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Animal cells are shaped by a thin layer of actin filaments underneath the plasma membrane known as the actin cortex. This cortex stiffens the cell surface and thus opposes cellular deformation, yet also actively generates membrane protrusions by exerting polymerization forces. It is unclear how the interplay between these two opposing mechanical functions plays out to shape the cell surface. To answer this question, we reconstitute biomimetic actin cortices nucleated by the Arp2/3 complex inside cell-sized lipid vesicles. We show that thin Arp2/3-nucleated actin cortices strongly deform and rigidify the shapes of giant unilamellar vesicles and impart a shape memory on time scales that exceeds the time of actin turnover. In addition, actin cortices can produce finger-like membrane protrusions, showing that Arp2/3-mediated actin polymerization forces alone are sufficient to initiate protrusions in the absence of actin bundling or membrane curving proteins. Combining mathematical modeling and our experimental results reveals that the concentration of actin nucleating proteins, rather than actin polymerization speed, is crucial for protrusion formation. This is because locally concentrated actin polymerization forces can drive a positive feedback loop between recruitment of actin and its nucleators to drive membrane deformation. Our work paints a picture where the actin cortex can either drive or inhibit deformations depending on the local distribution of nucleators.Significance StatementThe cells in our body must actively change shape in order to migrate, grow and divide, but they also need to maintain their shape to withstand external forces during tissue development. Cellular shape control results from an interplay between the plasma membrane and its underlying cortex, a shell composed of crosslinked actin filaments. Using cell-free reconstitution and mathematical modelling, we show that minimal biomimetic actin cortices can mechanically rigidify lipid vesicles while at the same time driving membrane protrusion formation. Our observations suggest that the spatial distribution of actin nucleation determines whether the actin cortex drives or inhibits membrane deformations.

The actin cortex is a complex cytoskeletal machinery that drives and responds to changes in cell shape. It must generate or adapt to plasma membrane curvature to facilitate diverse functions such as cell division, migration, and phagocytosis. Due to the complex molecular makeup of the actin cortex, it remains unclear whether actin networks are inherently able to sense and generate membrane curvature, or whether they rely on their diverse binding partners to accomplish this. Here, we show that curvature sensing is an inherent capability of branched actin networks nucleated by Arp2/3 and VCA. We develop a robust method to encapsulate actin inside giant unilamellar vesicles (GUVs) and assemble an actin cortex at the inner surface of the GUV membrane. We show that actin forms a uniform and thin cortical layer when present at high concentration and distinct patches associated with negative membrane curvature at low concentration. Serendipitously, we find that the GUV production method also produces dumbbell-shaped GUVs, which we explain using mathematical modeling in terms of membrane hemifusion of nested GUVs. We find that branched actin networks preferentially assemble at the neck of the dumbbells, which possess a micrometer-range convex curvature comparable with the curvature of the actin patches found in spherical GUVs. Minimal branched actin networks can thus sense membrane curvature, which may help mammalian cells to robustly recruit actin to curved membranes to facilitate diverse cellular functions such as cytokinesis and migration.

The actin cortex is a complex cytoskeletal machinery which drives and responds to changes in cell shape. It must generate or adapt to plasma membrane curvature to facilitate diverse functions such as cell division, migration and phagocytosis. Due to the complex molecular makeup of the actin cortex, it remains unclear whether actin networks are inherently able to sense and generate membrane curvature, or whether they rely on their diverse binding partners to accomplish this. Here, we show that curvature sensing and generation is an inherent capability of branched actin networks nucleated by Arp2/3 and VCA. We develop a robust method to encapsulate actin inside giant unilamellar vesicles (GUVs) and assemble an actin cortex at the inner surface of the GUV membrane. We show that actin forms a uniform and thin cortical layer when present at high concentration and distinct patches that generate negative membrane curvature at low concentration. Serendipitously, we find that the GUV production method also produces dumbbell-shaped GUVs, which we explain using mathematical modelling in terms of membrane hemifusion of nested GUVs. We find that dendritic actin networks preferentially assemble at the neck of the dumbbells, which possess a micron-range convex curvature that matches the curvature generated by actin patches in spherical GUVs. Minimal dendritic actin networks can thus both generate and sense membrane curvatures, which may help mammalian cells to robustly recruit actin to curved membranes in order to facilitate diverse cellular functions such as cytokinesis and migration.SIGNIFICANCEAnimal cells move, deform and divide using their actin cortex, a thin layer of filamentous proteins that supports the plasma membrane. For these actions, actin must often assemble at curved sections of the membrane, which is widely believed to require the action of dedicated actin- or membrane-bending proteins. Here, we use a bottom-up reconstitution approach to ask whether actin networks are intrinsically able to generate and sense membrane curvature. We show that membrane-nucleated actin cortices can indeed preferentially self-assemble at concave membranes generated by hemifusion of lipid vesicles. This raises intriguing questions about how such curvature recognition works, and whether cells exploit this intrinsic capability of branched actin networks to concentrate actin in specific cortical regions.

