Showing papers by "Frank Jülicher published in 2015"

Active gel physics

Abstract: The mechanical behaviour of cells is largely controlled by a structure that is fundamentally out of thermodynamic equilibrium: a network of crosslinked filaments subjected to the action of energy-transducing molecular motors. The study of this kind of active system was absent from conventional physics and there was a need for both new theories and new experiments. The field that has emerged in recent years to fill this gap is underpinned by a theory that takes into account the transduction of chemical energy on the molecular scale. This formalism has advanced our understanding of living systems, but it has also had an impact on research in physics per se. Here, we describe this developing field, its relevance to biology, the novelty it conveys to other areas of physics and some of the challenges in store for the future of active gel physics. Equilibrium physics is ill-equipped to explain all of life’s subtleties, largely because living systems are out of equilibrium. Attempts to overcome this problem have given rise to a lively field of research—and some surprising biological findings.

Interplay of cell dynamics and epithelial tension during morphogenesis of the Drosophila pupal wing.

Abstract: The individual cells in a developing animal embryo organize themselves into tissues with specific and reproducible shapes, which requires the cells to communicate with one another. Cells in tissues exert forces on their neighbors, and respond to being pushed and pulled by the cells around them. In the fruit fly Drosophila melanogaster, each wing consists mainly of a framework of proteins and other molecules that is built by epithelial cells. These epithelial cells divide and grow during the life of a fly larva, and then reorganize themselves into the shape of the wing after it forms into a pupa. During this reshaping, epithelial cells in some regions of the wing experience powerful contractions. Previous work had suggested that and these forces produced tension in the rest of the wing to pull it into its final elongated shape. But it wasn't clear what exactly these contractions were pulling against to produce the tension. Nor was it understood exactly how wing epithelial cells responded to tension to reorganize themselves into a different wing shape. Now, Etournay, Popovic, Merkel, Nandi et al. have analyzed the forces acting across the entire wing blade and how these forces shape the wing. All cell divisions, cell neighbor exchanges and changes in cell shape in the developing wing blade were tracked under a microscope; this revealed how each one of them contributed to the change in wing shape. Further experiments revealed that localized contractile forces produce tension in the wing because it is connected around its edge to surrounding structures via an extracellular protein called Dumpy. Releasing these contacts, by severing them with a laser or by mutating Dumpy, caused the wing to develop into abnormal shapes, showing that the tension in the wing blade has an important role in determining wing shape. Furthermore, by tracking cells in wings that had been severed by a laser, or mutated for Dumpy Etournay, Popovic, Merkel, Nandi et al. could figure out exactly which cellular processes were guided by epithelial tension. Etournay Popovic, Merkel, Nandi et al. also present a theoretical model that describes how the interplay between active force generation and the response of cells to the resulting tension shapes the wings of fruit flies. They propose that epithelial tension provides a mechanism through which cells can communicate with each other to ensure that together the combined behavior of these cells generates reproducible shapes. Further studies are required to analyze how active force generation is patterned and cells sense and respond to external forces during development.

Quantification of surface tension and internal pressure generated by single mitotic cells

Abstract: During mitosis, adherent cells round up, by increasing the tension of the contractile actomyosin cortex while increasing the internal hydrostatic pressure. In the simple scenario of a liquid cell interior, the surface tension is related to the local curvature and the hydrostatic pressure difference by Laplace's law. However, verification of this scenario for cells requires accurate measurements of cell shape. Here, we use wedged micro-cantilevers to uniaxially confine single cells and determine confinement forces while concurrently determining cell shape using confocal microscopy. We fit experimentally measured confined cell shapes to shapes obeying Laplace's law with uniform surface tension and find quantitative agreement. Geometrical parameters derived from fitting the cell shape and the measured force were used to calculate hydrostatic pressure excess and surface tension of cells. We find that HeLa cells increase their internal hydrostatic pressure excess and surface tension from ≈ 40 Pa and 0.2 mNm−1 during interphase to ≈ 400 Pa and 1.6 mNm−1 during metaphase. The method introduced provides a means to determine internal pressure excess and surface tension of rounded cells accurately and with minimal cellular perturbation and should be applicable to characterize the mechanical properties of various cellular systems.

