field can be explained by a simple model of fly epithelium as a linearly elastic sheet. This fact allows us to use measurements of the strain field around cellular events, such as cell divisions, to infer the magnitude and dynamics of the mechanical forces they generate. In particular, we find that cell divisions exert a transient isotropic force dipole field, corresponding to the temporary localisation of the cell nucleus to the tissue surface during the division, and traceless-symmetric force dipole field that remains detectable from the tissue strain field for up to about $3.5$ hours after the division. This is the timescale on which elastic strains are erased by other mechanical processes and therefore it corresponds to the tissue fluidization timescale. In summary, we have developed a method to infer force dipoles induced by cell divisions, by observing the strain field in the surrounding tissues. Using this method we quantitatively characterize mechanical forces generated during a cell division, and their effects on the tissue mechanics.

physics.bio-ph↗

arXiv2024

Particle transport in a correlated ratchet

One of the many measures of the non-equilibrium nature of a system is the existence of a non-zero steady state current which is especially relevant for many biological systems. To this end, we study the non-equilibrium dynamics of a particle moving in a tilted colored noise ratchet in two different situations. In the first, the colored noise variable is reset to a specific value every time the particle transitions from one well to another in the ratchet. Contrary to intuition, we find that the current magnitude decreases as the correlation time of the noise increases, and increases monotonically with noise strength. The average displacement of the particle is against the tilt, which implies that the particle performs work. We then consider a variation of the same problem in which the colored noise process is allowed to evolve freely without any resetting at the transitions. Again, the average displacement is against the potential. However, the current magnitude increases with the correlation time, and there is an optimal noise strength that maximizes the current magnitude. Finally, we provide quantitative arguments to explain these findings and their relevance to active biological matter such as tissues.

cond-mat.soft↗

arXiv2023

Ductile-to-brittle transition and yielding in soft amorphous materials: perspectives and open questions

Soft amorphous materials are viscoelastic solids ubiquitously found around us, from clays and cementitious pastes to emulsions and physical gels encountered in food or biomedical engineering. Under an external deformation, these materials undergo a noteworthy transition from a solid to a liquid state that reshapes the material microstructure. This yielding transition was the main theme of a workshop held from January 9 to 13, 2023 at the Lorentz Center in Leiden. The manuscript presented here offers a critical perspective on the subject, synthesizing insights from the various brainstorming sessions and informal discussions that unfolded during this week of vibrant exchange of ideas. The result of these exchanges takes the form of a series of open questions that represent outstanding experimental, numerical, and theoretical challenges to be tackled in the near future.

cond-mat.soft↗

arXiv2023

Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids

We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. In our framework, the growth of the dynamical correlation length $ξ$ and of the correlation volume $χ_4$ are controlled by a zero-temperature fixed point. We connect this critical behavior to the properties of the distribution of local energy barriers at zero temperature. Our description makes a direct connection between dynamical heterogeneities and avalanche-type relaxation associated to dynamic facilitation, allowing us to relate the size distribution of heterogeneities to their time evolution. Within an avalanche, a local region relaxes multiple times, the more the larger is the avalanche. This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation). Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elasto-plastic models.

cond-mat.soft↗

arXiv2023

Theory of rheology and aging of protein condensates

Biological condensates are assemblies of proteins and nucleic acids that form membraneless compartments in cells and play essential roles in cellular functions. In many cases they exhibit the physical properties of liquid droplets that coexist in a surrounding fluid. Recently, quantitative studies on the material properties of biological condensates have become available, revealing complex material properties. In vitro experiments have shown that protein condensates exhibit time dependent material properties, similar to aging in glasses. To understand this phenomenon from a theoretical perspective, we develop a rheological model based on the physical picture of protein diffusion and stochastic binding inside condensates. The complex nature of protein interactions is captured by a distribution of binding energies, incorporated in a trap model originally developed to study glass transitions. Our model can describe diffusion of constituent particles, as well as the material response to time-dependent forces, and it recapitulates the age dependent relaxation time of Maxwell glass observed experimentally both in active and passive rheology. We derive a generalized fluctuation-response relations of our model in which the relaxation function does not obey time translation invariance. Our study sheds light on the complex material properties of biological condensates and provides a theoretical framework for understanding their aging behavior.

