We discuss the mechano-chemical self-organization of an active fluid on a spherical sur-face. We find that a minimal model can generate patterns of flow, concentration and stress that exhibit key features of fundamental cellular processes such as cell symmetry breaking, cell division and cell locomotion. Furthermore, we show that this system provides insights in the mechanochemical self-organization of shapes. Our work thus provides a framework for the study of general principles of cellular self-organization.
A. Mietke, V. Jemseena, K. Vijay Kumar, I. F. Sbalzarini and F. Jülicher
Centrosomes play an key role for the organization of the mitotic spindle and serve as sites of microtubule nucleation. In order to understand centrosomal nucleation of microtubules it is important to know whether centrosomes locally enrich soluble tubulin. Here we deter-mine the spatial distribution of filamentous and soluble tubulin near the centrosome and show that soluble tubulin is locally enriched in centrosomes. We quantify tubulin concentra-tion inside and outside the centrosome. Our work suggests that centrosomal microtubule nucleation is mediated by locally increased tubulin concentrations.
J. Baumgart, M. Kirchner, S. Redemann, A. Bond, J. Woodruff, J.-M. Verbavatz, F. Jülicher,
T. Müller-Reichert, A. A. Hyman and J. Brugués
We discuss fluctuation theorems for non-equilibrium stochastic processes that follow from the Martingale property of the exponential of the stochastic entropy at stopping times. Our work reveals generic features of non-equilibrium processes.
I. Neri, E. Roldan, S. Pigolotti and F. Jülicher
Fluid filled lumen often form in tissues during development. They can serve as transport channels such as in the liver or the pancreas. Here we discuss the physical principles under-lying the nucleation of lumen in spherical cell assemblies. We show that in some regimes lumen nucleation is similar to classical nucleation theory. Surprisingly, we also find that tissue ferroelectricity, the coupling of bending to electric fields, can facilitate lumen nuclea-tion. Our results show that electro-hydraulic effects could play an important role in tissue morphogenesis.
C. Duclut, N. Sarkar, J. Prost and F. Jülicher
Using micropatterns of actin polymerization in vitro, we investigate stochastic transport of colloidal beads in antiparallel networks of overlapping actin filaments. A theoretical description of the system reveals the key physical rules for cargo transport and positioning in filament networks of mixed polarity.
M. Richard, C. Blanch-Mercader, H. Ennomani, W. Cao, E. M. De La Cruz J.-F. Joanny, F. Jülicher, L. Blanchoinc, and P. Martin
Three-dimensional tissues are amorphous arrangements of cells which can exhibit structural order that is linked to their function. Here, we investigate principles that underlie the organization of liver tissue. The liver has important metabolic functions that require transport networks of blood and bile that connect to liver cells. Here we show by quantifying cell polarity and cell nematics together with the morphology of transport networks that liver tissue has the organization of a nematic liquid crystal with large scale orientational order.
H. Morales-Navarrete, H. Nonaka, A. Scholich, F. Segovia-Miranda, W. de Back, K. Meyer, R. L. Bogorad, V. Koteliansky, L. Brusch, Y. Kalaidzidis, F. Jülicher, B. M. Friedrich, M. Zerial
Epithelia are sheet like tissue layers. Here we present a theoretical study of the dynamics of a thick polar epithelium that is subjected to the action of both an electric field and a hydrodynamic flow that permeates the tissue. We develop a generalized continuum hydrodynamic description and describe the tissue as a two-component fluid system. Considering a planar geometry, we find that finite thickness tissue layers exist only in a restricted region of phase space and that relatively modest electric fields or imposed external flows can induce either proliferation or death.
N. Sarkar, J. Prost and F. Jülicher
We study negative fluctuations of stochastic entropy production in an experimental system of a electronic double dot. The system operates at non-equilibrium steady-state conditions. We show that the average values of the minima of stochastic entropy production lie above the lower bound predicted by theory. We also extend our theory by deriving a general bound for the average value of the maximum heat absorbed by a mesoscopic system from the environment and compare this result with experimental data.
