Cell shape dynamics: from waves to migration

Machine learning based methodology to identify cell shape phenotypes associated with microenvironmental cues

Cell morphology has been identified as a potential indicator of stem cell response to biomaterials. However, determination of cell shape phenotype in biomaterials is complicated by heterogeneous cell populations, microenvironment heterogeneity, and multi-parametric definitions of cell morphology. To associate cell morphology with cell-material interactions, we developed a shape phenotyping framework based on support vector machines. A feature selection procedure was implemented to select the most significant combination of cell shape metrics to build classifiers with both accuracy and stability to identify and predict microenvironment-driven morphological differences in heterogeneous cell populations. The analysis was conducted at a multi-cell level, where a "supercell" method used average shape measurements of small groups of single cells to account for heterogeneous populations and microenvironment. A subsampling validation algorithm revealed the range of supercell sizes and sample sizes needed for classifier stability and generalization capability. As an example, the responses of human bone marrow stromal cells (hBMSCs) to fibrous vs flat microenvironments were compared on day 1. Our analysis showed that 57 cells (grouped into supercells of size 4) are the minimum needed for phenotyping. The analysis identified that a combination of minor axis length, solidity, and mean negative curvature were the strongest early shape-based indicator of hBMSCs response to fibrous microenvironment.

Quantitative analysis of B-lymphocyte migration directed by CXCL13

B-lymphocyte migration, directed by chemokine gradients, is essential for homing to sites of antigen presentation. B cells move rapidly, exhibiting amoeboid morphology like other leukocytes, yet quantitative studies addressing B-cell migration are currently lacking relative to neutrophils, macrophages, and T cells. Here, we used total internal reflection fluorescence (TIRF) microscopy to characterize the changes in shape (morphodynamics) of primary, murine B cells as they migrated on surfaces with adsorbed chemokine, CXCL13, and the adhesive ligand, ICAM-1. B cells exhibited frequent, spontaneous dilation and shrinking events at the sides of the leading membrane edge, a phenomenon that was predictive of turning versus directional persistence. To characterize directed B-cell migration, a microfluidic device was implemented to generate gradients of adsorbed CXCL13 gradients. Haptotaxis assays revealed a modest yet consistently positive bias of the cell's persistent random walk behavior towards CXCL13 gradients. Quantification of tactic fidelity showed that bias is optimized by steeper gradients without excessive midpoint density of adsorbed chemokine. Under these conditions, B-cell migration is more persistent when the direction of migration is better aligned with the gradient.

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.

Self-organization of chemoattractant waves in Dictyostelium depends on F-actin and cell-substrate adhesion

In the social amoeba Dictyostelium discoideum, travelling waves of extracellular cyclic adenosine monophosphate (cAMP) self-organize in cell populations and direct aggregation of individual cells to form multicellular fruiting bodies. In contrast to the large body of studies that addressed how movement of cells is determined by spatial and temporal cues encoded in the dynamic cAMP gradients, how cell mechanics affect the formation of a self-generated chemoattractant field has received less attention. Here, we show, by live cell imaging analysis, that the periodicity of the synchronized cAMP waves increases in cells treated with the actin inhibitor latrunculin. Detail analysis of the extracellular cAMP-induced transients of cytosolic cAMP (cAMP relay response) in well-isolated cells demonstrated that their amplitude and duration were markedly reduced in latrunculin-treated cells. Similarly, in cells strongly adhered to a poly-l-lysine-coated surface, the response was suppressed, and the periodicity of the population-level oscillations was markedly lengthened. Our results suggest that cortical F-actin is dispensable for the basic low amplitude relay response but essential for its full amplification and that this enhanced response is necessary to establish high-frequency signalling centres. The observed F-actin dependence may prevent aggregation centres from establishing in microenvironments that are incompatible with cell migration.

