An excitable cortex and memory model successfully predicts new pseudopod dynamics

Mechanobiology of the relocation of proteins in advecting cells: in vitro experiments, multi-physics modeling, and simulations

Cell motility-a cellular behavior of paramount relevance in embryonic development, immunological response, metastasis, or angiogenesis-demands a mechanical deformation of the cell membrane and influences the surface motion of molecules and their biochemical interactions. In this work, we develop a fully coupled multi-physics model able to capture and predict the protein flow on endothelial advecting plasma membranes. The model has been validated against co-designed in vitro experiments. The complete picture of the receptor dynamics has been understood, and limiting factors have been identified together with the laws that regulate receptor polarization. This computational approach might be insightful in the prediction of endothelial cell behavior in different tumoral environments, circumventing the time-consuming and expensive empirical characterization of each tumor.

A chemorepellent inhibits local Ras activation to inhibit pseudopod formation to bias cell movement away from the chemorepellent

The ability of cells to sense chemical gradients is essential during development, morphogenesis, and immune responses. Although much is known about chemoattraction, chemorepulsion remains poorly understood. Proliferating Dictyostelium cells secrete a chemorepellent protein called AprA. AprA prevents pseudopod formation at the region of the cell closest to the source of AprA, causing the random movement of cells to be biased away from the AprA. Activation of Ras proteins in a localized sector of a cell cortex helps to induce pseudopod formation, and Ras proteins are needed for AprA chemorepulsion. Here we show that AprA locally inhibits Ras cortical activation through the G protein–coupled receptor GrlH, the G protein subunits Gβ and Gα8, Ras protein RasG, protein kinase B, the p21-activated kinase PakD, and the extracellular signal–regulated kinase Erk1. Diffusion calculations and experiments indicate that in a colony of cells, high extracellular concentrations of AprA in the center can globally inhibit Ras activation, while a gradient of AprA that naturally forms at the edge of the colony allows cells to activate Ras at sectors of the cell other than the sector of the cell closest to the center of the colony, effectively inducing both repulsion from the colony and cell differentiation. Together, these results suggest that a pathway that inhibits local Ras activation can mediate chemorepulsion.

Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows

Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach.

Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.

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

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

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

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.

Short- and long-term memory of moving amoeboid cells

Amoeboid cells constantly change shape and extend protrusions. The direction of movement is not random, but is correlated with the direction of movement in the preceding minutes. The basis of this correlation is an underlying memory of direction. The presence of memory in movement is known for many decades, but its molecular mechanism is still largely unknown. This study reports in detail on the information content of directional memory, the kinetics of learning and forgetting this information, and the molecular basis for memory using Dictyostelium mutants. Two types of memory were characterized. A short-term memory stores for ~20 seconds the position of the last pseudopod using a local modification of the branched F-actin inducer SCAR/WAVE, which enhances one new pseudopod to be formed at the position of the previous pseudopod. A long term memory stores for ~2 minutes the activity of the last ~10 pseudopods using a cGMP-binding protein that induces myosin filaments in the rear of the cell; this inhibits pseudopods in the rear and thereby enhances pseudopods in the global front. Similar types of memory were identified in human neutrophils and mesenchymal stem cells, the protist Dictyostelium and the fungus B.d. chytrid. The synergy of short- and long-term memory explains their role in persistent movement for enhanced cell dispersal, food seeking and chemotaxis.

Symmetry Breaking during Cell Movement in the Context of Excitability, Kinetic Fine-Tuning and Memory of Pseudopod Formation

The path of moving eukaryotic cells depends on the kinetics and direction of extending pseudopods. Amoeboid cells constantly change their shape with pseudopods extending in different directions. Detailed analysis has revealed that time, place and direction of pseudopod extension are not random, but highly ordered with strong prevalence for only one extending pseudopod, with defined life-times, and with reoccurring events in time and space indicative of memory. Important components are Ras activation and the formation of branched F-actin in the extending pseudopod and inhibition of pseudopod formation in the contractile cortex of parallel F-actin/myosin. In biology, order very often comes with symmetry. In this essay, I discuss cell movement and the dynamics of pseudopod extension from the perspective of symmetry and symmetry changes of Ras activation and the formation of branched F-actin in the extending pseudopod. Combining symmetry of Ras activation with kinetics and memory of pseudopod extension results in a refined model of amoeboid movement that appears to be largely conserved in the fast moving Dictyostelium and neutrophils, the slow moving mesenchymal stem cells and the fungus B.d. chytrid.