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

In cytokinesis of animal cells, the cell is symmetrically divided into two. Since the cell's volume is conserved, the projected area has to increase to allow for the change of shape. Here we aim to predict how membrane gain and loss adapt during cytokinesis. We work with a kinetic model in which membrane turnover depends on membrane tension and cell shape. We apply this model to a series of calculated vesicle shapes as a proxy for the shape of dividing cells. We find that the ratio of kinetic turnover parameters changes nonmonotonically with cell shape, determined by the dependence of exocytosis and endocytosis on membrane curvature. Our results imply that controlling membrane turnover will be crucial for the successful division of artificial cells.

The ability to detect specific nucleic acid sequences allows for a wide range of applications such as the identification of pathogens, clinical diagnostics, and genotyping. CRISPR-Cas proteins Cas12a and Cas13a are RNA-guided endonucleases that bind and cleave specific DNA and RNA sequences, respectively. After recognition of a target sequence, both enzymes activate indiscriminate nucleic acid cleavage, which has been exploited for sequence-specific molecular diagnostics of nucleic acids. Here, we present a label-free detection approach that uses a readout based on solution turbidity caused by liquid-liquid phase separation (LLPS). Our approach relies on the fact that the LLPS of oppositely charged polymers requires polymers to be longer than a critical length. This length dependence is predicted by the Voorn-Overbeek model, which we describe in detail and validate experimentally in mixtures of polynucleotides and polycations. We show that the turbidity resulting from LLPS can be used to detect the presence of specific nucleic acid sequences by employing the programmable CRISPR-nucleases Cas12a and Cas13a. Because LLPS of polynucleotides and polycations causes solutions to become turbid, the detection of specific nucleic acid sequences can be observed with the naked eye. We furthermore demonstrate that there is an optimal polynucleotide concentration for detection. Finally, we provide a theoretical prediction that hints towards possible improvements of an LLPS-based detection assay. The deployment of LLPS complements CRISPR-based molecular diagnostic applications and facilitates easy and low-cost nucleotide sequence detection.

Biofilms can grow on virtually any surface available, with impacts ranging from endangering the lives of patients to degrading unwanted water contaminants. Biofilm research is challenging due to the high degree of biofilm heterogeneity. A method for the production of standardized, reproducible, and patterned biofilm-inspired materials could be a boon for biofilm research and allow for completely new engineering applications. Here, we present such a method, combining 3D printing with genetic engineering. We prototyped a low-cost 3D printer that prints bioink, a suspension of bacteria in a solution of alginate that solidifies on a calcium-containing substrate. We 3D-printed Escherichia coli in different shapes and in discrete layers, after which the cells survived in the printing matrix for at least 1 week. When printed bacteria were induced to form curli fibers, the major proteinaceous extracellular component of E. coli biofilms, they remained adherent to the printing substrate and stably spatially patterned even after treatment with a matrix-dissolving agent, indicating that a biofilm-mimicking structure had formed. This work is the first demonstration of patterned, biofilm-inspired living materials that are produced by genetic control over curli formation in combination with spatial control by 3D printing. These materials could be used as living, functional materials in applications such as water filtration, metal ion sequestration, or civil engineering, and potentially as standardizable models for certain curli-containing biofilms.

