Showing papers by "Frank Jülicher published in 2022"

A condensate dynamic instability orchestrates actomyosin cortex activation

Abstract: A key event at the onset of development is the activation of a contractile actomyosin cortex during the oocyte-to-embryo transition1-3. Here we report on the discovery that, in Caenorhabditis elegans oocytes, actomyosin cortex activation is supported by the emergence of thousands of short-lived protein condensates rich in F-actin, N-WASP and the ARP2/3 complex4-8 that form an active micro-emulsion. A phase portrait analysis of the dynamics of individual cortical condensates reveals that condensates initially grow and then transition to disassembly before dissolving completely. We find that, in contrast to condensate growth through diffusion9, the growth dynamics of cortical condensates are chemically driven. Notably, the associated chemical reactions obey mass action kinetics that govern both composition and size. We suggest that the resultant condensate dynamic instability10 suppresses coarsening of the active micro-emulsion11, ensures reaction kinetics that are independent of condensate size and prevents runaway F-actin nucleation during the formation of the first cortical actin meshwork.

Theory of nematic and polar active fluid surfaces

Abstract: We derive a fully covariant theory of the hydrodynamics of nematic and polar active surfaces, subjected to internal and external forces and torques. We study the symmetries of polar and nematic surfaces and find that in addition to 5 different types of in-plane isotropic surfaces, polar and nematic surfaces can be classified into 5 polar, 2 pseudopolar, 5 nematic and 2 pseudonematic types of surfaces. We give examples of physical realisations of the different types of surfaces we have identified. We obtain expressions for the equilibrium tensions, moments, and external forces and torques acting on a passive polar or nematic surface. We calculate the entropy production rate using the framework of thermodynamics close to equilibrium and find constitutive equations for polar and nematic active surfaces with different symmetries. We study the instabilities of a confined flat planar-chiral polar active layer and of a confined deformable polar active surface with broken up-down symmetry. with a tangent polar or nematic order. B . The distribution of stresses within a thin layer gives rise to tensions and torques acting within the surface, when integrated across the thick-ness of the layer. C . Internal and external forces and torques act on a surface element with surface area dS . D . The order parameter changes in time and is transported by the flow. Lagrangian time derivatives are taken by comparing the order parameter at two times t and t + dt , following the flow of the surface.

A gelation transition enables the self-organization of bipolar metaphase spindles

Abstract: Abstract The mitotic spindle is a highly dynamic bipolar structure that emerges from the self-organization of microtubules, molecular motors and other proteins. Sustained motor-driven poleward flows of dynamic microtubules play a key role in the bipolar organization of spindles. However, it is not understood how the local activity of motor proteins generates these large-scale coherent poleward flows. Here we show that a gelation transition enables long-range microtubule transport causing the spindles to self-organize into two oppositely polarized microtubule gels. Laser ablation experiments reveal that local active stresses generated at the spindle midplane propagate through the structure, thereby driving global coherent microtubule flows. Simulations show that microtubule gels undergoing rapid turnover can exhibit long stress relaxation times, in agreement with the long-range flows observed in experiments. Finally, our model predicts that in the presence of branching microtubule nucleation, either disrupting such flows or decreasing the network connectivity can lead to a microtubule polarity reversal in spindles. We experimentally confirm this inversion of polarity by abolishing the microtubule transport in spindles. Overall, we uncover a connection between spindle rheology and architecture in spindle self-organization.

Network Synchronization Revisited: Time Delays in Mutually Coupled Oscillators

Abstract: Coordinated and efficient operation in large, complex systems requires the synchronization of the rhythms of spatially distributed components. Such systems are the basis for critical infrastructure such as satellite navigation, mobile communications, and services like the precision time protocol and Universal Coordinated Time. Different concepts for the synchronization of oscillator networks have been proposed, in particular mutual synchronization without and hierarchical synchronization from a reference clock. Established network synchronization models in electrical engineering address the role of inevitable cross-coupling time delays for network synchronization. Mutual synchronization has been studied using linear approximations of the coupling functions of these models. We review previous work and present a general model in which we study synchronization taking into account nonlinearities and finite time delays. As a result, dynamical phenomena in networks of coupled electronic oscillators induced by time delays, such as the multistability and stabilization of synchronized states can be predicted and observed. We study the linear stability of nonlinear states and predict for which system parameters synchronized states can be stable. We use these results to discuss the implementation of mutual synchronization for complex system architectures. A key finding is that mutual synchronization can result in stable in- and anti-phase synchronized states in the presence of large time delays. We provide the condition for which such synchronized states are guaranteed to be stable.

Flagella-like beating of actin bundles driven by self-organized myosin waves

Abstract: Wave-like beating of eukaryotic cilia and flagella-threadlike protrusions found in many cells and microorganisms-is a classic example of spontaneous mechanical oscillations in biology. This type of self-organized active matter raises the question of the coordination mechanism between molecular motor activity and cytoskeletal filament bending. Here we show that in the presence of myosin motors, polymerizing actin filaments self-assemble into polar bundles that exhibit wave-like beating. Importantly, filament beating is associated with myosin density waves initiated at twice the frequency of the actin-bending waves. A theoretical description based on curvature control of motor binding to the filaments and of motor activity explains our observations in a regime of high internal friction. Overall, our results indicate that the binding of myosin to actin depends on the actin bundle shape, providing a feedback mechanism between the myosin activity and filament deformations for the self-organization of large motor filament assemblies.

Long-range morphogen gradient formation by cell-to-cell signal propagation

Abstract: Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradation rates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scale wnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay can generate stable morphogen and signaling gradients that are oriented by a local, morphogen-independent source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-range gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-range gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over.

