Different modes of state transitions determine pattern in the Phosphatidylinositide-Actin system

Competition and synergy of Arp2/3 and formins in nucleating actin waves

Actin assembly and dynamics are crucial for maintaining cell structure and changing physiological states. The broad impact of actin on various cellular processes makes it challenging to dissect the specific role of actin regulatory proteins. Using actin waves that propagate on the cortex of mast cells as a model, we discovered that formins (FMNL1 and mDia3) are recruited before the Arp2/3 complex in actin waves. GTPase Cdc42 interactions drive FMNL1 oscillations, with active Cdc42 and the constitutively active mutant of FMNL1 capable of forming waves on the plasma membrane independently of actin waves. Additionally, the delayed recruitment of Arp2/3 antagonizes FMNL1 and active Cdc42. This antagonism is not due to competition for monomeric actin but rather for their common upstream regulator, active Cdc42, whose levels are negatively regulated by Arp2/3 via SHIP1 recruitment. Collectively, our study highlights the complex feedback loops in the dynamic control of the actin cytoskeletal network.

Nonlinear dynamics in phosphoinositide metabolism

Phosphoinositides broadly impact membrane dynamics, signal transduction and cellular physiology. The orchestration of signaling complexity by this seemingly simple metabolic pathway remains an open question. It is increasingly evident that comprehending the complexity of the phosphoinositides metabolic network requires a systems view based on nonlinear dynamics, where the products of metabolism can either positively or negatively modulate enzymatic function. These feedback and feedforward loops may be paradoxical, leading to counterintuitive effects. In this review, we introduce the framework of nonlinear dynamics, emphasizing distinct dynamical regimes such as the excitable state, oscillations, and mixed-mode oscillations-all of which have been experimentally observed in phosphoinositide metabolisms. We delve into how these dynamical behaviors arise from one or multiple network motifs, including positive and negative feedback loops, coherent and incoherent feedforward loops. We explore the current understanding of the molecular circuits responsible for these behaviors. While mapping these circuits presents both conceptual and experimental challenges, redefining cellular behavior based on dynamical state, lipid fluxes, time delay, and network topology is likely essential for a comprehensive understanding of this fundamental metabolic network.

Periodicity, mixed-mode oscillations, and multiple timescales in a phosphoinositide-Rho GTPase network

While rhythmic contractile behavior is commonly observed at the cellular cortex, the primary focus has been on excitable or periodic events described by simple activator-delayed inhibitor mechanisms. We show that Rho GTPase activation in nocodazole-treated mitotic cells exhibits both simple oscillations and complex mixed-mode oscillations. Rho oscillations with a 20- to 30-s period are regulated by phosphatidylinositol (3,4,5)-trisphosphate (PIP3) via an activator-delayed inhibitor mechanism, while a slow reaction with period of minutes is regulated by phosphatidylinositol 4-kinase via an activator-substrate depletion mechanism. Conversion from simple to complex oscillations can be induced by modulating PIP3 metabolism or altering membrane contact site protein E-Syt1. PTEN depletion results in a period-doubling intermediate, which, like mixed-mode oscillations, is an intermediate state toward chaos. In sum, this system operates at the edge of chaos. Small changes in phosphoinositide metabolism can confer cells with the flexibility to rapidly enter ordered states with different periodicities.

Fluctuations of formin binding in the generation of membrane patterns

Circular actin waves that propagate on the substrate-attached membrane of Dictyostelium cells separate two distinct membrane domains from each other: an inner territory rich in phosphatidyl-(3,4,5) trisphosphate (PIP3) and an external area decorated with the PIP3-degrading 3-phosphatase PTEN. During wave propagation, the inner territory increases at the expense of the external area. Beyond a size limit, the inner territory becomes unstable, breaking into an inner and an external domain. The sharp boundary between these domains is demarcated by the insertion of an actin wave. During the conversion of inner territory to external area, the state of the membrane fluctuates, as visualized by dynamic landscapes of formin B binding. Here we analyze the formin B fluctuations in relation to three markers of the membrane state: activated Ras, PIP3, and PTEN.

From actin waves to mechanism and back: How theory aids biological understanding

Actin dynamics in cell motility, division, and phagocytosis is regulated by complex factors with multiple feedback loops, often leading to emergent dynamic patterns in the form of propagating waves of actin polymerization activity that are poorly understood. Many in the actin wave community have attempted to discern the underlying mechanisms using experiments and/or mathematical models and theory. Here, we survey methods and hypotheses for actin waves based on signaling networks, mechano-chemical effects, and transport characteristics, with examples drawn from Dictyostelium discoideum, human neutrophils, Caenorhabditis elegans, and Xenopus laevis oocytes. While experimentalists focus on the details of molecular components, theorists pose a central question of universality: Are there generic, model-independent, underlying principles, or just boundless cell-specific details? We argue that mathematical methods are equally important for understanding the emergence, evolution, and persistence of actin waves and conclude with a few challenges for future studies.

Nanotopography modulates intracellular excitable systems through cytoskeleton actuation

Cellular sensing of most environmental cues involves receptors that affect a signal-transduction excitable network (STEN), which is coupled to a cytoskeletal excitable network (CEN). We show that the mechanism of sensing of nanoridges is fundamentally different. CEN activity occurs preferentially on nanoridges, whereas STEN activity is constrained between nanoridges. In the absence of STEN, waves disappear, but long-lasting F-actin puncta persist along the ridges. When CEN is suppressed, wave propagation is no longer constrained by nanoridges. A computational model reproduces these experimental observations. Our findings indicate that nanotopography is sensed directly by CEN, whereas STEN is only indirectly affected due to a CEN-STEN feedback loop. These results explain why texture sensing is robust and acts cooperatively with multiple other guidance cues in complex, in vivo microenvironments.

Mechanochemical subcellular-element model of crawling cells

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Spontaneous transitions between amoeboid and keratocyte-like modes of migration

The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.