SUMMARYStem-cell derived in vitro systems, such as organoids or embryoids, hold great potential for modeling in vivo biology and engineering living systems with novel functions. To unlock that potential, we need new ways to elicit higher-level organization. Here we show that adding extraembryonic endoderm (XEN) cells to mouse gastruloids leads to the formation of neural epithelia. By single-cell RNA-seq, imaging and differentiation experiments, we demonstrate the neural characteristics and spatial patterning of the epithelial tissue. We further show that the XEN cells differentiate reciprocally to a visceral endoderm-like state. Finally, we demonstrate that local inhibition of WNT signaling and production of a basement membrane by the XEN cells underlie the formation of the neuroepithelial tissue. In summary, we establish “XEN Enhanced Gastruloids” (XEGs) to explore heterotypic cellular interactions as a means to achieve complex, tissue-level organization in vitro.

Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins influence the membrane shape, the membrane shape affects the interactions between the proteins. To study these membrane-mediated interactions on closed and anisotropically curved membranes, we use colloids adhered to ellipsoidal membrane vesicles as a model system. We find that two particles on a closed system always attract each other, and tend to align with the direction of largest curvature. Multiple particles form arcs, or, at large enough numbers, a complete ring surrounding the vesicle in its equatorial plane. The resulting vesicle shape resembles a snowman. Our results indicate that these physical interactions on membranes with anisotropic shapes can be exploited by cells to drive macromolecules to preferred regions of cellular or intracellular membranes, and utilized to initiate dynamic processes such as cell division. The same principle could be used to find the midplane of an artificial vesicle, as a first step towards dividing it into two equal parts.

Protein inclusions in the membranes of living cells interact via the deformations they impose on that membrane. Such membrane-mediated interactions lead to sorting and self-assembly of the inclusions, as well as to membrane remodelling, crucial for many biological processes. For the past decades, theory, numerical calculations and experiments have been using simplified models for proteins to gain quantitative insights into their behaviour. Despite challenges arising from nonlinearities in the equations, the multiple length scales involved and the nonadditive nature of the interactions, recent progress now enables for the first time a direct comparison between theoretical and numerical predictions and experiments. We review the current knowledge on the biologically most relevant case, inclusions on lipid membranes with a closed surface and discuss challenges and opportunities for further progress.

The ability to detect specific nucleic acid sequences allows for a wide range of applications including identification of pathogens, clinical diagnostics, and genotyping. CRISPR-Cas proteins Cas12a and Cas13a are RNA-guided endonucleases that bind and cleave specific DNA and RNA sequences, respectively. After recognition of a target sequence both enzymes activate a unique, indiscriminate nucleic acid cleavage activity, which has been exploited for detection of sequence specific nucleotides using labelled reporter molecules. We here present a label-free detection approach that uses a readout based on solution turbidity caused by liquid-liquid phase separation (LLPS). Turbidity arises from coacervates of positively charged polyelectrolytes with long poly(dT) or poly(U) oligonucleotides. In the presence of a target sequence, long oligonucleotides are progressively shortened, changing the solution from turbid to transparent. We explain how oligonucleotide cleavage resolves LLPS by using a mathematical model which we validate with poly(dT) phase separation experiments. The deployment of LLPS complements CRISPR-based molecular diagnostic applications and facilitates easy and low-cost nucleotide sequence detection.

The plasma membrane and cytoskeleton of living cells are closely coupled dynamical systems. Internal cytoskeletal elements such as actin filaments and microtubules continually exert forces on the membrane, resulting in the formation of membrane protrusions. In this paper we investigate the interplay between the shape of a cell distorted by pushing and pulling forces generated by microtubules and the resulting rearrangement of the microtubule network. From analytical calculations, we find that two microtubules that deform the vesicle can both attract or repel each other, depending on their angular separations and the direction of the imposed forces. We also show how the existence of attractive interactions between multiple microtubules can be deduced analytically, and further explore general interactions through Monte Carlo simulations. Our results suggest that the commonly reported parallel structures of microtubules in both biological and artificial systems can be a natural consequence of membrane mediated interactions.

