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Frank Jülicher

Publications and source records attributed to Frank Jülicher.

At least 19 recordsLinked to original sources
arXiv2026

Fluctuation-Response Theory of Non-Equilibrium Complex Fluids

A fundamental challenge in soft matter physics is to describe materials, such as the living cytoplasm and tissues, that are simultaneously active, chemically driven, and exhibit long-lasting memory of mechanical stresses. Here, we construct a generalized hydrodynamic framework at finite wavevectors and frequencies that is applicable to non-equilibrium fluids with memory. By leveraging stationary correlation identities, we derive a generalized linear response theory for non-equilibrium steady states. This framework serves as a formal extension of Onsager's regression hypothesis beyond thermal equilibrium. Our approach provides a direct pathway to derive transport coefficients from steady-state fluctuations without the traditional Mori-Zwanzig projection-operator formalism, generalizing the Green-Kubo relations to non-equilibrium systems. As a corollary, we derive two model-free variants of the non-equilibrium fluctuation-response relation for non-Markovian dynamics. These generalized relations explicitly capture the non-equilibrium circulating currents--an out-of-equilibrium signature that is invisible to conventional scalar formulations or frameworks that treat degrees of freedom independently. Applying our theory to chemically driven active fluids reveals the emergence of active viscoelastic memory, wherein chemical reaction cycles dynamically renormalize the macroscopic viscous response. Strikingly, this active memory can induce negative storage and loss moduli at finite frequencies, a behavior absent in ordinary viscoelastic fluids. Our first-principles framework rigorously extends linear rheology to non-equilibrium systems and provides a foundation for understanding non-Markovian dynamics across a broad range of biological and synthetic active matter.

cond-mat.soft↗
arXiv2026

Flow, dynamics and active fracture in hydraulic multicellular systems

From interstitial space to luminal cavities, fluid pressure and flow can remodel, reshape and even redefine a biological tissue. Fluids can either govern or react to mechanical interactions between cells. However, measuring flows at cellular scales is difficult, which makes it challenging to understand tissue hydraulics. Here, we develop a theoretical approach that captures cellular mechanics and fluid flow in one framework. We find that hydraulics can drastically influence tissue behavior. Hydraulic coupling between cell shape and size governs a tissue's response to osmotic shock, while tuning a tissue's permeabilities can channel fluid either between or across cell membranes. In active tissues, hydraulics can suppress cell mobility to the point of fracture, where we discover a hydraulic ratchet that drives fluid out of cells to generate small luminal spaces. We find experimental evidence that hydraulics can suppress cell motion in early stage zebrafish embryos injected with a thickening agent, which indicates that hydraulics may generally govern the behaviors of many multicellular systems.

physics.bio-ph↗
arXiv2026

Continuous Game of Life: cell emergence and self-organization at the edge of growth

Conway's Game of Life shows that simple rules can generate a rich diversity of emerging structures. This cellular automaton has been translated to continuous space by Rafler (2011) in a simulation called SmoothLife. The isotropic rule of this continuous Game of Life generates patterns whose beauty has attracted the attention of a growing community at the intersection of science and computer art. We study a minimal variant of this model, continuous in space and time, that generates cell-like patterns capable of self-replicating, gliding and disappearing. The phenomenology of these unit patterns is reported and related to homogeneous-state bifurcations, symmetry breaking, observed shape instabilities, finite-amplitude morphological changes, and a dilute-to-dense transition associated with cell proliferation. Its mapping onto a large reaction-diffusion system is interpreted in terms of homeostatic concentrations of morphogens, regulated by the nonlinear survival rule and generated through a cell-sourced cascade of auxiliary reactions. Introducing a global conservation law that limits resource availability causes the system to self-organize at this dilute-to-dense transition, which we call the edge of growth. A further exploration of parameter space reveals a variety of phases and the richness of life-like morphologies organized around this edge. Resemblance to biological processes such as division, motility, and death, together with a concise formulation and numerical implementation, makes the continuous Game of Life an appealing model system for investigating the emergence and self-organization of life-like patterns.

physics.bio-ph↗
arXiv2026

Flow-wave coupling synchronizes oscillations in growing active matter

Oscillatory biochemical signals and mechanical forces must coordinate robustly during development, yet the principles governing their mutual coupling remain poorly understood. In syncytial embryos and cell-free extracts, mitotic waves propagate across millimeter scales while simultaneously generating cytoplasmic flows, suggesting a two-way interaction between chemical oscillators and mechanics. Here, we combine experiments in Xenopus Laevis cytoplasmic extracts with a minimal particle-based model to reveal a mechanochemical feedback that stabilizes phase wave propagation. In contrast to previous models of oscillatory active matter, an asymmetric size cycle, slow growth and rapid shrinkage, combined with size-dependent mechanical interactions generates a net particle displacement and flows aligned with the wave direction, which in turn drive a synchronization transition. Our results show that mechanical forces actively maintain the coherence of biochemical waves, providing a general mechanism for long-range order in oscillating active matter.