Versatile Patterns in the Actin Cortex of Motile Cells: Self-Organized Pulses Can Coexist with Macropinocytic Ring-Shaped Waves

Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. However, identifying how qualitatively distinct actin patterns can coexist remains a challenge. Using bifurcation theory of a mass conserved activator-inhibitor system, we uncover a generic mechanism of how different actin waves-traveling waves and excitable pulses-organize and simultaneously emerge. Live-cell imaging experiments indeed reveal that narrow, planar, and fast-moving excitable pulses may coexist with ring-shaped macropinocytic actin waves in the cortex of motile amoeboid cells.

Gradients of PI(4,5)P2 and PI(3,5)P2 Jointly Participate in Shaping the Back State of Dictyostelium Cells

Polarity, which refers to the molecular or structural asymmetry in cells, is essential for diverse cellular functions. Dictyostelium has proven to be a valuable system for dissecting the molecular mechanisms of cell polarity. Previous studies in Dictyostelium have revealed a range of signaling and cytoskeletal proteins that function at the leading edge to promote pseudopod extension and migration. In contrast, how proteins are localized to the trailing edge is not well understood. By screening for asymmetrically localized proteins, we identified a novel trailing-edge protein we named Teep1. We show that a charged surface formed by two pleckstrin homology (PH) domains in Teep1 is necessary and sufficient for targeting it to the rear of cells. Combining biochemical and imaging analyses, we demonstrate that Teep1 interacts preferentially with PI(4,5)P2 and PI(3,5)P2in vitro and simultaneous elimination of these lipid species in cells blocks the membrane association of Teep1. Furthermore, a leading-edge localized myotubularin phosphatase likely mediates the removal of PI(3,5)P2 from the front, as well as the formation of a back-to-front gradient of PI(3,5)P2. Together our data indicate that PI(4,5)P2 and PI(3,5)P2 on the plasma membrane jointly participate in shaping the back state of Dictyostelium cells.

Using Live-Cell Imaging and Synthetic Biology to Probe Directed Migration in Dictyostelium

For decades, the social amoeba Dictyostelium discoideum has been an invaluable tool for dissecting the biology of eukaryotic cells. Its short growth cycle and genetic tractability make it ideal for a variety of biochemical, cell biological, and biophysical assays. Dictyostelium have been widely used as a model of eukaryotic cell motility because the signaling and mechanical networks which they use to steer and produce forward motion are highly conserved. Because these migration networks consist of hundreds of interconnected proteins, perturbing individual molecules can have subtle effects or alter cell morphology and signaling in major unpredictable ways. Therefore, to fully understand this network, we must be able to quantitatively assess the consequences of abrupt modifications. This ability will allow us better control cell migration, which is critical for development and disease, in vivo. Here, we review recent advances in imaging, synthetic biology, and computational analysis which enable researchers to tune the activity of individual molecules in single living cells and precisely measure the effects on cellular motility and signaling. We also provide practical advice and resources to assist in applying these approaches in Dictyostelium.

Cellular self-organization: generating order from the abyss

While the organization of inanimate systems such as gases or liquids is predominantly thermodynamically driven—a mixture of two gases will tend to mix until they reach equilibrium—biological systems frequently exhibit organization that is far from a well-mixed equilibrium. The anisotropies displayed by cells are evident in some of the dynamic processes that constitute life including cell development, movement, and division. These anisotropies operate at different length-scales, from the meso- to the nanoscale, and are proposed to reflect self-organization, a characteristic of living systems that is becoming accessible to reconstitution from purified components, and thus a more thorough understanding. Here, some examples of self-organization underlying cellular anisotropies at the cellular level are reviewed, with an emphasis on Rho-family GTPases operating at the plasma membrane. Given the technical challenges of studying these dynamic proteins, some of the successful approaches that are being employed to study their self-organization will also be considered.

The excitable signal transduction networks: movers and shapers of eukaryotic cell migration

In response to a variety of external cues, eukaryotic cells display varied migratory modes to perform their physiological functions during development and in the adult. Aberrations in cell migration result in embryonic defects and cancer metastasis. The molecular components involved in cell migration are remarkably conserved between the social amoeba Dictyostelium and mammalian cells. This makes the amoeba an excellent model system for studies of eukaryotic cell migration. These migration-associated components can be grouped into three networks: input, signal transduction and cytoskeletal. In migrating cells, signal transduction events such as Ras or PI3K activity occur at the protrusion tips, referred to as 'front', whereas events such as dissociation of PTEN from these regions are referred to as 'back'. Asymmetric distribution of such front and back events is crucial for establishing polarity and guiding cell migration. The triggering of these signaling events displays properties of biochemical excitability including all-or-nothing responsiveness to suprathreshold stimuli, refractoriness, and wave propagation. These signal transduction waves originate from a point and propagate towards the edge of the cell, thereby driving cytoskeletal activity and cellular protrusions. Any change in the threshold for network activation alters the range of the propagating waves and the size of cellular protrusions which gives rise to various migratory modes in cells. Thus, this review highlights excitable signal transduction networks as key players for coordinating cytoskeletal activities to drive cell migration in all eukaryotes.

How cortical waves drive fission of motile cells

Cytokinesis-the division of a cell into two daughter cells-is a key step in cell growth and proliferation. It typically occurs in synchrony with the cell cycle to ensure that a complete copy of the genetic information is passed on to the next generation of daughter cells. In animal cells, cytokinesis commonly relies on an actomyosin contractile ring that drives equatorial furrowing and separation into the two daughter cells. However, also contractile ring-independent forms of cell division are known that depend on substrate-mediated traction forces. Here, we report evidence of an as yet unknown type of contractile ring-independent cytokinesis that we termed wave-mediated cytofission. It is driven by self-organized cortical actin waves that travel across the ventral membrane of oversized, multinucleated Dictyostelium discoideum cells. Upon collision with the cell border, waves may initiate the formation of protrusions that elongate and eventually pinch off to form separate daughter cells. They are composed of a stable elongated wave segment that is enclosed by a cell membrane and moves in a highly persistent fashion. We rationalize our observations based on a noisy excitable reaction-diffusion model in combination with a dynamic phase field to account for the cell shape and demonstrate that daughter cells emerging from wave-mediated cytofission exhibit a well-controlled size.