Eukaryotic cells are densely packed with macromolecular complexes and intertwining organelles, continually transported and reshaped. Intriguingly, organelles avoid clashing and entangling with each other in such limited space. Mitochondria form extensive networks constantly remodeled by fission and fusion. Here, we show that mitochondrial fission is triggered by mechanical forces. Mechano-stimulation of mitochondria – via encounter with motile intracellular pathogens, via external pressure applied by an atomic force microscope, or via cell migration across uneven microsurfaces – results in the recruitment of the mitochondrial fission machinery, and subsequent division. We propose that MFF, owing to affinity for narrow mitochondria, acts as a membrane-bound force sensor to recruit the fission machinery to mechanically strained sites. Thus, mitochondria adapt to the environment by sensing and responding to biomechanical cues. Our findings that mechanical triggers can be coupled to biochemical responses in membrane dynamics may explain how organelles orderly cohabit in the crowded cytoplasm., eLife, 6, ISSN:2050-084X

SummaryIn development and differentiation, morphological changes often accompany mechanical changes [1], but it is unclear whether or when cells in embryos sense tissue elasticity. The earliest embryo is uniformly pliable, while adult tissues vary widely in mechanics from soft brain and stiff heart to rigid bone [2]. However, cell sensitivity to microenvironment elasticity is debated based in part on results from complex three-dimensional culture models [3]. Regenerative cardiology provides strong motivation to clarify any cell-level sensitivities to tissue elasticity because rigid postinfarct regions limit pumping by the adult heart [4]. Here, we focus on the spontaneously beating embryonic heart and sparsely cultured cardiomyocytes, including cells derived from pluripotent stem cells. Tissue elasticity, Et, increases daily for heart to 1–2 kPa by embryonic day 4 (E4), and although this is ∼10-fold softer than adult heart, the beating contractions of E4 cardiomyocytes prove optimal at ∼Et,E4 both in vivo and in vitro. Proteomics reveals daily increases in a small subset of proteins, namely collagen plus cardiac-specific excitation-contraction proteins. Rapid softening of the heart’s matrix with collagenase or stiffening it with enzymatic crosslinking suppresses beating. Sparsely cultured E4 cardiomyocytes on collagen-coated gels likewise show maximal contraction on matrices with native E4 stiffness, highlighting cell-intrinsic mechanosensitivity. While an optimal elasticity for striation proves consistent with the mathematics of force-driven sarcomere registration, contraction wave speed is linear in Et as theorized for excitation-contraction coupled to matrix elasticity. Pluripotent stem cell-derived cardiomyocytes also prove to be mechanosensitive to matrix and thus generalize the main observation that myosin II organization and contractile function are optimally matched to the load contributed by matrix elasticity.

The process of detecting and tracking biological features such as bacteria and nuclei is complicated by the fact that they constantly change their shape. Shape changes happen both continuously as the biological features grow and discontinuously as they divide or die. In this paper I present a new method of tracking such features for the case that they can be reasonably approximated by a relatively simple mathematical shape such as a cylinder or an ellipse. Using contour plots with multiple levels to detect the features and their shapes, rather than the commonly used single contour detection technique, this method can efficiently detect multiple features even if they have large differences in brightness, as well as reliably track divisions when both brightness and size drop dramatically.

Many biological systems form colonies at high density. Passive granular systems will be jammed at such densities, yet for the survival of biological systems it is crucial that they are dynamic. We construct a phase diagram for a system of active particles interacting via Vicsek alignment, and vary the density, self-propulsion force, and orientational noise. We find that the system exhibits four different phases, characterized by transitions in the effective diffusion constant and in the orientational order parameter. Our simulations show that there exists an optimal noise such that particles require a minimal force to unjam, allowing for rearrangements., 7 pages, 8 figures

The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 kBT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles.

The interplay of membrane proteins is vital for many biological processes, such as cellular transport, cell division, and signal transduction between nerve cells. Theoretical considerations have led to the idea that the membrane itself mediates protein self-organization in these processes through minimization of membrane curvature energy. Here, we present a combined experimental and numerical study in which we quantify these interactions directly for the first time. In our experimental model system we control the deformation of a lipid membrane by adhering colloidal particles. Using confocal microscopy, we establish that these membrane deformations cause an attractive interaction force leading to reversible binding. The attraction extends over 2.5 times the particle diameter and has a strength of three times the thermal energy (-3.3 kT). Coarse-grained Monte-Carlo simulations of the system are in excellent agreement with the experimental results and prove that the measured interaction is independent of length scale. Our combined experimental and numerical results reveal membrane curvature as a common physical origin for interactions between any membrane-deforming objects, from nanometre-sized proteins to micrometre-sized particles., 15 pages, 12 figures, Published in Scientific Reports (open access): http://www.nature.com/articles/srep32825 Supplementary Material available via the given URL