cond-mat.soft↗

arXiv2022

Electrohydraulic activity of biological cells

Fluid pumping and the generation of electric current by living tissues are required during morphogenetic processes and for maintainance of homeostasis. How these flows emerge from active and passive ion transport in cells has been well established. However, the interplay between flow and current generation is not well understood. Here, we study the electro-hydraulic coupling that arises from cell ion pumping. We develop a one-dimensional continuum model of fluid and ion transport across active cell membranes. Solving the Nernst-Planck and Poisson equations in the limit of weak charge imbalance allows us to derive approximate analytical solutions of the model. These approximations, consistent with the numerical results in physiologically relevant regime of parameters, allow us to describe electro-hydraulic activity of cells and tissues in terms of experimentally accessible parameters.

physics.bio-ph↗

arXiv2022

Random traction yielding transition in epithelial tissues

We investigate how randomly oriented cell traction forces lead to fluidisation in a vertex model of epithelial tissues. We find that the fluidisation occurs at a critical value of the traction force magnitude $F_c$. We show that this transition exhibits critical behaviour, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidisation mechanism through active force generation that could be relevant in biological tissues.

cond-mat.soft↗

arXiv2022

Scaling description of creep flow in amorphous solids

Amorphous solids such as coffee foam, toothpaste or mayonnaise display a transient creep flow when a stress $Σ$ is suddenly imposed. The associated strain rate is commonly found to decay in time as $\dotγ \sim t^{-ν}$, followed either by arrest or by a sudden fluidisation. Various empirical laws have been suggested for the creep exponent $ν$ and fluidisation time $τ_f$ in experimental and numerical studies. Here, we postulate that plastic flow is governed by the difference between $Σ$ and the transient yield stress $Σ_t(γ)$ that characterises the stability of configurations visited by the system at strain $γ$. Assuming the analyticity of $Σ_t(γ)$ allows us to predict $ν$ and asymptotic behaviours of $τ_f$ in terms of properties of stationary flows. We test successfully our predictions using elastoplastic models and published experimental results.

cond-mat.soft↗

arXiv2020

Thermal origin of quasi-localised excitations in glasses

Key aspects of glasses are controlled by the presence of excitations in which a group of particles can rearrange. Surprisingly, recent observations indicate that their density is dramatically reduced and their size decreases as the temperature of the supercooled liquid is lowered. Some theories predict these excitations to cause a gap in the spectrum of quasi-localised modes of the Hessian that grows upon cooling, while others predict a pseudo-gap ${D_L(ω)} \sim ω^α$. To unify these views and observations, we generate glassy configurations of controlled gap magnitude $ω_c$ at temperature ${T=0}$, using so-called `breathing' particles, and study how such gapped states respond to thermal fluctuations. We find that \textit{(i)}~the gap always fills up at finite $T$ with ${D_L(ω) \approx A_4(T) \, ω^4}$ and ${A_4 \sim \exp(-E_a / T)}$ at low $T$, \textit{(ii)}~$E_a$ rapidly grows with $ω_c$, in reasonable agreement with a simple scaling prediction ${E_a\sim ω_c^4}$ and \textit{(iii)}~at larger $ω_c$ excitations involve fewer particles, as we rationalise, and eventually become string-like. We propose an interpretation of mean-field theories of the glass transition, in which the modes beyond the gap act as an excitation reservoir, from which a pseudo-gap distribution is populated with its magnitude rapidly decreasing at lower $T$. We discuss how this picture unifies the rarefaction as well as the decreasing size of excitations upon cooling, together with a string-like relaxation occurring near the glass transition.

cond-mat.soft↗

arXiv2020

Thermally activated flow in models of amorphous solids

Amorphous solids yield at a critical value $Σ_c$ of the imposed stress $Σ$ through a dynamical phase transition. While sharp in athermal systems, the presence of thermal fluctuations leads to the rounding of the transition and thermally activated flow even below $Σ_c$. Here, we study the steady state thermal flow of amorphous solids using a mesoscopic elasto-plastic model. In the Hebraud-Lequex (HL) model we provide an analytical solution of the thermally activated flow at low temperature. We then propose a general scaling law that also describes the transition rounding. Finally, we find that the scaling law holds in numerical simulations of the HL model, a 2D elasto-plastic model, and in previously published molecular dynamics simulations of 2D Lennard-Jones glass.