Formins specify membrane patterns generated by propagating actin waves

Circular actin waves separate two distinct areas on the substrate-attached cell surface from each other: an external area from an inner territory that is circumscribed by the wave. These areas differ in composition of actin-associated proteins and of phosphoinositides in the membrane. At the propagating wave, one area is converted into the other. By photo-conversion of Eos-actin and analysis of actin network structures we show that both in the inner territory and the external area the actin network is subject to continuous turnover. To address the question of whether areas in the wave pattern are specified by particular actin polymerizing machines, we locate five members of the formin family to specific regions of the wave landscape using TIRF microscopy and constitutively active formin constructs tagged with fluorescent protein. Formin ForB favors the actin wave and ForG the inner territory, whereas ForA, ForE, and ForH are more strongly recruited to the external area. Fluctuations of membrane binding peculiar to ForB indicate transient states in the specification of membrane domains before differentiation into ForB decorated and depleted ones. Annihilation of the patterns by 1 µM of the formin inhibitor SMIFH2 supports the implication of formins in their generation.

Oscillatory Switches of Dorso-Ventral Polarity in Cells Confined between Two Surfaces

To maneuver in a three-dimensional space, migrating cells need to accommodate to multiple surfaces. In particular, phagocytes have to explore their environment in the search for particles to be ingested. To examine how cells decide between competing surfaces, we exposed single cells of Dictyostelium to a defined three-dimensional space by confining them between two planar surfaces: those of a cover glass and of a wedged microcantilever. These cells form propagating waves of filamentous actin and PIP3 on their ventral substrate-attached surface. The dynamics of wave formation in the confined cells was explored using two-focus fluorescence imaging. When waves formed on one substrate, wave formation on the other substrate was efficiently suppressed. The propensity for wave formation switched between the opposing cell surfaces with periods of 2-5 min by one of two modes: 1) a rolling mode involving the slipping of a wave along the nonattached plasma membrane and 2) de novo initiation of waves on the previously blank cell surface. These data provide evidence for a cell-autonomous oscillator that switches dorso-ventral polarity in a cell simultaneously exposed to multiple substrate surfaces.

The Architecture of Traveling Actin Waves Revealed by Cryo-Electron Tomography

Actin waves are dynamic supramolecular structures involved in cell migration, cytokinesis, adhesion, and neurogenesis. Although wave-like propagation of actin networks is a widespread phenomenon, the actin architecture underlying wave propagation remained unknown. In situ cryo-electron tomography of Dictyostelium cells unveils the wave architecture and provides evidence for wave progression by de novo actin nucleation. Subtomogram averaging reveals the structure of Arp2/3 complex-mediated branch junctions in their native state, and enables quantitative analysis of the 3D organization of branching within the waves. We find an excess of branches directed toward the substrate-attached membrane, and tent-like structures at sites of branch clustering. Fluorescence imaging shows that Arp2/3 clusters follow accumulation of the elongation factor VASP. We propose that filament growth toward the membrane lifts up the actin network as the wave propagates, until depolymerization of oblique filaments at the back causes the collapse of horizontal filaments into a compact layer.

Wave patterns organize cellular protrusions and control cortical dynamics

Cellular protrusions are typically considered as distinct structures associated with specific regulators. However, we found that these regulators coordinately localize as propagating cortical waves, suggesting a common underlying mechanism. These molecular events fell into two excitable networks, the signal transduction network STEN and the cytoskeletal network CEN with different wave substructures. Computational studies using a coupled-network model reproduced these features and showed that the morphology and kinetics of the waves depended on strengths of feedback loops. Chemically induced dimerization at multiple nodes produced distinct, coordinated alterations in patterns of other network components. Taken together, these studies indicate: STEN positive feedback is mediated by mutual inhibition between Ras/Rap and PIP2, while negative feedback depends on delayed PKB activation; PKBs link STEN to CEN; CEN includes positive feedback between Rac and F-actin, and exerts fast positive and slow negative feedbacks to STEN The alterations produced protrusions resembling filopodia, ruffles, pseudopodia, or lamellipodia, suggesting that these structures arise from a common regulatory mechanism and that the overall state of the STEN-CEN system determines cellular morphology.

Excitable dynamics of Ras triggers spontaneous symmetry breaking of PIP3 signaling in motile cells

Spontaneous cell movement is underpinned by an asymmetric distribution of signaling molecules including small G proteins and phosphoinositides on the cell membrane. However, the molecular network necessary for spontaneous symmetry breaking has not been fully elucidated. Here, we report that, in Dictyostelium discoideum, the spatiotemporal dynamics of GTP bound Ras (Ras-GTP) breaks the symmetry due its intrinsic excitability even in the absence of extracellular spatial cues and downstream signaling activities. A stochastic excitation of local and transient Ras activation induced phosphatidylinositol (3,4,5)-trisphosphate (PIP3) accumulation via direct interaction with Phosphoinositide 3-kinase (PI3K), causing tightly coupled traveling waves that propagated along the membrane. Comprehensive phase analysis of the waves of Ras-GTP and PIP3 metabolism-related molecules revealed the network structure of the excitable system including positive-feedback regulation of Ras-GTP by the downstream PIP3. A mathematical model reconstituted a series of the observed symmetry-breaking phenomena, illustrating the essential involvement of Ras excitability in the cellular decision-making process.

Insight from the maximal activation of the signal transduction excitable network in Dictyostelium discoideum

Cell migration requires the coordination of an excitable signal transduction network involving Ras and PI3K pathways with cytoskeletal activity. We show that expressing activated Ras GTPase-family proteins in cells lacking PTEN or other mutations which increase cellular protrusiveness transforms cells into a persistently activated state. Leading- and trailing-edge markers were found exclusively at the cell perimeter and the cytosol, respectively, of the dramatically flattened cells. In addition, the lifetimes of dynamic actin puncta were increased where they overlapped with actin waves, suggesting a mechanism for the coupling between these two networks. All of these phenotypes could be reversed by inhibiting signal transduction. Strikingly, maintaining cells in this state of constant activation led to a form of cell death by catastrophic fragmentation. These findings provide insight into the feedback loops that control excitability of the signal transduction network, which drives migration.