physics.bio-ph↗
arXiv2026

Control of morphology and topology in a lattice model of branching morphogenesis

We present a lattice model for morphogen-controlled branching morphogenesis which combines ideas and concepts from non-equilibrium physics and developmental biology. In this model, the stochastic occupation dynamics of cells is coupled with signaling molecules (morphogens) produced by the cells. We investigate growth patterns governed by morphogen concentration gradients, spanning regimes ranging from the diffusion-limited aggregation limit to the stochastic surface growth (Eden model) limit. Moreover, we introduce control over topology by a local operator and study growth, degrowth, and steady-state dynamics of branched patterns. The topology-preserving steady-state clusters exhibit a power-law scaling of radius of gyration with cluster size, yielding the exponents $0.68\pm0.01$ in square lattice and $0.67\pm 0.01$ in hexagonal lattice.

cond-mat.stat-mech↗
arXiv2026

DNA end tethering through break-induced DNA--protein condensation

Cells deploy robust mechanisms to repair DNA damage, safeguarding genomic stability and cellular health, but the physical principles underlying these processes remain incompletely understood. Experiments show \emph{in vitro} that upon a DNA double-strand break, a DNA--protein condensate can tether the broken DNA ends before they disperse away, a critical step for subsequent repair biochemistry. However, it remains puzzling how such condensation reliably achieves spatiotemporal localization at the break site and captures both broken ends despite intrinsic stochasticity. Here, we propose that broken DNA ends can trigger a conversion of proteins from a soluble state to a condensate-competent state. Combining this idea with Brownian dynamics simulations and theory, we propose a physical mechanism for reliable DNA-end tethering. Simulations show that such break-induced conversion can drive local DNA--protein condensation with two possible outcomes: successful or failed tethering. To rationalize this, we construct an effective free energy landscape, identify the corresponding stationary states, and demonstrate that tethering is governed by a kinetic competition between polymer relaxation and condensation dynamics. Together, our study shows that DNA end-dependent conversion, coupled with DNA--protein condensation, can reliably tether broken DNA ends.

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

Spatiotemporal Control of Charge +1 Topological Defects in Polar Active Matter

Topological defects are a conspicuous feature of active liquid crystals that have been associated with important morphogenetic transitions in organismal development. Robust development thus requires a tight control of the motion and placement of topological defects. In this manuscript, we study a mechanism to control +1 topological defects in an active polar fluid confined to a disk. If activity is localized in an annulus within the disk, the defect moves on a circular trajectory around the center of the disk. Using an ansatz for the polar field, we determine the dependence of the angular speed and the circle radius on the boundary orientation of the polar field and the active annulus. Using a proportional integral controller, we guide the defect along complex trajectories by changing the active annulus size and the boundary orientation.

cond-mat.soft↗
arXiv2026

Electrohydraulic Fields Generated by Active Transport at Tissue Interfaces

Living cells and tissues can generate complex patterns of electric fields and fluid flows which can play important role in physiology. Both, fields and flows are rooted in ion transport across biological interfaces: cell membranes and epithelial cell layers. Here we develop a unified electrohydraulic framework that combines electric fields, osmotic pressures, and fluid flows, emphasising their couplings. We consider an active, permeable interface that drives electrohydraulic fields in the surrounding bulk. We show that spatially heterogeneous ion transport acts as a distributed current source, generating long-range electric fields, osmotic gradients, and fluid flows. Using this framework, we show that patterns of ion pumping at cell and tissue boundaries can simultaneously produce large-scale electric fields and fluid flows due to electrohydraulic coupling. A key insight is that an external electric field and an internal dipolar pumping pattern can be physically equivalent and can generate the same pattern of ion current and fluid flows. The induced dipolar osmotic pressure can drive self-propulsion through bulk osmotic coupling, with a mobility determined by interfacial permeability and system size, a mechanism distinct from classical electrophoresis or electro-osmosis. We further show that for strong fields a new effect emerges. Nonlinear coupling can lead to isotropic swelling of a hollow ball of cells. This can explain recent experiments on epithelial organoids. Finally, we show that feedback between ion transport and resulting electric fields can drive spontaneous symmetry breaking, generating dipolar or multipolar fields and patterns. Our work highlights the importance of electrohydraulic coupling in the emergence in currents and fields in the biological systems.

