Diverse sensitivity thresholds in dynamic signaling responses by social amoebae

Rate thresholds in cell signaling have functional and phenotypic consequences in non-linear time-dependent environments

All cells employ signal transduction pathways to respond to physiologically relevant extracellular cytokines, stressors, nutrient levels, hormones, morphogens, and other stimuli that vary in concentration and rate in healthy and diseased states. A central unsolved fundamental question in cell signaling is whether and how cells sense and integrate information conveyed by changes in the rate of extracellular stimuli concentrations, in addition to the absolute difference in concentration. We propose that different environmental changes over time influence cell behavior in addition to different signaling molecules or different genetic backgrounds. However, most current biomedical research focuses on acute environmental changes and does not consider how cells respond to environments that change slowly over time. As an example of such environmental change, we review cell sensitivity to environmental rate changes, including the novel mechanism of rate threshold. A rate threshold is defined as a threshold in the rate of change in the environment in which a rate value below the threshold does not activate signaling and a rate value above the threshold leads to signal activation. We reviewed p38/Hog1 osmotic stress signaling in yeast, chemotaxis and stress response in bacteria, cyclic adenosine monophosphate signaling in Amoebae, growth factors signaling in mammalian cells, morphogen dynamics during development, temporal dynamics of glucose and insulin signaling, and spatio-temproral stressors in the kidney. These reviewed examples from the literature indicate that rate thresholds are widespread and an underappreciated fundamental property of cell signaling. Finally, by studying cells in non-linear environments, we outline future directions to understand cell physiology better in normal and pathophysiological conditions.

Propagation dynamics of electrotactic motility in large epithelial cell sheets

Directional migration initiated at the wound edge leads epithelia to migrate in wound healing. How such coherent migration is achieved is not well understood. Here, we used electric fields to induce robust migration of sheets of human keratinocytes and developed an in silico model to characterize initiation and propagation of epithelial collective migration. Electric fields initiate an increase in migration directionality and speed at the leading edge. The increases propagate across the epithelial sheets, resulting in directional migration of cell sheets as coherent units. Both the experimental and in silico models demonstrated vector-like integration of the electric and default directional cues at free edge in space and time. The resultant collective migration is consistent in experiments and modeling, both qualitatively and quantitatively. The keratinocyte model thus faithfully reflects key features of epithelial migration as a coherent tissue in vivo, e.g. that leading cells lead, and that epithelium maintains cell-cell junction.

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 rate threshold mechanism regulates MAPK stress signaling and survival

Cells are exposed to changes in extracellular stimulus concentration that vary as a function of rate. However, how cells integrate information conveyed from stimulation rate along with concentration remains poorly understood. Here, we examined how varying the rate of stress application alters budding yeast mitogen-activated protein kinase (MAPK) signaling and cell behavior at the single-cell level. We show that signaling depends on a rate threshold that operates in conjunction with stimulus concentration to determine the timing of MAPK signaling during rate-varying stimulus treatments. We also discovered that the stimulation rate threshold and stimulation rate-dependent cell survival are sensitive to changes in the expression levels of the Ptp2 phosphatase, but not of another phosphatase that similarly regulates osmostress signaling during switch-like treatments. Our results demonstrate that stimulation rate is a regulated determinant of cell behavior and provide a paradigm to guide the dissection of major stimulation rate dependent mechanisms in other systems.

Diverse Cell Stimulation Kinetics Identify Predictive Signal Transduction Models

Computationally understanding the molecular mechanisms that give rise to cell signaling responses upon different environmental, chemical, and genetic perturbations is a long-standing challenge that requires models that fit and predict quantitative responses for new biological conditions. Overcoming this challenge depends not only on good models and detailed experimental data but also on the rigorous integration of both. We propose a quantitative framework to perturb and model generic signaling networks using multiple and diverse changing environments (hereafter "kinetic stimulations") resulting in distinct pathway activation dynamics. We demonstrate that utilizing multiple diverse kinetic stimulations better constrains model parameters and enables predictions of signaling dynamics that would be impossible using traditional dose-response or individual kinetic stimulations. To demonstrate our approach, we use experimentally identified models to predict signaling dynamics in normal, mutated, and drug-treated conditions upon multitudes of kinetic stimulations and quantify which proteins and reaction rates are most sensitive to which extracellular stimulations.

Migration of Microparticle-Containing Amoeba through Constricted Environments

In many situations, cells migrate through tiny orifices. Examples include the extravasation of immune cells from the bloodstream for fighting infections, the infiltration of cancer cells during metastasis, and the migration of human pathogens. An extremely motile and medically relevant type of human pathogen is Acanthamoeba castellanii. In the study presented here, we investigated how a combination of microparticles and microstructured interfaces controls the migration of A. castellanii trophozoites. The microinterfaces comprised well-defined micropillar arrays, and the trophozoites easily migrated through the given constrictions by adapting the shape and size of their intracellular vacuoles and by adapting intracellular motion. After feeding the trophozoite cells in microinterfaces with synthetic, stiff microparticles of various sizes and shapes, their behavior changed drastically: if the particles were smaller than the micropillar gap, migration was still possible. If the cells incorporated particles larger than the pillar gap, they could become immobilized but could also display remarkable problem-solving capabilities. For example, they turned rod-shaped microparticles such that their short axis fit through the pillar gap or they transported the particles above the structure. As migration is a crucial contribution to A. castellanii pathogenicity and is also relevant to other biological processes in microenvironments, such as cancer metastasis, our results provide an interesting strategy for controlling the migration of cells containing intracellular particles by microstructured interfaces that serve as migration-limiting environments.