cond-mat.soft↗

arXiv2020

Inferring the flow properties of epithelial tissues from their geometry

Amorphous materials exhibit complex material proprteties with strongly nonlinear behaviors. Below a yield stress they behave as plastic solids, while they start to yield above a critical stress $Σ_c$. A key quantity controlling plasticity which is, however, hard to measure is the density $P(x)$ of weak spots, where $x$ is the additional stress required for local plastic failure. In the thermodynamic limit $P(x)\sim x^θ$ is singular at $x= 0$ in the solid phase below the yield stress $Σ_c$. This singularity is related to the presence of system spannig avalanches of plastic events. Here we address the question if the density of weak spots and the flow properties of a material can be determined from the geometry of an amporphous structure alone. We show that a vertex model for cell packings in tissues exhibits the phenomenology of plastic amorphous systems. As the yield stress is approached from above, the strain rate vanishes and the avalanches size $S$ and their duration $τ$ diverge. We then show that in general, in materials where the energy functional depend on topology, the value $x$ is proportional to the length $L$ of a bond that vanishes in a plastic event. For this class of models $P(x)$ is therefore readily measurable from geometry alone. Applying this approach to a quantification of the cell packing geometry in the developing wing epithelium of the fruit fly, we find that in this tissue $P(L)$ exhibits a power law with exponents similar to those found numerically for a vertex model in its solid phase. This suggests that this tissue exhibits plasticity and non-linear material properties that emerge from collective cell behaviors and that these material properties govern developmental processes. Our approach based on the relation between topology and energetics suggests a new route to outstanding questions associated with the yielding transition.

physics.bio-ph↗

arXiv2019

How collective asperity detachments nucleate slip at frictional interfaces

Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius $A_c$ governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding $x_σ$ presents a pseudo-gap $P(x_σ) \sim (x_σ)^θ$, where $θ$ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius $A_c$ diverges as a $θ$-dependent power law of the system size. We discuss how these predictions can be tested experimentally.

cond-mat.dis-nn↗

arXiv2019

Theory for the density of interacting quasi-localised modes in amorphous solids

Quasi-localised modes appear in the vibrational spectrum of amorphous solids at low-frequency. Though never formalised, these modes are believed to have a close relationship with other important local excitations, including shear transformations and two-level systems. We provide a theory for their frequency density, $D_{L}(ω)\simω^α$, that establishes this link for systems at zero temperature under quasi-static loading. It predicts two regimes depending on the density of shear transformations $P(x)\sim x^θ$ (with $x$ the additional stress needed to trigger a shear transformation). If $θ>1/4$, $α=4$ and a finite fraction of quasi-localised modes form shear transformations, whose amplitudes vanish at low frequencies. If $θ<1/4$, $α=3+ 4 θ$ and all quasi-localised modes form shear transformations with a finite amplitude at vanishing frequencies. We confirm our predictions numerically.

cond-mat.soft↗

arXiv2018

Elasto-plastic description of brittle failure in amorphous materials

The response of amorphous materials to an applied strain can be continuous, or instead display a macroscopic stress drop when a shear band nucleates. Such discontinuous response can be observed if the initial configuration is very stable. We study theoretically how such brittleness emerges in athermal, quasi-statically driven, materials as their initial stability is increased. We show that this emergence is well reproduced by elasto-plastic models and is predicted by a mean field approximation, where it corresponds to a continuous transition. In mean field, failure can be forecasted from the avalanche statistics. We show that this is not the case for very brittle materials in finite dimensions due to rare weak regions where a shear band nucleates. Their critical radius is predicted to follow $a_c\sim (Σ-Σ_b)^{-2}$, where $Σ$ is the stress and $Σ_b$ the stress a shear band can carry.

cond-mat.soft↗