Directional sensing in eukaryotic chemotaxis: a balanced inactivation model

Receptor polarization through localized activity and global sensitization

Eukaryotic cells chemosense concentration gradients of extracellular ligands using membrane-bound receptors that polarize their activity. Receptors from several chemosensing families are preferentially degraded after activation and undergo significant lateral diffusion, both of which may blunt their polarization. To explore the combined role of these two seemingly detrimental phenomena on active receptor polarization, we use a reaction/diffusion model. The model elucidates a counterintuitive principle that governs receptor polarization under external gradients: Localized Activity and Global Sensitization (LAGS). In LAGS, receptor activity is localized through receptor degradation or ligand unbinding. In contrast, uniform sensitivity to ligands is maintained over the plasma membrane through lateral receptor diffusion. Surprisingly, increasing preferential degradation of active receptors and increasing lateral diffusion of all receptors both sharpen active receptor polarization. Additionally, when combined with receptor oligomerization, an increase in preferential degradation allows cells to sense relative ligand gradients over a larger range of background ligand concentrations. An analytical model identifies parameter regimes that dictate which processes dominate receptor polarization. A survey of kinetic parameters suggests that receptor polarization in many mammalian pathways can be modeled using LAGS.

Dynamic cluster field modeling of collective chemotaxis

Collective migration of eukaryotic cells is often guided by chemotaxis, and is critical in several biological processes, such as cancer metastasis, wound healing, and embryogenesis. Understanding collective chemotaxis has challenged experimental, theoretical and computational scientists because cells can sense very small chemoattractant gradients that are tightly controlled by cell-cell interactions and the regulation of the chemoattractant distribution by the cells. Computational models of collective cell migration that offer a high-fidelity resolution of the cell motion and chemoattractant dynamics in the extracellular space have been limited to a small number of cells. Here, we present Dynamic cluster field modeling (DCF), a novel computational method that enables simulations of collective chemotaxis of cellular systems with O ( 1000 ) cells and high-resolution transport dynamics of the chemoattractant in the time-evolving extracellular space. We illustrate the efficiency and predictive capabilities of our approach by comparing our numerical simulations with experiments in multiple scenarios that involve chemoattractant secretion and uptake by the migrating cells, cell migration in confined spaces, regulation of the attractant distribution by cell motion, and interactions of the chemoattractant with an enzyme. The proposed algorithm opens new opportunities to address outstanding problems that involve collective cell migration in the central nervous system, immune response and cancer metastasis.

Eukaryotic Chemotaxis under Periodic Stimulation Shows Temporal Gradient Dependence

When cells of the social amoeba Dictyostelium discoideum are starved of nutrients they start to synthesize and secrete the chemical messenger and chemoattractant cyclic adenosine monophosphate (cAMP). This signal is relayed by other cells, resulting in the establishment of periodic waves. The cells aggregate through chemotaxis toward the center of these waves. We investigated the chemotactic response of individual cells to repeated exposure to waves of cAMP generated by a microfluidic device. For fast-moving waves (short period), the chemotactic ability of the cells was found to increase upon exposure to more waves, suggesting the development of a memory over several cycles. This effect was not significant for slow-moving waves (large period). We show that the experimental results are consistent with a local excitation global inhibition-based model, extended by including a component that rises and decays slowly and that is activated by the temporal gradient of cAMP concentration. The observed enhancement in chemotaxis is relevant to populations in the wild: once sustained, periodic waves of the chemoattractant are established, it is beneficial to cells to improve their chemotactic ability in order to reach the aggregation center sooner.

Integrins regulate hERG1 dynamics by girdin-dependent Gαi3: signaling and modeling in cancer cells

The hERG1 potassium channel is aberrantly over expressed in tumors and regulates the cancer cell response to integrin-dependent adhesion. We unravel a novel signaling pathway by which integrin engagement by the ECM protein fibronectin promotes hERG1 translocation to the plasma membrane and its association with β1 integrins, by activating girdin-dependent Gαi3 proteins and protein kinase B (Akt). By sequestering hERG1, β1 integrins make it avoid Rab5-mediated endocytosis, where unbound channels are degraded. The cycle of hERG1 expression determines the resting potential (Vrest) oscillations and drives the cortical f-actin dynamics and thus cell motility. To interpret the slow biphasic kinetics of hERG1/β1 integrin interplay, we developed a mathematical model based on a generic balanced inactivation-like module. Integrin-mediated cell adhesion triggers two contrary responses: a rapid stimulation of hERG1/β1 complex formation, followed by a slow inhibition which restores the initial condition. The protracted hERG1/β1 integrin cycle determines the slow time course and cyclic behavior of cell migration in cancer cells.

Single-cell directional sensing from just a few receptor binding events

Identifying the directionality of signaling sources from noisy input to membrane receptors is an essential task performed by many cell types. A variety of models have been proposed to explain directional sensing in cells. However, many of these require significant computational and memory capacities for the cell. We propose and analyze a simple mechanism in which a cell adopts the direction associated with the first few membrane binding events. This model yields an accurate angular estimate to the source long before steady state is reached in biologically relevant scenarios. Our proposed mechanism allows for reliable estimates of the directionality of external signals using temporal information and assumes minimal computational capacities of the cell.