cond-mat.soft↗
arXiv2026

Hydrodynamic theory of chemically active emulsions

We present a systematic theory of chemically active emulsions in the hydrodynamic limit by constructing a thermodynamically consistent framework in which the equilibrium is broken by chemo-stating of fuel molecules. For ternary solutions with active chemical reactions, we obtain an effective dynamics of the conserved field dynamics at long length and time scales. The effective dynamics takes into account the broken time reversal symmetry that manifests itself by the emergence of gradient terms akin to those of Active Model B+, which is a generic theory of active phase separation. In addition to the active coefficients modifying the interfacial energy coefficient, the theory contains higher order terms in the gradient expansion that are necessary to correctly describe the dynamics of chemically active emulsions, extending thus Active Model B+. We study numerically a Flory-Huggins model with active chemical reactions. Our theory predicts the formation of microphases when the effective interfacial energy coefficient becomes negative. Moreover, including noise, we show the existence of bubbly phase separation. We also identify a new type of phase behavior, a dynamic active filament phase. Finally, we discuss the steady state entropy production rate in the system resulting from the active chemical reactions. We observe that the total entropy production rate increases with the driving chemical potential and exhibits a kink-like singularity at the transition to the dynamic active filament phase. Our work shows that the generic behaviors of active phase separation can emerge in chemically active emulsions.

cond-mat.soft↗
arXiv2026

Edge Currents Shape Condensates in Chiral Active Matter

Chiral active matter, which breaks both parity symmetry and time-reversal symmetry, is ubiquitous in living systems. Here, we introduce a minimal two-dimensional chiral active lattice gas by incorporating stochastic, biased local rotations. At low temperatures, the system coarsens into condensates with chiral orientations and faceted, crystal-like shapes. The interfaces align at characteristic angles with respect to the lattice axes and exhibit edge currents that are persistent, unidirectional, and angle-dependent. To generalise these findings, we propose a continuum theory by adding an active chiral edge current term to Model B, which reveals the essential role of active chiral transport in the interfacial dynamics of phase separation. Edge currents with $n$-fold symmetry produce condensates whose shapes resemble regular $n$-sided polygons. In the thin-interface limit, we construct an effective interface potential governing edge currents, from which the steady-state condensate geometry can be obtained, both in the lattice model and the continuum description.

cond-mat.stat-mech↗
arXiv2026

Physical Approaches to Metabolic Scaling in Living Systems

Living systems continuously transform matter and energy through the chemical processes that constitute their metabolism. The overall metabolic rate of an organism correlates positively with its body mass, however both the exact scaling behavior and possible explanations for this behavior have been under intense debate for two centuries. This review synthesizes empirical findings and theoretical frameworks on the energetics of living systems from an interdisciplinary perspective, with a focus on physical concepts. A general thermodynamic framework to study metabolism is laid out, together with a coarse-grained description of metabolic biochemistry. The rich history of experimental work in this field is surveyed, revealing a variety of metabolic scaling patterns at different levels of biological organization, from individual cells to whole populations. Several biophysical models proposed to explain the sublinear scaling of metabolic rate with body mass are summarized. Though the traditional focus has been on adult organisms, the review also highlights recent advances that probe metabolism during development. Improvements in experimental techniques, extensive datasets, and a host of open questions, suggest the field will continue gaining momentum in the near term. The review concludes with an outlook for this future progress: an interdisciplinary approach to elucidate metabolic scaling across different developmental stages and organism sizes.

cond-mat.soft↗
arXiv2026

In vitro binding energies capture Klf4 occupancy across the human genome

Transcription factors (TFs) regulate gene expression by binding to specific genomic loci determined by DNA sequence. Their sequence specificity is commonly summarized by a consensus binding motif. However, eukaryotic genomes contain billions of low-affinity DNA sequences to which TFs associate with a sequence-dependent binding energy. We currently lack insight into how the genomic sequence defines this spectrum of binding energies and the resulting pattern of TF localization. Here, we set out to obtain a quantitative understanding of sequence-dependent TF binding to both motif and non-motif sequences. We achieve this by first pursuing accurate measurements of physical binding energies of the human TF Klf4 to a library of short DNA sequences in a fluorescence-anisotropy-based bulk competitive binding assay. Second, we show that the highly non-linear sequence dependence of Klf4 binding energies can be captured by combining a linear model of binding energies with an Ising model of the coupled recognition of nucleotides by a TF. We find that this statistical mechanics model parametrized by our in vitro measurements captures Klf4 binding patterns on individual long DNA molecules stretched in the optical tweezer, and is predictive for Klf4 occupancy across the entire human genome without additional fit parameters.

