A conceptual molecular network for chemotactic behaviors characterized by feedback of molecules cycling between the membrane and the cytosol

Particle-based simulations reveal two positive feedback loops allow relocation and stabilization of the polarity site during yeast mating

Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site is often not oriented towards the eventual mating partner, and cells relocate the polarity site in an indecisive manner before developing a stable orientation. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior and moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are unlikely to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Surprisingly, inclusion of a second pathway that promotes polarity site orientation generated relocating polarity sites with properties similar to those observed experimentally. This pathway forms a second positive feedback loop involving the recruitment of receptors to the cell membrane and couples polarity establishment to gradient sensing. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.

Comparative mapping of crawling-cell morphodynamics in deep learning-based feature space

Navigation of fast migrating cells such as amoeba Dictyostelium and immune cells are tightly associated with their morphologies that range from steady polarized forms that support high directionality to those more complex and variable when making frequent turns. Model simulations are essential for quantitative understanding of these features and their origins, however systematic comparisons with real data are underdeveloped. Here, by employing deep-learning-based feature extraction combined with phase-field modeling framework, we show that a low dimensional feature space for 2D migrating cell morphologies obtained from the shape stereotype of keratocytes, Dictyostelium and neutrophils can be fully mapped by an interlinked signaling network of cell-polarization and protrusion dynamics. Our analysis links the data-driven shape analysis to the underlying causalities by identifying key parameters critical for migratory morphologies both normal and aberrant under genetic and pharmacological perturbations. The results underscore the importance of deciphering self-organizing states and their interplay when characterizing morphological phenotypes.

Migratory cells that move by crawling do so by extending and retracting their plasma membrane. When and where these events take place determine the cell shape, and this is directly linked to the movement patterns. Understanding how the highly plastic and interconvertible morphologies appear from their underlying dynamics remains a challenge partly because their inherent complexity makes quantitatively comparison against the outputs of mathematical models difficult. To this end, we employed machine-learning based classification to extract features that characterize the basic migrating morphologies. The obtained features were then used to compare real cell data with outputs of a conceptual model that we introduced which describes coupling via feedback between local protrusive dynamics and polarity. The feature mapping showed that the model successfully recapitulates the shape dynamics that were not covered by previous related models and also hints at the critical parameters underlying state transitions. The ability of the present approach to compare model outputs with real cell data systematically and objectively is important as it allows outputs of future mathematical models to be quantitatively tested in an accessible and common reference frame.

How cells determine the number of polarity sites

The diversity of cell morphologies arises, in part, through regulation of cell polarity by Rho-family GTPases. A poorly understood but fundamental question concerns the regulatory mechanisms by which different cells generate different numbers of polarity sites. Mass-conserved activator-substrate (MCAS) models that describe polarity circuits develop multiple initial polarity sites, but then those sites engage in competition, leaving a single winner. Theoretical analyses predicted that competition would slow dramatically as GTPase concentrations at different polarity sites increase toward a 'saturation point', allowing polarity sites to coexist. Here, we test this prediction using budding yeast cells, and confirm that increasing the amount of key polarity proteins results in multiple polarity sites and simultaneous budding. Further, we elucidate a novel design principle whereby cells can switch from competition to equalization among polarity sites. These findings provide insight into how cells with diverse morphologies may determine the number of polarity sites.

Screening by changes in stereotypical behavior during cell motility

Stereotyped behaviors are series of postures that show very little variability between repeats. They have been used to classify the dynamics of individuals, groups and species without reference to the lower-level mechanisms that drive them. Stereotypes are easily identified in animals due to strong constraints on the number, shape, and relative positions of anatomical features, such as limbs, that may be used as landmarks for posture identification. In contrast, the identification of stereotypes in single cells poses a significant challenge as the cell lacks these landmark features, and finding constraints on cell shape is a non-trivial task. Here, we use the maximum caliber variational method to build a minimal model of cell behavior during migration. Without reference to biochemical details, we are able to make behavioral predictions over timescales of minutes using only changes in cell shape over timescales of seconds. We use drug treatment and genetics to demonstrate that maximum caliber descriptors can discriminate between healthy and aberrant migration, thereby showing potential applications for maximum caliber methods in automated disease screening, for example in the identification of behaviors associated with cancer metastasis.

Principles that govern competition or co-existence in Rho-GTPase driven polarization

Rho-GTPases are master regulators of polarity establishment and cell morphology. Positive feedback enables concentration of Rho-GTPases into clusters at the cell cortex, from where they regulate the cytoskeleton. Different cell types reproducibly generate either one (e.g. the front of a migrating cell) or several clusters (e.g. the multiple dendrites of a neuron), but the mechanistic basis for unipolar or multipolar outcomes is unclear. The design principles of Rho-GTPase circuits are captured by two-component reaction-diffusion models based on conserved aspects of Rho-GTPase biochemistry. Some such models display rapid winner-takes-all competition between clusters, yielding a unipolar outcome. Other models allow prolonged co-existence of clusters. We investigate the behavior of a simple class of models and show that while the timescale of competition varies enormously depending on model parameters, a single factor explains a large majority of this variation. The dominant factor concerns the degree to which the maximal active GTPase concentration in a cluster approaches a "saturation point" determined by model parameters. We suggest that both saturation and the effect of saturation on competition reflect fundamental properties of the Rho-GTPase polarity machinery, regardless of the specific feedback mechanism, which predict whether the system will generate unipolar or multipolar outcomes.