Non-asymptotic transients away from steady states determine cellular responsiveness to dynamic spatial-temporal signals

Majority of the theory on cell polarization and the understanding of cellular sensing and responsiveness to localized chemical cues has been based on the idea that non-polarized and polarized cell states can be represented by stable asymptotic switching between them. The existing model classes that describe the dynamics of signaling networks underlying polarization are formulated within the framework of autonomous systems. However these models do not simultaneously capture both, robust maintenance of polarized state longer than the signal duration, and retained responsiveness to signals with complex spatial-temporal distribution. Based on recent experimental evidence for criticality organization of biochemical networks, we challenge the current concepts and demonstrate that non-asymptotic signaling dynamics arising at criticality uniquely ensures optimal responsiveness to changing chemoattractant fields. We provide a framework to characterize non-asymptotic dynamics of system's state trajectories through a non-autonomous treatment of the system, further emphasizing the importance of (long) transient dynamics, as well as the necessity to change the mathematical formalism when describing biological systems that operate in changing environments.

Computational methods and diffusion theory in triangulation sensing to model neuronal navigation

Computational methods are now recognized as powerful and complementary approaches in various applied sciences such as biology. These computing methods are used to explore the gap between scales such as the one between molecular and cellular. Here we present recent progress in the development of computational approaches involving diffusion modeling, asymptotic analysis of the model partial differential equations, hybrid methods and simulations in the generic context of cell sensing and guidance via external gradients. Specifically, we highlight the reconstruction of the location of a point source in two and three dimensions from the steady-state diffusion fluxes arriving to narrow windows located on the cell. We discuss cases in which these windows are located on the boundary of a two-dimensional plane or three-dimensional half-space, on a disk in free space or inside a two-dimensional corridor, or a ball in three dimensions. The basis of this computational approach is explicit solutions of the Neumann-Green's function for the mentioned geometry. This analysis can be used to design hybrid simulations where Brownian paths are generated only in small regions in which the local spatial organization is relevant. Particle trajectories outside of this region are only implicitly treated by generating exit points at the boundary of this domain of interest. This greatly accelerates the simulation time by avoiding the explicit computation of Brownian paths in an infinite domain and serves to generate statistics, without following all trajectories at the same time, a process that can become numerically expensive quickly. Moreover, these computational approaches are used to reconstruct a point source and estimating the uncertainty in the source reconstruction due to an additive noise perturbation present in the fluxes. We also discuss the influence of various window configurations (cluster vs uniform distributions) on recovering the source position. Finally, the applications in developmental biology are formulated into computational principles that could underly neuronal navigation in the brain.

Cells use molecular working memory to navigate inchanging chemoattractant fields

In order to migrate over large distances, cells within tissues and organisms rely on sensing local gradient cues which are irregular, conflicting, and changing over time and space. The mechanism how they generate persistent directional migration when signals are disrupted, while still remaining adaptive to signal's localization changes remain unknown. Here we find that single cells utilize a molecular mechanism akin to a working memory to satisfy these two opposing demands. We derive theoretically that this is characteristic for receptor networks maintained away from steady states. Time-resolved live-cell imaging of Epidermal growth factor receptor (EGFR) phosphorylation dynamics shows that cells transiently memorize position of encountered signals via slow-escaping remnant of the polarized signaling state, a dynamical 'ghost', driving memory-guided persistent directional migration. The metastability of this state further enables migrational adaptation when encountering new signals. We thus identify basic mechanism of real-time computations underlying cellular navigation in changing chemoattractant fields.

A systems approach to investigate GPCR-mediated Ras signaling network in chemoattractant sensing

A GPCR-mediated signaling network enables a chemotactic cell to generate adaptative Ras signaling in response to a large range of concentrations of a chemoattractant. To explore potential regulatory mechanisms of GPCR-controlled Ras signaling in chemosensing, we applied a software package, Simmune, to construct detailed spatiotemporal models simulating responses of the cAR1-mediated Ras signaling network. We first determined the dynamics of G-protein activation and Ras signaling in Dictyostelium cells in response to cAMP stimulations using live-cell imaging and then constructed computation models by incorporating potential mechanisms. Using simulations, we validated the dynamics of signaling events and predicted the dynamic profiles of those events in the cAR1-mediated Ras signaling networks with defective Ras inhibitory mechanisms, such as without RasGAP, with RasGAP overexpression, or with RasGAP hyperactivation. We describe a method of using Simmune to construct spatiotemporal models of a signaling network and run computational simulations without writing mathematical equations. This approach will help biologists to develop and analyze computational models that parallel live-cell experiments.