A minimal computational model for three-dimensional cell migration

During migration, eukaryotic cells can continuously change their three-dimensional morphology, resulting in a highly dynamic and complex process. Further complicating this process is the observation that the same cell type can rapidly switch between different modes of migration. Modelling this complexity necessitates models that are able to track deforming membranes and that can capture the intracellular dynamics responsible for changes in migration modes. Here we develop an efficient three-dimensional computational model for cell migration, which couples cell mechanics to a simple intracellular activator-inhibitor signalling system. We compare the computational results to quantitative experiments using the social amoeba Dictyostelium discoideum. The model can reproduce the observed migration modes generated by varying either mechanical or biochemical model parameters and suggests a coupling between the substrate and the biomechanics of the cell.

Mutually inhibitory Ras-PI(3,4)P2 feedback loops mediate cell migration

Signal transduction and cytoskeleton networks in a wide variety of cells display excitability, but the mechanisms are poorly understood. Here, we show that during random migration and in response to chemoattractants, cells maintain complementary spatial and temporal distributions of Ras activity and phosphatidylinositol (3,4)-bisphosphate [PI(3,4)P₂]. In addition, depletion of PI(3,4)P₂ by disruption of the 5-phosphatase, Dd5P4, or by recruitment of 4-phosphatase INPP4B to the plasma membrane, leads to elevated Ras activity, cell spreading, and altered migratory behavior. Furthermore, RasGAP2 and RapGAP3 bind to PI(3,4)P₂, and the phenotypes of cells lacking these genes mimic those with low PI(3,4)P₂ levels, providing a molecular mechanism. These findings suggest that Ras activity drives PI(3,4)P₂ down, causing the PI(3,4)P₂-binding GAPs to dissociate from the membrane, further activating Ras, completing a positive-feedback loop essential for excitability. Consistently, a computational model incorporating such a feedback loop in an excitable network model accurately simulates the dynamic distributions of active Ras and PI(3,4)P₂ as well as cell migratory behavior. The mutually inhibitory Ras-PI(3,4)P₂ mechanisms we uncovered here provide a framework for Ras regulation that may play a key role in many physiological processes.

The threshold of an excitable system serves as a control mechanism for noise filtering during chemotaxis

Chemotaxis, the migration of cells in the direction of a chemical gradient, is of utmost importance in various biological processes. In recent years, research has demonstrated that the underlying mechanism that controls cell migration is an excitable network. One of the properties that characterizes excitability is the presence of a threshold for activation. Here, we show that excitable systems possess noise filtering capabilities that enable faster and more efficient directed migration compared to other systems that also include a threshold, such as ultrasensitive switches. We demonstrate that this filtering ability is a consequence of the varying responses of excitable systems to step and pulse stimuli. Whereas the response to step inputs is determined solely by the magnitude of the stimulus, for pulse stimuli, the response depends on both the magnitude and duration of the stimulus. We then show that these two forms of threshold behavior can be decoupled from one another, allowing finer control in chemotaxis. Finally, we use a simple model of chemotaxis to demonstrate that cells that rely on an excitable system display faster and more effective directed migration that a hypothetical cell guided by an ultra-sensitive switch.

Adaptation of Living Systems

Adaptation refers to the biological phenomenon where living systems change their internal states in response to changes in their environments in order to maintain certain key functions critical for their survival and fitness. Adaptation is one of the most ubiquitous and arguably one of the most fundamental properties of living systems. It occurs throughout all biological scales, from adaptation of populations of species over evolutionary time to adaptation of a single cell to different environmental stresses during its life span. In this article, we review some of the recent progress made in understanding molecular mechanisms of cellular level adaptation. We take the minimalist (or the physicist) approach and study the simplest systems that exhibit generic adaptive behaviors. We focus on understanding the basic biochemical interaction networks in living matter that are responsible for adaptation dynamics. By combining theoretical modeling with quantitative experimentation, we demonstrate universal features in adaptation as well as important differences in different cellular systems, including chemotaxis in bacterium cells (Escherichia coli) and eukaryotic cells (Dictyostelium). Future work in extending the modeling framework to study adaptation in more complex systems such as sensory neurons are discussed.