S. Singh, É. Roldán, I. Neri, I. M Khaymovich, D. S. Golubev, V. F. Maisi, J. T. Peltonen, F. Jülicher and J. P. Pekola
The metabolic rate of organisms varies with body mass. This dependence is well captured by a 3/4-power law scaling relation called Kleiber’s law. The physiological basis of Kleiber’s law are not understood. Here we show that the metabolic rate of flatworms obeys Kleiber’s law. In these animals Kleiber’s law does results from an increase of mass per cell with body mass but not from a decrease of metabolic rate per cell. An analysis of the energy balance combined with experiments shows that body size dependent energy stores are key to the emergence of Kleiber’s law in flatworms.
Biological form emerges from dynamic processes that couple chemical signals to active mechanical processes. Here we present a simple framework to study the mechanochemical self-organization of surfaces. Surface shape is governed by force and torque balances in the presence of active surface stresses. These stresses are themselves regulated by diffusing molecular species. Our work reveals general principles of the mechano-chemical self-organization of geometries.
We present a quantitative theory of cell polarity establishment. Our model accounts for the dynamics of flows and concentration profiles in the cell cortex that emerge from mechano-chemical self-organization. We show that this self-organized process is guided by symmetry breaking cues. This system provides a paradynamic example for an important class of pattern forming systems in biology.
We develop a method based on optical tweezers to study the frequency dependent rheology of micron sized droplets. We use this method to determine the rheology of protein condensates that serve as simple models for membraneless organelles in cells. Our work shows that protein condensates are visco-elastic fluids with a viscosity that strongly depends on salt concentration.
We consider a simple model of a closed polymer loop that is pinned at one point and is subject to an external force. We show that this model can be formally mapped to an asymmetric simple exclusion process. This link provides a link between the statistics of many particle systems and polymer physics. Our result can be applied to the dynamics of DNA loops under forcing.
Droplets which form by liquid-liquid phase separation from a solution can provide chemical compartments that localize chemical reactions in space. We consider a simple model of such chemically active droplets in which small colloidal particles are immersed. We show that chemical reactions can lead to a positioning of particles to the geometric center of the droplet. Our work is relevant to the centering of centrioles inside centrosomes of cells.
We investigate the process by which a flat sheet of cells can undergo a shape change that leads to the formation of a fold in the tissue. Using a combination of experiments and theory we focus on folds that form in the developing fly wing tissue. Our work reveals that a localized reduction of contractile tension on the basal side of the tissue is a key mechanism for fold formation. Furthermore, an increase in lateral contractile tension provides a second mechanism. Our combination of lateral and basal tension estimates with a mechanical tissue model reveals how simple modulations of surface and edge tension drive complex three-dimensional morphological changes.
Chemically active droplets provide simple models for protocells. They are maintained away from thermodynamic equilibrium, they take up material, turn over my chemical processes and release reaction products. Most interestingly, they can spontaneously divide and undergo cycles of growth and division. Here, we study the role of hydrodynamic flows for the shape changes and division of chemically active droplets. Our work shows that hydrodynamic flows tends to stabilize spherical shapes and that droplet division occurs for sufficiently strong chemical driving, sufficiently large droplet viscosity or sufficiently small surface tension.
We investigate how the positions of a condensed phase can be controlled by using concentration gradients of a regulator that influences phase separation. We find a novel first order phase transition at which the position of the condensed phase switches in a discontinuous manner. This mechanism could have implications for the spatial organisation of biological cells and provides a control mechanism for droplets in microfluidic systems.
We present a theory of growth control inspired by biological tissues during development. We identify a critical point of the feedback dynamics where a graded profile of a secreted molecule regulates growth. At this critical point, growth is spatially homogeneous and concentration profiles exhibit exact scaling with size. We propose that the observed approximate growth homogeneity and scaling in the fly wing imaginal disk are signatures of this critical point.
We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We study the quality of noisy oscilations in different parameter regimes. we show that key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.
We present a stochastic differential equation for the time evolution of entropy in Langevin processes. We show that entropy fluctuation exhibit universal properties which are a conse-quence of a simple stochastic time transformation.
Active matter is driven at molecular scales away from thermodynamic equilibrium by energy transfusing processes. The theory of bulk active matter is well developed and reveals uncon-ventional material properties and the emergence of active stresses. Here we study active matter that is organised in thin films or sheets that are embedded in three dimensional space. We derive a general theory of the mechanics and the material properties of active surfaces that can account for the interplay of active mechanics and surface deformations.