Polarity establishment in many cells is thought to occur via positive feedback that reinforces even tiny asymmetries in polarity protein distribution. Cdc42 and related GTPases are activated and accumulate in a patch of the cortex that defines the front of the cell. Positive feedback enables spontaneous polarization triggered by stochastic fluctuations, but as such fluctuations can occur at multiple locations, how do cells ensure that they make only one front? In polarizing cells of the model yeast Saccharomyces cerevisiae, positive feedback can trigger growth of several Cdc42 clusters at the same time, but this multi-cluster stage rapidly evolves to a single-cluster state, which then promotes bud emergence. By manipulating polarity protein dynamics, we show that resolution of multi-cluster intermediates occurs through a greedy competition between clusters to recruit and retain polarity proteins from a shared intracellular pool.

Rho GTPases play important roles in many aspects of cell migration, including polarity establishment and organizing actin cytoskeleton. In particular, the Rho GTPase Rac1 has been associated with the generation of protrusions at leading edge of migrating cells. Previously we showed the mobility of Rac1 molecules is not uniform throughout a migrating cell (Hinde E et. al. PNAS 2013). Specifically, the closer a Rac1 molecule is to the leading edge, the slower the molecule diffuses. Because actin-bound Rac1 diffuses slower than unbound Rac1, we hypothesized that regions of high actin concentration, called "actin islands", act as diffusive traps and are responsible for the non-uniform diffusion observed in vivo. Here, in silico model simulations demonstrate that equally spaced actin islands can regulate the time scale for Rac1 diffusion in a manner consistent with data from live-cell imaging experiments. Additionally, we find this mechanism is robust; different patterns of Rac1 mobility can be achieved by changing the actin islands' positions or their affinity for Rac1.

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.

We describe an approach to study the conformation of individual proteins during single particle tracking (SPT) in living cells. "Binder/tag" is based on incorporation of a 7-mer peptide (the tag) into a protein where its solvent exposure is controlled by protein conformation. Only upon exposure can the peptide specifically interact with a reporter protein (the binder). Thus, simple fluorescence localization reflects protein conformation. Through direct excitation of bright dyes, the trajectory and conformation of individual proteins can be followed. Simple protein engineering provides highly specific biosensors suitable for SPT and FRET. We describe tagSrc, tagFyn, tagSyk, tagFAK, and an orthogonal binder/tag pair. SPT showed slowly diffusing islands of activated Src within Src clusters and dynamics of activation in adhesions. Quantitative analysis and stochastic modeling revealed in vivo Src kinetics. The simplicity of binder/tag can provide access to diverse proteins.

Mitogen-activated protein kinase (MAPK) pathways control many cellular processes, including differentiation and proliferation. These pathways commonly activate MAPK isoforms that have redundant or overlapping function. However, recent studies have revealed circumstances in which MAPK isoforms have specialized, nonoverlapping roles in differentiation. The mechanisms that underlie this specialization are not well understood. To address this question, we sought to establish regulatory mechanisms that are unique to the MAPK Fus3 in pheromone-induced mating and chemotropic fate transitions of the budding yeast Saccharomyces cerevisiae. Our investigations reveal a previously unappreciated role for inactive Fus3 as a potent negative regulator of pheromone-induced chemotropism. We show that this inhibitory role is dependent on inactive Fus3 binding to the α-subunit of the heterotrimeric G-protein. Further analysis revealed that the binding of catalytically active Fus3 to the G-protein is required for gradient tracking and serves to suppress cell-to-cell variability between mating and chemotropic fates in a population of pheromone-responding cells.

Cell migration is essential for development and tissue repair, but it also contributes to disease. Rho GTPases regulate cell migration, but a comprehensive analysis of how each Rho signalling component affects migration has not been carried out.

Many cells undergo symmetry-breaking polarization toward a randomly oriented "front" in the absence of spatial cues. In budding yeast, such polarization involves a positive feedback loop that enables amplification of stochastically arising clusters of polarity factors. Previous mathematical modeling suggested that, if more than one cluster were amplified, the clusters would compete for limiting resources and the largest would "win," explaining why yeast cells always make one and only one bud. Here, using imaging with improved spatiotemporal resolution, we show the transient coexistence of multiple clusters during polarity establishment, as predicted by the model. Unexpectedly, we also find that initial polarity factor clustering is oscillatory, revealing the presence of a negative feedback loop that disperses the factors. Mathematical modeling predicts that negative feedback would confer robustness to the polarity circuit and make the kinetics of competition between polarity factor clusters relatively insensitive to polarity factor concentration. These predictions are confirmed experimentally.