The Sealing Zone in Osteoclasts: A Self-Organized Structure on the Bone

Osteoclasts form a specialized cell-matrix adhesion structure, known as the "sealing zone", during bone resorption. The sealing zone is a dynamic actin-rich structure that defines the resorption area of the bone. The detailed dynamics and fine structure of the sealing zone have been elusive. Osteoclasts plated on glass do not form a sealing zone, but generate a separate supra-molecular structure called the "podosome belt". Podosomes are integrin-based adhesion complexes involved in matrix adhesion, cell migration, matrix degradation, and mechanosensing. Invadopodia, podosome-like protrusions in cancer cells, are involved in cell invasion into other tissues by promoting matrix degradation. Both podosomes and invadopodia exhibit actin pattern transitions during maturation. We previously found that Arp2/3-dependent actin flow occurs in all observed assembly patterns of podosomes in osteoclasts on glass. It is known that the actin wave in Dictyostelium cells exhibits a similar pattern transition in its evolution. Because of significant advances in our understanding regarding the mechanism of podosomes/invadopodia formation over the last decade, we revisited the structure and function of the sealing zone in this review, highlighting the possible involvement of self-organized actin waves in the organogenesis of the sealing zone.

Parallel signaling pathways regulate excitable dynamics differently for pseudopod formation in eukaryotic chemotaxis

In eukaryotic chemotaxis, parallel signaling pathways regulate the spatiotemporal pseudopod dynamics at the leading edge of a motile cell through characteristic dynamics of an excitable system; however, differences in the excitability and the physiological roles of individual pathways remain to be elucidated. Here we found that two different pathways, soluble guanylyl cyclase (sGC) and phosphatidylinositol 3-kinase (PI3K), exhibited similar all-or-none responses but different refractory periods by simultaneous observations of their excitable properties. Due to the shorter refractory period, sGC signaling responded more frequently to chemoattractants, leading to pseudopod formation with higher frequency. sGC excitability was regulated negatively by its product, cGMP, and cGMP-binding protein C (GbpC) through the suppression of F-actin polymerization, providing the underlying delayed negative feedback mechanism for the cyclical pseudopod formation. These results suggest that parallel pathways respond on different time-scales to environmental cues for chemotactic motility based on their intrinsic excitability. Key words: cGMP signaling, chemotaxis, excitability, pseudopod formation

Assessment of Dictyostelium discoideum Response to Acute Mechanical Stimulation

Chemotaxis, or migration up a gradient of a chemoattractant, is the best understood mode of directed migration. Studies using social amoeba Dictyostelium discoideum revealed that a complex signal transduction network of parallel pathways amplifies the response to chemoattractants, and leads to biased actin polymerization and protrusion of a pseudopod in the direction of a gradient. In contrast, molecular mechanisms driving other types of directed migration, for example, due to exposure to shear flow or electric fields, are not known. Many regulators of chemotaxis exhibit localization at the leading or lagging edge of a migrating cell, as well as show transient changes in localization or activation following global stimulation with a chemoattractant. To understand the molecular mechanisms of other types of directed migration we developed a method that allows examination of cellular response to acute mechanical stimulation based on brief (2 - 5 s) exposure to shear flow. This stimulation can be delivered in a channel while imaging cells expressing fluorescently-labeled biosensors to examine individual cell behavior. Additionally, cell population can be stimulated in a plate, lysed, and immunoblotted using antibodies that recognize active versions of proteins of interest. By combining both assays, one can examine a wide array of molecules activated by changes in subcellular localization and/or phosphorylation. Using this method we determined that acute mechanical stimulation triggers activation of the chemotactic signal transduction and actin cytoskeleton networks. The ability to examine cellular responses to acute mechanical stimulation is important for understanding the initiating events necessary for shear flow-induced motility. This approach also provides a tool for studying the chemotactic signal transduction network without the confounding influence of the chemoattractant receptor.

Excitable Signal Transduction Networks in Directed Cell Migration

Although directed migration of eukaryotic cells may have evolved to escape nutrient depletion, it has been adopted for an extensive range of physiological events during development and in the adult organism. The subversion of these movements results in disease, such as cancer. Mechanisms of propulsion and sensing are extremely diverse, but most eukaryotic cells move by extending actin-filled protrusions termed macropinosomes, pseudopodia, or lamellipodia or by extension of blebs. In addition to motility, directed migration involves polarity and directional sensing. The hundreds of gene products involved in these processes are organized into networks of parallel and interconnected pathways. Many of these components are activated or inhibited coordinately with stimulation and on each spontaneously extended protrusion. Moreover, these networks display hallmarks of excitability, including all-or-nothing responsiveness and wave propagation. Cellular protrusions result from signal transduction waves that propagate outwardly from an origin and drive cytoskeletal activity. The range of the propagating waves and hence the size of the protrusions can be altered by lowering or raising the threshold for network activation, with larger and wider protrusions favoring gliding or oscillatory behavior over amoeboid migration. Here, we evaluate the variety of models of excitable networks controlling directed migration and outline critical tests. We also discuss the utility of this emerging view in producing cell migration and in integrating the various extrinsic cues that direct migration.

Symmetrical retrograde actin flow in the actin fusion structure is involved in osteoclast fusion

The aim of this study was to elucidate the role of the zipper-like structure (ZLS), a podosome-related structure that transiently appears at the cell contact zone, in osteoclast fusion. Live-cell imaging of osteoclasts derived from RAW264.7 cells transfected with EGFP-actin revealed consistent symmetrical retrograde actin flow in the ZLS, but not in the podosome cluster, the podosome ring or the podosome belt. Confocal imaging showed that the distributions of F-actin, vinculin, paxillin and zyxin in the ZLS were different from those in the podosome belt. Thick actin filament bundles running outside the ZLS appeared to recruit non-muscle myosin IIA. The F-actin-rich domain of the ZLS contained actin-related protein 2/3 complex (Arp2/3). Inhibition of Arp2/3 activity disorganized the ZLS, disrupted actin flow, deteriorated cell-cell adhesion and inhibited osteoclast hypermultinucleation. In contrast, ML-7, an inhibitor of myosin light chain kinase, had little effect on the structure of ZLS and promoted osteoclast hypermultinucleation. These results reveal a link between actin flow in the ZLS and osteoclast fusion. Osteoclast fusion was promoted by branched actin elongation and negatively regulated by actomyosin contraction.

