Frank Jülicher

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, emphasizing 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—They 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 of currents and fields in the biological systems.

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 cross-linkers. The cross-linkers' 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.

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 nonmotif sequences. We achieve this by first pursuing accurate measurements of physical binding energies of human TF Krüppel-like factor 4 (Klf4) to a library of short DNA sequences in a fluorescence-anisotropy-based bulk competitive binding assay. Second, we show that the highly nonlinear 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. In this model, nucleotide–TF interfaces collectively switch between two states, weak binding and strong nucleotide-specific binding, and the states of neighboring interfaces are coupled with J ∼ 2 k B T . We find that this statistical mechanics model parameterized by our in vitro measurements captures Klf4 binding patterns on an individual long DNA molecule stretched in the optical tweezer, and is predictive for Klf4 occupancy across the entire human genome without additional fit parameters.

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, crystallike 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 generalize 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.

Clathrin-mediated endocytosis (CME) is the primary pathway for internalization of extracellular and membrane cargo in eukaryotic cells. It is characterized by a patch of the plasma membrane invaginating and pinching off to generate a cytoplasmic vesicle. Recently, experimental evidence has begun to accumulate in support of proteins assembling into liquid-like condensates at nascent CME sites, but potential functional consequences are not understood. Given that condensate capillary forces can influence membrane bending, we constructed complementary analytical and numerical model systems to probe the mechanical influence of a protein droplet on endocytosis. Model evaluations and analysis reveal that a droplet can regulate the progression of endocytosis by stalling invagination until the droplet grows past a threshold size. After the droplet-mediated brake is released, the droplet provides a force that can drive the membrane bud toward scission. Thus, we propose a “mechanical timer” mechanism as a function for protein phase separation in cellular membrane trafficking. Statement of Significance: Clathrin-mediated endocytosis is the essential pathway through which a patch of plasma membrane deforms into a vesicle in all eukaryotic cells. Recent experimental studies suggest that cytoplasmic components of the endocytic machinery condense into a liquid-like droplet on the membrane prior to internalization, raising questions about the droplet’s biological function. Using complementary numerical and analytical modeling approaches, we show that an endocytic droplet can regulate the pathway via capillary force. The droplet volume sets the strength of this force, providing the cell with a handle to switch from stalling to driving membrane invagination. While the biological role of liquid condensates is typically attributed to organizing biochemistry, this work demonstrates a novel purely mechanical function.

The actin cytoskeleton drives shape changes and transport in cells and supports mechanical signal transmission. However, how cells control and use active cytoskeletal flows at the mesoscale is not well understood. We reconstituted an active cytoskeleton in water-in-oil emulsion droplets of Xenopus laevis egg extract and observed, above a critical droplet size, the emergence of a 3D radially convergent steady-state flow of polymeric actin, maintained by continuous actin turnover. The flow condensed lipid-rich cellular debris into a centered inclusion. Steady-state F-actin density and flow velocity profiles roughly collapse onto scale-invariant master curves. This behavior can be explained by a physical model representing the network as an isotropic active viscous fluid with a percolation threshold. The contracting network behaves as an active swimmer with complex internal dynamics that centers itself and the central inclusion inside the droplets without physical boundary attachment. Active contraction, crosslinking and polymerization dynamics in an actin network can thus generate cell-scale flow patterns that sense the confining geometry and external signals and exert forces that are likely sufficient to move and localize organelles in cells.

I. Dense, well-ordered material states of proteins form the amyloid fibers that are a hallmark of neurodegenerative disease in the brain. Beyond forming amyloid fibers, some of these proteins can also adopt other material states termed condensates which are initially liquid-like but evolve to a soft, glassy phase. Fiber growth requires a large supply of monomers and, thus, it is often speculated that fibers emerge from within a dense condensate as it ages and its microscopic dynamics slow into a glassy state. Here, we use the well-established model system Fused in Sarcoma (FUS) to directly observe, quantify and theoretically describe fiber growth and its interplay with condensates. We report the discovery that fibers grow overwhelmingly in the dilute phase surrounding the condensates while the condensates concurrently evolve to a glassy arrested solid. The resulting protein fibers and glassy condensates are both distinct solid-like phases that coexist but do not directly interconvert. Taken together, these findings reveal that there are two competitive aging pathways in FUS condensation that are linked through phase separation kinetics.

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.

We study phase-separating fluid mixtures as they demix in the presence of chemical reactions that maintain them away from thermodynamic equilibrium. We show that in such chemically active emulsions the interplay of chemical reactions, phase separation, and hydrodynamics effects complex self-organization and pattern formation that can give rise to spatiotemporal chaos. This chaotic dynamics, unlike in classical turbulence, is not due to fluid inertia—we analyze the system in the Stokes flow regime—and it is different from the of active nematics at low Reynolds number, for our fluid mixtures lack any orientational order. To explore the generic features of nonlinear dynamics in our system, we derive amplitude equations which we find to be identical to those obtained for Rayleigh-Benard convection with mean flow and stress-free conditions at the top and bottom plates. Chemically active emulsions possessing no internal order, we thus establish, can exhibit chaoticity that is driven by interfacial stresses in the fluid mixture.