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.

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.

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.

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 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.

Type V myosin focuses the polarisome and shapes the tip of yeast cells.

The polarisome is a cortical proteinaceous microcompartment that organizes the growth of actin filaments and the fusion of secretory vesicles in yeasts and filamentous fungi. Polarisomes are compact, spotlike structures at the growing tips of their respective cells. The molecular forces that control the form and size of this microcompartment are not known. Here we identify a complex between the polarisome subunit Pea2 and the type V Myosin Myo2 that anchors Myo2 at the cortex of yeast cells. We discovered a point mutation in the cargo-binding domain of Myo2 that impairs the interaction with Pea2 and consequently the formation and focused localization of the polarisome. Cells carrying this mutation grow round instead of elongated buds. Further experiments and biophysical modeling suggest that the interactions between polarisome-bound Myo2 motors and dynamic actin filaments spatially focus the polarisome and sustain its compact shape.

Cortical excitability and cell division.

As the interface between the cell and its environment, the cell cortex must be able to respond to a variety of external stimuli. This is made possible in part by cortical excitability, a behavior driven by coupled positive and negative feedback loops that generate propagating waves of actin assembly in the cell cortex. Cortical excitability is best known for promoting cell protrusion and allowing the interpretation of and response to chemoattractant gradients in migrating cells. It has recently become apparent, however, that cortical excitability is involved in the response of the cortex to internal signals from the cell-cycle regulatory machinery and the spindle during cell division. Two overlapping functions have been ascribed to cortical excitability in cell division: control of cell division plane placement, and amplification of the activity of the small GTPase Rho at the equatorial cortex during cytokinesis. Here, we propose that cortical excitability explains several important yet poorly understood features of signaling during cell division. We also consider the potential advantages that arise from the use of cortical excitability as a signaling mechanism to regulate cortical dynamics in cell division.

Rho and F-actin self-organize within an artificial cell cortex.

The cell cortex, comprised of the plasma membrane and underlying cytoskeleton, undergoes dynamic reorganizations during a variety of essential biological processes including cell adhesion, cell migration, and cell division.1,2 During cell division and cell locomotion, for example, waves of filamentous-actin (F-actin) assembly and disassembly develop in the cell cortex in a process termed "cortical excitability."3-7 In developing frog and starfish embryos, cortical excitability is generated through coupled positive and negative feedback, with rapid activation of Rho-mediated F-actin assembly followed in space and time by F-actin-dependent inhibition of Rho.7,8 These feedback loops are proposed to serve as a mechanism for amplification of active Rho signaling at the cell equator to support furrowing during cytokinesis while also maintaining flexibility for rapid error correction in response to movement of the mitotic spindle during chromosome segregation.9 In this paper, we develop an artificial cortex based on Xenopus egg extract and supported lipid bilayers (SLBs), to investigate cortical Rho and F-actin dynamics.10 This reconstituted system spontaneously develops two distinct types of self-organized cortical dynamics: singular excitable Rho and F-actin waves, and non-traveling oscillatory Rho and F-actin patches. Both types of dynamic patterns have properties and dependencies similar to the excitable dynamics previously characterized in vivo.7 These findings directly support the long-standing speculation that the cell cortex is a self-organizing structure and present a novel approach for investigating mechanisms of Rho-GTPase-mediated cortical dynamics.

Compete or Coexist? Why the Same Mechanisms of Symmetry Breaking Can Yield Distinct Outcomes.

Cellular morphogenesis is governed by the prepattern based on the symmetry-breaking emergence of dense protein clusters. Thus, a cluster of active GTPase Cdc42 marks the site of nascent bud in the baker's yeast. An important biological question is which mechanisms control the number of pattern maxima (spots) and, thus, the number of nascent cellular structures. Distinct flavors of theoretical models seem to suggest different predictions. While the classical Turing scenario leads to an array of stably coexisting multiple structures, mass-conserved models predict formation of a single spot that emerges via the greedy competition between the pattern maxima for the common molecular resources. Both the outcome and the kinetics of this competition are of significant biological importance but remained poorly explored. Recent theoretical analyses largely addressed these questions, but their results have not yet been fully appreciated by the broad biological community. Keeping mathematical apparatus and jargon to the minimum, we review the main conclusions of these analyses with their biological implications in mind. Focusing on the specific example of pattern formation by small GTPases, we speculate on the features of the patterning mechanisms that bypass competition and favor formation of multiple coexisting structures and contrast them with those of the mechanisms that harness competition to form unique cellular structures.