Summary: Multinucleated osteoclasts form a podosome-derived fusion structure during cell fusion. Juxtaposition of fusion partner cells is probably maintained via force generated by symmetrical retrograde actin flow in the fusion structure.

Altering the threshold of an excitable signal transduction network changes cell migratory modes

The diverse migratory modes displayed by different cell types are generally believed to be idiosyncratic. Here we show that the migratory behavior of Dictyostelium was switched from amoeboid to keratocyte-like and oscillatory modes by synthetically decreasing PIP2 levels or increasing Ras/Rap-related activities. The perturbations at these key nodes of an excitable signal transduction network initiated a causal chain of events: The threshold for network activation was lowered, the speed and range of propagating waves of signal transduction activity increased, actin driven cellular protrusions expanded and, consequently, the cell migratory mode transitions ensued. Conversely, innately keratocyte-like and oscillatory cells were promptly converted to amoeboid by inhibition of Ras effectors with restoration of directed migration. We use computational analysis to explain how thresholds control cell migration and discuss the architecture of the signal transduction network that gives rise to excitability.

Actin Organization in Cells Responding to a Perforated Surface, Revealed by Live Imaging and Cryo-Electron Tomography

In a 3D environment, motile cells accommodate their protruding and retracting activities to geometrical cues. Dictyostelium cells migrating on a perforated film explored its holes by forming actin rings around their border and extending protrusions through the free space. The response was initiated when an actin wave passed a hole, and the rings persisted only in the PIP3-rich territories surrounded by a wave. To reconstruct actin structures from cryo-electron tomograms, actin rings were identified by cryo-correlative light and electron microscopy, and thin wedges of relevant regions were obtained by cryo-focused ion-beam milling. Retracting stages were distinguished from protruding ones by the accumulation of myosin-II. Early actin rings consisted of filaments pointing upright from the membrane, entangled with a meshwork of filaments close to the membrane. Branches identified at later stages suggested that formin-based nucleation of filaments was followed by Arp2/3-mediated network stabilization, which prevented buckling of the force-generating filaments.

Spatiotemporal relationships between the cell shape and the actomyosin cortex of periodically protruding cells

We investigate the dynamics of cell shape and analyze the actin and myosin distributions of cells exhibiting cortical density traveling waves. These waves propagate by repeated cycles of cortical compression (folding) and dilation (unfolding) that lead to periodic protrusions (oscillations) of the cell boundary. The focus of our detailed analysis is the remarkable periodicity of this phenotype, in which both the overall shape transformation and distribution of actomyosin density are repeated from cycle to cycle even though the characteristics of the shape transformation vary significantly for different regions of the cell. We show, using correlation analysis, that during traveling wave propagation cortical actin and plasma membrane densities are tightly coupled at each point along the cell periphery. We also demonstrate that the major protrusion appears at the wave trailing edge just after the actin cortex density has reached a maximum. Making use of the extraordinary periodicity, we employ latrunculin to demonstrate that sequestering actin monomers can have two distinct effects: low latrunculin concentrations can trigger and enhance traveling waves but higher concentrations of this drug retard the waves. The fundamental mechanism underlying this periodically protruding phenotype, involving folding and unfolding of the cortex‐membrane couple, is likely to hold important clues for diverse phenomena including cell division and amoeboid‐type migration. © 2015 The Authors. Cytoskeleton Published by Wiley Periodicals, Inc.

F-actin waves, actin cortex disassembly and focal exocytosis driven by actin-phosphoinositide positive feedback

Actin polymerization is controlled by the phosphoinositide composition of the plasma membrane. However, the molecular mechanisms underlying the spatiotemporal regulation of actin network organization over extended length scales are still unclear. To observe phosphoinositide-dependent cytoskeletal dynamics we combined the model system of frustrated phagocytosis, total internal reflection microscopy and manipulation of the buffer tonicity. We found that macrophages interacting with IgG-coated glass substrates formed circular F-actin waves on their ventral surface enclosing a region of plasma membrane devoid of cortical actin. Plasma membrane free of actin cortex was strongly depleted of PI(4,5)P2 , but enriched in PI(3,4)P2 and displayed a fivefold increase in exocytosis. Wave formation could be promoted by application of a hypotonic shock. The actin waves were characteristic of a bistable wavefront at the boundary between the regions of membrane containing and lacking cortical actin. Phosphoinositide modifiers and RhoGTPase activities dramatically redistributed with respect to the wavefronts, which often exhibited spatial oscillations. Perturbation of either lipid or actin cytoskeleton-related pathways led to rapid loss of both the polarized lipid distribution and the wavefront. As waves travelled over the plasma membrane, wavefront actin was seen to rapidly polymerize and depolymerize at pre-existing clusters of FcγRIIA, coincident with rapid changes in lipid composition. Thus the potential of receptors to support rapid F-actin polymerization appears to depend acutely on the local concentrations of multiple lipid species. We propose that interdependence through positive feedback from the cytoskeleton to lipid modifiers leads to coordinated local cortex remodeling, focal exocytosis, and organizes extended actin networks.

