Patterning of the cell cortex by Rho GTPases.

The Rho GTPases - RHOA, RAC1 and CDC42 - are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.

Microtubule detyrosination drives symmetry breaking to polarize cells for directed cell migration.

To initiate directed movement, cells must become polarized, establishing a protrusive leading edge and a contractile trailing edge. This symmetry-breaking process involves reorganization of cytoskeleton and asymmetric distribution of regulatory molecules. However, what triggers and maintains this asymmetry during cell migration remains largely elusive. Here, we established a micropatterning-based 1D motility assay to investigate the molecular basis of symmetry breaking required for directed cell migration. We show that microtubule (MT) detyrosination drives cell polarization by directing kinesin-1-based transport of the adenomatous polyposis coli (APC) protein to cortical sites. This is essential for the formation of cell's leading edge during 1D and 3D cell migration. These data, combined with biophysical modeling, unveil a key role for MT detyrosination in the generation of a positive feedback loop linking MT dynamics and kinesin-1-based transport. Thus, symmetry breaking during cell polarization relies on a feedback loop driven by MT detyrosination that supports directed cell migration.

Singularity in polarization: rewiring yeast cells to make two buds.

For budding yeast to ensure formation of only one bud, cells must polarize toward one, and only one, site. Polarity establishment involves the Rho family GTPase Cdc42, which concentrates at polarization sites via a positive feedback loop. To assess whether singularity is linked to the specific Cdc42 feedback loop, we disabled the yeast cell's endogenous amplification mechanism and synthetically rewired the cells to employ a different positive feedback loop. Rewired cells violated singularity, occasionally making two buds. Even cells that made only one bud sometimes initiated two clusters of Cdc42, but then one cluster became dominant. Mathematical modeling indicated that, given sufficient time, competition between clusters would promote singularity. In rewired cells, competition occurred slowly and sometimes failed to develop a single "winning" cluster before budding. Slowing competition in normal cells also allowed occasional formation of two buds, suggesting that singularity is enforced by rapid competition between Cdc42 clusters.

Local and global Cdc42 guanine nucleotide exchange factors for fission yeast cell polarity are coordinated by microtubules and the Tea1-Tea4-Pom1 axis.

The conserved Rho-family GTPase Cdc42 plays a central role in eukaryotic cell polarity. The rod-shaped fission yeast Schizosaccharomyces pombe has two Cdc42 guanine nucleotide exchange factors (GEFs), Scd1 and Gef1, but little is known about how they are coordinated in polarized growth. Although the microtubule cytoskeleton is normally not required for polarity maintenance in fission yeast, we show here that when scd1 function is compromised, disruption of microtubules or the polarity landmark proteins Tea1, Tea4 or Pom1 leads to disruption of polarized growth. Instead, cells adopt an isotropic-like pattern of growth, which we term PORTLI growth. Surprisingly, PORTLI growth is caused by spatially inappropriate activity of Gef1. Although most Cdc42 GEFs are membrane associated, we find that Gef1 is a broadly distributed cytosolic protein rather than a membrane-associated protein at cell tips like Scd1. Microtubules and the Tea1-Tea4-Pom1 axis counteract inappropriate Gef1 activity by regulating the localization of the Cdc42 GTPase-activating protein Rga4. Our results suggest a new model of fission yeast cell polarity regulation, involving coordination of 'local' (Scd1) and 'global' (Gef1) Cdc42 GEFs via microtubules and microtubule-dependent polarity landmarks.

Pattern formation in active model C with anchoring: bands, aster networks, and foams.

We study the dynamics of pattern formation in a minimal model for active mixtures made of microtubules and molecular motors. We monitor the evolution of the (conserved) microtubule density and of the (non-conserved) nematic order parameter, focusing on the effects of an "anchoring" term that provides a direct coupling between the preferred microtubule direction and their density gradient. The key control parameter is the ratio between activity and elasticity. When elasticity dominates, the interplay between activity and anchoring leads to formation of banded structures that can undergo additional bending, rotational or splaying instabilities. When activity dominates, the nature of anchoring instead gives rise to a range of active cellular solids, including aster-like networks, disordered foams and spindle-like patterns. We speculate that the introduced "active model C" with anchoring is a minimal model to describe pattern formation in a biomimetic analogue of the microtubule cytoskeleton.

