Showing papers by "Frank Jülicher published in 2016"

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

Abstract: Cilia and flagella are model systems for studying how mechanical forces control morphology. The periodic bending motion of cilia and flagella is thought to arise from mechanical feedback: dynein motors generate sliding forces that bend the flagellum, and bending leads to deformations and stresses, which feed back and regulate the motors. Three alternative feedback mechanisms have been proposed: regulation by the sliding forces, regulation by the curvature of the flagellum, and regulation by the normal forces that deform the cross-section of the flagellum. In this work, we combined theoretical and experimental approaches to show that the curvature control mechanism is the one that accords best with the bending waveforms of Chlamydomonas flagella. We make the surprising prediction that the motors respond to the time derivative of curvature, rather than curvature itself, hinting at an adaptation mechanism controlling the flagellar beat.

TissueMiner: A multiscale analysis toolkit to quantify how cellular processes create tissue dynamics

Abstract: Cells interact, divide, rearrange and change shape to build an organ during development. Modern microscopy and computer technology can follow each individual cell of an entire organ in a living organism. However, to understand how the complex choreography of cells leads to well-shaped organs, researchers need tools to help the store and analyze the large amounts of data generated. Tools are also needed to visualize and quantify the complex cell behaviors in an easy and flexible manner. During its development, a fruit fly’s wings become divided into distinct regions separated by tubular supports called veins. Early on in development, the vein cells are indistinguishable from their neighbors, but at late stages, vein cells become a different shape. Veins also become narrower, which is assumed to be due to the number of vein cells falling. However, the way in which cells behave to bring about these changes has not been studied in detail. Etournay, Merkel, Popovic, Brandl et al. have now developed a toolkit called TissueMiner that enables users to store large amounts of data about cells and analyze how cells collectively shape an organ. TissueMiner was then used to identify vein cells at late stages of wing development and follow them backward in time to reveal their position at early stages. This showed that veins become narrower and more elongated because the cells that make up the veins shrink more than cells in other regions. TissueMiner was then used to show that vein cells specifically rearrange and elongate to produce thinner regions, while the number of cells increases slightly because the cells divide. These results suggest that the cell behaviors responsible for making veins elongate and narrow are likely to be different from what had previously been assumed. TissueMiner can be used in future studies to help understand the molecule signals that influence how cells behave in veins during wing development. The toolkit could also now be used to explore the changes involved in the development of other organs in other organisms.

Persistence, period and precision of autonomous cellular oscillators from the zebrafish segmentation clock

Abstract: In vertebrate development, the sequential and rhythmic segmentation of the body axis is regulated by a "segmentation clock". This clock is comprised of a population of coordinated oscillating cells that together produce rhythmic gene expression patterns in the embryo. Whether individual cells autonomously maintain oscillations, or whether oscillations depend on signals from neighboring cells is unknown. Using a transgenic zebrafish reporter line for the cyclic transcription factor Her1, we recorded single tailbud cells in vitro. We demonstrate that individual cells can behave as autonomous cellular oscillators. We described the observed variability in cell behavior using a theory of generic oscillators with correlated noise. Single cells have longer periods and lower precision than the tissue, highlighting the role of collective processes in the segmentation clock. Our work reveals a population of cells from the zebrafish segmentation clock that behave as self-sustained, autonomous oscillators with distinctive noisy dynamics.

Correction: Corrigendum: Paired arrangement of kinetochores together with microtubule pivoting and dynamics drive kinetochore capture in meiosis I

Abstract: Scientific Reports 6: Article number: 25736; published online: 11 May 2016; updated: 22 September 2016 In this Article, the Acknowledgments section is incomplete. “We thank M. Sato, S. Hauf, G. Rodel and the Yeast Genetic Resource Center for strains and plasmids; B. Schroth-Diez, Bert Nitzsche and Jan Peychl from the Light Microscopy Facility of MPI-CBG; V.