Selective localization of myosin-I proteins in macropinosomes and actin waves

Class I myosins are widely expressed with roles in endocytosis and cell migration in a variety of cell types. Dictyostelium express multiple myosin Is, including three short-tailed (Myo1A, Myo1E, Myo1F) and three long-tailed (Myo1B, Myo1C, Myo1D). Here we report the molecular basis of the specific localizations of short-tailed Myo1A, Myo1E, and Myo1F compared to our previously determined localization of long-tailed Myo1B. Myo1A and Myo1B have common and unique localizations consistent with the various features of their tail region; specifically the BH sites in their tails are required for their association with the plasma membrane and heads are sufficient for relocalization to the front of polarized cells. Myo1A does not localize to actin waves and macropinocytic protrusions, in agreement with the absence of a tail region which is required for these localizations of Myo1B. However, in spite of the overall similarity of their domain structures, the cellular distributions of Myo1E and Myo1F are quite different from Myo1A. Myo1E and Myo1F, but not Myo1A, are associated with macropinocytic cups and actin waves. The localizations of Myo1E and Myo1F in macropinocytic structures and actin waves differ from the localization of Myo1B. Myo1B colocalizes with F-actin in the actin waves and at the tips of mature macropinocytic cups whereas Myo1E and Myo1F are in the interior of actin waves and along the entire surface of macropinocytic cups. Our results point to different mechanisms of targeting of short- and long-tailed myosin Is, and are consistent with these myosins having both shared and divergent cellular functions.

Frequency and amplitude control of cortical oscillations by phosphoinositide waves

Rhythmicity is prevalent in the cortical dynamics of diverse single and multicellular systems. Current models of cortical oscillations focus primarily on cytoskeleton-based feedbacks, but information on signals upstream of the actin cytoskeleton is limited. In addition, inhibitory mechanisms--especially local inhibitory mechanisms, which ensure proper spatial and kinetic controls of activation--are not well understood. Here, we identified two phosphoinositide phosphatases, synaptojanin 2 and SHIP1, that function in periodic traveling waves of rat basophilic leukemia (RBL) mast cells. The local, phase-shifted activation of lipid phosphatases generates sequential waves of phosphoinositides. By acutely perturbing phosphoinositide composition using optogenetic methods, we showed that pulses of PtdIns(4,5)P2 regulate the amplitude of cyclic membrane waves while PtdIns(3,4)P2 sets the frequency. Collectively, these data suggest that the spatiotemporal dynamics of lipid metabolism have a key role in governing cortical oscillations and reveal how phosphatidylinositol 3-kinases (PI3K) activity could be frequency-encoded by a phosphatase-dependent inhibitory reaction.

Wave Patterns in Cell Membrane and Actin Cortex Uncoupled from Chemotactic Signals

When cells of Dictyostelium discoideum orientate in a gradient of chemoattractant, they are polarized into a protruding front pointing toward the source of attractant, and into a retracting tail. Under the control of chemotactic signal inputs, Ras is activated and PIP3 is synthesized at the front, while the PIP3-degrading phosphatase PTEN decorates the tail region. As a result of signal transduction, actin filaments assemble at the front into dendritic structures associated with the Arp2/3 complex, in contrast to the tail region where a loose actin meshwork is associated with myosin-II and cortexillin, an antiparallel actin-bundling protein. In axenically growing strains of D. discoideum, wave patterns built by the same components evolve in the absence of any external signal input. Since these autonomously generated patterns are constrained to the plane of the substrate-attached cell surface, they are optimally suited to the optical analysis of state transitions between front-like and tail-like states of the membrane and the actin cortex. Here, we describe imaging techniques using fluorescent proteins to probe for the state of the membrane, the reorganization of the actin network, and the dynamics of wave patterns.

The mechanisms of spatial and temporal patterning of cell-edge dynamics

Adherent cells migrate and change their shape by means of protrusion and retraction at their edges. When and where these activities occur defines the shape of the cell and the way it moves. Despite a great deal of knowledge about the structural organization, components, and biochemical reactions involved in protrusion and retraction, the origins of their spatial and temporal patterns are still poorly understood. Chemical signaling circuitry is believed to be an important source of patterning, but recent studies highlighted mechanisms based on physical forces, motion, and mechanical feedback.

Signaling networks that regulate cell migration

SUMMARY

Stimuli that promote cell migration, such as chemokines, cytokines, and growth factors in metazoans and cyclic AMP in Dictyostelium, activate signaling pathways that control organization of the actin cytoskeleton and adhesion complexes. The Rho-family GTPases are a key convergence point of these pathways. Their effectors include actin regulators such as formins, members of the WASP/WAVE family and the Arp2/3 complex, and the myosin II motor protein. Pathways that link to the Rho GTPases include Ras GTPases, TorC2, and PI3K. Many of the molecules involved form gradients within cells, which define the front and rear of migrating cells, and are also established in related cellular behaviors such as neuronal growth cone extension and cytokinesis. The signaling molecules that regulate migration can be integrated to provide a model of network function. The network displays biochemical excitability seen as spontaneous waves of activation that propagate along the cell cortex. These events coordinate cell movement and can be biased by external cues to bring about directed migration.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Dynamic membrane patterning, signal localization and polarity in living cells

We review the molecular and physical aspects of the dynamic localization of signaling molecules on the plasma membranes of living cells. At the nanoscale, clusters of receptors and signaling proteins play an essential role in the processing of extracellular signals. At the microscale, "soft" and highly dynamic signaling domains control the interaction of individual cells with their environment. At the multicellular scale, individual polarity patterns control the forces that shape multicellular aggregates and tissues.

Signaling in chemotactic amoebae remains spatially confined to stimulated membrane regions

Recent work has demonstrated that the receptor-mediated signaling system in chemotactic amoeboid cells shows typical properties of an excitable system. Here, we delivered spatially confined stimuli of the chemoattractant cAMP to the membrane of differentiated Dictyostelium discoideum cells to investigate whether localized receptor stimuli can induce the spreading of excitable waves in the G-protein-dependent signal transduction system. By imaging the spatiotemporal dynamics of fluorescent markers for phosphatidylinositol (3,4,5)-trisphosphate (PIP₃), PTEN and filamentous actin, we observed that the activity of the signaling pathway remained spatially confined to the stimulated membrane region. Neighboring parts of the membrane were not excited and no receptor-initiated spatial spreading of excitation waves was observed. To generate localized cAMP stimuli, either particles that carried covalently bound cAMP molecules on their surface were brought into contact with the cell or a patch of the cell membrane was aspirated into a glass micropipette to shield this patch against freely diffusing cAMP molecules in the surrounding medium. Additionally, the binding site of the cAMP receptor was probed with different surface-immobilized cAMP molecules, confirming results from earlier ligand-binding studies.