Dry active turbulence in a model for microtubule-motor mixtures.

We study the dynamics and phase behaviour of a dry suspension of microtubules and molecular motors. We obtain a set of continuum equations by rigorously coarse graining a microscopic model where motor-induced interactions lead to parallel or antiparallel ordering. Through numerical simulations, we show that this model generically creates either stable stripes, or a never-settling pattern where stripes periodically form, rotate and then split up. We derive a minimal model which displays the same instability as the full model, and clarifies the underlying physical mechanism. The necessary ingredients are an extensile flux arising from microtubule sliding and an interfacial torque favouring ordering along density gradients. We argue that our minimal model unifies various previous observations of chaotic behaviour in dry active matter into a general universality class.

CDC-42 and RAC-1 regulate opposite chemotropisms in Neurospora crassa.

Cell polarization and fusion are crucial developmental processes that occur in response to intracellular and extracellular signals. Asexual spores (conidia) of the mold Neurospora crassa differentiate two types of polarized cell protrusions, germ tubes and conidial anastomosis tubes (CATs), which exhibit negative and positive chemotropism, respectively. We provide the first evidence that shared and separate functions of the Rho-type GTPases CDC-42 and RAC-1 regulate these opposite chemotropisms. We demonstrate that RAC-1 is essential for CAT formation and cell fusion, whereas CDC-42 is necessary and sufficient for normal germ tube development. Cdc42-Rac-interactive-binding (CRIB) reporters were constructed to exclusively label locally activated GTP-bound GTPases. Time course analyses showed that repositioning of these activated GTPase clusters within germ tube and CAT tip apices controls directional growth in the absence of a tip-localized vesicle supply center (Spitzenkörper). We propose a model in which the local assembly of a plasma-membrane-associated GTPase-PAK-MAPK signaling platform regulates chemoattractant perception and secretion in order to synchronize oscillatory cell-cell communication and directional CAT tip growth.

Curvature-driven positioning of Turing patterns in phase-separating curved membranes.

We introduce a new finite difference scheme to study the dynamics of Turing patterns of a two-species activator-inhibitor system embedded on a phase-separating curved membrane, modelling for instance a lipid bilayer. We show that the underlying binary fluid can strongly affect both the dynamical and the steady state properties of the ensuing Turing patterns. Furthermore, geometry plays a key role, as a large enough local membrane curvature can both arrest the coarsening of the lipid domains and position the patterns selectively at areas of high or small local curvature. The physical phenomena we observe are due to a minimal coupling, between the diffusivity of the Turing components and the local membrane composition. While our study is theoretical in nature, it can provide a framework within which to address intracellular pattern formation in systems of interacting membrane proteins.

Correction: Curvature-driven positioning of Turing patterns in phase-separating curved membranes.

Correction for 'Curvature-driven positioning of Turing patterns in phase-separating curved membranes' by Giulio Vandin et al., Soft Matter, 2016, DOI: .

Excitable behavior can explain the "ping-pong" mode of communication between cells using the same chemoattractant.

Here we elucidate a paradox: how a single chemoattractant-receptor system in two individuals is used for communication despite the seeming inevitability of self-excitation. In the filamentous fungus Neurospora crassa, genetically identical cells that produce the same chemoattractant fuse via the homing of individual cell protrusions toward each other. This is achieved via a recently described "ping-pong" pulsatile communication. Using a generic activator-inhibitor model of excitable behavior, we demonstrate that the pulse exchange can be fully understood in terms of two excitable systems locked into a stable oscillatory pattern of mutual excitation. The most puzzling properties of this communication are the sudden onset of oscillations with final amplitude, and the absence of seemingly inevitable self-excitation. We show that these properties result directly from both the excitability threshold and refractory period characteristic of excitable systems. Our model suggests possible molecular mechanisms for the ping-pong communication.

Actomyosin cortex: Inherently oscillatory?

A new analysis of cytokinetic furrow ingression in the Caenorhabditis elegans zygote at high spatiotemporal resolution demonstrates that, rather than being a process of steady, spatially uniform constriction, furrow ingression is modulated by complex contractile oscillations that move around the furrow, possibly in the form of propagating waves.

Testing models of cell cortex wave generation by Rho GTPases.