Linking morphodynamics and directional persistence of T lymphocyte migration

T cells play a central role in the adaptive immune response, and their directed migration is essential for homing to sites of antigen presentation. Like neutrophils, T lymphocytes are rapidly moving cells that exhibit amoeboid movement, characterized by a definitive polarity with F-actin concentrated at the front and myosin II elsewhere. In this study, we used total internal reflection fluorescence (TIRF) microscopy to monitor the cells' areas of contact with a surface presenting adhesive ICAM-1 and the chemokine, CXCL12/SDF-1. Our analysis reveals that T-cell migration and reorientation are achieved by bifurcation and lateral separation of protrusions along the leading membrane edge, followed by cessation of one of the protrusions, which acts as a pivot for cell turning. We show that the distribution of bifurcation frequencies exhibits characteristics of a random, spontaneous process; yet, the waiting time between bifurcation events depends on whether or not the pivot point remains on the same side of the migration axis. Our analysis further suggests that switching of the dominant protrusion between the two sides of the migration axis is associated with persistent migration, whereas the opposite is true of cell turning. To help explain the bifurcation phenomenon and how distinct migration behaviours might arise, a spatio-temporal, stochastic model describing F-actin dynamics is offered.

Cooperative cell motility during tandem locomotion of amoeboid cells

Tandem pairs of Dictyostelium cells migrate synchronously with an ~54-s time delay between the formation of their frontal protrusions. Each cell establishes two active adhesions, with the trailing cell reusing the location of the adhesions of the leading cell. This coordinated motility is mechanically driven and aided by cell–cell adhesions.

Streams of migratory cells are initiated by the formation of tandem pairs of cells connected head to tail to which other cells subsequently adhere. The mechanisms regulating the transition from single to streaming cell migration remain elusive, although several molecules have been suggested to be involved. In this work, we investigate the mechanics of the locomotion of Dictyostelium tandem pairs by analyzing the spatiotemporal evolution of their traction adhesions (TAs). We find that in migrating wild-type tandem pairs, each cell exerts traction forces on stationary sites (∼80% of the time), and the trailing cell reuses the location of the TAs of the leading cell. Both leading and trailing cells form contractile dipoles and synchronize the formation of new frontal TAs with ∼54-s time delay. Cells not expressing the lectin discoidin I or moving on discoidin I–coated substrata form fewer tandems, but the trailing cell still reuses the locations of the TAs of the leading cell, suggesting that discoidin I is not responsible for a possible chemically driven synchronization process. The migration dynamics of the tandems indicate that their TAs’ reuse results from the mechanical synchronization of the leading and trailing cells’ protrusions and retractions (motility cycles) aided by the cell–cell adhesions.

Time series modeling of live-cell shape dynamics for image-based phenotypic profiling

Live-cell imaging can be used to capture spatio-temporal aspects of cellular responses that are not accessible to fixed-cell imaging. As the use of live-cell imaging continues to increase, new computational procedures are needed to characterize and classify the temporal dynamics of individual cells. For this purpose, here we present the general experimental-computational framework SAPHIRE (Stochastic Annotation of Phenotypic Individual-cell Responses) to characterize phenotypic cellular responses from time series imaging datasets. Hidden Markov modeling is used to infer and annotate morphological state and state-switching properties from image-derived cell shape measurements. Time series modeling is performed on each cell individually, making the approach broadly useful for analyzing asynchronous cell populations. Two-color fluorescent cells simultaneously expressing actin and nuclear reporters enabled us to profile temporal changes in cell shape following pharmacological inhibition of cytoskeleton-regulatory signaling pathways. Results are compared with existing approaches conventionally applied to fixed-cell imaging datasets, and indicate that time series modeling captures heterogeneous dynamic cellular responses that can improve drug classification and offer additional important insight into mechanisms of drug action. The software is available at http://saphire-hcs.org.

T Lymphocyte Migration: An Action Movie Starring the Actin and Associated Actors

The actin cytoskeleton is composed of a dynamic filament meshwork that builds the architecture of the cell to sustain its fundamental properties. This physical structure is characterized by a continuous remodeling, which allows cells to accomplish complex motility steps such as directed migration, crossing of biological barriers, and interaction with other cells. T lymphocytes excel in these motility steps to ensure their immune surveillance duties. In particular, actin cytoskeleton remodeling is a key to facilitate the journey of T lymphocytes through distinct tissue environments and to tune their stop and go behavior during the scanning of antigen-presenting cells. The molecular mechanisms controlling actin cytoskeleton remodeling during T lymphocyte motility have been only partially unraveled, since the function of many actin regulators has not yet been assessed in these cells. Our review aims to integrate the current knowledge into a comprehensive picture of how the actin cytoskeleton drives T lymphocyte migration. We will present the molecular actors that control actin cytoskeleton remodeling, as well as their role in the different T lymphocyte motile steps. We will also highlight which challenges remain to be addressed experimentally and which approaches appear promising to tackle them.