Excitable signal transduction induces both spontaneous and directional cell asymmetries in the phosphatidylinositol lipid signaling system for eukaryotic chemotaxis

Intracellular asymmetry in the signaling network works as a compass to navigate eukaryotic chemotaxis in response to guidance cues. Although the compass variable can be derived from a self-organization dynamics, such as excitability, the responsible mechanism remains to be clarified. Here, we analyzed the spatiotemporal dynamics of the phosphatidylinositol 3,4,5-trisphosphate (PtdInsP3) pathway, which is crucial for chemotaxis. We show that spontaneous activation of PtdInsP3-enriched domains is generated by an intrinsic excitable system. Formation of the same signal domain could be triggered by various perturbations, such as short impulse perturbations that triggered the activation of intrinsic dynamics to form signal domains. We also observed the refractory behavior exhibited in typical excitable systems. We show that the chemotactic response of PtdInsP3 involves biasing the spontaneous excitation to orient the activation site toward the chemoattractant. Thus, this biased excitability embodies the compass variable that is responsible for both random cell migration and biased random walk. Our finding may explain how cells achieve high sensitivity to and robust coordination of the downstream activation that allows chemotactic behavior in the noisy environment outside and inside the cells.

PTEN redundancy: overexpressing lpten, a homolog of Dictyostelium discoideum ptenA, the ortholog of human PTEN, rescues all behavioral defects of the mutant ptenA-

Mutations in the tumor suppressor gene PTEN are associated with a significant proportion of human cancers. Because the human genome also contains several homologs of PTEN, we considered the hypothesis that if a homolog, functionally redundant with PTEN, can be overexpressed, it may rescue the defects of a PTEN mutant. We have performed an initial test of this hypothesis in the model system Dictyostelium discoideum, which contains an ortholog of human PTEN, ptenA. Deletion of ptenA results in defects in motility, chemotaxis, aggregation and multicellular morphogenesis. D. discoideum also contains lpten, a newly discovered homolog of ptenA. Overexpressing lpten completely rescues all developmental and behavioral defects of the D. discoideum mutant ptenA⁻. This hypothesis must now be tested in human cells.

Actin and PIP3 waves in giant cells reveal the inherent length scale of an excited state

The membrane and actin cortex of a motile cell can autonomously differentiate into two states, one typical of the front, the other of the tail. On the substrate-attached surface of Dictyostelium discoideum cells, dynamic patterns of front-like and tail-like states are generated that are well suited to monitor transitions between these states. To image large-scale pattern dynamics independently of boundary effects, we produced giant cells by electric-pulse-induced cell fusion. In these cells, actin waves are coupled to the front and back of phosphatidylinositol (3,4,5)-trisphosphate (PIP3)-rich bands that have a finite width. These composite waves propagate across the plasma membrane of the giant cells with undiminished velocity. After any disturbance, the bands of PIP3 return to their intrinsic width. Upon collision, the waves locally annihilate each other and change direction; at the cell border they are either extinguished or reflected. Accordingly, expanding areas of progressing PIP3 synthesis become unstable beyond a critical radius, their center switching from a front-like to a tail-like state. Our data suggest that PIP3 patterns in normal-sized cells are segments of the self-organizing patterns that evolve in giant cells.

Modeling self-organized spatio-temporal patterns of PIP₃ and PTEN during spontaneous cell polarization

During spontaneous cell polarization of Dictyostelium discoideum cells, phosphatidylinositol (3,4,5)-triphoshpate (PIP3) and PTEN (phosphatase tensin homolog) have been identified as key signaling molecules which govern the process of polarization in a self-organized manner. Recent experiments have quantified the spatio-temporal dynamics of these signaling components. Surprisingly, it was found that membrane-bound PTEN can be either in a high or low state, that PIP3 waves were initiated in areas lacking PTEN through an excitable mechanism, and that PIP3 was degraded even though the PTEN concentration remained low. Here we develop a reaction-diffusion model that aims to explain these experimental findings. Our model contains bistable dynamics for PTEN, excitable dynamics for PIP3, and postulates the existence of two species of PTEN with different dephosphorylation rates. We show that our model is able to produce results that are in good qualitative agreement with the experiments, suggesting that our reaction-diffusion model underlies the self-organized spatio-temporal patterns observed in experiments.

The association of myosin IB with actin waves in dictyostelium requires both the plasma membrane-binding site and actin-binding region in the myosin tail

F-actin structures and their distribution are important determinants of the dynamic shapes and functions of eukaryotic cells. Actin waves are F-actin formations that move along the ventral cell membrane driven by actin polymerization. Dictyostelium myosin IB is associated with actin waves but its role in the wave is unknown. Myosin IB is a monomeric, non-filamentous myosin with a globular head that binds to F-actin and has motor activity, and a non-helical tail comprising a basic region, a glycine-proline-glutamine-rich region and an SH3-domain. The basic region binds to acidic phospholipids in the plasma membrane through a short basic-hydrophobic site and the Gly-Pro-Gln region binds F-actin. In the current work we found that both the basic-hydrophobic site in the basic region and the Gly-Pro-Gln region of the tail are required for the association of myosin IB with actin waves. This is the first evidence that the Gly-Pro-Gln region is required for localization of myosin IB to a specific actin structure in situ. The head is not required for myosin IB association with actin waves but binding of the head to F-actin strengthens the association of myosin IB with waves and stabilizes waves. Neither the SH3-domain nor motor activity is required for association of myosin IB with actin waves. We conclude that myosin IB contributes to anchoring actin waves to the plasma membranes by binding of the basic-hydrophobic site to acidic phospholipids in the plasma membrane and binding of the Gly-Pro-Gln region to F-actin in the wave.