Two Complementary Signaling Pathways Depict Eukaryotic Chemotaxis: A Mechanochemical Coupling Model

Many eukaryotic cells, including neutrophils and Dictyostelium cells, are able to undergo correlated random migration in the absence of directional cues while reacting to shallow gradients of chemoattractants with exquisite precision. Although progress has been made with regard to molecular identities, it remains elusive how molecular mechanics are integrated with cell mechanics to initiate and manipulate cell motility. Here, we propose a two dimensional (2D) cell migration model wherein a multilayered dynamic seesaw mechanism is accompanied by a mechanical strain-based inhibition mechanism. In biology, these two mechanisms can be mapped onto the biochemical feedback between phosphoinositides (PIs) and Rho GTPase and the mechanical interplay between filamin A (FLNa) and FilGAP. Cell migration and the accompanying morphological changes are demonstrated in numerical simulations using a particle-spring model, and the diffusion in the cell membrane are simulations using a one dimensional (1D) finite differences method (FDM). The fine balance established between endogenous signaling and a mechanically governed inactivation scheme ensures the endogenous cycle of self-organizing pseudopods, accounting for the correlated random migration. Furthermore, this model cell manifests directional and adaptable responses to shallow graded signaling, depending on the overwhelming effect of the graded stimuli guidance on strain-based inhibition. Finally, the model cell becomes trapped within an obstacle-ridden spatial region, manifesting a shuttle run for local explorations and can chemotactically “escape”, illustrating again the balance required in the complementary signaling pathways.

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.

How Phagocytes Acquired the Capability of Hunting and Removing Pathogens From a Human Body: Lessons Learned From Chemotaxis and Phagocytosis of Dictyostelium discoideum (Review)

How phagocytes find invading microorganisms and eliminate pathogenic ones from human bodies is a fundamental question in the study of infectious diseases. About 2.5 billion years ago, eukaryotic unicellular organisms-protozoans-appeared and started to interact with various bacteria. Less than 1 billion years ago, multicellular animals-metazoans-appeared and acquired the ability to distinguish self from non-self and to remove harmful organisms from their bodies. Since then, animals have developed innate immunity in which specialized white-blood cells phagocytes- patrol the body to kill pathogenic bacteria. The social amoebae Dictyostelium discoideum are prototypical phagocytes that chase various bacteria via chemotaxis and consume them as food via phagocytosis. Studies of this genetically amendable organism have revealed evolutionarily conserved mechanisms underlying chemotaxis and phagocytosis and shed light on studies of phagocytes in mammals. In this review, we briefly summarize important studies that contribute to our current understanding of how phagocytes effectively find and kill pathogens via chemotaxis and phagocytosis.

Using Dictyostelium to Develop Therapeutics for Acute Respiratory Distress Syndrome

Acute respiratory distress syndrome (ARDS) involves damage to lungs causing an influx of neutrophils from the blood into the lung airspaces, and the neutrophils causing further damage, which attracts more neutrophils in a vicious cycle. There are ∼190,000 cases of ARDS per year in the US, and because of the lack of therapeutics, the mortality rate is ∼40%. Repelling neutrophils out of the lung airspaces, or simply preventing neutrophil entry, is a potential therapeutic. In this minireview, we discuss how our lab noticed that a protein called AprA secreted by growing Dictyostelium cells functions as a repellent for Dictyostelium cells, causing cells to move away from a source of AprA. We then found that AprA has structural similarity to a human secreted protein called dipeptidyl peptidase IV (DPPIV), and that DPPIV is a repellent for human neutrophils. In animal models of ARDS, inhalation of DPPIV or DPPIV mimetics blocks neutrophil influx into the lungs. To move DPPIV or DPPIV mimetics into the clinic, we need to know how this repulsion works to understand possible drug interactions and side effects. Combining biochemistry and genetics in Dictyostelium to elucidate the AprA signal transduction pathway, followed by drug studies in human neutrophils to determine similarities and differences between neutrophil and Dictyostelium chemorepulsion, will hopefully lead to the safe use of DPPIV or DPPIV mimetics in the clinic.

Three-dimensional stochastic simulation of chemoattractant-mediated excitability in cells

During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our simulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration.

Though the term noise usually carries negative connotations, it can also contribute positively to the characteristic dynamics of a system. In biological systems, where noise arises from the stochastic interactions between molecules, its study is usually confined to genetic regulatory systems in which copy numbers are small and fluctuations large. However, noise can have important roles when the number of signaling molecules is large. The extension of pseudopods and the subsequent motion of amoeboid cells arises from the noise-induced trigger of an excitable system. Chemoattractant signals bias this triggering thereby directing cell motion. To date, this paradigm has not been tested by mathematical models that account accurately for the noise that arises in the corresponding reactions. In this study, we employ a reaction-diffusion master equation approach to investigate the effects of noise. Using a modular approach and a three-dimensional cell model with specific subdomains attributed to the cell membrane and cortex, we explore the spatiotemporal dynamics of the system. Our simulations recreate many experimentally-observed cell behaviors thereby supporting the biased-excitable network hypothesis.

A mathematical model for bleb regulation in zebrafish primordial germ cells

Blebs are cell protrusions generated by local membrane-cortex detachments followed by expansion of the plasma membrane. Blebs are formed by some migrating cells, e.g. primordial germ cells of the zebrafish. While blebs occur randomly at each part of the membrane in unpolarized cells, a polarization process guarantees the occurrence of blebs at a preferential site and thereby facilitates migration toward a specified direction. Little is known about the factors involved in the controlled and directed bleb generation, yet recent studies revealed the influence of an intracellular flow and the stabilizing role of the membrane-cortex linker molecule Ezrin. Based on this information, we develop and analyse a coupled bulk-surface model describing a potential cellular mechanism by which a bleb could be induced at a controlled site. The model rests upon intracellular Darcy flow and a diffusion-advection-reaction system, describing the temporal evolution from a homogeneous to a strongly anisotropic Ezrin distribution. We prove the well-posedness of the mathematical model and show that simulations qualitatively correspond to experimental observations, suggesting that indeed the interaction of an intracellular flow with membrane proteins can be the cause of the Ezrin redistribution accompanying bleb formation.