Quantifying Modes of 3D Cell Migration

Although it is widely appreciated that cells migrate in a variety of diverse environments in vivo, we are only now beginning to use experimental workflows that yield images with sufficient spatiotemporal resolution to study the molecular processes governing cell migration in 3D environments. Since cell migration is a dynamic process, it is usually studied via microscopy, but 3D movies of 3D processes are difficult to interpret by visual inspection. In this review, we discuss the technologies required to study the diversity of 3D cell migration modes with a focus on the visualization and computational analysis tools needed to study cell migration quantitatively at a level comparable to the analyses performed today on cells crawling on flat substrates.

Pulsatile cell-autonomous contractility drives compaction in the mouse embryo

Mammalian embryos initiate morphogenesis with compaction, which is essential for specifying the first lineages of the blastocyst. The 8-cell-stage mouse embryo compacts by enlarging its cell-cell contacts in a Cdh1-dependent manner. It was therefore proposed that Cdh1 adhesion molecules generate the forces driving compaction. Using micropipette aspiration to map all tensions in a developing embryo, we show that compaction is primarily driven by a twofold increase in tension at the cell-medium interface. We show that the principal force generator of compaction is the actomyosin cortex, which gives rise to pulsed contractions starting at the 8-cell stage. Remarkably, contractions emerge as periodic cortical waves when cells are disengaged from adhesive contacts. In line with this, tension mapping of mzCdh1(-/-) embryos suggests that Cdh1 acts by redirecting contractility away from cell-cell contacts. Our study provides a framework to understand early mammalian embryogenesis and original perspectives on evolutionary conserved pulsed contractions.

Determining local geometrical features of grain boundaries from microscopy

Grain boundaries are solid-solid interfaces whose dynamics is driven by their local curvature. As they are fluctuating interfaces and have a width comparable to the lattice spacing of the surrounding grains, the determination of their local geometrical characteristics is difficult. Here we present a method to determine the local normal direction, tangent plane and curvature of grain boundaries from microscopy images using point sampled surface analysis techniques. We apply our algorithm to study the boundary of a shrinking grain in a two-dimensional colloidal polycrystalline material. Our method is easily generalized to three dimensions, which makes it applicable to the wide range of interfaces encountered in soft matter.

The interplay of cell-cell and cell-substrate adhesion in collective cell migration

Collective cell migration often involves notable cell-cell and cell-substrate adhesions and highly coordinated motion of touching cells. We focus on the interplay between cell-substrate adhesion and cell-cell adhesion. We show that the loss of cell-surface contact does not significantly alter the dynamic pattern of protrusions and retractions of fast migrating amoeboid cells (Dictyostelium discoideum), but significantly changes their ability to adhere to other cells. Analysis of the dynamics of cell shapes reveals that cells that are adherent to a surface may coordinate their motion with neighbouring cells through protrusion waves that travel across cell-cell contacts. However, while shape waves exist if cells are detached from surfaces, they do not couple cell to cell. In addition, our investigation of actin polymerization indicates that loss of cell-surface adhesion changes actin polymerization at cell-cell contacts. To further investigate cell-cell/cell-substrate interactions, we used optical micromanipulation to form cell-substrate contact at controlled locations. We find that both cell-shape dynamics and cytoskeletal activity respond rapidly to the formation of cell-substrate contact.