In cells, membrane tubes are extracted by molecular motors. Although individual motors cannot provide enough force to pull a tube, clusters of such motors can. Here,weinvestigate, using a minimal in vitro model system, how the tube pulling process depends on fundamental properties of the motor species involved. Previously, it has been shown that processive motors can pull tubes by dynamic association at the tube tip. We demonstrate that, remarkably, nonprocessive motors can also cooperatively extract tubes. Moreover, the tubes pulled by nonprocessive motors exhibit rich dynamics as compared to those pulled by their processive counterparts. We report distinct phases of persistent growth, retraction, and an intermediate regime characterized by highly dynamic switching between the two. We interpret the different phases in the context of a single-species model. The model assumes only a simple motor clustering mechanism along the length of the entire tube and the presence of a length-dependent tube tension. The resulting dynamic distribution of motor clusters acts as both a velocity and distance regulator for the tube. We show the switching phase to be an attractor of the dynamics of this model, suggesting that the switching observed experimentally is a robust characteristic of nonprocessive motors. A similar system could regulate in vivo biological membrane networks.

Swarming behaviour is abundant in nature. Over many different length scales, in for example herds, flocking birds and swimming bacteria, roughly identical individuals interact locally to achieve group behaviour. The similarities between these examples suggests the existence of a general underlying principle. We propose here a local interaction model for self-propelling, elliptical particles that results in collective motion. Any particle interacts with its neighbours only, experiences noise on its orientation and pushes inwards if it is in the outer layer of the group. Initially, alignment between particles is the result of steric repulsion. We observe two types of group behaviour. The first type is a migrating group, where particles in the bulk are aligned over large length scales, but do not rearrange. The second type has very little net motion. The elliptical particles form smaller regions of aligned and antialigned particles, effectively cancelling the net motion of the group. Finally, we compare the group behaviour of elliptical particles to circular ones and investigate the importance of polar alignment. We conclude that polar alignment is a requirement for large-scale collective dynamics, like collective migration and rotation.

Contact inhibition is the process by which cells switch from a motile growing state to a passive and stabilized state upon touching their neighbors. When two cells touch, an adhesion link is created between them by means of transmembrane E-cadherin proteins. Simultaneously, their actin filaments stop polymerizing in the direction perpendicular to the membrane and reorganize to create an apical belt that colocalizes with the adhesion links. Here, we propose a detailed quantitative model of the role of the cytoplasmic $\beta$-catenin and $\alpha$-catenin proteins in this process, treated as a reaction-diffusion system. Upon cell-cell contact, the concentration in $\alpha$-catenin dimers increases, inhibiting actin branching and thereby reducing cellular motility and expansion pressure. This model provides a mechanism for contact inhibition that could explain previously unrelated experimental findings on the role played by E-cadherin, $\beta$-catenin and $\alpha$-catenin in the cellular phenotype and in tumorigenesis. In particular, we address the effect of a knockout of the adenomatous polyposis coli tumor suppressor gene. Potential direct tests of our model are discussed.

We analytically study membrane mediated interactions between inclusions embedded in a tubular membrane. We model inclusions as constraints coupled to the curvature tensor of the membrane tube. First, as special test cases, we analyze the interaction between ring and rod shaped inclusions. Using Monte Carlo simulations, we further show how point-like inclusions interact to form linear aggregates. Our results reveal that depending on the hard-core radius of the inclusions, they arrange into either lines or rings to globally minimize the curvature energy of the membrane., Comment: 5 + 4 pages, 4 + 3 figures

We present a model of soft active particles that leads to a rich array of collective behavior found also in dense biological swarms of bacteria and other unicellular organisms. Our model uses only local interactions, such as Vicsek-type nearest neighbor alignment, short-range repulsion, and a local boundary term. Changing the relative strength of these interactions leads to migrating swarms, rotating swarms and jammed swarms, as well as swarms that exhibit run-and-tumble motion, alternating between migration and either rotating or jammed states. Interestingly, although a migrating swarm moves slower than an individual particle, the diffusion constant can be up to three orders of magnitude larger, suggesting that collective motion can be highly advantageous, for example, when searching for food., 8 pages, 7 figures