Statistics of Infima and Stopping Times of Entropy Production and Applications to Active Molecular Processes

Abstract: We study the statistics of infima, stopping times and passage probabilities of entropy production in nonequilibrium steady states, and show that they are universal. We consider two examples of stopping times: first-passage times of entropy production and waiting times of stochastic processes, which are the times when a system reaches for the first time a given state. Our main results are: (i) the distribution of the global infimum of entropy production is exponential with mean equal to minus Boltzmann's constant; (ii) we find the exact expressions for the passage probabilities of entropy production to reach a given value; (iii) we derive a fluctuation theorem for stopping-time distributions of entropy production. These results have interesting implications for stochastic processes that can be discussed in simple colloidal systems and in active molecular processes. In particular, we show that the timing and statistics of discrete chemical transitions of molecular processes, such as, the steps of molecular motors, are governed by the statistics of entropy production. We also show that the extreme-value statistics of active molecular processes are governed by entropy production, for example, the infimum of entropy production of a motor can be related to the maximal excursion of a motor against the direction of an external force. Using this relation, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases, which follows from our universal results for entropy-production infima.

Polo-like kinase phosphorylation determines Caenorhabditis elegans centrosome size and density by biasing SPD-5 toward an assembly-competent conformation.

Abstract: Centrosomes are major microtubule-organizing centers composed of centrioles surrounded by an extensive proteinacious layer called the pericentriolar material (PCM). In Caenorhabditis elegans embryos, the mitotic PCM expands by Polo-like kinase 1 (PLK-1) phosphorylation-accelerated assembly of SPD-5 molecules into supramolecular scaffolds. However, how PLK-1 phosphorylation regulates SPD-5 assembly is not known. We found that a mutant version of SPD-5 that is insensitive to PLK-1 phosphorylation (SPD-54A) could localize to PCM but was unable to rescue the reduction in PCM size and density when wild-type SPD-5 levels were decreased. In vitro, purified SPD-54A self-assembled into functional supramolecular scaffolds over long time scales, suggesting that phosphorylation only controls the rate of SPD-5 scaffold assembly. Furthermore, the SPD-5 scaffold, once assembled, remained intact and supported microtubule nucleation in the absence of PLK-1 activity in vivo We conclude that PLK-1 is required for rapid assembly of the PCM scaffold but not for scaffold maintenance or function. Based on this idea, we developed a theoretical model that adequately predicted PCM growth rates in different mutant conditions in vivo We propose that PLK-1 phosphorylation-dependent conversion of SPD-5 into an assembly-competent form underlies PCM formation in vivo and that the rate of this conversion determines final PCM size and density.

Autonomous Chemical Oscillator Circuit Based on Bidirectional Chemical-Microfluidic Coupling

Abstract: DOI: 10.1002/admt.201600005 The mechanical microfl uidic oscillators developed by Mosadegh et al. [ 3 ] are relaxation oscillators (akin to astable multivibrators in electronics) based on two fi eld-effect-type valves and two membranes acting as compliances. The oscillators have been used to control subordinate fl uid circuits, [ 3 ] to analyze endothelial cell elongation, [ 5 ] and to deliver temporally patterned chemical concentration profi les to living cells. [ 4 ] It was also shown that four independent oscillators on a single chip with periods between 0.4 and 2 h could be operated in parallel, purely driven by gravity. [ 5 ] A different approach for a mechanical microfl uidic oscillator based on a simple setup with a single overshooting elastic diaphragm was shown by Xia et al. [ 6,7 ] The device produces fast stable oscillations with a period of about 10 ms with a limited frequency tunability of about 30%. Though frequencies in this range are ideal for rapid fl ow mixing, they are much too fast compared to many chemical or biological processes. Both microfl uidic oscillators discussed can be used to transport reagents, but they are not themselves responsive to chemical concentrations. Autonomous oscillators are a key component of signal processing systems in electronics and biology. [ 1,2 ] The development of oscillators that couple chemical or biological systems with the mechanical domain of microfl uidics could stimulate novel concepts for the “smart” handling of fl uids and their ingredients. In technology, the realization of chemical oscillators is challenging, in contrast to electronic oscillators. Recently, the construction of microfl uidic oscillators has been demonstrated. [ 3–7 ]