Membrane Tension Can Enhance Adaptation to Maintain Polarity of Migrating Cells

Migratory cells are known to adapt to environments that contain wide-ranging levels of chemoattractant. Although biochemical models of adaptation have been previously proposed, here, we discuss a different mechanism based on mechanosensing, in which the interaction between biochemical signaling and cell tension facilitates adaptation. We describe and analyze a model of mechanochemical-based adaptation coupling a mechanics-based physical model of cell tension coupled with the wave-pinning reaction-diffusion model for Rac GTPase activity. The mathematical analysis of this model, simulations of a simplified one-dimensional cell geometry, and two-dimensional finite element simulations of deforming cells reveal that as a cell protrudes under the influence of high stimulation levels, tension-mediated inhibition of Rac signaling causes the cell to polarize even when initially overstimulated. Specifically, tension-mediated inhibition of Rac activation, which has been experimentally observed in recent years, facilitates this adaptation by countering the high levels of environmental stimulation. These results demonstrate how tension-related mechanosensing may provide an alternative (and potentially complementary) mechanism for cell adaptation.

The purinergic receptor P2Y11 choreographs the polarization, mitochondrial metabolism, and migration of T lymphocytes

T cells must migrate to encounter antigen-presenting cells and perform their roles in host defense. Here, we found that autocrine stimulation of the purinergic receptor P2Y11 regulates the migration of human CD4 T cells. P2Y11 receptors redistributed from the front to the back of polarized cells where they triggered intracellular cAMP/PKA signals that attenuated mitochondrial metabolism at the back. The absence of P2Y11 receptors at the front of cells resulted in hotspots of mitochondrial metabolism and localized ATP production that stimulated P2X4 receptors, Ca²⁺ influx, and pseudopod protrusion at the front. This regulatory function of P2Y11 receptors depended on their subcellular redistribution and autocrine stimulation by cellular ATP release and was perturbed by indiscriminate global stimulation. We conclude that excessive extracellular ATP-such as in response to inflammation, sepsis, and cancer-disrupts this autocrine feedback mechanism, which results in defective T cell migration, impaired T cell function, and loss of host immune defense.

A computational study of amoeboid motility in 3D: the role of extracellular matrix geometry, cell deformability, and cell-matrix adhesion

Amoeboid cells often migrate using pseudopods, which are membrane protrusions that grow, bifurcate, and retract dynamically, resulting in a net cell displacement. Many cells within the human body, such as immune cells, epithelial cells, and even metastatic cancer cells, can migrate using the amoeboid phenotype. Amoeboid motility is a complex and multiscale process, where cell deformation, biochemistry, and cytosolic and extracellular fluid motions are coupled. Furthermore, the extracellular matrix (ECM) provides a confined, complex, and heterogeneous environment for the cells to navigate through. Amoeboid cells can migrate without significantly remodeling the ECM using weak or no adhesion, instead utilizing their deformability and the microstructure of the ECM to gain enough traction. While a large volume of work exists on cell motility on 2D substrates, amoeboid motility is 3D in nature. Despite recent progress in modeling cellular motility in 3D, there is a lack of systematic evaluations of the role of ECM microstructure, cell deformability, and adhesion on 3D motility. To fill this knowledge gap, here we present a multiscale, multiphysics modeling study of amoeboid motility through 3D-idealized ECM. The model is a coupled fluid‒structure and coarse-grain biochemistry interaction model that accounts for large deformation of cells, pseudopod dynamics, cytoplasmic and extracellular fluid motion, stochastic dynamics of cell-ECM adhesion, and microstructural (pore-scale) geometric details of the ECM. The key finding of the study is that cell deformation and matrix porosity strongly influence amoeboid motility, while weak adhesion and microscale structural details of the ECM have secondary but subtle effects.

A computational model of amoeboid cell motility in the presence of obstacles

Locomotion of amoeboid cells is mediated by finger-like protrusions of the cell body, known as pseudopods, which grow, bifurcate, and retract in a dynamic fashion. Pseudopods are the primary mode of locomotion for many cells within the human body, such as leukocytes, embryonic cells, and metastatic cancer cells. Amoeboid motility is a complex and multiscale process, which involves bio-molecular reactions, cell deformation, and cytoplasmic and extracellular fluid motion. Additionally, cells within the human body are subject to a confined 3D environment known as the extra-cellular matrix (ECM), which resembles a fluid-filled porous medium. In this article, we present a 3D, multiphysics computational approach coupling fluid mechanics, solid mechanics, and a pattern formation model to simulate locomotion of amoeboid cells through a porous matrix composed of a viscous fluid and an array of finite-sized spherical obstacles. The model combines reaction-diffusion of activator/inhibitors, extreme deformation of the cell, pseudopod dynamics, cytoplasmic and extracellular fluid motion, and fully resolved extracellular matrix. A surface finite-element method is used to obtain the cell deformation and activator/inhibitor concentrations, while the fluid motion is solved using a combined finite-volume and spectral method. The immersed-boundary methods are used to couple the cell deformation, obstacles, and fluid. The model is able to recreate squeezing and weaving motion of cells through the matrix. We study the influence of matrix porosity, obstacle size, and cell deformability on the motility behavior. It is found that below certain values of these parameters, cell motion is completely inhibited. Phase diagrams are presented depicting such motility limits. Interesting dynamics seen in the presence of obstacles but absent in unconfined medium, such as freezing or cell arrest, probing, doubling-back, and tug-of-war are predicted. Furthermore, persistent unidirectional motion of cells that is often observed in an unconfined medium is shown to be lost in presence of obstacles, and is attributed to an alteration of the pseudopod dynamics. The same mechanism, however, allows the cell to find a new direction to penetrate further into the matrix without being stuck in one place. The results and analysis presented here show a strong coupling between cell deformability and ECM properties, and provide new fluid mechanical insights on amoeboid motility in confined medium.