Mitosis in the early syncytial Drosophila embryo is highly correlated in space and time, as manifested in mitotic wavefronts that propagate across the embryo. In this paper we investigate the idea that the embryo can be considered a mechanically-excitable medium, and that mitotic wavefronts can be understood as nonlinear wavefronts that propagate through this medium. We study the wavefronts via both image analysis of confocal microscopy videos and theoretical models. We find that the mitotic waves travel across the embryo at a well-defined speed that decreases with replication cycle. We find two markers of the wavefront in each cycle, corresponding to the onsets of metaphase and anaphase. Each of these onsets is followed by displacements of the nuclei that obey the same wavefront pattern. To understand the mitotic wavefronts theoretically we analyze wavefront propagation in excitable media. We study two classes of models, one with biochemical signaling and one with mechanical signaling. We find that the dependence of wavefront speed on cycle number is most naturally explained by mechanical signaling, and that the entire process suggests a scenario in which biochemical and mechanical signaling are coupled.

Cellular membranes exhibit a variety of morphologies, from a simple spherical liposome to bewildering complex structures like interconnected tubular networks found in the Endoplasmic Reticulum, or connected stacks of perforated membrane sheets as in the Golgi apparatus. Membranes form these structures through different mechanisms, the most important of which is through the interplay between membrane lipids and inclusions like proteins. Spatial organization of such proteins in biological membranes is essential for stabilizing the membrane and for the dynamic behavior of cellular organelles. Despite making significant strides in understanding membrane mediated interactions, it is not completely understood how inclusions interact in a highly curved regime. It is, therefore, warranted to investigate how proteins in strongly bent membranes self-organize. We do so using both analytical calculations based on the course-grained Helfrich model, and with Monte Carlo simulations. First, we find that the forces between identical inclusions, which are known to be always repulsive on a flat membrane, become attractive on curved and closed membranes. Second, we show how many point-like inclusions embedded in a tubular membrane spontaneously self-assemble into rings and lines. Finally, we quantitatively show how inclusions adhered to an ellipsoidal membrane likewise self-assemble into a ring perpendicular to its semi-major axis. The structures we find are highly relevant in biology, and are found for instance in endocytosis and cell division. Our results therefore reveal that purely physical interactions underlie these biological phenomena.

Inclusions in biological membranes may interact via deformations they induce on the shape of that very membrane. Such deformations are a purely physical effect, resulting in nonspecific forces between the inclusions. In this Letter we show that this type of interaction can organize membrane domains and hence may play an important biological role. Using a simple analytical model we predict that membrane inclusions sort according to the curvature they impose. We verify this prediction by both numerical simulations and experimental observations of membrane domains in phase separated vesicles.

The ternary system consisting of cholesterol, a saturated lipid, and an unsaturated one exhibits a rich phase behavior with multiple phase coexistence regimes. Remarkably, phase separation even occurs when each of the three binary systems consisting of two of these components is a uniform mixture. We use a Flory-Huggins like model in which the phase separation of the ternary system is a consequence of an interaction between all three components to describe the system. From the associated Gibbs free energy we calculate phase diagrams, spinodals, and critical points. Moreover, we use a Van der Waals/Cahn-Hilliard like construction to derive an expression for the line tension between coexisting phases. We show how the line tension depends on the position in the phase diagram, and give an explicit expression for the concentration profile at the phase boundary.

Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line tension and the bending moduli, are crucially involved in the kinetics and the asymptotic behavior of phase separation. In this Letter we present a combined analytical and experimental approach to determine the properties of phase-separated vesicle systems. First we develop an analytical model for the vesicle shape of weakly budded biphasic vesicles. Subsequently experimental data on vesicle shape and membrane fluctuations are taken and compared to the model. The combined approach allows for a reproducible and reliable determination of the physical parameters of complex vesicle systems. The parameters obtained set limits for the size and stability of nanodomains in the plasma membrane of living cells., Comment: (*) authors contributed equally, 6 pages, 3 figures, 1 table; added insets to figure 3

While it is a well known fact that membrane proteins interact via electrostatic, hydrophobic and van der Waals forces, only recently attention was drawn to a new kind of fundamental interaction that is mediated by the membrane itself. Proteins that locally impose a membrane curvature create a deformation that is probed by other, similar proteins. Since it is very difficult to quantitatively measure and discriminate the different types of interactions in the case of proteins, we study a model system which allows the exclusive observation of membrane mediated interactions alone. Building on our earlier experiments on fully phase separated vesicles (Semrau et al., PRL, 2008) we study biomimetic vesicles with bulging liquid ordered domains. These domains deform the surrounding membrane and create a repulsive force between them. This leads to a wealth of measurable effects: we observe hindered domain fusion, a preferred domain size and, most importantly, an intriguing sorting mechanism. Domains of different sizes spontaneously demix and form regions of equally sized domains. Quantitative measurements of the repulsive force allow us to build a model for the sorting that is independently confirmed in Monte Carlo simulations. The observed sorting provides a new mechanism for protein sorting in the endoplasmic reticulum and for membrane mediated protein aggregation.