Curvature regulation of the ciliary beat through axonemal twist

Abstract: Cilia and flagella are hairlike organelles that propel cells through fluid. The active motion of the axoneme, the motile structure inside cilia and flagella, is powered by molecular motors of the axonemal dynein family. These motors generate forces and torques that slide and bend the microtubule doublets within the axoneme. To create regular waveforms, the activities of the dyneins must be coordinated. It is thought that coordination is mediated by stresses due to radial, transverse, or sliding deformations, and which build up within the moving axoneme and feed back on dynein activity. However, which particular components of the stress regulate the motors to produce the observed waveforms of the many different types of flagella remains an open question. To address this question, we describe the axoneme as a three-dimensional bundle of filaments and characterize its mechanics. We show that regulation of the motors by radial and transverse stresses can lead to a coordinated flagellar motion only in the presence of twist. We show that twist, which could arise from torque produced by the dyneins, couples curvature to transverse and radial stresses. We calculate emergent beating patterns in twisted axonemes resulting from regulation by transverse stresses. The resulting waveforms are similar to those observed in flagella of Chlamydomonas and sperm. Due to the twist, the waveform has nonplanar components, which result in swimming trajectories such as twisted ribbons and helices, which agree with observations.

Interface dynamics of competing tissues

Abstract: Tissues can be characterized by their homeostatic stress, i.e. the value of stress for which cell division and cell death balance. When two different tissues grow in competition, a difference of their homeostatic stresses determines which tissue grows at the expense of the second. This then leads to the propagation of the interface separating the tissues. Here, we study structural and dynamical properties of this interface by combining continuum theory with mesoscopic simulations of a cell-based model. Using a simulation box that moves with the interface, we find that a stationary state exists in which the interface has a finite width and propagates with a constant velocity. The propagation velocity in the simulations depends linearly on the homeostatic stress difference, in excellent agreement with the analytical predictions. This agreement is also seen for the stress and velocity profiles. Finally, we analyzed the interface growth and roughness as a function of time and system size. We estimated growth and roughness exponents, which differ from those previously obtained for simple tissue growth.

Activity induces traveling waves, vortices and spatiotemporal chaos in a model actomyosin layer

Abstract: Inspired by the actomyosin cortex in biological cells, we investigate the spatiotemporal dynamics of a model describing a contractile active polar fluid sandwiched between two external media. The external media impose frictional forces at the interface with the active fluid. The fluid is driven by a spatially-homogeneous activity measuring the strength of the active stress that is generated by processes consuming a chemical fuel. We observe that as the activity is increased over two orders of magnitude the active polar fluid first shows spontaneous flow transition followed by transition to oscillatory dynamics with traveling waves and traveling vortices in the flow field. In the flow-tumbling regime, the active polar fluid also shows transition to spatiotemporal chaos at sufficiently large activities. These results demonstrate that level of activity alone can be used to tune the operating point of actomyosin layers with qualitatively different spatiotemporal dynamics.

Active dynamics of tissue shear flow

Abstract: We present a hydrodynamic theory to describe shear flows in developing epithelial tissues. We introduce hydrodynamic fields corresponding to state properties of constituent cells as well as a contribution to overall tissue shear flow due to rearrangements in cell network topology. We then construct a generic linear constitutive equation for the shear rate due to topological rearrangements and we investigate a novel rheological behaviour resulting from memory effects in the tissue. We identify two distinct active cellular processes: generation of active stress in the tissue, and actively driven topological rearrangements. We find that these two active processes can produce distinct cellular and tissue shape changes, depending on boundary conditions applied on the tissue. Our findings have consequences for the understanding of tissue morphogenesis during development.

Hydrodynamic theory of tissue shear flow

Abstract: We present a hydrodynamic theory to describe shear flows in developing epithelial tissues. We introduce hydrodynamic fields corresponding to state properties of constituent cells as well as a contribution to overall tissue shear flow due to rearrangements in cell network topology. We then construct a generic linear constitutive equation for the shear rate due to topological rearrangements and we investigate a novel rheological behaviour resulting from memory effects in the tissue. We identify two distinct active cellular processes: generation of active stress in the tissue, and actively driven topological rearrangements. We find that these two active processes can produce distinct cellular and tissue shape changes, depending on boundary conditions applied on the tissue. Our findings have consequences for the understanding of tissue morphogenesis during development.