Actomyosin-based cortical contractility is a common feature of eukaryotic cells and is involved in cell motility, cell division, and apoptosis. In nonmuscle cells, oscillations in contractility are induced by microtubule depolymerization during cell spreading. We developed an ordinary differential equation model to describe this behavior. The computational model includes 36 parameters. The values for all but two of the model parameters were taken from experimental measurements found in the literature. Using these values, we demonstrate that the model generates oscillatory behavior consistent with current experimental observations. The rhythmic behavior occurs because of the antagonistic effects of calcium-induced contractility and stretch-activated calcium channels. The model makes several experimentally testable predictions: 1), buffering intracellular calcium increases the period and decreases the amplitude of cortical oscillations; 2), increasing the number or activity of stretch activated channels leads to an increase in period and amplitude of cortical oscillations; 3), inhibiting Ca(2+) pump activity increases the period and amplitude of oscillations; and 4), a threshold exists for the calcium concentration below which oscillations cease.

Chemotaxis of fibroblasts and other mesenchymal cells is critical for embryonic development and wound healing. Fibroblast chemotaxis directed by a gradient of platelet-derived growth factor (PDGF) requires signaling through the phospholipase C (PLC)/protein kinase C (PKC) pathway. Diacylglycerol (DAG), the lipid product of PLC that activates conventional PKCs, is focally enriched at the up-gradient leading edge of fibroblasts responding to a shallow gradient of PDGF, signifying polarization. To explain the underlying mechanisms, we formulated reaction-diffusion models including as many as three putative feedback loops based on known biochemistry. These include the previously analyzed mechanism of substrate-buffering by myristoylated alanine-rich C kinase substrate (MARCKS) and two newly considered feedback loops involving the lipid, phosphatidic acid (PA). DAG kinases and phospholipase D, the enzymes that produce PA, are identified as key regulators in the models. Paradoxically, increasing DAG kinase activity can enhance the robustness of DAG/active PKC polarization with respect to chemoattractant concentration while decreasing their whole-cell levels. Finally, in simulations of wound invasion, efficient collective migration is achieved with thresholds for chemotaxis matching those of polarization in the reaction-diffusion models. This multi-scale modeling framework offers testable predictions to guide further study of signal transduction and cell behavior that affect mesenchymal chemotaxis.

Cells transition from spread to rounded morphologies in diverse physiological contexts including mitosis and mesenchymal-to-amoeboid transitions. When these drastic shape changes occur rapidly, cell volume and surface area are approximately conserved. Consequently, the rounded cells are suddenly presented with a several-fold excess of cell surface whose area far exceeds that of a smooth sphere enclosing the cell volume. This excess is stored in a population of bleb-like protrusions (BLiPs), whose size distribution is shown by electron micrographs to be skewed. We introduce three complementary models of rounded cell morphologies with a prescribed excess surface area. A 2D Hamiltonian model provides a mechanistic description of how discrete attachment points between the cell surface and cortex together with surface bending energy can generate a morphology that satisfies a prescribed excess area and BLiP number density. A 3D random seed-and-growth model simulates efficient packing of BLiPs over a primary rounded shape, demonstrating a pathway for skewed BLiP size distributions that recapitulate 3D morphologies. Finally, a phase field model (2D and 3D) posits energy-based constitutive laws for the cell membrane, nematic F-actin cortex, interior cytosol, and external aqueous medium. The cell surface is equipped with a spontaneous curvature function, a proxy for the cell surface-cortex couple, that is a priori unknown, which the model "learns" from the thin section transmission electron micrograph image (2D) or the "seed and growth" model image (3D). Converged phase field simulations predict self-consistent amplitudes and spatial localization of pressure and stress throughout the cell for any posited stationary morphology target and cell compartment constitutive properties. The models form a general framework for future studies of cell morphological dynamics in a variety of biological contexts.

G protein-coupled receptor (GPCR) signaling is fundamental to physiological processes such as vision, the immune response, and wound healing. In the budding yeast Saccharomyces cerevisiae, GPCRs detect and respond to gradients of pheromone during mating. After pheromone stimulation, the GPCR Ste2 is removed from the cell membrane, and new receptors are delivered to the growing edge. The regulator of G protein signaling (RGS) protein Sst2 acts by accelerating GTP hydrolysis and facilitating pathway desensitization. Sst2 is also known to interact with the receptor Ste2. Here we show that Sst2 is required for proper receptor recovery at the growing edge of pheromone-stimulated cells. Mathematical modeling suggested pheromone-induced synthesis of Sst2 together with its interaction with the receptor function to reestablish a receptor pool at the site of polarized growth. To validate the model, we used targeted genetic perturbations to selectively disrupt key properties of Sst2 and its induction by pheromone. Together our results reveal that a regulator of G protein signaling can also regulate the G protein-coupled receptor. Whereas Sst2 negatively regulates G protein signaling, it acts in a positive manner to promote receptor retention at the growing edge.