Minimal Network Topologies for Signal Processing during Collective Cell Chemotaxis

Cell-cell communication plays an important role in collective cell migration. However, it remains unclear how cells in a group cooperatively process external signals to determine the group's direction of motion. Although the topology of signaling pathways is vitally important in single-cell chemotaxis, the signaling topology for collective chemotaxis has not been systematically studied. Here, we combine mathematical analysis and simulations to find minimal network topologies for multicellular signal processing in collective chemotaxis. We focus on border cell cluster chemotaxis in the Drosophila egg chamber, in which responses to several experimental perturbations of the signaling network are known. Our minimal signaling network includes only four elements: a chemoattractant, the protein Rac (indicating cell activation), cell protrusion, and a hypothesized global factor responsible for cell-cell interaction. Experimental data on cell protrusion statistics allows us to systematically narrow the number of possible topologies from more than 40,000,000 to only six minimal topologies with six interactions between the four elements. This analysis does not require a specific functional form of the interactions, and only qualitative features are needed; it is thus robust to many modeling choices. Simulations of a stochastic biochemical model of border cell chemotaxis show that the qualitative selection procedure accurately determines which topologies are consistent with the experiment. We fit our model for all six proposed topologies; each produces results that are consistent with all experimentally available data. Finally, we suggest experiments to further discriminate possible pathway topologies.

Regulation of flagellar motor switching by c-di-GMP phosphodiesterases in Pseudomonas aeruginosa

The second messenger cyclic diguanylate (c-di-GMP) plays a prominent role in regulating flagellum-dependent motility in the single-flagellated pathogenic bacterium Pseudomonas aeruginosa The c-di-GMP-mediated signaling pathways and mechanisms that control flagellar output remain to be fully unveiled. Studying surface-tethered and free-swimming P. aeruginosa PAO1 cells, we found that the overexpression of an exogenous diguanylate cyclase (DGC) raises the global cellular c-di-GMP concentration and thereby inhibits flagellar motor switching and decreases motor speed, reducing swimming speed and reversal frequency, respectively. We noted that the inhibiting effect of c-di-GMP on flagellar motor switching, but not motor speed, is exerted through the c-di-GMP-binding adaptor protein MapZ and associated chemotactic pathways. Among the 22 putative c-di-GMP phosphodiesterases, we found that three of them (DipA, NbdA, and RbdA) can significantly inhibit flagellar motor switching and swimming directional reversal in a MapZ-dependent manner. These results disclose a network of c-di-GMP-signaling proteins that regulate chemotactic responses and flagellar motor switching in P. aeruginosa and establish MapZ as a key signaling hub that integrates inputs from different c-di-GMP-signaling pathways to control flagellar output and bacterial motility. We rationalized these experimental findings by invoking a model that postulates the regulation of flagellar motor switching by subcellular c-di-GMP pools.

3DμF - Interactive Design Environment for Continuous Flow Microfluidic Devices

The design of microfluidic Lab on a Chip (LoC) systems is an onerous task requiring specialized skills in fluid dynamics, mechanical design drafting, and manufacturing. Engineers face significant challenges during the labor-intensive process of designing microfluidic devices, with very few specialized tools that help automate the process. Typical design iterations require the engineer to research the architecture, manually draft the device layout, optimize for manufacturing processes, and manually calculate and program the valve sequences that operate the microfluidic device. The problem compounds when engineers not only have to test the functionality of the chip but are also expected to optimize them for the robust execution of biological assays. In this paper, we present an interactive tool for designing continuous flow microfluidic devices. 3DμF is the first completely open source interactive microfluidic system designer that readily supports state of the art design automation algorithms. Through various case studies, we show 3DμF can be used to reproduce designs from literature, provide metrics for evaluating microfluidic design complexity and showcase how 3DμF is a platform for integrating a wide assortment of engineering techniques used in the design of microfluidic devices as a part of the standard design workflow.

Adaptive information processing of network modules to dynamic and spatial stimuli

BACKGROUND

Adaptation and homeostasis are basic features of information processing in cells and seen in a broad range of contexts. Much of the current understanding of adaptation in network modules/motifs is based on their response to simple stimuli. Recently, there have also been studies of adaptation in dynamic stimuli. However a broader synthesis of how different circuits of adaptation function, and which circuits enable a broader adaptive behaviour in classes of more complex and spatial stimuli is largely missing.

RESULTS

We study the response of a variety of adaptive circuits to time-varying stimuli such as ramps, periodic stimuli and static and dynamic spatial stimuli. We find that a variety of responses can be seen in ramp stimuli, making this a basis for discriminating between even similar circuits. We also find that a number of circuits adapt exactly to ramp stimuli, and dissect these circuits to pinpoint what characteristics (architecture, feedback, biochemical aspects, information processing ingredients) allow for this. These circuits include incoherent feedforward motifs, inflow-outflow motifs and transcritical circuits. We find that changes in location in such circuits where a signal acts can result in non-adaptive behaviour in ramps, even though the location was associated with exact adaptation in step stimuli. We also demonstrate that certain augmentations of basic inflow-outflow motifs can alter the behaviour of the circuit from exact adaptation to non-adaptive behaviour. When subject to periodic stimuli, some circuits (inflow-outflow motifs and transcritical circuits) are able to maintain an average output independent of the characteristics of the input. We build on this to examine the response of adaptive circuits to static and dynamic spatial stimuli. We demonstrate how certain circuits can exhibit a graded response in spatial static stimuli with an exact maintenance of the spatial mean-value. Distinct features which emerge from the consideration of dynamic spatial stimuli are also discussed. Finally, we also build on these results to show how different circuits which show any combination of presence or absence of exact adaptation in ramps, exact mainenance of time average output in periodic stimuli and exact maintenance of spatial average of output in static spatial stimuli may be realized.