Mechanochemical modeling of neutrophil migration based on four signaling layers, integrin dynamics, and substrate stiffness

Directional neutrophil migration during human immune responses is a highly coordinated process regulated by both biochemical and biomechanical environments. In this paper, we developed an integrative mathematical model of neutrophil migration using a lattice Boltzmann-particle method built in-house to solve the moving boundary problem with spatiotemporal regulation of biochemical components. The mechanical features of the cell cortex are modeled by a series of spring-connected nodes representing discrete cell-substrate adhesive sites. The intracellular signaling cascades responsible for cytoskeletal remodeling [e.g., small GTPases, phosphoinositide-3-kinase (PI3K), and phosphatase and tensin homolog] are built based on our previous four-layered signaling model centered on the bidirectional molecular transport mechanism and implemented as reaction-diffusion equations. Focal adhesion dynamics are determined by force-dependent integrin-ligand binding kinetics and integrin recycling and are thus integrated with cell motion. Using numerical simulations, the model reproduces the major features of cell migration in response to uniform and gradient biochemical stimuli based on the quantitative spatiotemporal regulation of signaling molecules, which agree with experimental observations. The existence of multiple types of integrins with different binding kinetics could act as an adaptation mechanism for substrate stiffness. Moreover, cells can perform reversal, U-turn, or lock-on behaviors depending on the steepness of the reversal biochemical signals received. Finally, this model is also applied to predict the responses of mutants in which PTEN is overexpressed or disrupted.

Dynamic seesaw model for rapid signaling responses in eukaryotic chemotaxis

Directed movement of eukaryotic cells toward spatiotemporally varied chemotactic stimuli enables rapid intracellular signaling responses. While macroscopic cellular manifestation is shaped by balancing external stimuli strength with finite internal delays, the organizing principles of the underlying molecular mechanisms remain to be clarified. Here, we developed a novel modeling framework based on a simple seesaw mechanism to elucidate how cells repeatedly reverse polarity. As a key feature of the modeling, the bottom module of bidirectional molecular transport is successively controlled by three upstream modules of signal reception, initial signal processing, and Rho GTPase regulation. Our simulations indicated that an isotropic cell is polarized in response to a graded input signal. By applying a reversal gradient to a chemoattractant signal, lamellipod-specific molecules (i.e. PIP₃ and PI3K) disappear, first from the cell front, and then they redistribute at the opposite side, whereas functional molecules at the rear of the cell (i.e. PIP₂ and PTEN) act oppositely. In particular, the model cell exhibits a seesaw-like spatiotemporal pattern for the establishment of front and rear and interconversion, consistent with those related experimental observations. Increasing the switching frequency of the chemotactic gradient causes the cell to stay in a trapped state, further supporting the proposed dynamics of eukaryotic chemotaxis with the underlying cytoskeletal remodeling.

Role of metabolic spatiotemporal dynamics in regulating biofilm colony expansion

Cell fate determination is typically regulated by biological networks, yet increasing evidences suggest that cell-cell communication and environmental stresses play crucial roles in the behavior of a cell population. A recent microfluidic experiment showed that the metabolic codependence of two cell populations generates a collective oscillatory dynamic during the expansion of a Bacillus subtilis biofilm. We develop a modeling framework for the spatiotemporal dynamics of the associated metabolic circuit for cells in a colony. We elucidate the role of metabolite diffusion and the need of two distinct cell populations to observe oscillations. Uniquely, this description captures the onset and thereafter stable oscillatory dynamics during expansion and predicts the existence of damping oscillations under various environmental conditions. This modeling scheme provides insights to understand how cells integrate the information from external signaling and cell-cell communication to determine the optimal survival strategy and/or maximize cell fitness in a multicellular system.