Geometry-Driven Polarity in Motile Amoeboid Cells

Motile eukaryotic cells, such as leukocytes, cancer cells, and amoeba, typically move inside the narrow interstitial spacings of tissue or soil. While most of our knowledge of actin-driven eukaryotic motility was obtained from cells that move on planar open surfaces, recent work has demonstrated that confinement can lead to strongly altered motile behavior. Here, we report experimental evidence that motile amoeboid cells undergo a spontaneous symmetry breaking in confined interstitial spaces. Inside narrow channels, the cells switch to a highly persistent, unidirectional mode of motion, moving at a constant speed along the channel. They remain in contact with the two opposing channel side walls and alternate protrusions of their leading edge near each wall. Their actin cytoskeleton exhibits a characteristic arrangement that is dominated by dense, stationary actin foci at the side walls, in conjunction with less dense dynamic regions at the leading edge. Our experimental findings can be explained based on an excitable network model that accounts for the confinement-induced symmetry breaking and correctly recovers the spatio-temporal pattern of protrusions at the leading edge. Since motile cells typically live in the narrow interstitial spacings of tissue or soil, we expect that the geometry-driven polarity we report here plays an important role for movement of cells in their natural environment.

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.

Both contractile axial and lateral traction force dynamics drive amoeboid cell motility

Chemotaxing Dictyostelium discoideum cells adapt their morphology and migration speed in response to intrinsic and extrinsic cues. Using Fourier traction force microscopy, we measured the spatiotemporal evolution of shape and traction stresses and constructed traction tension kymographs to analyze cell motility as a function of the dynamics of the cell's mechanically active traction adhesions. We show that wild-type cells migrate in a step-wise fashion, mainly forming stationary traction adhesions along their anterior-posterior axes and exerting strong contractile axial forces. We demonstrate that lateral forces are also important for motility, especially for migration on highly adhesive substrates. Analysis of two mutant strains lacking distinct actin cross-linkers (mhcA(-) and abp120(-) cells) on normal and highly adhesive substrates supports a key role for lateral contractions in amoeboid cell motility, whereas the differences in their traction adhesion dynamics suggest that these two strains use distinct mechanisms to achieve migration. Finally, we provide evidence that the above patterns of migration may be conserved in mammalian amoeboid cells.

Membrane nanowaves in single and collective cell migration

We report the characterization of three-dimensional membrane waves for migrating single and collective cells and describe their propagation using wide-field optical profiling technique with nanometer resolution. We reveal the existence of small and large membrane waves the amplitudes of which are in the range of ∼3–7 nm to ∼16–25 nm respectively, through the cell. For migrating single-cells, the amplitude of these waves is about 30 nm near the cell edge. Two or more different directions of propagation of the membrane nanowaves inside the same cell can be observed. After increasing the migration velocity by BMP-2 treatment, only one wave direction of propagation exists with an increase in the average amplitude (more than 80 nm near the cell edge). Furthermore for collective-cell migration, these membrane nanowaves are attenuated on the leader cells and poor transmission of these nanowaves to follower cells was observed. After BMP-2 treatment, the membrane nanowaves are transmitted from the leader cell to several rows of follower cells. Surprisingly, the vast majority of the observed membrane nanowaves is shared between the adjacent cells. These results give a new view on how single and collective-cells modulate their motility. This work has significant implications for the therapeutic use of BMPs for the regeneration of skin tissue.

Cellular contact guidance through dynamic sensing of nanotopography

We investigate the effects of surface nanotopography on the migration and cell shape dynamics of the amoeba Dictyostelium discoideum. Multiple prior studies have implicated the patterning of focal adhesions in contact guidance. However, we observe significant contact guidance of Dictyostelium along surfaces with nanoscale ridges or grooves, even though this organism lacks integrin-based adhesions. Cells that move parallel to nanoridges are faster, more protrusive at their fronts, and more elongated than are cells that move perpendicular to nanoridges. Quantitative studies show that nanoridges spaced 1.5 μm apart exhibit the greatest contact guidance efficiency. Because Dictyostelium cells exhibit oscillatory shape dynamics, we model contact guidance as a process in which stochastic cellular harmonic oscillators couple to the periodicity of the nanoridges. In support of this connection, we find that nanoridges nucleate actin polymerization waves of nanoscale width that propagate parallel to the nanoridges.