During the proliferative phase of cutaneous wound healing, dermal fibroblasts are recruited into the clotted wound by a concentration gradient of platelet-derived growth factor (PDGF), together with other spatial cues. Despite the importance of this chemotactic process, the mechanisms controlling the directed migration of slow-moving mesenchymal cells such as fibroblasts are not well understood. Here, we develop and analyze a reaction-diffusion model of phospholipase C/protein kinase C (PKC) signaling, which was recently identified as a requisite PDGF-gradient-sensing pathway, with the goal of identifying mechanisms that can amplify its sensitivity in the shallow external gradients typical of chemotaxis experiments. We show that phosphorylation of myristoylated alanine-rich C kinase substrate by membrane-localized PKC constitutes a positive feedback that is sufficient for local pathway amplification. The release of phosphorylated myristoylated alanine-rich C kinase substrate and its subsequent diffusion and dephosphorylation in the cytosol also serves to suppress the pathway in down-gradient regions of the cell. By itself, this mechanism only weakly amplifies signaling in a shallow PDGF gradient, but it synergizes with other feedback mechanisms to enhance amplification. This model offers a framework for a mechanistic understanding of phospholipase C/PKC signaling in chemotactic gradient sensing and can guide the design of experiments to assess the roles of putative feedback loops.

Podosomes are actin-enriched adhesion structures important for multiple cellular processes, including migration, bone remodeling, and phagocytosis. Here, we characterize the structure and organization of phagocytic podosomes using interferometric photoactivated localization microscopy, a super-resolution microscopy technique capable of 15-20 nm resolution, together with structured illumination microscopy and localization-based super-resolution microscopy. Phagocytic podosomes are observed during frustrated phagocytosis, a model in which cells attempt to engulf micropatterned IgG antibodies. For circular patterns, this results in regular arrays of podosomes with well-defined geometry. Using persistent homology, we develop a pipeline for semi-automatic identification and measurement of podosome features. These studies reveal an hourglass shape of the podosome actin core, a protruding knob at the bottom of the core, and two actin networks extending from the core. Additionally, the distributions of paxillin, talin, myosin II, α-actinin, cortactin, and microtubules relative to actin are characterized.

Phagocytosis, the biological process in which cells ingest large particles such as bacteria, is a key component of the innate immune response. Fcγ receptor (FcγR)-mediated phagocytosis is initiated when these receptors are activated after binding immunoglobulin G (IgG). Receptor activation initiates a signaling cascade that leads to the formation of the phagocytic cup and culminates with ingestion of the foreign particle. In the experimental system termed "frustrated phagocytosis", cells attempt to internalize micropatterned disks of IgG. Cells that engage in frustrated phagocytosis form "rosettes" of actin-enriched structures called podosomes around the IgG disk. The mechanism that generates the rosette pattern is unknown. We present data that supports the involvement of Cdc42, a member of the Rho family of GTPases, in pattern formation. Cdc42 acts downstream of receptor activation, upstream of actin polymerization, and is known to play a role in polarity establishment. Reaction-diffusion models for GTPase spatiotemporal dynamics exist. We demonstrate how the addition of negative feedback and minor changes to these models can generate the experimentally observed rosette pattern of podosomes. We show that this pattern formation can occur through two general mechanisms. In the first mechanism, an intermediate species forms a ring of high activity around the IgG disk, which then promotes rosette organization. The second mechanism does not require initial ring formation but relies on spatial gradients of intermediate chemical species that are selectively activated over the IgG patch. Finally, we analyze the models to suggest experiments to test their validity.

Structured illumination microscopy (SIM) surpasses the optical diffraction limit and offers a two-fold enhancement in resolution over diffraction limited microscopy. However, it requires both intense illumination and multiple acquisitions to produce a single high-resolution image. Using deep learning to augment SIM, we obtain a five-fold reduction in the number of raw images required for super-resolution SIM, and generate images under extreme low light conditions (at least 100× fewer photons). We validate the performance of deep neural networks on different cellular structures and achieve multi-color, live-cell super-resolution imaging with greatly reduced photobleaching.