CONCLUSIONS

By studying a range of network circuits/motifs on one hand and a range of stimuli on the other, we isolate characteristics of these circuits (structural) which enable different degrees of exact adaptive and homeostatic behaviour in such stimuli, how they may be combined, and also identify cases associated with non-homeostatic behaviour. We also reveal constraints associated with locations where signals may act to enable homeostatic behaviour and constraints associated with augmentations of circuits. This consideration of multiple experimentally/naturally relevant stimuli along with circuits of adaptation of relevance in natural and engineered biology, provides a platform for deepening our understanding of adaptive and homeostatic behaviour in natural systems, bridging the gap between models of adaptation and experiments and in engineering homeostatic synthetic circuits.

Biological signal generators: integrating synthetic biology tools and in silico control

Biological networks sense extracellular stimuli and generate appropriate outputs within the cell that determine cellular response. Biological signal generators are becoming an important tool for understanding how information is transmitted in these networks and controlling network behavior. Signal generators produce well-defined, dynamic, intracellular signals of important network components, such as kinase activity or the concentration of a specific transcription factor. Synthetic biology tools coupled with in silico control have enabled the construction of these sophisticated biological signal generators. Here we review recent advances in biological signal generator construction and their use in systems biology studies. Challenges for constructing signal generators for a wider range of biological networks and generalizing their use are discussed.

Integrating chemical and mechanical signals through dynamic coupling between cellular protrusions and pulsed ERK activation

The Ras-ERK signaling pathway regulates diverse cellular processes in response to environmental stimuli and contains important therapeutic targets for cancer. Recent single cell studies revealed stochastic pulses of ERK activation, the frequency of which determines functional outcomes such as cell proliferation. Here we show that ERK pulses are initiated by localized protrusive activities. Chemically and optogenetically induced protrusions trigger ERK activation through various entry points into the feedback loop involving Ras, PI3K, the cytoskeleton, and cellular adhesion. The excitability of the protrusive signaling network drives stochastic ERK activation in unstimulated cells and oscillations upon growth factor stimulation. Importantly, protrusions allow cells to sense combined signals from substrate stiffness and the growth factor. Thus, by uncovering the basis of ERK pulse generation we demonstrate how signals involved in cell growth and differentiation are regulated by dynamic protrusions that integrate chemical and mechanical inputs from the environment.

Cellular ERK activation occurs as discrete pulses but their relationship to upstream Ras signaling is still under debate. Here, the authors show that Ras signaling associated with cellular protrusions triggers pulsed ERK activation, thereby enabling cells to integrate chemical and mechanical stimuli.

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.

A computational model for how cells choose temporal or spatial sensing during chemotaxis

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.

Unicellular organisms and other single cells often have to migrate towards food sources or away from predators by sensing chemicals present in the environment. There are two ways for a cell to sense these external chemicals: temporal sensing, where the cell senses the external chemical at two different time points after it has moved through a certain distance, or spatial sensing, where the cell senses the external chemical at two different locations on its cellular surface (e.g., the front and rear of the cell) simultaneously. It has been thought that small unicellular organisms employ temporal sensing as their small size prohibits sensing at two different locations on the cellular surface. Using computational modeling, we find that the choice between temporal and spatial sensing is determined by the ratio of cell velocity to the product of cell diameter and rate of signaling, as well as the diffusivities of the signaling proteins. Predictions from our model agree with experimental observations over a wide range of cells, where a fast-moving, small cell performs better comparing the chemoattractant at different times in its trajectory; whereas, a slow-moving, big cell performs better by comparing the chemoattractant concentration at its two ends.

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.

Collective behaviour and swarm intelligence in slime moulds

The study of collective behaviour aims to understand how individual-level behaviours can lead to complex group-level patterns. Collective behaviour has primarily been studied in animal groups such as colonies of insects, flocks of birds and schools of fish. Although less studied, collective behaviour also occurs in microorganisms. Here, we argue that slime moulds are powerful model systems for solving several outstanding questions in collective behaviour. In particular, slime mould may hold the key to linking individual-level mechanisms to colony-level behaviours. Using well-established principles of collective animal behaviour as a framework, we discuss the extent to which slime mould collectives are comparable to animal groups, and we highlight some potentially fruitful areas for future research.

Elastic Multi-scale Mechanisms: Computation and Biological Evolution

Explanations based on low-level interacting elements are valuable and powerful since they contribute to identify the key mechanisms of biological functions. However, many dynamic systems based on low-level interacting elements with unambiguous, finite, and complete information of initial states generate future states that cannot be predicted, implying an increase of complexity and open-ended evolution. Such systems are like Turing machines, that overlap with dynamical systems that cannot halt. We argue that organisms find halting conditions by distorting these mechanisms, creating conditions for a constant creativity that drives evolution. We introduce a modulus of elasticity to measure the changes in these mechanisms in response to changes in the computed environment. We test this concept in a population of predators and predated cells with chemotactic mechanisms and demonstrate how the selection of a given mechanism depends on the entire population. We finally explore this concept in different frameworks and postulate that the identification of predictive mechanisms is only successful with small elasticity modulus.