The Rho GTPases pattern the cell cortex in a variety of fundamental cell-morphogenetic processes including division, wound repair, and locomotion. It has recently become apparent that this patterning arises from the ability of the Rho GTPases to self-organize into static and migrating spots, contractile pulses, and propagating waves in cells from yeasts to mammals 1 . These self-organizing Rho GTPase patterns have been explained by a variety of theoretical models which require multiple interacting positive and negative feedback loops. However, it is often difficult, if not impossible, to discriminate between different models simply because the available experimental data do not simultaneously capture the dynamics of multiple molecular concentrations and biomechanical variables at fine spatial and temporal resolution. Specifically, most studies typically provide either the total Rho GTPase signal or the Rho GTPase activity as reported by various sensors, but not both. Therefore, it remains largely unknown how membrane accumulation of Rho GTPases (i.e., Rho membrane enrichment) is related to Rho activity. Here we dissect the dynamics of RhoA by simultaneously imaging both total RhoA and active RhoA in the regime of acute cortical excitability 2 , characterized by pronounced waves of Rho activity and F-actin polymerization 3-5 . We find that within nascent waves, accumulation of active RhoA precedes that of total RhoA, and we exploit this finding to distinguish between two popular theoretical models previously used to explain propagating cortical Rho waves.

Cell cycle and developmental control of cortical excitability in Xenopus laevis.

Interest in cortical excitability-the ability of the cell cortex to generate traveling waves of protein activity-has grown considerably over the past 20 years. Attributing biological functions to cortical excitability requires an understanding of the natural behavior of excitable waves and the ability to accurately quantify wave properties. Here we have investigated and quantified the onset of cortical excitability in Xenopus laevis eggs and embryos and the changes in cortical excitability throughout early development. We found that cortical excitability begins to manifest shortly after egg activation. Further, we identified a close relationship between wave properties-such as wave frequency and amplitude-and cell cycle progression as well as cell size. Finally, we identified quantitative differences between cortical excitability in the cleavage furrow relative to nonfurrow cortical excitability and showed that these wave regimes are mutually exclusive.

Mechanosensitive calcium flashes promote sustained RhoA activation during tight junction remodeling.

Epithelial cell-cell junctions remodel in response to mechanical stimuli to maintain barrier function. Previously, we found that local leaks in tight junctions (TJs) are rapidly repaired by local, transient RhoA activation, termed "Rho flares," but how Rho flares are regulated is unknown. Here, we discovered that intracellular calcium flashes and junction elongation are early events in the Rho flare pathway. Both laser-induced and naturally occurring TJ breaks lead to local calcium flashes at the site of leaks. Additionally, junction elongation induced by optogenetics increases Rho flare frequency, suggesting that Rho flares are mechanically triggered. Depletion of intracellular calcium or inhibition of mechanosensitive calcium channels (MSCs) reduces the amplitude of calcium flashes and diminishes the sustained activation of Rho flares. MSC-dependent calcium influx is necessary to maintain global barrier function by regulating reinforcement of local TJ proteins via junction contraction. In all, we uncovered a novel role for MSC-dependent calcium flashes in TJ remodeling, allowing epithelial cells to repair local leaks induced by mechanical stimuli.

A versatile cortical pattern-forming circuit based on Rho, F-actin, Ect2, and RGA-3/4.

Many cells can generate complementary traveling waves of actin filaments (F-actin) and cytoskeletal regulators. This phenomenon, termed cortical excitability, results from coupled positive and negative feedback loops of cytoskeletal regulators. The nature of these feedback loops, however, remains poorly understood. We assessed the role of the Rho GAP RGA-3/4 in the cortical excitability that accompanies cytokinesis in both frog and starfish. RGA-3/4 localizes to the cytokinetic apparatus, "chases" Rho waves in an F-actin-dependent manner, and when coexpressed with the Rho GEF Ect2, is sufficient to convert the normally quiescent, immature Xenopus oocyte cortex into a dramatically excited state. Experiments and modeling show that changing the ratio of RGA-3/4 to Ect2 produces cortical behaviors ranging from pulses to complex waves of Rho activity. We conclude that RGA-3/4, Ect2, Rho, and F-actin form the core of a versatile circuit that drives a diverse range of cortical behaviors, and we demonstrate that the immature oocyte is a powerful model for characterizing these dynamics.