Mutual Synchronization of Spatially Distributed 24 GHz Oscillators up to Distances of 500 m

Abstract: This brief studies how mutual synchronization of oscillators can be achieved for cross-coupling time delays much larger than the period of the oscillations. Using the closed loop transfer function for a system of two mutually delay-coupled phase-locked loops (PLLs) and applying the Nyquist stability criterion, the critical time delay for which stable in- and anti-phase synchronized states become unstable is calculated. The analysis reveals the range of feed-forward loop gains for a given time delay value so that stable in- or anti-phase synchronized states can exist. These theoretical predictions are then verified by measurements with PLLs operating at 24GHz and for cross-coupling time delays ranging from the nano- to the microseconds domain. Such delays are equivalent to coupling at distances of up to 500m. The experimental results show a good agreement with the theoretical predictions. Hence, this brief shows how to setup a network of mutually delay-coupled PLLs and achieve stable synchronized states for a given time delay.

Stability Analysis of Mutually Synchronized Spatially Distributed 24 GHz Oscillators

Abstract: In this work the basin of stability of synchronized states in a system of two mutually delay-coupled phase-locked loops (PLLs) is studied. For sufficiently large cross-coupling time delays several synchronized states with different frequencies and phase relations can exist. This is termed multistability. Using PLL nodes with voltage-controlled oscillators operating at 24 GHz the basin of stability of in- and anti-phase synchronized states is measured. The PLL nodes were modified accordingly to measure the transient dynamics during synchronization. A comparison to the results of time domain simulations of the transient dynamics reveals that such dynamics can be predicted qualitatively and quantitatively. Based on these results, a deeper understanding of the synchronization process at time delays resulting in multistable states in coupled PLL networks, can be obtained.

Emergent chirality in active solid rotation of pancreas spheres

Abstract: Collective cell dynamics play a crucial role in many developmental and physiological contexts. While two-dimensional (2D) cell migration has been widely studied, how three-dimensional (3D) geometry and topology interplay with collective cell behavior to determine dynamics and functions remains an open question. In this work, we elucidate the biophysical mechanism underlying rotation in spherical tissues, a phenomenon widely reported both in vivo and in vitro. Using murine pancreas-derived organoids as a model system, we find that epithelial spheres exhibit persistent rotation, rotational axis drift and rotation arrest. Using a 3D vertex model, we demonstrate how the interplay between traction force and polarity alignment can account for these distinct rotational dynamics. Furthermore, our analysis shows that the spherical tissue rotates as an active solid and exhibits spontaneous chiral symmetry breaking. Using a continuum model, we demonstrate how the types and location of topological defects in the polarity field underlie this symmetry breaking process. Altogether, our work shows that tissue chirality can arise via topological defects in the pattern of cell traction forces, with potential implications for left-right symmetry breaking processes in morphogenetic events.

Core PCP mutations affect short time mechanical properties but not tissue morphogenesis in the Drosophila pupal wing

Abstract: How morphogenetic movements are robustly coordinated in space and time is a fundamental open question in biology. We study this question using the wing of Drosophila melanogaster, an epithelial tissue that undergoes large-scale tissue flows during pupal stages. We showed previously (Etournay et al., 2015) that pupal wing morphogenesis involves both cellular behaviors that allow relaxation of mechanical tissue stress, as well as cellular behaviors that appear to be actively patterned. The core planar cell polarity (PCP) pathway influences morphogenetic cell movements in many other contexts, which suggests that it could globally pattern active cellular behaviors during pupal wing morphogenesis. We show here, however, that this is not the case: there is no significant phenotype on the cellular dynamics underlying pupal morphogenesis in mutants of core PCP. Furthermore, using laser ablation experiments, coupled with a rheological model to describe the dynamics of the response to laser ablation, we conclude that while core PCP mutations affect the fast timescale response to laser ablation, they do not affect overall tissue mechanics. In conclusion, our work shows that cellular dynamics and tissue shape changes during Drosophila pupal wing morphogenesis are independent of one potential chemical guiding cue, core PCP.

Active T1 transitions in cellular networks

Abstract: In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy.

How to Implement Mutual Network Synchronization in the Presence of Large Cross-Coupling Delays

Abstract: SummaryMutual synchronization without a reference oscillator has shown to scale advantageously with system size while being robust to noise. However, the complexity of its implementation has so far hindered its way into technical application. We show that the issue can be addressed using concepts from delay dynamical systems theory. These allow to predict the properties of self-organized synchronization, necessary to guide the architecture design of networks that implement the mutual synchronization concept. We confirm the theoretical predictions with numerical simulations.

Broken living layers: Dislocations in active smectic liquid crystals.

Abstract: We show that dislocations in active two-dimensional (2D) smectic liquid crystals with underlying rotational symmetry are always unbound in the presence of noise, meaning the active smectic phase does not exist for nonzero noise in d=2. The active smectic phase can, like equilibrium smectics in 2D, be stabilized by applying rotational symmetry-breaking fields; however, even in the presence of such fields, active smectics are still much less stable against noise than equilibrium ones, when the symmetry-breaking field(s) are weak.

Heat fluctuations in chemically active systems.

Abstract: Chemically active systems such as living cells are maintained out of thermal equilibrium due to chemical events which generate heat and lead to active fluctuations. A key question is to understand on which time and length scales active fluctuations dominate thermal fluctuations. Here, we formulate a stochastic field theory with Poisson white noise to describe the heat fluctuations which are generated by stochastic chemical events and lead to active temperature fluctuations. We find that on large length- and timescales, active fluctuations always dominate thermal fluctuations. However, at intermediate length- and timescales, multiple crossovers exist which highlight the different characteristics of active and thermal fluctuations. Our work provides a framework to characterize fluctuations in active systems and reveals that local equilibrium holds at certain length- and timescales.