The IQGAP-related protein DGAP1 mediates signaling to the actin cytoskeleton as an effector and a sequestrator of Rac1 GTPases

Proteins are typically categorized into protein families based on their domain organization. Yet, evolutionarily unrelated proteins can also be grouped together according to their common functional roles. Sequestering proteins constitute one such functional class, acting as macromolecular buffers and serving as an intracellular reservoir ready to release large quantities of bound proteins or other molecules upon appropriate stimulation. Another functional protein class comprises effector proteins, which constitute essential components of many intracellular signal transduction pathways. For instance, effectors of small GTP-hydrolases are activated upon binding a GTP-bound GTPase and thereupon participate in downstream interactions. Here we describe a member of the IQGAP family of scaffolding proteins, DGAP1 from Dictyostelium, which unifies the roles of an effector and a sequestrator in regard to the small GTPase Rac1. Unlike classical effectors, which bind their activators transiently leading to short-lived signaling complexes, interaction between DGAP1 and Rac1-GTP is stable and induces formation of a complex with actin-bundling proteins cortexillins at the back end of the cell. An oppositely localized Rac1 effector, the Scar/WAVE complex, promotes actin polymerization at the cell front. Competition between DGAP1 and Scar/WAVE for the common activator Rac1-GTP might provide the basis for the oscillatory re-polarization typically seen in randomly migrating Dictyostelium cells. We discuss the consequences of the dual roles exerted by DGAP1 and Rac1 in the regulation of cell motility and polarity, and propose that similar signaling mechanisms may be of general importance in regulating spatiotemporal dynamics of the actin cytoskeleton by small GTPases.

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.

Chemotaxis: movement, direction, control

This review focuses on basic principles of motility in different cell types, formation of the specific cell structures that enable directed migration, and how external signals are transduced into cells and coupled to the motile machinery. Feedback mechanisms and their potential role in maintenance of internal chemotactic gradients and persistence of directed migration are highlighted.

An excitable cortex and memory model successfully predicts new pseudopod dynamics

Motile eukaryotic cells migrate with directional persistence by alternating left and right turns, even in the absence of external cues. For example, Dictyostelium discoideum cells crawl by extending distinct pseudopods in an alternating right-left pattern. The mechanisms underlying this zig-zag behavior, however, remain unknown. Here we propose a new Excitable Cortex and Memory (EC&M) model for understanding the alternating, zig-zag extension of pseudopods. Incorporating elements of previous models, we consider the cell cortex as an excitable system and include global inhibition of new pseudopods while a pseudopod is active. With the novel hypothesis that pseudopod activity makes the local cortex temporarily more excitable--thus creating a memory of previous pseudopod locations--the model reproduces experimentally observed zig-zag behavior. Furthermore, the EC&M model makes four new predictions concerning pseudopod dynamics. To test these predictions we develop an algorithm that detects pseudopods via hierarchical clustering of individual membrane extensions. Data from cell-tracking experiments agrees with all four predictions of the model, revealing that pseudopod placement is a non-Markovian process affected by the dynamics of previous pseudopods. The model is also compatible with known limits of chemotactic sensitivity. In addition to providing a predictive approach to studying eukaryotic cell motion, the EC&M model provides a general framework for future models, and suggests directions for new research regarding the molecular mechanisms underlying directional persistence.

FRET imaging and statistical signal processing reveal positive and negative feedback loops regulating the morphology of randomly migrating HT-1080 cells

Cell migration plays an important role in many physiological processes. Rho GTPases (Rac1, Cdc42, RhoA) and phosphatidylinositols have been extensively studied in directional cell migration. However, it remains unclear how Rho GTPases and phosphatidylinositols regulate random cell migration in space and time. We have attempted to address this issue using fluorescence resonance energy transfer (FRET) imaging and statistical signal processing. First, we acquired time-lapse images of random migration of HT-1080 fibrosarcoma cells expressing FRET biosensors of Rho GTPases and phosphatidyl inositols. We developed an image-processing algorithm to extract FRET values and velocities at the leading edge of migrating cells. Auto- and cross-correlation analysis suggested the involvement of feedback regulations among Rac1, phosphatidyl inositols and membrane protrusions. To verify the feedback regulations, we employed an acute inhibition of the signaling pathway with pharmaceutical inhibitors. The inhibition of actin polymerization decreased Rac1 activity, indicating the presence of positive feedback from actin polymerization to Rac1. Furthermore, treatment with PI3-kinase inhibitor induced an adaptation of Rac1 activity, i.e. a transient reduction of Rac1 activity followed by recovery to the basal level. In silico modeling that reproduced the adaptation predicted the existence of a negative feedback loop from Rac1 to actin polymerization. Finally, we identified MLCK as the probable controlling factor in the negative feedback. These findings quantitatively demonstrate positive and negative feedback loops that involve actin, Rac1 and MLCK, and account for the ordered patterns of membrane dynamics observed in randomly migrating cells.

How cells use pseudopods for persistent movement and navigation

Pseudopods are cell extensions used for movement. The direction and trajectory of cell movement depend on how cells extend pseudopods. Experimental data show that new pseudopods are frequently formed by the splitting of an existing pseudopod, often as a series of left-right extensions. Here, these data on pseudopod extensions are discussed in the context of a theoretical model for pseudopod splitting.