Understanding health and disease with multidimensional single-cell methods

Current efforts in the biomedical sciences and related interdisciplinary fields are focused on gaining a molecular understanding of health and disease, which is a problem of daunting complexity that spans many orders of magnitude in characteristic length scales, from small molecules that regulate cell function to cell ensembles that form tissues and organs working together as an organism. In order to uncover the molecular nature of the emergent properties of a cell, it is essential to measure multiple-cell components simultaneously in the same cell. In turn, cell heterogeneity requires multiple-cells to be measured in order to understand health and disease in the organism. This review summarizes current efforts towards a data-driven framework that leverages single-cell technologies to build robust signatures of healthy and diseased phenotypes. While some approaches focus on multicolor flow cytometry data and other methods are designed to analyze high-content image-based screens, we emphasize the so-called Supercell/SVM paradigm (recently developed by the authors of this review and collaborators) as a unified framework that captures mesoscopic-scale emergence to build reliable phenotypes. Beyond their specific contributions to basic and translational biomedical research, these efforts illustrate, from a larger perspective, the powerful synergy that might be achieved from bringing together methods and ideas from statistical physics, data mining, and mathematics to solve the most pressing problems currently facing the life sciences.

Bone morphogenetic protein signaling suppresses wound-induced skin repair by inhibiting keratinocyte proliferation and migration

Bone morphogenetic protein (BMP) signalling plays a key role in the control of skin development and postnatal remodelling by regulating keratinocyte proliferation, differentiation and apoptosis. To study the role of BMPs in wound-induced epidermal repair, we used transgenic mice overexpressing the BMP downstream component Smad1 under the control of a K14 promoter as an in vivo model, as well as ex vivo and in vitro assays. K14-caSmad1 mice exhibited retarded wound healing associated with significant inhibition of proliferation and increased apoptosis in healing wound epithelium. Furthermore, microarray and qRT-PCR analyses revealed decreased expression of a number of cytoskeletal/cell motility-associated genes including wound-associated keratins (Krt16, Krt17) and Myo5a, in the epidermis of K14-caSmad1 mice versus wild-type controls during wound healing. BMP treatment significantly inhibited keratinocyte migration ex vivo, and primary keratinocytes of K14-caSmad1 mice showed retarded migration compared to wild-type controls. Finally, siRNA-mediated silencing of Bmpr-1B in primary mouse keratinocytes accelerated cell migration and was associated with increased expression of Krt16, Krt17 and Myo5a compared to controls. Thus, this study demonstrates that BMPs inhibit keratinocyte proliferation, cytoskeletal organization and migration in regenerating skin epithelium during wound healing, and raises a possibility for using BMP antagonists for the management of chronic wounds.

A model for intracellular actin waves explored by nonlinear local perturbation analysis

Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem.

Modeling and measuring signal relay in noisy directed migration of cell groups

We develop a coarse-grained stochastic model for the influence of signal relay on the collective behavior of migrating Dictyostelium discoideum cells. In the experiment, cells display a range of collective migration patterns, including uncorrelated motion, formation of partially localized streams, and clumping, depending on the type of cell and the strength of the external, linear concentration gradient of the signaling molecule cyclic adenosine monophosphate (cAMP). From our model, we find that the pattern of migration can be quantitatively described by the competition of two processes, the secretion rate of cAMP by the cells and the degradation rate of cAMP in the gradient chamber. Model simulations are compared to experiments for a wide range of strengths of an external linear-gradient signal. With degradation, the model secreting cells form streams and efficiently transverse the gradient, but without degradation, we find that model secreting cells form clumps without streaming. This indicates that the observed effective collective migration in streams requires not only signal relay but also degradation of the signal. In addition, our model allows us to detect and quantify precursors of correlated motion, even when cells do not exhibit obvious streaming.

Collective cell migration is observed in various biological processes including angiogenesis, gastrulation, fruiting body formation, and wound healing. Dictyostelium discoideum, for example, exhibits highly dynamic patterns such as streams and clumps during its early phases of collective motion and has served as a model organism for the study of collective migration. In this study, facilitated by experiments, we develop a conceptual, minimalistic, computational model to analyze the dynamical processes leading to the emergence of collective patterns and the associated dependence on the external injection of a cAMP signal, the intercellular cAMP secretion rate, and the cAMP degradation rate. We demonstrate that degradation is necessary to reproduce the experimentally observed collective migration patterns, and show how our model can be utilized to uncover basic dependences of migration modes on cell characteristics. Our numerical observations elucidate the different possible types of motion and quantify the onset of collective motion. Thus, the model allows us to distinguish noisy motion guided by the external signal from weakly correlated motion.