Chemotactic droplet swimmers in complex geometries

Chemotaxis¹ and auto-chemotaxis are key mechanisms in the dynamics of micro-organisms, e.g. in the acquisition of nutrients and in the communication between individuals, influencing the collective behaviour. However, chemical signalling and the natural environment of biological swimmers are generally complex, making them hard to access analytically. We present a well-controlled, tunable artificial model to study chemotaxis and autochemotaxis in complex geometries, using microfluidic assays of self-propelling oil droplets in an aqueous surfactant solution (Herminghaus et al 2014 Soft Matter 10 7008-22; Krüger et al 2016 Phys. Rev. Lett. 117). Droplets propel via interfacial Marangoni stresses powered by micellar solubilisation. Moreover, filled micelles act as a chemical repellent by diffusive phoretic gradient forces. We have studied these chemotactic effects in a series of microfluidic geometries, as published in Jin et al (2017 Proc. Natl Acad. Sci. 114 5089-94): first, droplets are guided along the shortest path through a maze by surfactant diffusing into the maze from the exit. Second, we let auto-chemotactic droplet swimmers pass through bifurcating microfluidic channels and record anticorrelations between the branch choices of consecutive droplets. We present an analytical Langevin model matching the experimental data. In a previously unpublished experiment, pillar arrays of variable sizes and shapes provide a convex wall interacting with the swimmer and, in the case of attachment, bending its trajectory and forcing it to revert to its own trail. We observe different behaviours based on the interplay of wall curvature and negative autochemotaxis, i.e. no attachment for highly curved interfaces, stable trapping at large pillars, and a narrow transition region where negative autochemotaxis makes the swimmers detach after a single orbit.

Migrating Myeloid Cells Sense Temporal Dynamics of Chemoattractant Concentrations

Chemoattractant-mediated recruitment of hematopoietic cells to sites of pathogen growth or tissue damage is critical to host defense and organ homeostasis. Chemotaxis is typically considered to rely on spatial sensing, with cells following concentration gradients as long as these are present. Utilizing a microfluidic approach, we found that stable gradients of intermediate chemokines (CCL19 and CXCL12) failed to promote persistent directional migration of dendritic cells or neutrophils. Instead, rising chemokine concentrations were needed, implying that temporal sensing mechanisms controlled prolonged responses to these ligands. This behavior was found to depend on G-coupled receptor kinase-mediated negative regulation of receptor signaling and contrasted with responses to an end agonist chemoattractant (C5a), for which a stable gradient led to persistent migration. These findings identify temporal sensing as a key requirement for long-range myeloid cell migration to intermediate chemokines and provide insights into the mechanisms controlling immune cell motility in complex tissue environments.

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.

Mechanisms of Cell Polarization

Cell polarization is a key step in the migration, development, and organization of eukaryotic cells, both at the single cell and multicellular level. Research on the mechanisms that give rise to polarization of a given cell, and organization of polarity within a tissue has led to new understanding across cellular and developmental biology. In this review, we describe some of the history of theoretical and experimental aspects of the field, as well as some interesting questions and challenges for the future.

Rescaling of Spatio-Temporal Sensing in Eukaryotic Chemotaxis

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient—an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies.

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation, Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of "collective guidance" computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster's size-clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.

Directed migration of cancer cells guided by the graded texture of the underlying matrix

Living cells and the extracellular matrix (ECM) can exhibit complex interactions that define key developmental, physiological and pathological processes. Here, we report a new type of directed migration-which we term 'topotaxis'-guided by the gradient of the nanoscale topographic features in the cells' ECM environment. We show that the direction of topotaxis is reflective of the effective cell stiffness, and that it depends on the balance of the ECM-triggered signalling pathways PI(3)K-Akt and ROCK-MLCK. In melanoma cancer cells, this balance can be altered by different ECM inputs, pharmacological perturbations or genetic alterations, particularly a loss of PTEN in aggressive melanoma cells. We conclude that topotaxis is a product of the material properties of cells and the surrounding ECM, and propose that the invasive capacity of many cancers may depend broadly on topotactic responses, providing a potentially attractive mechanism for controlling invasive and metastatic behaviour.

A Model for Direction Sensing in Dictyostelium discoideum: Ras Activity and Symmetry Breaking Driven by a Gβγ-Mediated, Gα2-Ric8 -- Dependent Signal Transduction Network

Chemotaxis is a dynamic cellular process, comprised of direction sensing, polarization and locomotion, that leads to the directed movement of eukaryotic cells along extracellular gradients. As a primary step in the response of an individual cell to a spatial stimulus, direction sensing has attracted numerous theoretical treatments aimed at explaining experimental observations in a variety of cell types. Here we propose a new model of direction sensing based on experiments using Dictyostelium discoideum (Dicty). The model is built around a reaction-diffusion-translocation system that involves three main component processes: a signal detection step based on G-protein-coupled receptors (GPCR) for cyclic AMP (cAMP), a transduction step based on a heterotrimetic G protein Gα2βγ, and an activation step of a monomeric G-protein Ras. The model can predict the experimentally-observed response of cells treated with latrunculin A, which removes feedback from downstream processes, under a variety of stimulus protocols. We show that [Formula: see text] cycling modulated by Ric8, a nonreceptor guanine exchange factor for [Formula: see text] in Dicty, drives multiple phases of Ras activation and leads to direction sensing and signal amplification in cAMP gradients. The model predicts that both [Formula: see text] and Gβγ are essential for direction sensing, in that membrane-localized [Formula: see text], the activated GTP-bearing form of [Formula: see text], leads to asymmetrical recruitment of RasGEF and Ric8, while globally-diffusing Gβγ mediates their activation. We show that the predicted response at the level of Ras activation encodes sufficient 'memory' to eliminate the 'back-of-the wave' problem, and the effects of diffusion and cell shape on direction sensing are also investigated. In contrast with existing LEGI models of chemotaxis, the results do not require a disparity between the diffusion coefficients of the Ras activator GEF and the Ras inhibitor GAP. Since the signal pathways we study are highly conserved between Dicty and mammalian leukocytes, the model can serve as a generic one for direction sensing.