Discrete Modeling of Amoeboid Locomotion and Chemotaxis in Dictyostelium discoideum by Tracking Pseudopodium Growth Direction

Dictyostelium discoideum amoeba is a well-established model organism for studying the crawling locomotion of eukaryotic cells. These amoebae extend pseudopodium - a temporary actin-based protrusion of their body membrane to probe the medium and crawl through it. Experiments show highly-ordered patterns in the growth direction of these pseudopodia, which results in persistence cell motility. Here, we propose a discrete model for studying and investigating the cell locomotion based on the experimental evidences. According to our model, Dictyostelium selects its pseudopodium growth direction based on a second-order Markov chain process, in the absence of external cues. Consequently, compared to a random walk process, our model indicates stronger growth in the mean-square displacement of cells, which is consistent with empirical findings. In the presence of external chemical stimulants, cells tend to align with the gradient of chemoattractant molecules. To quantify this tendency, we define a coupling coefficient between the pseudopodium extension direction and the gradient of an external stimulant, which depends on the local stimulant concentration and its gradient. Additionally, we generalize the model to weak-coupling regime by utilizing perturbation methods.

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.

A critical-like collective state leads to long-range cell communication in Dictyostelium discoideum aggregation

The transition from single-cell to multicellular behavior is important in early development but rarely studied. The starvation-induced aggregation of the social amoeba Dictyostelium discoideum into a multicellular slug is known to result from single-cell chemotaxis towards emitted pulses of cyclic adenosine monophosphate (cAMP). However, how exactly do transient, short-range chemical gradients lead to coherent collective movement at a macroscopic scale? Here, we developed a multiscale model verified by quantitative microscopy to describe behaviors ranging widely from chemotaxis and excitability of individual cells to aggregation of thousands of cells. To better understand the mechanism of long-range cell—cell communication and hence aggregation, we analyzed cell—cell correlations, showing evidence of self-organization at the onset of aggregation (as opposed to following a leader cell). Surprisingly, cell collectives, despite their finite size, show features of criticality known from phase transitions in physical systems. By comparing wild-type and mutant cells with impaired aggregation, we found the longest cell—cell communication distance in wild-type cells, suggesting that criticality provides an adaptive advantage and optimally sized aggregates for the dispersal of spores.

A multiscale model and imaging data show that cells of the slime mold Dictyostelium discoideum maximize their cell—cell communication range during aggregation by a critical-like state known from phase transitions in physical systems.

Cells are often coupled to each other in cell collectives, such as aggregates during early development, tissues in the developed organism, and tumors in disease. How do cells communicate over macroscopic distances much larger than the typical cell—cell distance to decide how they should behave? Here, we developed a multiscale model of social amoeba, spanning behavior from individuals to thousands of cells. We show that local cell—cell coupling via secreted chemicals may be tuned to a critical value, resulting in emergent long-range communication and heightened sensitivity. Hence, these aggregates are remarkably similar to bacterial biofilms and neuronal networks, all communicating in a pulselike fashion. Similar organizing principles may also aid our understanding of the remarkable robustness in cancer development.

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

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

Coupled excitable Ras and F-actin activation mediates spontaneous pseudopod formation and directed cell movement

Chemotaxis is the mechanism by which cells move in the direction of chemical gradients. The central circuit connecting basal movement and gradient sensing is unknown. Ras activation and F-actin form one coupled excitable system, which is the beating heart of cell movement in both the absence and presence of external cues.

Many eukaryotic cells regulate their mobility by external cues. Genetic studies have identified >100 components that participate in chemotaxis, which hinders the identification of the conceptual framework of how cells sense and respond to shallow chemical gradients. The activation of Ras occurs during basal locomotion and is an essential connector between receptor and cytoskeleton during chemotaxis. Using a sensitive assay for activated Ras, we show here that activation of Ras and F-actin forms two excitable systems that are coupled through mutual positive feedback and memory. This coupled excitable system leads to short-lived patches of activated Ras and associated F-actin that precede the extension of protrusions. In buffer, excitability starts frequently with Ras activation in the back/side of the cell or with F-actin in the front of the cell. In a shallow gradient of chemoattractant, local Ras activation triggers full excitation of Ras and subsequently F-actin at the side of the cell facing the chemoattractant, leading to directed pseudopod extension and chemotaxis. A computational model shows that the coupled excitable Ras/F-actin system forms the driving heart for the ordered-stochastic extension of pseudopods in buffer and for efficient directional extension of pseudopods in chemotactic gradients.