Cell-to-cell variation sets a tissue-rheology-dependent bound on collective gradient sensing

When a single cell senses a chemical gradient and chemotaxes, stochastic receptor-ligand binding can be a fundamental limit to the cell's accuracy. For clusters of cells responding to gradients, however, there is a critical difference: Even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate, the resulting bias can be much larger than the effects of ligand-receptor binding. Specifically, when a strongly responding cell is at one end of a cell cluster, cluster motion is biased toward that cell. These errors are mitigated if clusters average measurements over times long enough for cells to rearrange. In consequence, fluid clusters are better able to sense gradients: We derive a link between cluster accuracy, cell-to-cell variation, and the cluster rheology. Because of this connection, increasing the noisiness of individual cell motion can actually increase the collective accuracy of a cluster by improving fluidity.

Structural analyses unravel the molecular mechanism of cyclic di-GMP regulation of bacterial chemotaxis via a PilZ adaptor protein

The bacterial second messenger cyclic di-GMP (c-di-GMP) has emerged as a prominent mediator of bacterial physiology, motility, and pathogenicity. c-di-GMP often regulates the function of its protein targets through a unique mechanism that involves a discrete PilZ adaptor protein. However, the molecular mechanism for PilZ protein-mediated protein regulation is unclear. Here, we present the structure of the PilZ adaptor protein MapZ cocrystallized in complex with c-di-GMP and its protein target CheR1, a chemotaxis-regulating methyltransferase in Pseudomonas aeruginosa This cocrystal structure, together with the structure of free CheR1, revealed that the binding of c-di-GMP induces dramatic structural changes in MapZ that are crucial for CheR1 binding. Importantly, we found that restructuring and repositioning of two C-terminal helices enable MapZ to disrupt the CheR1 active site by dislodging a structural domain. The crystallographic observations are reinforced by protein-protein binding and single cell-based flagellar motor switching analyses. Our studies further suggest that the regulation of chemotaxis by c-di-GMP through MapZ orthologs/homologs is widespread in proteobacteria and that the use of allosterically regulated C-terminal motifs could be a common mechanism for PilZ adaptor proteins. Together, the findings provide detailed structural insights into how c-di-GMP controls the activity of an enzyme target indirectly through a PilZ adaptor protein.

Timescale Separation of Positive and Negative Signaling Creates History-Dependent Responses to IgE Receptor Stimulation

The high-affinity receptor for IgE expressed on the surface of mast cells and basophils interacts with antigens, via bound IgE antibody, and triggers secretion of inflammatory mediators that contribute to allergic reactions. To understand how past inputs (memory) influence future inflammatory responses in mast cells, a microfluidic device was used to precisely control exposure of cells to alternating stimulatory and non-stimulatory inputs. We determined that the response to subsequent stimulation depends on the interval of signaling quiescence. For shorter intervals of signaling quiescence, the second response is blunted relative to the first response, whereas longer intervals of quiescence induce an enhanced second response. Through an iterative process of computational modeling and experimental tests, we found that these memory-like phenomena arise from a confluence of rapid, short-lived positive signals driven by the protein tyrosine kinase Syk; slow, long-lived negative signals driven by the lipid phosphatase Ship1; and slower degradation of Ship1 co-factors. This work advances our understanding of mast cell signaling and represents a generalizable approach for investigating the dynamics of signaling systems.

Variability and Order in Cytoskeletal Dynamics of Motile Amoeboid Cells

The chemotactic motion of eukaryotic cells such as leukocytes or metastatic cancer cells relies on membrane protrusions driven by the polymerization and depolymerization of actin. Here we show that the response of the actin system to a receptor stimulus is subject to a threshold value that varies strongly from cell to cell. Above the threshold, we observe pronounced cell-to-cell variability in the response amplitude. The polymerization time, however, is almost constant over the entire range of response amplitudes, while the depolymerization time increases with increasing amplitude. We show that cell-to-cell variability in the response amplitude correlates with the amount of Arp2/3, a protein that enhances actin polymerization. A time-delayed feedback model for the cortical actin concentration is consistent with all our observations and confirms the role of Arp2/3 in the observed cell-to-cell variability. Taken together, our observations highlight robust regulation of the actin response that enables a reliable timing of cell movement.

Oscillatory stimuli differentiate adapting circuit topologies

Adapting pathways consist of negative feedback loops (NFLs) or incoherent feedforward loops (IFFLs), which we show can be differentiated using oscillatory stimulation: NFLs but not IFFLs generically show ‘refractory period stabilization’ or ‘period skipping’. Using these signatures and genetic rewiring we identified the circuit dominating cell cycle timing in yeast. In C. elegans AWA neurons we uncovered a Ca2+-NFL, diffcult to find by other means, especially in wild-type, intact animals. (70 words)

Physical models of collective cell motility: from cell to tissue

In this article, we review physics-based models of collective cell motility. We discuss a range of techniques at different scales, ranging from models that represent cells as simple self-propelled particles to phase field models that can represent a cell's shape and dynamics in great detail. We also extensively review the ways in which cells within a tissue choose their direction, the statistics of cell motion, and some simple examples of how cell-cell signaling can interact with collective cell motility. This review also covers in more detail selected recent works on collective cell motion of small numbers of cells on micropatterns, in wound healing, and the chemotaxis of clusters of cells.