Sequential pattern formation governed by signaling gradients.

Abstract: Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the interplay of cell oscillations with tissue elongation and shortening and with signaling gradients, is still missing. Here we show that a set of coupled genetic oscillators in an elongating tissue that is regulated by diffusing and advected signaling molecules can account for segmentation as a self-organized patterning process. This system can form a finite number of segments and the dynamics of segmentation and the total number of segments formed depend strongly on kinetic parameters describing tissue elongation and signaling molecules. The model accounts for existing experimental perturbations to signaling gradients, and makes testable predictions about novel perturbations. The variety of different patterns formed in our model can account for the variability of segmentation between different animal species.

The Selector Gene apterous and Notch Are Required to Locally Increase Mechanical Cell Bond Tension at the Drosophila Dorsoventral Compartment Boundary

Abstract: The separation of cells with distinct fates and functions is important for tissue and organ formation during animal development. Regions of different fates within tissues are often separated from another along straight boundaries. These compartment boundaries play a crucial role in tissue patterning and growth by stably positioning organizers. In Drosophila, the wing imaginal disc is subdivided into a dorsal and a ventral compartment. Cells of the dorsal, but not ventral, compartment express the selector gene apterous. Apterous expression sets in motion a gene regulatory cascade that leads to the activation of Notch signaling in a few cell rows on either side of the dorsoventral compartment boundary. Both Notch and apterous mutant clones disturb the separation of dorsal and ventral cells. Maintenance of the straight shape of the dorsoventral boundary involves a local increase in mechanical tension at cell bonds along the boundary. The mechanisms by which cell bond tension is locally increased however remain unknown. Here we use a combination of laser ablation of cell bonds, quantitative image analysis, and genetic mutants to show that Notch and Apterous are required to increase cell bond tension along the dorsoventral compartment boundary. Moreover, clonal expression of the Apterous target gene capricious results in cell separation and increased cell bond tension at the clone borders. Finally, using a vertex model to simulate tissue growth, we find that an increase in cell bond tension at the borders of cell clones, but not throughout the cell clone, can lead to cell separation. We conclude that Apterous and Notch maintain the characteristic straight shape of the dorsoventral compartment boundary by locally increasing cell bond tension.

Paired arrangement of kinetochores together with microtubule pivoting and dynamics drive kinetochore capture in meiosis I

Abstract: Kinetochores are protein complexes on the chromosomes, whose function as linkers between spindle microtubules and chromosomes is crucial for proper cell division The mechanisms that facilitate kinetochore capture by microtubules are still unclear In the present study, we combine experiments and theory to explore the mechanisms of kinetochore capture at the onset of meiosis I in fission yeast We show that kinetochores on homologous chromosomes move together, microtubules are dynamic and pivot around the spindle pole, and the average capture time is 3-4 minutes Our theory describes paired kinetochores on homologous chromosomes as a single object, as well as angular movement of microtubules and their dynamics For the experimentally measured parameters, the model reproduces the measured capture kinetics and shows that the paired configuration of kinetochores accelerates capture, whereas microtubule pivoting and dynamics have a smaller contribution Kinetochore pairing may be a general feature that increases capture efficiency in meiotic cells

Triangles bridge the scales: how cellular processes cause tissue deformation

Abstract: In this article, we propose a general framework to study the dynamics and topology of cellular networks that capture the geometry of cell packings in two-dimensional tissues. Such epithelia undergo large-scale deformation during morphogenesis of a multicellular organism. Large-scale deformations emerge from many individual cellular events such as cell shape changes, cell rearrangements, cell divisions, and cell extrusions. Using a triangle-based representation of cellular network geometry, we obtain an exact decomposition of large-scale material deformation. Interestingly, our approach reveals contributions of correlations between cellular rotations and elongation as well as cellular growth and elongation to tissue deformation. Using this Triangle Method, we discuss tissue remodeling in the developing pupal wing of the fly Drosophila melanogaster.