On Having No Head: Cognition throughout Biological Systems

The central nervous system (CNS) underlies memory, perception, decision-making, and behavior in numerous organisms. However, neural networks have no monopoly on the signaling functions that implement these remarkable algorithms. It is often forgotten that neurons optimized cellular signaling modes that existed long before the CNS appeared during evolution, and were used by somatic cellular networks to orchestrate physiology, embryonic development, and behavior. Many of the key dynamics that enable information processing can, in fact, be implemented by different biological hardware. This is widely exploited by organisms throughout the tree of life. Here, we review data on memory, learning, and other aspects of cognition in a range of models, including single celled organisms, plants, and tissues in animal bodies. We discuss current knowledge of the molecular mechanisms at work in these systems, and suggest several hypotheses for future investigation. The study of cognitive processes implemented in aneural contexts is a fascinating, highly interdisciplinary topic that has many implications for evolution, cell biology, regenerative medicine, computer science, and synthetic bioengineering.

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.

Know the Single-Receptor Sensing Limit? Think Again

How cells reliably infer information about their environment is a fundamentally important question. While sensing and signaling generally start with cell-surface receptors, the degree of accuracy with which a cell can measure external ligand concentration with even the simplest device-a single receptor-is surprisingly hard to pin down. Recent studies provide conflicting results for the fundamental physical limits. Comparison is made difficult as different studies either suggest different readout mechanisms of the ligand-receptor occupancy, or differ on how ligand diffusion is implemented. Here we critically analyse these studies and present a unifying perspective on the limits of sensing, with wide-ranging biological implications.

Re-membering the body: applications of computational neuroscience to the top-down control of regeneration of limbs and other complex organs

A major goal of regenerative medicine and bioengineering is the regeneration of complex organs, such as limbs, and the capability to create artificial constructs (so-called biobots) with defined morphologies and robust self-repair capabilities. Developmental biology presents remarkable examples of systems that self-assemble and regenerate complex structures toward their correct shape despite significant perturbations. A fundamental challenge is to translate progress in molecular genetics into control of large-scale organismal anatomy, and the field is still searching for an appropriate theoretical paradigm for facilitating control of pattern homeostasis. However, computational neuroscience provides many examples in which cell networks - brains - store memories (e.g., of geometric configurations, rules, and patterns) and coordinate their activity towards proximal and distant goals. In this Perspective, we propose that programming large-scale morphogenesis requires exploiting the information processing by which cellular structures work toward specific shapes. In non-neural cells, as in the brain, bioelectric signaling implements information processing, decision-making, and memory in regulating pattern and its remodeling. Thus, approaches used in computational neuroscience to understand goal-seeking neural systems offer a toolbox of techniques to model and control regenerative pattern formation. Here, we review recent data on developmental bioelectricity as a regulator of patterning, and propose that target morphology could be encoded within tissues as a kind of memory, using the same molecular mechanisms and algorithms so successfully exploited by the brain. We highlight the next steps of an unconventional research program, which may allow top-down control of growth and form for numerous applications in regenerative medicine and synthetic bioengineering.

Cell blebbing upon addition of cryoprotectants: a self-protection mechanism

In this work, the mechanism of cell bleb formation upon the addition of cryoprotectants (CPAs) was investigated, and the role of cell blebs in protecting cells was determined. The results show that after adding CPAs, the hyperosmotic stress results in the breakage of the cortical cytoskeleton and the detachment of the cell membrane from the cortical cytoskeleton, causing the formation of cell blebs. Multiple blebs decrease the intracellular hydrostatic pressure induced by the extracellular hyperosmotic shock and alleviate the osmotic damage to cells, which reduces the cell mortality rate. In the presence of a low concentration of CPAs, cell blebs can effectively protect cells. In contrast, in the presence of a high concentration of CPAs, the protective effect is limited because of severe disruption in the cortical cytoskeleton. To determine the relationship between blebs and the mortality rate of cells, we defined a bleb index and found that the bleb index of 0.065 can be regarded as a reference value for the safe addition of DMSO to HeLa cells. The bleb index can also explain why the stepwise addition of CPAs is better than the single-step addition of CPAs. Moreover, the mechanism of the autophagy of cells induced by the hyperosmotic stress was studied, and the protective effect associated with the autophagy was compared with the effect of the blebbing. The findings reported here elucidate a self-protection mechanism of cells experiencing the hyperosmotic stress in the presence of CPAs, and they provide significant evidence for cell tolerance in the field of cryopreservation.

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.

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.

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.