A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis

In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.

Dynamic regulation of neutrophil polarity and migration by the heterotrimeric G protein subunits Gαi-GTP and Gβγ

Activation of the Gi family of heterotrimeric guanine nucleotide-binding proteins (G proteins) releases βγ subunits, which are the major transducers of chemotactic G protein-coupled receptor (GPCR)-dependent cell migration. The small molecule 12155 binds directly to Gβγ and activates Gβγ signaling without activating the Gαi subunit in the Gi heterotrimer. We used 12155 to examine the relative roles of Gαi and Gβγ activation in the migration of neutrophils on surfaces coated with the integrin ligand intercellular adhesion molecule-1 (ICAM-1). We found that 12155 suppressed basal migration by inhibiting the polarization of neutrophils and increasing their adhesion to ICAM-1-coated surfaces. GPCR-independent activation of endogenous Gαi and Gβγ with the mastoparan analog Mas7 resulted in normal migration. Furthermore, 12155-treated cells expressing a constitutively active form of Gαi1 became polarized and migrated. The extent and duration of signaling by the second messenger cyclic adenosine monophosphate (cAMP) were enhanced by 12155. Inhibiting the activity of cAMP-dependent protein kinase (PKA) restored the polarity of 12155-treated cells but did not decrease their adhesion to ICAM-1 and failed to restore migration. Together, these data provide evidence for a direct role of activated Gαi in promoting cell polarization through a cAMP-dependent mechanism and in inhibiting adhesion through a cAMP-independent mechanism.

Fluorescence Readout of a Patch Clamped Membrane by Laser Scanning Microscopy

In this chapter, we describe how to shield a patch of a cell membrane against extracellularly applied chemoattractant stimuli. Classical patch clamp methodology is applied to allow for controlled shielding of a membrane patch by measuring the seal resistivity. In Dictyostelium cells, a seal resistivity of 50 MΩ proved to be tight enough to exclude molecules from diffusing into the shielded membrane region. This allowed for separating a shielded and a non-shielded region of a cell membrane to study the spatiotemporal dynamics of intracellular chemotactic signaling events at the interface between shielded and non-shielded areas. The spatiotemporal dynamics of signaling events in the membrane was read out by means of appropriate fluorescent markers using laser scanning confocal microscopy.

Modeling Excitable Dynamics of Chemotactic Networks

The study of chemotaxis has benefited greatly from computational models that describe the response of cells to chemoattractant stimuli. These models must keep track of spatially and temporally varying distributions of numerous intracellular species. Moreover, recent evidence suggests that these are not deterministic interactions, but also include the effect of stochastic variations that trigger an excitable network. In this chapter we illustrate how to create simulations of excitable networks using the Virtual Cell modeling environment.

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.

Methodologies for the modeling and simulation of biochemical networks, illustrated for signal transduction pathways: a primer

Biochemical networks depict the chemical interactions that take place among elements of living cells. They aim to elucidate how cellular behavior and functional properties of the cell emerge from the relationships between its components, i.e. molecules. Biochemical networks are largely characterized by dynamic behavior, and exhibit high degrees of complexity. Hence, the interest in such networks is growing and they have been the target of several recent modeling efforts. Signal transduction pathways (STPs) constitute a class of biochemical networks that receive, process, and respond to stimuli from the environment, as well as stimuli that are internal to the organism. An STP consists of a chain of intracellular signaling processes that ultimately result in generating different cellular responses. This primer presents the methodologies used for the modeling and simulation of biochemical networks, illustrated for STPs. These methodologies range from qualitative to quantitative, and include structural as well as dynamic analysis techniques. We describe the different methodologies, outline their underlying assumptions, and provide an assessment of their advantages and disadvantages. Moreover, publicly and/or commercially available implementations of these methodologies are listed as appropriate. In particular, this primer aims to provide a clear introduction and comprehensive coverage of biochemical modeling and simulation methodologies for the non-expert, with specific focus on relevant literature of STPs.

Local perturbation analysis: a computational tool for biophysical reaction-diffusion models

Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model's behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.

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.

Scanning x-ray nanodiffraction on Dictyostelium discoideum

We have performed scanning x-ray nanobeam diffraction experiments on single cells of the amoeba Dictyostelium discoideum. Cells have been investigated in 1), freeze-dried, 2), frozen-hydrated (vitrified), and 3), initially alive states. The spatially resolved small-angle x-ray scattering signal shows characteristic streaklike patterns in reciprocal space, which we attribute to fiber bundles of the actomyosin network. From the intensity distributions, an anisotropy parameter can be derived that indicates pronounced local variations within the cell. In addition to nanobeam small-angle x-ray scattering, we have evaluated the x-ray differential phase contrast in view of the projected electron density. Different experimental aspects of the x-ray experiment, sample preparation, and data analysis are discussed. Finally, the x-ray results are correlated with optical microscopy (differential phase contrast and confocal microscopy of mutant strains with fluorescently labeled actin and myosin II), which have been carried out in live and fixed states, including optical microscopy under cryogenic conditions.