Modeling Contact Inhibition of Locomotion of Colliding Cells Migrating on Micropatterned Substrates

In cancer metastasis, embryonic development, and wound healing, cells can coordinate their motion, leading to collective motility. To characterize these cell-cell interactions, which include contact inhibition of locomotion (CIL), micropatterned substrates are often used to restrict cell migration to linear, quasi-one-dimensional paths. In these assays, collisions between polarized cells occur frequently with only a few possible outcomes, such as cells reversing direction, sticking to one another, or walking past one another. Using a computational phase field model of collective cell motility that includes the mechanics of cell shape and a minimal chemical model for CIL, we are able to reproduce all cases seen in two-cell collisions. A subtle balance between the internal cell polarization, CIL and cell-cell adhesion governs the collision outcome. We identify the parameters that control transitions between the different cases, including cell-cell adhesion, propulsion strength, and the rates of CIL. These parameters suggest hypotheses for why different cell types have different collision behavior and the effect of interventions that modulate collision outcomes. To reproduce the heterogeneity in cell-cell collision outcomes observed experimentally in neural crest cells, we must either carefully tune our parameters or assume that there is significant cell-to-cell variation in key parameters like cell-cell adhesion.

Many cells cooperate with their neighbors to move as a group. However, the mechanisms of these cell-cell interactions are not well understood. One experimental tool to analyze interactions is to allow cells to collide with one another, and see what happens. In order to better understand what features these experiments measure, we develop a computational model of cell-cell collisions, and identify the biochemical and mechanical parameters that lead to different outcomes of collisions. We can recreate all known types of collisions seen in experiments, including cells reversing on contact, sticking, or walking past each other. Our model suggests that what happens in a collision may depend strongly on the mechanical forces between the two cells.

Modeling Cellular Noise Underlying Heterogeneous Cell Responses in the Epidermal Growth Factor Signaling Pathway

Cellular heterogeneity, which plays an essential role in biological phenomena, such as drug resistance and migration, is considered to arise from intrinsic (i.e., reaction kinetics) and extrinsic (i.e., protein variability) noise in the cell. However, the mechanistic effects of these types of noise to determine the heterogeneity of signal responses have not been elucidated. Here, we report that the output of epidermal growth factor (EGF) signaling activity is modulated by cellular noise, particularly by extrinsic noise of particular signaling components in the pathway. We developed a mathematical model of the EGF signaling pathway incorporating regulation between extracellular signal-regulated kinase (ERK) and nuclear pore complex (NPC), which is necessary for switch-like activation of the nuclear ERK response. As the threshold of switch-like behavior is more sensitive to perturbations than the graded response, the effect of biological noise is potentially critical for cell fate decision. Our simulation analysis indicated that extrinsic noise, but not intrinsic noise, contributes to cell-to-cell heterogeneity of nuclear ERK. In addition, we accurately estimated variations in abundance of the signal proteins between individual cells by direct comparison of experimental data with simulation results using Apparent Measurement Error (AME). AME was constant regardless of whether the protein levels varied in a correlated manner, while covariation among proteins influenced cell-to-cell heterogeneity of nuclear ERK, suppressing the variation. Simulations using the estimated protein abundances showed that each protein species has different effects on cell-to-cell variation in the nuclear ERK response. In particular, variability of EGF receptor, Ras, Raf, and MEK strongly influenced cellular heterogeneity, while others did not. Overall, our results indicated that cellular heterogeneity in response to EGF is strongly driven by extrinsic noise, and that such heterogeneity results from variability of particular protein species that function as sensitive nodes, which may contribute to the pathogenesis of human diseases.

Individual cell behaviors are controlled by a variety of noise, such as fluctuations in biochemical reactions, protein variability, molecular diffusion, transcriptional noise, cell-to-cell contact, temperature, and pH. Such cellular noise often interferes with signal responses from external stimuli, and such heterogeneity functions in induction of drug resistance, survival, and migration of cells. Thus, heterogeneous cellular responses have positive and negative roles. However, the regulatory mechanisms that produce cellular heterogeneity are unclear. By mathematical modeling and simulations, we investigated how heterogeneous signaling responses are evoked in the EGF signaling pathway and influence the switch-like activation of nuclear ERK. This study demonstrated that cellular heterogeneity of the EGF signaling response is evoked by cell-to-cell variation of particular signaling proteins, such as EGFR, Ras, Raf, and MEK, which act as sensitive nodes in the pathway. These results suggest that signaling responses in individual cells can be predicted from the levels of proteins of sensitive nodes. This study also suggested that proteins of sensitive nodes may serve as cell survival mechanisms.

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.

A cyclic di-GMP-binding adaptor protein interacts with a chemotaxis methyltransferase to control flagellar motor switching

The bacterial messenger cyclic diguanylate monophosphate (c-di-GMP) binds to various effectors, the most common of which are single-domain PilZ proteins. These c-di-GMP effectors control various cellular functions and multicellular behaviors at the transcriptional or posttranslational level. We found that MapZ (methyltransferase-associated PilZ; formerly known as PA4608), a single-domain PilZ protein from the opportunistic pathogen Pseudomonas aeruginosa, directly interacted with the methyltransferase CheR1 and that this interaction was enhanced by c-di-GMP. In vitro assays indicated that, in the presence of c-di-GMP, MapZ inhibited CheR1 from methylating the chemoreceptor PctA, which would be expected to increase its affinity for chemoattractants and promote chemotaxis. MapZ localized to the poles of P. aeruginosa cells, where the flagellar motor and other chemotactic proteins, including PctA and CheR1, are also located. P. aeruginosa cells exhibit a random walk behavior by frequently switching the direction of flagellar rotation in a uniform solution. We showed that binding of c-di-GMP to MapZ decreased the frequency of flagellar motor switching and that MapZ was essential for generating the heterogeneous motility typical of P. aeruginosa cell populations and for efficient surface attachment during biofilm formation. Collectively, the studies revealed that c-di-GMP affects flagellar motor output by regulating the methylation of chemoreceptors through a single-domain PilZ adaptor protein.