physics.bio-ph↗
arXiv2026

Nonequilibrium noise emerging from broken detailed balance in active gels

In thermodynamic equilibrium, the fluctuation-dissipation theorem links thermal fluctuations and dissipation. Biological systems, however, are driven out of equilibrium by internal processes that produce additional, active fluctuations. Despite being relevant for biological functions such as intracellular transport, predicting the statistical properties of active fluctuations remains challenging. Here, we address this challenge in a minimal model of an active gel as a network of elastic elements connected by transient crosslinks. The crosslinkers' binding and unbinding rates break detailed balance, which drives the system out of equilibrium. Through coarse-graining, we derive fluctuating hydrodynamic equations including an active noise term, which emerges explicitly from the breaking of detailed balance. Finally, we provide predictions for the stochastic motion of a tracer particle embedded in the active gel, which enables comparisons with microrheology experiments both in synthetic active gels and in cells. Overall, our work provides an explicit link between the statistical properties of active fluctuations and the molecular breaking of detailed balance. Thus, it paves the way toward complementing the fluctuation-dissipation theorem with a fluctuation-activity relation in active systems.

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↗
arXiv2026

Roadmap for Condensates in Cell Biology

Biomolecular condensates govern essential cellular processes yet elude description by traditional equilibrium models. This roadmap, distilled from structured discussions at a workshop and reflecting the consensus of its participants, clarifies key concepts for researchers, funding bodies, and journals. After unifying terminology that often separates disciplines, we outline the core physics of condensate formation, review their biological roles, and identify outstanding challenges in nonequilibrium theory, multiscale simulation, and quantitative in-cell measurements. We close with a forward-looking outlook to guide coordinated efforts toward predictive, experimentally anchored understanding and control of biomolecular condensates.

physics.bio-ph↗
arXiv2025

Marrying critical oscillators with traveling waves shapes nonlinear sound processing in the cochlea

The cochlea's capacity to process a broad range of sound intensities has been linked to nonlinear amplification by critical oscillators. However, while the increasing sensitivity of a critical oscillator upon decreasing the stimulus magnitude comes with proportionally sharper frequency tuning and slower responsiveness -- critical slowing down, the observed bandwidth of cochlear frequency tuning and the cochlear response time vary little with sound level. Because the cochlea operates as a distributed system rather than a single critical oscillator, it remains unclear whether criticality can serve as a fundamental principle for cochlear amplification. Here we tackle this challenge by integrating tonopically distributed critical oscillators in a traveling-wave model of the cochlea. Importantly, critical oscillators generically provide spatial buildup of energy gain from energy pumping into the waves and a key nonlinearity. In addition, our nonlinear model accounts for viscoelastic coupling between the oscillators. The model produces, with a single set of parameters, a family of cochlear tuning curves that quantitatively describe experimental data over a broad range of input levels. Overall, the interplay between generic nonlinear properties of local critical oscillators and distributed effects from traveling waves gives rise to a collective nonlinear response that preserves the power-law responsiveness afforded by criticality, but without paying the price of critical slowing down.

physics.bio-ph↗
arXiv2025

Kinetic theory of emulsions with matter supply

In this work, we propose a theory for the kinetics of emulsions in which a continuous supply of matter feeds droplet growth. We consider cases where growth is either limited by bulk diffusion or the transport through the droplets' interfaces. Our theory extends the Lifshitz-Slyozov-Wagner (LSW) theory by two types of matter supply, where either the supersaturation is maintained or the supply rate is constant. In emulsions with maintained supersaturation, we find a decoupling of droplets at all times, with the droplet size distribution narrowing in the diffusion-limited regime and a drifting distribution of a fixed shape in the interface-resistance-limited case. In emulsions with a constant matter supply, there is a transition between narrowing and broadening in the diffusion-limited regime, and the distribution is non-universal. For the interface-resistance-limited regime, there is no transition to narrowing, and we find a universal law governing coarsening kinetics that is valid for any constant matter supply. The average radius evolves according to a power law that is independent of the matter supply, and we find a closed-form expression for the droplet size distribution function. Our theory is relevant to biological systems, such as biomolecular condensates in living cells, since droplet material is not conserved and the growth of small droplets is proposed to be interface-resistance-limited.

cond-mat.soft↗