Suppression of Ostwald ripening in active emulsions

Abstract: Emulsions consisting of droplets immersed in a fluid are typically unstable since they coarsen over time. One important coarsening process is Ostwald ripening, which is driven by the surface tension of the droplets. Stability of emulsions is relevant not only in complex fluids but also in biological cells, which contain liquidlike compartments, e.g., germ granules, Cajal bodies, and centrosomes. Such cellular systems are driven away from equilibrium, e.g., by chemical reactions, and thus can be called active emulsions. In this paper, we study such active emulsions by developing a coarse-grained description of the droplet dynamics, which we analyze for two different chemical reaction schemes. We first consider the simple case of first-order reactions, which leads to stable, monodisperse emulsions in which Ostwald ripening is suppressed within a range of chemical reaction rates. We then consider autocatalytic droplets, which catalyze the production of their own droplet material. Spontaneous nucleation of autocatalytic droplets is strongly suppressed and their emulsions are typically unstable. We show that autocatalytic droplets can be nucleated reliably and their emulsions stabilized by the help of chemically active cores, which catalyze the production of droplet material. In summary, different reaction schemes and catalytic cores can be used to stabilize emulsions and to control their properties.

Polarized endosome dynamics by spindle asymmetry during asymmetric cell division

Abstract: During asymmetric division, fate determinants at the cell cortex segregate unequally into the two daughter cells. It has recently been shown that Sara (Smad anchor for receptor activation) signalling endosomes in the cytoplasm also segregate asymmetrically during asymmetric division. Biased dispatch of Sara endosomes mediates asymmetric Notch/Delta signalling during the asymmetric division of sensory organ precursors in Drosophila. In flies, this has been generalized to stem cells in the gut and the central nervous system, and, in zebrafish, to neural precursors of the spinal cord. However, the mechanism of asymmetric endosome segregation is not understood. Here we show that the plus-end kinesin motor Klp98A targets Sara endosomes to the central spindle, where they move bidirectionally on an antiparallel array of microtubules. The microtubule depolymerizing kinesin Klp10A and its antagonist Patronin generate central spindle asymmetry. This asymmetric spindle, in turn, polarizes endosome motility, ultimately causing asymmetric endosome dispatch into one daughter cell. We demonstrate this mechanism by inverting the polarity of the central spindle by polar targeting of Patronin using nanobodies (single-domain antibodies). This spindle inversion targets the endosomes to the wrong cell. Our data uncover the molecular and physical mechanism by which organelles localized away from the cellular cortex can be dispatched asymmetrically during asymmetric division.

Decision Making in the Arrow of Time

Abstract: We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore, the steady-state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.

Scaling and Regeneration of Self-Organized Patterns

Abstract: A modification to the classical Turing pattern mechanism is proposed to address body plan regeneration in flatworms. In particular, how these spontaneously forming patterns automatically and reliably adjust to animal size ensuring only one head forms.

Continuum theory of gene expression waves during vertebrate segmentation

Abstract: The segmentation of the vertebrate body plan during embryonic development is a rhythmic and sequential process governed by genetic oscillations. These genetic oscillations give rise to traveling waves of gene expression in the segmenting tissue. Here we present a minimal continuum theory of vertebrate segmentation that captures the key principles governing the dynamic patterns of gene expression including the effects of shortening of the oscillating tissue. We show that our theory can quantitatively account for the key features of segmentation observed in zebrafish, in particular the shape of the wave patterns, the period of segmentation and the segment length as a function of time.

A local difference in Hedgehog signal transduction increases mechanical cell bond tension and biases cell intercalations along the Drosophila anteroposterior compartment boundary.

Abstract: Tissue organization requires the interplay between biochemical signaling and cellular force generation. The formation of straight boundaries separating cells with different fates into compartments is important for growth and patterning during tissue development. In the developing Drosophila wing disc, maintenance of the straight anteroposterior (AP) compartment boundary involves a local increase in mechanical tension at cell bonds along the boundary. The biochemical signals that regulate mechanical tension along the AP boundary, however, remain unknown. Here, we show that a local difference in Hedgehog signal transduction activity between anterior and posterior cells is necessary and sufficient to increase mechanical tension along the AP boundary. This difference in Hedgehog signal transduction is also required to bias cell rearrangements during cell intercalations to keep the characteristic straight shape of the AP boundary. Moreover, severing cell bonds along the AP boundary does not reduce tension at neighboring bonds, implying that active mechanical tension is upregulated, cell bond by cell bond. Finally, differences in the expression of the homeodomain-containing protein Engrailed also contribute to the straight shape of the AP boundary, independently of Hedgehog signal transduction and without modulating cell bond tension. Our data reveal a novel link between local differences in Hedgehog signal transduction and a local increase in active mechanical tension of cell bonds that biases junctional rearrangements. The large-scale shape of the AP boundary thus emerges from biochemical signals inducing patterns of active tension on cell bonds.