Small-amplitude and mixed-mode pH oscillations in the bromate-sulfite-ferrocyanide-aluminum(III) system.

The BrO(3)(-)-SO(3)(2-)-Fe(CN)(6)(4-) (BSF) pH-oscillatory system is coupled to the Al(OH)(3) precipitation equilibrium (BSFA system) and studied in a stirred flow reactor. The dynamic behavior of the BSFA system differs significantly from that of the BSF system. In addition to the large-amplitude pH oscillations found in the BSF system, new small-amplitude and mixed-mode oscillations occur. A detailed mechanism of the BSFA system is developed and investigated.

High-frequency oscillations in the Belousov-Zhabotinsky reaction.

Chemical oscillations in the classic Belousov-Zhabotinsky (BZ) system typically have a period of a few minutes, which can be increased significantly by changing the organic substrate. Here we show that by changing the temperature and concentrations, an increase of 3-4 orders of magnitude in the frequency of BZ oscillations can be obtained. At elevated temperatures, in high concentration mixtures, the cerium-catalyzed reaction exhibits sinusoidal oscillations with frequencies of 10 Hz or greater. We report the effect of temperature on the frequency and shape of oscillations in experiments under batch conditions and in a four-variable model. We show that our simple model accurately captures the complex temporal behavior of the system and suggests paths toward even higher frequencies.

Autoactivation of small GTPases by the GEF-effector positive feedback modules.

Small GTPases are organizers of a plethora of cellular processes. The time and place of their activation are tightly controlled by the localization and activation of their regulators, guanine-nucleotide exchange factors (GEFs) and GTPase-activating proteins (GAPs). Remarkably, in some systems, the upstream regulators of GTPases are also found downstream of their activity. Resulting feedback loops can generate complex spatiotemporal dynamics of GTPases with important functional consequences. Here we discuss the concept of positive autoregulation of small GTPases by the GEF-effector feedback modules and survey recent developments in this exciting area of cell biology.

Rho Flares Repair Local Tight Junction Leaks.

Tight junctions contribute to epithelial barrier function by selectively regulating the quantity and type of molecules that cross the paracellular barrier. Experimental approaches to evaluate the effectiveness of tight junctions are typically global, tissue-scale measures. Here, we introduce Zinc-based Ultrasensitive Microscopic Barrier Assay (ZnUMBA), which we used in Xenopus laevis embryos to visualize short-lived, local breaches in epithelial barrier function. These breaches, or leaks, occur as cell boundaries elongate, correspond to visible breaks in the tight junction, and are followed by transient localized Rho activation, or Rho flares. We discovered that Rho flares restore barrier function by driving concentration of tight junction proteins through actin polymerization and ROCK-mediated localized contraction of the cell boundary. We conclude that Rho flares constitute a damage control mechanism that reinstates barrier function when tight junctions become locally compromised because of normally occurring changes in cell shape and tissue tension.

Fission Yeast NDR/LATS Kinase Orb6 Regulates Exocytosis via Phosphorylation of the Exocyst Complex.