Noisy Oscillations in the Actin Cytoskeleton of Chemotactic Amoeba

Biological systems with their complex biochemical networks are known to be intrinsically noisy. Here we investigate the dynamics of actin polymerization of amoeboid cells, which are close to the onset of oscillations. We show that the large phenotypic variability in the polymerization dynamics can be accurately captured by a generic nonlinear oscillator model in the presence of noise. We determine the relative role of the noise with a single dimensionless, experimentally accessible parameter, thus providing a quantitative description of the variability in a population of cells. Our approach, which rests on a generic description of a system close to a Hopf bifurcation and includes the effect of noise, can characterize the dynamics of a large class of noisy systems close to an oscillatory instability.

What Scales the T Cell Response?

T cells are known to scale their clonal expansion and effector cytokine response according to the dose and strength of antigenic signal so as to balance their role of affecting protection with the intertwined and immunologically driven tissue damage. How T cells achieve this is now beginning to be understood. We underscore temporal integration of digital T cell receptor (TCR) signaling as the basis for achieving scaled response by means of accumulating crucial mediators over time. We also discuss the role of temporally integrated crosstalk between TCR and IL2 signaling in mediating a scaled, coherent, collective response by T cells. Finally, we highlight numerous known and putative regulatory interactions in the transcriptional program that are expected to quantitatively scale the T cell response, and also offer new mechanisms to hitherto unexplained observations.

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.

Gβ Regulates Coupling between Actin Oscillators for Cell Polarity and Directional Migration

For directional movement, eukaryotic cells depend on the proper organization of their actin cytoskeleton. This engine of motility is made up of highly dynamic nonequilibrium actin structures such as flashes, oscillations, and traveling waves. In Dictyostelium, oscillatory actin foci interact with signals such as Ras and phosphatidylinositol 3,4,5-trisphosphate (PIP₃) to form protrusions. However, how signaling cues tame actin dynamics to produce a pseudopod and guide cellular motility is a critical open question in eukaryotic chemotaxis. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. We implement an inducible sequestration system to inactivate the heterotrimeric G protein subunit Gβ and find that this acute perturbation triggers persistent, high-amplitude cortical oscillations of F-actin. Actin oscillators that are normally weakly coupled to one another in wild-type cells become strongly synchronized following acute inactivation of Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. A simple mathematical model of coupled actin oscillators reveals the importance of appropriate coupling strength for chemotaxis: moderate coupling can increase sensitivity to noisy inputs. Taken together, our data suggest that Gβ regulates the strength of coupling between actin oscillators for efficient polarity and directional migration. As these observations are only possible following acute inhibition of Gβ and are masked by slow compensation in genetic knockouts, our work also shows that acute loss-of-function approaches can complement and extend the reach of classical genetics in Dictyostelium and likely other systems as well.

Coupling of individual oscillators regulates biological functions ranging from crickets chirping in unison to the coordination of pacemaker cells of the heart. This study finds that a similar concept—coupling between actin oscillators—is at work within single slime mold cells to establish polarity and guide their direction of migration.

The actin cytoskeleton of motile cells is comprised of highly dynamic structures. Recently, small oscillating actin foci have been discovered around the periphery of Dictyostelium cells. These oscillators are thought to enable pseudopod formation, but how their dynamics are regulated for this is unknown. Here, we demonstrate that the strength of coupling between individual actin oscillators controls cell polarization and directional movement. Actin oscillators are weakly coupled to one another in wild-type cells, but they become strongly synchronized after acute inactivation of the signaling protein Gβ. This global coupling impairs sensing of internal cues during spontaneous polarization and sensing of external cues during directional motility. Supported by a mathematical model, our data suggest that wild-type cells are tuned to an optimal coupling strength for patterning by upstream cues. These observations are only possible following acute inhibition of Gβ, which highlights the value of revisiting classical mutants with acute loss-of-function perturbations.

Limits to the precision of gradient sensing with spatial communication and temporal integration

Gradient sensing requires at least two measurements at different points in space. These measurements must then be communicated to a common location to be compared, which is unavoidably noisy. Although much is known about the limits of measurement precision by cells, the limits placed by the communication are not understood. Motivated by recent experiments, we derive the fundamental limits to the precision of gradient sensing in a multicellular system, accounting for communication and temporal integration. The gradient is estimated by comparing a "local" and a "global" molecular reporter of the external concentration, where the global reporter is exchanged between neighboring cells. Using the fluctuation-dissipation framework, we find, in contrast to the case when communication is ignored, that precision saturates with the number of cells independently of the measurement time duration, because communication establishes a maximum length scale over which sensory information can be reliably conveyed. Surprisingly, we also find that precision is improved if the local reporter is exchanged between cells as well, albeit more slowly than the global reporter. The reason is that whereas exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation-global inhibition." Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account.

Regulation of Spatiotemporal Patterns by Biological Variability: General Principles and Applications to Dictyostelium discoideum

Spatiotemporal patterns often emerge from local interactions in a self-organizing fashion. In biology, the resulting patterns are also subject to the influence of the systematic differences between the system’s constituents (biological variability). This regulation of spatiotemporal patterns by biological variability is the topic of our review. We discuss several examples of correlations between cell properties and the self-organized spatiotemporal patterns, together with their relevance for biology. Our guiding, illustrative example will be spiral waves of cAMP in a colony of Dictyostelium discoideum cells. Analogous processes take place in diverse situations (such as cardiac tissue, where spiral waves occur in potentially fatal ventricular fibrillation) so a deeper understanding of this additional layer of self-organized pattern formation would be beneficial to a wide range of applications. One of the most striking differences between pattern-forming systems in physics or chemistry and those in biology is the potential importance of variability. In the former, system components are essentially identical with random fluctuations determining the details of the self-organization process and the resulting patterns. In biology, due to variability, the properties of potentially very few cells can have a driving influence on the resulting asymptotic collective state of the colony. Variability is one means of implementing a few-element control on the collective mode. Regulatory architectures, parameters of signaling cascades, and properties of structure formation processes can be "reverse-engineered" from observed spatiotemporal patterns, as different types of regulation and forms of interactions between the constituents can lead to markedly different correlations. The power of this biology-inspired view of pattern formation lies in building a bridge between two scales: the patterns as a collective state of a very large number of cells on the one hand, and the internal parameters of the single cells on the other.