A continuum model of actin waves in Dictyostelium discoideum

Actin waves are complex dynamical patterns of the dendritic network of filamentous actin in eukaryotes. We developed a model of actin waves in PTEN-deficient Dictyostelium discoideum by deriving an approximation of the dynamics of discrete actin filaments and combining it with a signaling pathway that controls filament branching. This signaling pathway, together with the actin network, contains a positive feedback loop that drives the actin waves. Our model predicts the structure, composition, and dynamics of waves that are consistent with existing experimental evidence, as well as the biochemical dependence on various protein partners. Simulation suggests that actin waves are initiated when local actin network activity, caused by an independent process, exceeds a certain threshold. Moreover, diffusion of proteins that form a positive feedback loop with the actin network alone is sufficient for propagation of actin waves at the observed speed of . Decay of the wave back can be caused by scarcity of network components, and the shape of actin waves is highly dependent on the filament disassembly rate. The model allows retraction of actin waves and captures formation of new wave fronts in broken waves. Our results demonstrate that a delicate balance between a positive feedback, filament disassembly, and local availability of network components is essential for the complex dynamics of actin waves.

Phase geometries of two-dimensional excitable waves govern self-organized morphodynamics of amoeboid cells

In both randomly moving Dictyostelium and mammalian cells, phosphatidylinositol (3,4,5)-trisphosphate and F-actin are known to propagate as waves at the membrane and act to push out the protruding edge. To date, however, the relationship between the wave geometry and the patterns of amoeboid shape change remains elusive. Here, by using phase map analysis, we show that morphology dynamics of randomly moving Dictyostelium discoideum cells can be characterized by the number, topology, and position of spatial phase singularities, i.e., points that represent organizing centers of rotating waves. A single isolated singularity near the cellular edge induced a rotational protrusion, whereas a pair of singularities supported a symmetric extension. These singularities appeared by strong phase resetting due to de novo nucleation at the back of preexisting waves. Analysis of a theoretical model indicated excitability of the system that is governed by positive feedback from phosphatidylinositol (3,4,5)-trisphosphate to PI3-kinase activation, and we showed experimentally that this requires F-actin. Furthermore, by incorporating membrane deformation into the model, we demonstrated that geometries of competing waves explain most of the observed semiperiodic changes in amoeboid morphology.

PIP3 waves and PTEN dynamics in the emergence of cell polarity

In a motile eukaryotic cell, front protrusion and tail retraction are superimposed on each other. To single out mechanisms that result in front to tail or in tail to front transition, we separated the two processes in time using cells that oscillate between a full front and a full tail state. State transitions were visualized by total internal reflection fluorescence microscopy using as a front marker PIP3 (phosphatidylinositol [3,4,5] tris-phosphate), and as a tail marker the tumor-suppressor PTEN (phosphatase tensin homolog) that degrades PIP3. Negative fluctuations in the PTEN layer of the membrane gated a local increase in PIP3. In a subset of areas lacking PTEN (PTEN holes), PIP3 was amplified until a propagated wave was initiated. Wave propagation implies that a PIP3 signal is transmitted by a self-sustained process, such that the temporal and spatial profiles of the signal are maintained during passage of the wave across the entire expanse of the cell membrane. Actin clusters were remodeled into a ring along the perimeter of the expanding PIP3 wave. The reverse transition of PIP3 to PTEN was linked to the previous site of wave initiation: where PIP3 decayed first, the entry of PTEN was primed.

Modeling the self-organized phosphatidylinositol lipid signaling system in chemotactic cells using quantitative image analysis

A key signaling event that is responsible for gradient sensing in eukaryotic cell chemotaxis is a phosphatidylinositol (PtdIns) lipid reaction system. The self-organization activity of this PtdIns lipid system induces an inherent polarity, even in the absence of an external chemoattractant gradient, by producing a localized PtdIns (3,4,5)-trisphosphate [PtdIns(3,4,5)P(3)]-enriched domain on the membrane. Experimentally, we found that such a domain could exhibit two types of behavior: (1) it could be persistent and travel on the membrane, or (2) be stochastic and transient. Taking advantage of the simultaneous visualization of PtdIns(3,4,5)P(3) and the enzyme phosphatase and tensin homolog (PTEN), for which PtdIns(3,4,5)P(3) is a substrate, we statistically demonstrated the inter-dependence of their spatiotemporal dynamics. On the basis of this statistical analysis, we developed a theoretical model for the self-organization of PtdIns lipid signaling that can accurately reproduce both persistent and transient domain formation; these types of formations can be explained by the oscillatory and excitability properties of the system, respectively.

Molecular basis of dynamic relocalization of Dictyostelium myosin IB

Class I myosins have a single heavy chain comprising an N-terminal motor domain with actin-activated ATPase activity and a C-terminal globular tail with a basic region that binds to acidic phospholipids. These myosins contribute to the formation of actin-rich protrusions such as pseudopodia, but regulation of the dynamic localization to these structures is not understood. Previously, we found that Acanthamoeba myosin IC binds to acidic phospholipids in vitro through a short sequence of basic and hydrophobic amino acids, BH site, based on the charge density of the phospholipids. The tail of Dictyostelium myosin IB (DMIB) also contains a BH site. We now report that the BH site is essential for DMIB binding to the plasma membrane and describe the molecular basis of the dynamic relocalization of DMIB in live cells. Endogenous DMIB is localized uniformly on the plasma membrane of resting cells, at active protrusions and cell-cell contacts of randomly moving cells, and at the front of motile polarized cells. The BH site is required for association of DMIB with the plasma membrane at all stages where it colocalizes with phosphoinositide bisphosphate/phosphoinositide trisphosphate (PIP(2)/PIP(3)). The charge-based specificity of the BH site allows for in vivo specificity of DMIB for PIP(2)/PIP(3) similar to the PH domain-based specificity of other class I myosins. However, DMIB-head is required for relocalization of DMIB to the front of migrating cells. Motor activity is not essential, but the actin binding site in the head is important. Thus, dynamic relocalization of DMIB is determined principally by the local PIP(2)/PIP(3) concentration in the plasma membrane and cytoplasmic F-actin.