Cellular memory in eukaryotic chemotaxis

Natural chemical gradients to which cells respond chemotactically are often dynamic, with both spatial and temporal components. A primary example is the social amoeba Dictyostelium, which migrates to the source of traveling waves of chemoattractant as part of a self-organized aggregation process. Despite its physiological importance, little is known about how cells migrate directionally in response to traveling waves. The classic back-of-the-wave problem is how cells chemotax toward the wave source, even though the spatial gradient reverses direction in the back of the wave. Here, we address this problem by using microfluidics to expose cells to traveling waves of chemoattractant with varying periods. We find that cells exhibit memory and maintain directed motion toward the wave source in the back of the wave for the natural period of 6 min, but increasingly reverse direction for longer wave periods. Further insights into cellular memory are provided by experiments quantifying cell motion and localization of a directional-sensing marker after rapid gradient switches. The results can be explained by a model that couples adaptive directional sensing to bistable cellular memory. Our study shows how spatiotemporal cues can guide cell migration over large distances.

Memory improves precision of cell sensing in fluctuating environments

Biological cells are often found to sense their chemical environment near the single-molecule detection limit. Surprisingly, this precision is higher than simple estimates of the fundamental physical limit, hinting towards active sensing strategies. In this work, we analyse the effect of cell memory, e.g. from slow biochemical processes, on the precision of sensing by cell-surface receptors. We derive analytical formulas, which show that memory significantly improves sensing in weakly fluctuating environments. However, surprisingly when memory is adjusted dynamically, the precision is always improved, even in strongly fluctuating environments. In support of this prediction we quantify the directional biases in chemotactic Dictyostelium discoideum cells in a flow chamber with alternating chemical gradients. The strong similarities between cell sensing and control engineering suggest universal problem-solving strategies of living matter.

Interaction of motility, directional sensing, and polarity modules recreates the behaviors of chemotaxing cells

Chemotaxis involves the coordinated action of separable but interrelated processes: motility, gradient sensing, and polarization. We have hypothesized that these are mediated by separate modules that account for these processes individually and that, when combined, recreate most of the behaviors of chemotactic cells. Here, we describe a mathematical model where the modules are implemented in terms of reaction-diffusion equations. Migration and the accompanying changes in cellular morphology are demonstrated in simulations using a mechanical model of the cell cortex implemented in the level set framework. The central module is an excitable network that accounts for random migration. The response to combinations of uniform stimuli and gradients is mediated by a local excitation, global inhibition module that biases the direction in which excitability is directed. A polarization module linked to the excitable network through the cytoskeleton allows unstimulated cells to move persistently and, for cells in gradients, to gradually acquire distinct sensitivity between front and back. Finally, by varying the strengths of various feedback loops in the model we obtain cellular behaviors that mirror those of genetically altered cell lines.

Chemotaxis is the movement of cells in response to spatial gradients of chemical cues. While single-celled organisms rely on sensing and responding to chemical gradients to search for nutrients, chemotaxis is also an essential component of the mammalian immune system. However, chemotaxis can also be deleterious, since chemotactic tumor cells can lead to metastasis. Due to its importance, understanding the process by which cells sense and respond to chemical gradients has attracted considerable interest. Moreover, because of the complexity of chemotactic signaling, which includes multiple feedback loops and redundant pathways, this has been a research area in which computational models have had a significant impact in understanding experimental findings. Here, we propose a modular description of the signaling network that regulates chemotaxis. The modules describe different processes that are observed in chemotactic cells. In addition to accounting for these behaviors individually, we show that the overall system recreates many features of the directed motion of migrating cells. The signaling described by our modules is implemented as a series of equations, whereas movement and the accompanying cellular deformations are simulated using a mechanical model of the cell and implemented using level set methods, a method that allows simulations of cells as they change morphology.

Excitable behavior in amoeboid chemotaxis

Chemotaxis, the directed motion of cells in response to chemical gradients, is a fundamental process. Eukaryotic cells detect spatial differences in chemoattractant receptor occupancy with high precision and use these differences to bias the location of actin-rich protrusions to guide their movement. Research into chemotaxis has benefitted greatly from a systems biology approach that combines novel experimental and computational tools to pose and test hypotheses. Recently, one such hypothesis has been postulated proposing that chemotaxis in eukaryotic cells is mediated by locally biasing the activity of an underlying excitable system. The excitable system hypothesis can account for a number of cellular behaviors related to chemotaxis, including the stochastic nature of the movement of unstimulated cells, the directional bias imposed by chemoattractant gradients, and the observed spatial and temporal distribution of signaling and cytoskeleton proteins.