Compression and dilation of the membrane-cortex layer generates rapid changes in cell shape

A cyclic process of membrane-cortex compression and dilation generates a traveling wave of cortical actin density that in turn generates oscillations in cell morphology.

Rapid changes in cellular morphology require a cell body that is highly flexible yet retains sufficient strength to maintain structural integrity. We present a mechanism that meets both of these requirements. We demonstrate that compression (folding) and subsequent dilation (unfolding) of the coupled plasma membrane–cortex layer generates rapid shape transformations in rounded cells. Two- and three-dimensional live-cell images showed that the cyclic process of membrane-cortex compression and dilation resulted in a traveling wave of cortical actin density. We also demonstrate that the membrane-cortex traveling wave led to amoeboid-like cell migration. The compression–dilation hypothesis offers a mechanism for large-scale cell shape transformations that is complementary to blebbing, where the plasma membrane detaches from the actin cortex and is initially unsupported when the bleb extends as a result of cytosolic pressure. Our findings provide insight into the mechanisms that drive the rapid morphological changes that occur in many physiological contexts, such as amoeboid migration and cytokinesis.

A dictionary of behavioral motifs reveals clusters of genes affecting Caenorhabditis elegans locomotion

Visible phenotypes based on locomotion and posture have played a critical role in understanding the molecular basis of behavior and development in Caenorhabditis elegans and other model organisms. However, it is not known whether these human-defined features capture the most important aspects of behavior for phenotypic comparison or whether they are sufficient to discover new behaviors. Here we show that four basic shapes, or eigenworms, previously described for wild-type worms, also capture mutant shapes, and that this representation can be used to build a dictionary of repetitive behavioral motifs in an unbiased way. By measuring the distance between each individual's behavior and the elements in the motif dictionary, we create a fingerprint that can be used to compare mutants to wild type and to each other. This analysis has revealed phenotypes not previously detected by real-time observation and has allowed clustering of mutants into related groups. Behavioral motifs provide a compact and intuitive representation of behavioral phenotypes.

Traveling waves in actin dynamics and cell motility

Much of current understanding of cell motility arose from studying steady treadmilling of actin arrays. Recently, there have been a growing number of observations of a more complex, non-steady, actin behavior, including self-organized waves. It is becoming clear that these waves result from activation and inhibition feedbacks in actin dynamics acting on different scales, but the exact molecular nature of these feedbacks and the respective roles of biomechanics and biochemistry are still unclear. Here, we review recent advances achieved in experimental and theoretical studies of actin waves and discuss mechanisms and physiological significance of wavy protrusions.

Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour

Patterns of waves, patches, and peaks of actin are observed experimentally in many living cells. Models of this phenomenon have been based on the interplay between filamentous actin (F-actin) and its nucleation promoting factors (NPFs) that activate the Arp2/3 complex. Here we present an alternative biologically-motivated model for F-actin-NPF interaction based on properties of GTPases acting as NPFs. GTPases (such as Cdc42, Rac) are known to promote actin nucleation, and to have active membrane-bound and inactive cytosolic forms. The model is a natural extension of a previous mathematical mini-model of small GTPases that generates static cell polarization. Like other modellers, we assume that F-actin negative feedback shapes the observed patterns by suppressing the trailing edge of NPF-generated wave-fronts, hence localizing the activity spatially. We find that our NPF-actin model generates a rich set of behaviours, spanning a transition from static polarization to single pulses, reflecting waves, wave trains, and oscillations localized at the cell edge. The model is developed with simplicity in mind to investigate the interaction between nucleation promoting factor kinetics and negative feedback. It explains distinct types of pattern initiation mechanisms, and identifies parameter regimes corresponding to distinct behaviours. We show that weak actin feedback yields static patterning, moderate feedback yields dynamical behaviour such as travelling waves, and strong feedback can lead to wave trains or total suppression of patterning. We use a recently introduced nonlinear bifurcation analysis to explore the parameter space of this model and predict its behaviour with simulations validating those results.