Lateral dynamics of proteins with polybasic domain on anionic membranes: a dynamic Monte-Carlo study.

Positively charged polybasic domains are essential for recruiting multiple signaling proteins, such as Ras GTPases and Src kinase, to the negatively charged cellular membranes. Much less, however, is known about the influence of electrostatic interactions on the lateral dynamics of these proteins. We developed a dynamic Monte-Carlo automaton that faithfully simulates lateral diffusion of the adsorbed positively charged oligopeptides as well as the dynamics of mono- (phosphatidylserine) and polyvalent (PIP(2)) anionic lipids within the bilayer. In agreement with earlier results, our simulations reveal lipid demixing that leads to the formation of a lipid shell associated with the peptide. The computed association times and average numbers of bound lipids demonstrate that tetravalent PIP(2) interacts with the peptide much more strongly than monovalent lipid. On the spatially homogeneous membrane, the lipid shell affects the behavior of the peptide only by weakly reducing its lateral mobility. However, spatially heterogeneous distributions of monovalent lipids are found to produce peptide drift, the velocity of which is determined by the total charge of the peptide-lipid complex. We hypothesize that this predicted phenomenon may affect the spatial distribution of proteins with polybasic domains in the context of cell-signaling events that alter the local density of monovalent anionic lipids.

Lateral dynamics of charged lipids and peripheral proteins in spatially heterogeneous membranes: comparison of continuous and Monte Carlo approaches.

Biological membranes are complex environments whose physico-chemical properties are of utmost importance for the understanding of many crucial biological processes. Much attention has been given in the literature to the description of membranes along the z-axis perpendicular to the membrane. Here, we instead consider the lateral dynamics of lipids and peripheral proteins due to their electrostatic interaction. Previously, we constructed a Monte Carlo automaton capable of simulating mutual diffusive dynamics of charged lipids and associated positively charged peptides. Here, we derive and numerically analyze a system of Poisson-Boltzmann-Nernst-Planck (PBNP) equations that provide a mean-field approximation compatible with our Monte Carlo model. The thorough comparison between the mean-field PBNP equations and Monte Carlo simulations demonstrates that both the approaches are in a good qualitative agreement in all tested scenarios. We find that the two methods quantitatively deviate when the local charge density is high, presumably because the Poisson-Boltzmann formalism is applicable in the so-called weak coupling limit, whose validity is restricted to low charge densities. Nevertheless, we conclude that the mean-field PBNP approach provides a good approximation for the considerably more detailed Monte Carlo model at only a fraction of the associated computational cost and allows simulation of the membrane lateral dynamics on the space and time scales relevant for the realistic biological problems.

Symmetry Breaking as an Interdisciplinary Concept Unifying Cell and Developmental Biology.

The concept of "symmetry breaking" has become a mainstay of modern biology, yet you will not find a definition of this concept specific to biological systems in Wikipedia [...].

Stochastic contraction of myosin minifilaments drives evolution of microridge protrusion patterns in epithelial cells.

Actin-based protrusions vary in morphology, stability, and arrangement on cell surfaces. Microridges are laterally elongated protrusions on mucosal epithelial cells, where they form evenly spaced, mazelike patterns that dynamically remodel by fission and fusion. To characterize how microridges form their highly ordered, subcellular patterns and investigate the mechanisms driving fission and fusion, we imaged microridges in the maturing skin of zebrafish larvae. After their initial development, microridge spacing and alignment became increasingly well ordered. Imaging F-actin and non-muscle myosin II (NMII) revealed that microridge fission and fusion were associated with local NMII activity in the apical cortex. Inhibiting NMII blocked fission and fusion rearrangements, reduced microridge density, and altered microridge spacing. High-resolution imaging allowed us to image individual NMII minifilaments in the apical cortex of cells in live animals, revealing that minifilaments are tethered to protrusions and often connect adjacent microridges. NMII minifilaments connecting the ends of two microridges fused them together, whereas minifilaments oriented perpendicular to microridges severed them or pulled them closer together. These findings demonstrate that as cells mature, cortical NMII activity orchestrates a remodeling process that creates an increasingly orderly microridge arrangement.