Cell membrane organization is the result of the collective effect of many driving forces. Several of these, such as electrostatic and van der Waals forces, have been identified and studied in detail. In this article, we investigate and quantify another force, the interaction between inclusions via deformations of the membrane shape. For electrically neutral systems, this interaction is the dominant organizing force. As a model system to study membrane-mediated interactions, we use phase-separated biomimetic vesicles that exhibit coexistence of liquid-ordered and liquid-disordered lipid domains. The membrane-mediated interactions between these domains lead to a rich variety of effects, including the creation of long-range order and the setting of a preferred domain size. Our findings also apply to the interaction of membrane protein patches, which induce similar membrane shape deformations and hence experience similar interactions.

Collections of motors dynamically organize to extract membrane tubes. These tubes grow but often pause or change direction as they traverse an underlying microtubule (MT) network. In vitro, membrane tubes also stall: they stop growing in length despite a large group of motors available at the tip to pull them forward. In these stationary membrane tubes in vitro, we find that clusters of processive kinesin motors form and reach the tip of the tube at regular time intervals. The average times between cluster arrivals depends on the time over which motors depart from the tip, suggesting that motors are recycled toward the tip. Numerical simulations of the motor dynamics in the membrane tube and on the MTs show that the presence of cooperative binding between motors quantitatively accounts for the clustering observed experimentally. Cooperative binding along the length of the MT and a nucleation point at a distance behind the tip define the recycling period. Based on comparison of the numerical results and experimental data, we estimate a cooperative binding probability and concentration regime where the recycling phenomenon occurs.

In Mechanics and Relativity, the reader is taken on a tour through time and space. Starting from the basic axioms formulated by Newton and Einstein, the theory of motion at both the everyday and the highly relativistic level is developed without the need of prior knowledge. The relevant mathematics is provided in an appendix. The text contains various worked examples and a large number of original problems to help the reader develop an intuition for the physics. Applications covered in the book span a wide range of physical phenomena, including rocket motion, spinning tennis rackets and high-energy particle collisions.

Many developmental processes use signaling for synchronization. One possible and well-known method is for each component to measure the local concentration of some diffusing biochemical species, and if that concentration exceeds a certain threshold, to release more of the same biochemical, giving rise to wavefront propagation in the chemically excitable medium. There are however more ways in which a medium can be excited and wavefronts can be formed. We suggest a new kind of signaling based not on diffusion of a chemical species, but on the propagation of mechanical stress. We construct a theoretical approach to describe mechanical signaling in an overdamped system as a nonlinear wavefront propagation problem. We apply the theory to mitosis in the early syncytial Drosophila embryo, which is highly correlated in space and time, as manifested in mitotic wavefronts that propagate across the embryo. We compare our results to data taken on Drosophila embryos in which histones in the nuclear chromosomes are labeled with GFP. By analyzing confocal microscopy videos of the mitotic wavefront, we find that the wavefront can be resolved into two distinct wavefronts in each cycle, corresponding to the onset of metaphase and of anaphase, respectively. The two wavefronts have the same speed and are separated by a time interval that is independent of cycle, indicating that they are two different markers for the same process. We find that the dependence of wavefront speed on cell cycle number is most naturally explained by mechanical signaling via stress diffusion, and that the entire process suggests a scenario in which biochemical and mechanical signaling are coupled.

Based on the Canham-Helfrich free energy, we derive analytical expressions for the shapes of axisymmetric membranes consisting of multiple domains. We give explicit equations for both closed vesicles and almost cylindrical tubes. Using these expressions, we also find the shape of a tube attached to a spherical vesicle. The resulting shapes compare well to numerical data, and our expressions can be used to easily determine membrane parameters from experimentally obtained shapes.