NDR/LATS kinases regulate multiple aspects of cell polarity and morphogenesis from yeast to mammals. Fission yeast NDR/LATS kinase Orb6 has been proposed to control cell polarity by regulating the Cdc42 guanine nucleotide exchange factor Gef1. Here, we show that Orb6 regulates polarity largely independently of Gef1 and that Orb6 positively regulates exocytosis. Through Orb6 inhibition in vivo and quantitative global phosphoproteomics, we identify Orb6 targets, including proteins involved in membrane trafficking. We confirm Sec3 and Sec5, conserved components of the exocyst complex, as substrates of Orb6 both in vivo and in vitro, and we show that Orb6 kinase activity is important for exocyst localization to cell tips and for exocyst activity during septum dissolution after cytokinesis. We further find that Orb6 phosphorylation of Sec3 contributes to exocyst function in concert with exocyst protein Exo70. We propose that Orb6 contributes to polarized growth by regulating membrane trafficking at multiple levels.

Autoamplification and Competition Drive Symmetry Breaking: Initiation of Centriole Duplication by the PLK4-STIL Network.

Centrioles, the cores of centrosomes and cilia, duplicate every cell cycle to ensure their faithful inheritance. How only a single procentriole is produced on each mother centriole remains enigmatic. We propose the first mechanistic biophysical model for procentriole initiation which posits that interactions between kinase PLK4 and its activator-substrate STIL are central for procentriole initiation. The model recapitulates the transition from a uniform "ring" of PLK4 surrounding the mother centriole to a single PLK4 "spot" that initiates procentriole assembly. This symmetry breaking requires autocatalytic activation of PLK4 and enhanced centriolar anchoring of PLK4 by phosphorylated STIL. We find that in situ degradation of active PLK4 cannot break symmetry. The model predicts that competition between transient PLK4 activity maxima for PLK4-STIL complexes destabilizes the PLK4 ring and produces instead a single PLK4 spot. Weakening of competition by overexpression of PLK4 and STIL causes progressive addition of supernumerary procentrioles, as observed experimentally.

Cell Polarity: Spot-On Cdc42 Polarization Achieved on Demand.

A new study deploys optogenetics to induce the yeast bud on demand, at a site determined by a laser spot. The authors definitively prove that the initiation of cell polarization is driven by the Bem1-mediated positive feedback loop and reveal novel features of its regulation by the cell cycle.

Many roads to symmetry breaking: molecular mechanisms and theoretical models of yeast cell polarity.

Mathematical modeling has been instrumental in identifying common principles of cell polarity across diverse systems. These principles include positive feedback loops that are required to destabilize a spatially uniform state of the cell. The conserved small G-protein Cdc42 is a master regulator of eukaryotic cellular polarization. Here we discuss recent developments in studies of Cdc42 polarization in budding and fission yeasts and demonstrate that models describing symmetry-breaking polarization can be classified into six minimal classes based on the structure of positive feedback loops that activate and localize Cdc42. Owing to their generic system-independent nature, these model classes are also likely to be relevant for the G-protein-based symmetry-breaking systems of higher eukaryotes. We review experimental evidence pro et contra different theoretically plausible models and conclude that several parallel and non-mutually exclusive mechanisms are likely involved in cellular polarization of yeasts. This potential redundancy needs to be taken into consideration when interpreting the results of recent cell-rewiring studies.

Periodic spatiotemporal patterns in a two-dimensional two-variable reaction-diffusion model.

Periodic spatiotemporal two-dimensional (2D) asymptotic patterns in an excitable two-variable thermochemical (reaction-diffusion) system are shown. In a one-dimensional system the traveling impulse which reflects from impermeable boundaries is a stable asymptotic solution if the diffusion coefficient of the reactant is greater than the thermal diffusivity of the system. Periodic patterns of two symmetries are presented in the 2D system: the impulse of excitation propagating along the diagonal of a square spatial domain and a structure consisting of curved impulses which propagate in the direction perpendicular to one side of a rectangular domain.

Breaking of translational symmetry of a traveling planar impulse in a two-dimensional two-variable reaction-diffusion model.

The stability of a planar impulse in rectangular spatial domains for a two-variable excitable reaction-diffusion system is numerically studied. The dependence of the stability on the size of the domain perpendicular to the direction of the propagation of the impulse is shown. The instability results in asymptotic stable curved impulses or an asymptotic spatiotemporal structure, which is generated similarly to the one-dimensional backfiring phenomenon.