Pattern formation is abundant in nature—from the rich ornaments of sea shells and the diversity of animal coat patterns to the myriad of fractal structures in biology and pattern-forming colonies of bacteria. Particularly fascinating are patterns changing with time, spatiotemporal patterns, like propagating waves and aggregation streams. Bacteria form large branched and nested aggregation-like patterns to immobilize themselves against water flow. The individual amoeba in Dictyostelium discoideum colonies initiates a transition to a collective multicellular state via a quorum-sensing form of communication—a cAMP signal propagating through the community in the form of spiral waves—and the subsequent chemotactic response of the cells leads to branch-like aggregation streams. The theoretical principle underlying most of these spatial and spatiotemporal patterns is self-organization, in which local interactions lead to patterns as large-scale collective”modes” of the system. Over more than half a century, these patterns have been classified and analyzed according to a”physics paradigm,” investigating such questions as how parameters regulate the transitions among patterns, which (types of) interactions lead to such large-scale patterns, and whether there are "critical parameter values" marking the sharp, spontaneous onset of patterns. A fundamental discovery has been that simple local interaction rules can lead to complex large-scale patterns. The specific pattern "layouts" (i.e., their spatial arrangement and their geometric constraints) have received less attention. However, there is a major difference between patterns in physics and chemistry on the one hand and patterns in biology on the other: in biology, patterns often have an important functional role for the biological system and can be considered to be under evolutionary selection. From this perspective, we can expect that individual biological elements exert some control on the emerging patterns. Here we explore spiral wave patterns as a prominent example to illustrate the regulation of spatiotemporal patterns by biological variability. We propose a new approach to studying spatiotemporal data in biology: analyzing the correlation between the spatial distribution of the constituents’ properties and the features of the spatiotemporal pattern. This general concept is illustrated by simulated patterns and experimental data of a model organism of biological pattern formation, the slime mold Dictyostelium discoideum. We introduce patterns starting from Turing (stripe and spot) patterns, together with target waves and spiral waves. The biological relevance of these patterns is illustrated by snapshots from real and theoretical biological systems. The principles of spiral wave formation are first explored in a stylized cellular automaton model and then reproduced in a model of Dictyostelium signaling. The shaping of spatiotemporal patterns by biological variability (i.e., by a spatial distribution of cell-to-cell differences) is demonstrated, focusing on two Dictyostelium models. Building up on this foundation, we then discuss in more detail how the nonlinearities in biological models translate the distribution of cell properties into pattern events, leaving characteristic geometric signatures.

A G-protein subunit translocation embedded network motif underlies GPCR regulation of calcium oscillations

G-protein βγ subunits translocate reversibly from the plasma membrane to internal membranes on receptor activation. Translocation rates differ depending on the γ subunit type. There is limited understanding of the role of the differential rates of Gβγ translocation in modulating signaling dynamics in a cell. Bifurcation analysis of the calcium oscillatory network structure predicts that the translocation rate of a signaling protein can regulate the damping of system oscillation. Here, we examined whether the Gβγ translocation rate regulates calcium oscillations induced by G-protein-coupled receptor activation. Oscillations in HeLa cells expressing γ subunit types with different translocation rates were imaged and quantitated. The results show that differential Gβγ translocation rates can underlie the diversity in damping characteristics of calcium oscillations among cells. Mathematical modeling shows that a translocation embedded motif regulates damping of G-protein-mediated calcium oscillations consistent with experimental data. The current study indicates that such a motif may act as a tuning mechanism to design oscillations with varying damping patterns by using intracellular translocation of a signaling component.

Modeling oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales-from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Ptch1 and Gli regulate Shh signalling dynamics via multiple mechanisms

In the vertebrate neural tube, the morphogen Sonic Hedgehog (Shh) establishes a characteristic pattern of gene expression. Here we quantify the Shh gradient in the developing mouse neural tube and show that while the amplitude of the gradient increases over time, the activity of the pathway transcriptional effectors, Gli proteins, initially increases but later decreases. Computational analysis of the pathway suggests three mechanisms that could contribute to this adaptation: transcriptional upregulation of the inhibitory receptor Ptch1, transcriptional downregulation of Gli and the differential stability of active and inactive Gli isoforms. Consistent with this, Gli2 protein expression is downregulated during neural tube patterning and adaptation continues when the pathway is stimulated downstream of Ptch1. Moreover, the Shh-induced upregulation of Gli2 transcription prevents Gli activity levels from adapting in a different cell type, NIH3T3 fibroblasts, despite the upregulation of Ptch1. Multiple mechanisms therefore contribute to the intracellular dynamics of Shh signalling, resulting in different signalling dynamics in different cell types.