Accurate detection of extracellular chemical gradients is essential for many cellular behaviors. Gradient sensing is challenging for small cells, which can experience little difference in ligand concentrations on the up-gradient and down-gradient sides of the cell. Nevertheless, the tiny cells of the yeast Saccharomyces cerevisiae reliably decode gradients of extracellular pheromones to find their mates. By imaging the behavior of polarity factors and pheromone receptors, we quantified the accuracy of initial polarization during mating encounters. We found that cells bias the orientation of initial polarity up-gradient, even though they have unevenly distributed receptors. Uneven receptor density means that the gradient of ligand-bound receptors does not accurately reflect the external pheromone gradient. Nevertheless, yeast cells appear to avoid being misled by responding to the fraction of occupied receptors rather than simply the concentration of ligand-bound receptors. Such ratiometric sensing also serves to amplify the gradient of active G protein. However, this process is quite error-prone, and initial errors are corrected during a subsequent indecisive phase in which polarity clusters exhibit erratic mobile behavior.

Many cells are remarkably proficient at tracking very shallow chemical gradients, despite considerable noise from stochastic receptor-ligand interactions. Motile cells appear to undergo a biased random walk: spatial noise in receptor activity may determine the instantaneous direction, but because noise is spatially unbiased, it is filtered out by time averaging, resulting in net movement upgradient. How nonmotile cells might filter out noise is unknown.

Cell biologists increasingly rely on computer-aided image analysis, allowing them to collect precise, unbiased quantitative results. However, despite great progress in image processing and computer vision, current computational approaches fail to address many key aspects of cell behavior, including the cell protrusions that guide cell migration and drive morphogenesis. We developed the open source MATLAB application CellGeo, a user-friendly computational platform to allow simultaneous, automated tracking and analysis of dynamic changes in cell shape, including protrusions ranging from filopodia to lamellipodia. Our method maps an arbitrary cell shape onto a tree graph that, unlike traditional skeletonization algorithms, preserves complex boundary features. CellGeo allows rigorous but flexible definition and accurate automated detection and tracking of geometric features of interest. We demonstrate CellGeo's utility by deriving new insights into (a) the roles of Diaphanous, Enabled, and Capping protein in regulating filopodia and lamellipodia dynamics in Drosophila melanogaster cells and (b) the dynamic properties of growth cones in catecholaminergic a-differentiated neuroblastoma cells.

All cells must detect and respond to changes in their environment, often through changes in gene expression. The yeast pheromone pathway has been extensively characterized, and is an ideal system for studying transcriptional regulation. Here we combine computational and experimental approaches to study transcriptional regulation mediated by Ste12, the key transcription factor in the pheromone response. Our mathematical model is able to explain multiple counterintuitive experimental results and led to several novel findings. First, we found that the transcriptional repressors Dig1 and Dig2 positively affect transcription by stabilizing Ste12. This stabilization through protein-protein interactions creates a large pool of Ste12 that is rapidly activated following pheromone stimulation. Second, we found that protein degradation follows saturating kinetics, explaining the long half-life of Ste12 in mutants expressing elevated amounts of Ste12. Finally, our model reveals a novel mechanism for robust perfect adaptation through protein-protein interactions that enhance complex stability. This mechanism allows the transcriptional response to act on a shorter time scale than upstream pathway activity.

Cell migration refers to the ability of cells to translocate across a substrate or through a matrix. To achieve net movement requires spatiotemporal regulation of the actin cytoskeleton. Computational approaches are necessary to identify and quantify the regulatory mechanisms that generate directed cell movement. To address this need, we developed computational tools, based on stochastic modeling, to analyze time series data for the position of randomly migrating cells. Our approach allows parameters that characterize cell movement to be efficiently estimated from cell track data. We applied our methods to analyze the random migration of Mouse Embryonic Fibroblasts (MEFS) and HeLa cells. Our analysis revealed that MEFs exist in two distinct states of migration characterized by differences in cell speed and persistence, whereas HeLa cells only exhibit a single state. Further analysis revealed that the Rho-family GTPase RhoG plays a role in determining the properties of the two migratory states of MEFs. An important feature of our computational approach is that it provides a method for predicting the current migration state of an individual cell from time series data. Finally, we applied our computational methods to HeLa cells expressing a Rac1 biosensor. The Rac1 biosensor is known to perturb movement when expressed at overly high concentrations; at these expression levels the HeLa cells showed two migratory states, which correlated with differences in the spatial distribution of active Rac1.