Infimum Law and First-Passage-Time Fluctuation Theorem for Entropy Production

Abstract: We derive an infimum law and a first-passage-time fluctuation theorem for entropy production of stochastic processes at steady state. We show that the ratio between the probability densities of the first-passage time to produce $S_{\rm tot}$ of entropy and of the first-passage time to produce $-S_{\rm tot}$ of entropy equals $e^{S_{\rm tot}/k}$, with $k$ Boltzmann's constant. This first-passage-time fluctuation relation is valid for processes with one or higher order passages. In addition, we derive universal bounds for the infimum statistics of entropy production using the fact that at steady state $e^{-S_{\rm tot}/k}$ is a martingale process. We show that the mean value of the entropy-production infimum obeys $\langle{\rm inf}\:S_{\rm tot}\rangle\geq -k$ and derive a bound on the cumulative distribution of entropy-production infima. Our results are derived using a measure-theoretic formalism of stochastic thermodynamics. We illustrate our results with a drift-diffusion process and with numerical simulations of a Smoluchowski-Feynman ratchet.

Polo kinase phosphorylation determines C. elegans centrosome size and density by biasing SPD-5 toward an assembly-competent conformation

Abstract: Centrosomes are major microtubule-organizing centers composed of centrioles surrounded by an extensive proteinacious layer called the pericentriolar material (PCM). In C. elegans embryos, the mitotic PCM expands by Polo-kinase (PLK-1) phosphorylation-accelerated assembly of SPD-5 molecules into supramolecular scaffolds. However, how PLK-1 phosphorylation regulates SPD-5 assembly is not known. We found that a mutant version of SPD-5 that is insensitive to PLK-1 phosphorylation (SPD-54A) could localize to PCM but was unable to rescue the reduction in PCM size and density when wild-type SPD-5 levels were decreased. In vitro, purified SPD-54A self-assembled into functional supramolecular scaffolds over long time scales, suggesting that phosphorylation only controls the rate of SPD-5 scaffold assembly. Furthermore, the SPD-5 scaffold, once assembled, remained intact and supported microtubule nucleation in the absence of PLK-1 activity in vivo. We conclude that Polo Kinase is required for rapid assembly of the PCM scaffold but not for scaffold maintenance or function. Based on this idea, we developed a theoretical model that adequately predicted PCM growth rates in different mutant conditions in vivo. We propose that PLK-1 phosphorylation-dependent conversion of SPD-5 into an assembly-competent form underlies PCM formation in vivo and that the rate of this conversion determines final PCM size and density.

Theory of Cargo and Membrane Trafficking

Abstract: Endocytosis underlies many cellular functions including signaling and nutrient uptake. The endocytosed cargo gets redistributed across a dynamic network of endosomes undergoing fusion and fission. Here, a theoretical approach is reviewed which can explain how the microscopic properties of endosome interactions cause the emergent macroscopic properties of cargo trafficking in the endosomal network. The theory has been tested experimentally. Parameters of the microscopic processes and their dependencies on endosome properties have been quantified for specific experimental conditions. This theory could also be used to infer mechanisms of signal-trafficking crosstalk. It is applicable to in vivo systems since fixed samples at few time points suffice as input data.

Sequential pattern formation governed by signaling gradients

Abstract: Rhythmic and sequential segmentation of the embryonic body plan is a vital developmental patterning process in all vertebrate species. However, a theoretical framework capturing the emergence of dynamic patterns of gene expression from the interplay of cell oscillations with tissue elongation and shortening and with signaling gradients, is still missing. Here we show that a set of coupled genetic oscillators in an elongating tissue that is regulated by diffusing and advected signaling molecules can account for segmentation as a self-organized patterning process. This system can form a finite number of segments and the dynamics of segmentation and the total number of segments formed depend strongly on kinetic parameters describing tissue elongation and signaling molecules. The model accounts for existing experimental perturbations to signaling gradients, and makes testable predictions about novel perturbations. The variety of different patterns formed in our model can account for the variability of segmentation between different animal species.