How to train your microbe: methods for dynamically characterizing gene networks

Gene networks regulate biological processes dynamically. However, researchers have largely relied upon static perturbations, such as growth media variations and gene knockouts, to elucidate gene network structure and function. Thus, much of the regulation on the path from DNA to phenotype remains poorly understood. Recent studies have utilized improved genetic tools, hardware, and computational control strategies to generate precise temporal perturbations outside and inside of live cells. These experiments have, in turn, provided new insights into the organizing principles of biology. Here, we introduce the major classes of dynamical perturbations that can be used to study gene networks, and discuss technologies available for creating them in a wide range of microbial pathways.

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.

Rectified directional sensing in long-range cell migration

How spatial and temporal information are integrated to determine the direction of cell migration remains poorly understood. Here, by precise microfluidics emulation of dynamic chemoattractant waves, we demonstrate that, in Dictyostelium, directional movement as well as activation of small guanosine triphosphatase Ras at the leading edge is suppressed when the chemoattractant concentration is decreasing over time. This 'rectification' of directional sensing occurs only at an intermediate range of wave speed and does not require phosphoinositide-3-kinase or F-actin. From modelling analysis, we show that rectification arises naturally in a single-layered incoherent feedforward circuit with zero-order ultrasensitivity. The required stimulus time-window predicts ~5 s transient for directional sensing response close to Ras activation and inhibitor diffusion typical for protein in the cytosol. We suggest that the ability of Dictyostelium cells to move only in the wavefront is closely associated with rectification of adaptive response combined with local activation and global inhibition.

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.

A generalizable, tunable microfluidic platform for delivering fast temporally varying chemical signals to probe single-cell response dynamics

Understanding how biological systems transduce dynamic, soluble chemical cues into physiological processes requires robust experimental tools for generating diverse temporal chemical patterns. The advent of microfluidics has seen the development of platforms for rapid fluid exchange allowing ease of changes in the cellular microenvironment and precise cell handling. Rapid exchange is important for exposing systems to temporally varying signals. However, direct coupling of macroscale fluid flow with microstructures is potentially problematic due to the high shear stresses that inevitably add confounding mechanical perturbation effects to the biological system of interest. Here, we have devised a method of translating fast and precise macroscale flows to microscale flows using a monolithically integrated perforated membrane. We integrated a high-density cell trap array for nonadherent cells that are challenging to handle under flow conditions with a soluble chemical signal generator module. The platform enables fast and repeatable switching of stimulus and buffer at low shear stresses for quantitative live, single-cell fluorescent studies. This modular design allows facile integration of any cell-handling chip design with any chemical delivery module. We demonstrate the utility of this device by characterizing heterogeneity of oscillatory response for cells exposed to alternating Ca²⁺ waveforms at various periodicities. This platform enables the analysis of cell responses to chemical perturbations at a single-cell resolution that is necessary in understanding signal transduction pathways.

Excitable signal transduction induces both spontaneous and directional cell asymmetries in the phosphatidylinositol lipid signaling system for eukaryotic chemotaxis

Intracellular asymmetry in the signaling network works as a compass to navigate eukaryotic chemotaxis in response to guidance cues. Although the compass variable can be derived from a self-organization dynamics, such as excitability, the responsible mechanism remains to be clarified. Here, we analyzed the spatiotemporal dynamics of the phosphatidylinositol 3,4,5-trisphosphate (PtdInsP3) pathway, which is crucial for chemotaxis. We show that spontaneous activation of PtdInsP3-enriched domains is generated by an intrinsic excitable system. Formation of the same signal domain could be triggered by various perturbations, such as short impulse perturbations that triggered the activation of intrinsic dynamics to form signal domains. We also observed the refractory behavior exhibited in typical excitable systems. We show that the chemotactic response of PtdInsP3 involves biasing the spontaneous excitation to orient the activation site toward the chemoattractant. Thus, this biased excitability embodies the compass variable that is responsible for both random cell migration and biased random walk. Our finding may explain how cells achieve high sensitivity to and robust coordination of the downstream activation that allows chemotactic behavior in the noisy environment outside and inside the cells.

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.

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.

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.

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.

How to understand and outwit adaptation

Adaptation is the ability of a system to respond and reset itself even in the continuing presence of a stimulus. On one hand, adaptation is a physiological necessity that enables proper neuronal signaling and cell movement. On the other hand, adaptation can be a source of annoyance, as it can make biological systems resistant to experimental perturbations. Here we speculate where adaptation might live in eukaryotic chemotaxis and how it can be encoded in the signaling network. We then discuss tools and strategies that can be used to both understand and outwit adaptation in a wide range of cellular contexts.

Interpreting frequency responses to dose-conserved pulsatile input signals in simple cell signaling motifs

Many hormones are released in pulsatile patterns. This pattern can be modified, for instance by changing pulse frequency, to encode relevant physiological information. Often other properties of the pulse pattern will also change with frequency. How do signaling pathways of cells targeted by these hormones respond to different input patterns? In this study, we examine how a given dose of hormone can induce different outputs from the target system, depending on how this dose is distributed in time. We use simple mathematical models of feedforward signaling motifs to understand how the properties of the target system give rise to preferences in input pulse pattern. We frame these problems in terms of frequency responses to pulsatile inputs, where the amplitude or duration of the pulses is varied along with frequency to conserve input dose. We find that the form of the nonlinearity in the steady state input-output function of the system predicts the optimal input pattern. It does so by selecting an optimal input signal amplitude. Our results predict the behavior of common signaling motifs such as receptor binding with dimerization, and protein phosphorylation. The findings have implications for experiments aimed at studying the frequency response to pulsatile inputs, as well as for understanding how pulsatile patterns drive biological responses via feedforward signaling pathways.