Microtubules stabilize cell polarity by localizing rear signals

Microtubules are known to play an important role in cell polarity; however, the mechanism remains unclear. Using cells migrating persistently on micropatterned strips, we found that depolymerization of microtubules caused cells to change from persistent to oscillatory migration. Mathematical modeling in the context of a local-excitation-global-inhibition control mechanism indicated that this mechanism can account for microtubule-dependent oscillation, assuming that microtubules remove inhibitory signals from the front after a delayed generation. Experiments further supported model predictions that the period of oscillation positively correlates with cell length and that oscillation may be induced by inhibiting retrograde motors. We suggest that microtubules are required not for the generation but for the maintenance of cell polarity, by mediating the global distribution of inhibitory signals. Disassembly of microtubules induces cell oscillation by allowing inhibitory signals to accumulate at the front, which stops frontal protrusion and allows the polarity to reverse.

The structure of dynamic GPCR signaling networks

G-protein-coupled receptors (GPCRs) stimulate signaling networks that control a variety of critical physiological processes. Static information on the map of interacting signaling molecules at the basis of many cellular processes exists, but little is known about the dynamic operation of these networks. Here we focus on two questions. First, Is the network architecture underlying GPCR-activated cellular processes unique in comparison with others such as transcriptional networks? We discuss how spatially localized GPCR signaling requires uniquely organized networks to execute polarized cell responses. Second, What approaches overcome challenges in deciphering spatiotemporally dynamic networks that govern cell behavior? We focus on recently developed microfluidic and optical approaches that allow GPCR signaling pathways to be triggered and perturbed with spatially and temporally variant input while simultaneously visualizing molecular and cellular responses. When integrated with mathematical modeling, these approaches can help identify design principles that govern cell responses to extracellular signals. We outline why optical approaches that allow the behavior of a selected cell to be orchestrated continually are particularly well suited for probing network organization in single cells.

Evolutionarily conserved coupling of adaptive and excitable networks mediates eukaryotic chemotaxis

Numerous models explain how cells sense and migrate towards shallow chemoattractant gradients. Studies show that an excitable signal transduction network acts as a pacemaker that controls the cytoskeleton to drive motility. Here we show that this network is required to link stimuli to actin polymerization and chemotactic motility and we distinguish the various models of chemotaxis. First, signalling activity is suppressed towards the low side in a gradient or following removal of uniform chemoattractant. Second, signalling activities display a rapid shut off and a slower adaptation during which responsiveness to subsequent test stimuli decline. Simulations of various models indicate that these properties require coupled adaptive and excitable networks. Adaptation involves a G-protein-independent inhibitor, as stimulation of cells lacking G-protein function suppresses basal activities. The salient features of the coupled networks were observed for different chemoattractants in Dictyostelium and in human neutrophils, suggesting an evolutionarily conserved mechanism for eukaryotic chemotaxis.

The directional response of chemotactic cells depends on a balance between cytoskeletal architecture and the external gradient

Polarized migrating cells display signal transduction events, such as activation of phosphatidylinositol 3-kinase (PI3K) and Scar/Wave, and respond more readily to chemotactic stimuli at the leading edge. We sought to determine the basis of this polarized sensitivity. Inhibiting actin polymerization leads to uniform sensitivity. However, when human neutrophils were "stalled" by simultaneously blocking actin and myosin dynamics, they maintained the gradient of responsiveness to chemoattractant and also displayed noise-driven PIP3 flashes on the basal membrane, localized toward the front. Thus, polarized sensitivity does not require migration or cytoskeletal dynamics. The threshold for response is correlated with the static F-actin distribution, but not cell shape or volume changes, membrane fluidity, or the preexisting distribution of PI3K. The kinetics of responses to temporal and spatial stimuli were consistent with the local excitation global inhibition model, but the overall direction of the response was biased by the internal axis of polarity.

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.

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.

Subcellular optogenetic inhibition of G proteins generates signaling gradients and cell migration

Cells sense gradients of extracellular cues and generate polarized responses such as cell migration and neurite initiation. There is static information on the intracellular signaling molecules involved in these responses, but how they dynamically orchestrate polarized cell behaviors is not well understood. A limitation has been the lack of methods to exert spatial and temporal control over specific signaling molecules inside a living cell. Here we introduce optogenetic tools that act downstream of native G protein-coupled receptor (GPCRs) and provide direct control over the activity of endogenous heterotrimeric G protein subunits. Light-triggered recruitment of a truncated regulator of G protein signaling (RGS) protein or a Gβγ-sequestering domain to a selected region on the plasma membrane results in localized inhibition of G protein signaling. In immune cells exposed to spatially uniform chemoattractants, these optogenetic tools allow us to create reversible gradients of signaling activity. Migratory responses generated by this approach show that a gradient of active G protein αi and βγ subunits is sufficient to generate directed cell migration. They also provide the most direct evidence so for a global inhibition pathway triggered by Gi signaling in directional sensing and adaptation. These optogenetic tools can be applied to interrogate the mechanistic basis of other GPCR-modulated cellular functions.