Dynamic force balances and cell shape changes during cytokinesis.

Abstract: During the division of animal cells, an actomyosin ring is formed in the cell cortex. The contraction of this ring induces shape changes of the cell and the formation of a cytokinesis furrow. In many cases, a cell-cell interface forms that separates the two new cells. Here we present a simple physical description of the cell shape changes and the dynamics of the interface closure, based on force balances involving active stresses and viscous friction. We discuss conditions in which the interface closure is either axially symmetric or asymmetric. We show that our model can account for the observed dynamics of ring contraction and interface closure in the C. elegans embryo.

Pulled Polymer Loops as a Model for the Alignment of Meiotic Chromosomes.

Abstract: During recombination, the DNA of parents exchange their genetic information to give rise to a genetically unique offspring. For recombination to occur, homologous chromosomes need to find each other and align with high precision. Fission yeast solves this problem by folding chromosomes in loops and pulling them through the viscous nucleoplasm. We propose a theory of pulled polymer loops to quantify the effect of drag forces on the alignment of chromosomes. We introduce an external force field to the concept of a Brownian bridge and thus solve for the statistics of loop configurations in space.

The wing and the eye: a parsimonious theory for scaling and growth control?

Abstract: How a developing organ grows and patterns to its final shape is an important question in developmental biology. Studies of growth and patterning in the Drosophila wing imaginal disc have identified a key player, the morphogen Decapentaplegic (Dpp). These studies provided insights into our understanding of growth control and scaling: expansion of the Dpp gradient correlated with the growth of the tissue. A recent report on growth of a Drosophila organ other than the wing, the eye imaginal disc, prompts a reconsideration of our models of growth control. Despite striking differences between the two, the Dpp gradient scales with the target tissues of both organs and the growth of both the wing and the eye is controlled by Dpp. The goal of this review is to discuss whether a parsimonious model of scaling and growth control can explain the relationship between the Dpp gradient and growth in these two different developmental systems.

Synchronization of mutually coupled digital PLLs in massive MIMO systems

Abstract: For next-generation wireless networks, massive multiple-input multiple-output (MIMO) promises significant performance gains compared to today's wireless communication standards. In this paper, we address the challenge of how to synchronize the carrier signals of all antenna units in a large network. We show that mutually coupled digital phase-locked loops (DPLLs) can enable in-phase synchronous clocking in largescale systems with transmission delay. Using a phase model of coupled DPLLs including signal filtering and signal transmission delays, we show how the collective frequency and the time scales of synchronization depend on system specifications. To test our theoretical predictions, we designed and carried out experiments, thereby providing a proof-of-principle that mutually delay-coupled DPLLs can provide self-organized synchronous clocking.

Information Density and Optimality of Sequential Decision-Making

Abstract: We provide an information theoretic analysis of Wald's sequential probability ratio test. The optimality of the Wald test in the sense that it yields the minimum average decision time for a binary decision problem is reflected by the evolution of the information densities over time. Information densities are considered as they take into account the fact that the termination time of the Wald test depends on the actual realization of the observation sequence. Based on information densities we show that in case the test terminates at time instant $k$ the probability to decide for hypothesis $\mathcal{H}_1$ (or the counter-hypothesis $\mathcal{H}_0$) is independent of time. We use this characteristic to evaluate the evolution of the mutual information between the binary random variable and the decision variable of the Wald test. Our results establish a connection between minimum mean decision times and the corresponding information processing.

Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella

Abstract: Axonemal dyneins are the molecular motors responsible for the beating of cilia and flagella. These motors generate sliding forces between adjacent microtubule doublets within the axoneme, the motile cytoskeletal structure inside the flagellum. To create regular, oscillatory beating patterns, the activities of the axonemal dyneins must be coordinated both spatially and temporally. It is thought that coordination is mediated by stresses or strains that build up within the moving axoneme, but it is not known which components of stress or strain are involved, nor how they feed back on the dyneins. To answer this question, we used isolated, reactivate axonemes of the unicellular alga Chlamydomonas as a model system. We derived a theory for beat regulation in a two-dimensional model of the axoneme. We then tested the theory by measuring the beat waveforms of wild type axonemes, which have asymmetric beats, and mutant axonemes, in which the beat is nearly symmetric, using high-precision spatial and temporal imaging. We found that regulation by sliding forces fails to account for the measured beat, due to the short lengths of Chlamydomonas cilia. We found that regulation by normal forces (which tend to separate adjacent doublets) cannot satisfactorily account for the symmetric waveforms of the mbo2 mutants. This is due to the model's failure to produce reciprocal inhibition across the axes of the symmetrically beating axonemes. Finally, we show that regulation by curvature accords with the measurements. Unexpectedly, we found that the phase of the curvature feedback indicates that the dyneins are regulated by the dynamic (i.e. time-varying) component of axonemal curvature, but not by the static one. We conclude that a high-pass filtered curvature signal is a good candidate for the signal that feeds back to coordinate motor activity in the axoneme.

An Information Theoretic Analysis of Sequential Decision-Making

Abstract: We provide a novel analysis of Wald's sequential probability ratio test based on information theoretic measures for symmetric thresholds, symmetric noise, and equally likely hypotheses under the assumption that the test exactly terminates at one of the thresholds. This test is optimal in the sense that it yields the minimum mean decision time. To analyze the decision-making process we consider information densities, which represent the stochastic information content of the observations yielding a stochastic termination time of the test. Based on this, we show that the conditional probability to decide for hypothesis $\mathcal{H}_1$ (or the counter-hypothesis $\mathcal{H}_0$) given that the test terminates at time instant $k$ is independent of time $k$. An analogous property has been found for a continuous-time first passage problem with two absorbing boundaries in the contexts of non-equilibrium statistical physics and communication theory. Moreover, we study the evolution of the mutual information between the binary variable to be tested and the output of the Wald test. Notably, we show that the decision time of the Wald test contains no information on which hypothesis is true beyond the decision outcome.

Hair-Bundle Friction from Transduction Channels' Gating Forces

Abstract: Hearing starts when sound-evoked mechanical vibrations of the hair-cell bundle activate mechanosensitive ion channels, giving birth to an electrical signal. As for any mechanical system, friction impedes movements of the hair bundle and thus constrains the sensitivity and frequency selectivity of auditory transduction. We have shown recently that the opening and closing of the transduction channels produce internal frictional forces that can dominate viscous drag on the micrometer-sized hair bundle and thus provide a major source of damping [2]. We develop here a physical theory of passive hair-bundle mechanics that explains the origin of channel friction. We show that channel friction can be understood quantitatively by coupling the dynamics of the conformational change associated with channel gating to tip-link tension. As a result, varying channel properties affects friction, with faster channels producing smaller friction. The analysis emphasizes the dual role of transduction channels’ gating forces, which affect both hair-bundle stiffness and drag. Friction originating from gating of ion channels is a general concept that is relevant to all mechanosensitive channels.

Spontaneous otoacoustic emissions in an active nonlinear cochlear model in the time domain

Abstract: A large fraction of human cochleas emits sounds even in the absence of external stimulation. These so-called spontaneous otoacoustic emissions (SOAEs) are a hallmark of the active nonlinear amplification process taking place in the cochlea. Here, we extend a previously proposed frequency domain model and put forward an active nonlinear one-dimensional model of the cochlea in the time domain describing human SOAEs [5]. In our model, oscillatory elements are close to an instability (Hopf bifurcation), they are subject to dynamical noise and coupled by hydrodynamic, elastic and dissipative interactions. Furthermore, oscillators are subject to a weak spatial irregularity in their activity (normally distributed and exponentially correlated in space) that gives rise to the individuality of each simulated cochlea. Our model captures main statistical features of the distribution of emission frequencies, the distribution of the numbers of emissions per cochlea, and the distribution of the distances between neighboring emissions as were previously measured in experiment [14].