Control parameter description of eukaryotic chemotaxis

A sub-population of Dictyostelium discoideum cells shows extremely high sensitivity to cAMP for directional migration

The chemotaxis of Dictysotelium discoideum cells in response to a chemical gradient of cyclic adenosine 3',5'-monophosphate (cAMP) was studied using a newly designed microfluidic device. The device consists of 800 cell-sized channels in parallel, each 4 μm wide, 5 μm high, and 100 μm long, allowing us to prepare the same chemical gradient in all channels and observe the motility of 500-1000 individual cells simultaneously. The percentage of cells that exhibited directed migration was determined for various cAMP concentrations ranging from 0.1 pM to 10 μM. The results show that chemotaxis was highest at 100 nM cAMP, consistent with previous observations. At concentrations as low as 10 pM, about 16% of cells still exhibited chemotaxis, suggesting that the receptor occupancy of only 6 cAMP molecules/cell can induce chemotaxis in very sensitive cells. At 100 pM cAMP, chemotaxis was suppressed due to the self-production and secretion of intracellular cAMP induced by extracellular cAMP. Overall, systematic observations of a large number of individual cells under the same chemical gradients revealed the heterogeneity of chemotaxis responses in a genetically homogeneous cell population, especially the existence of a sub-population with extremely high sensitivity for chemotaxis.

Sperm chemotaxis is driven by the slope of the chemoattractant concentration field

Spermatozoa of marine invertebrates are attracted to their conspecific female gamete by diffusive molecules, called chemoattractants, released from the egg investments in a process known as chemotaxis. The information from the egg chemoattractant concentration field is decoded into intracellular Ca²⁺ concentration ([Ca²⁺]_i) changes that regulate the internal motors that shape the flagellum as it beats. By studying sea urchin species-specific differences in sperm chemoattractant-receptor characteristics we show that receptor density constrains the steepness of the chemoattractant concentration gradient detectable by spermatozoa. Through analyzing different chemoattractant gradient forms, we demonstrate for the first time that Strongylocentrotus purpuratus sperm are chemotactic and this response is consistent with frequency entrainment of two coupled physiological oscillators: i) the stimulus function and ii) the [Ca²⁺]_i changes. We demonstrate that the slope of the chemoattractant gradients provides the coupling force between both oscillators, arising as a fundamental requirement for sperm chemotaxis.

Leader cells in collective chemotaxis: Optimality and trade-offs

Clusters of cells can work together in order to follow a signal gradient, chemotaxing even when single cells do not. Cells in different regions of collectively migrating neural crest streams show different gene expression profiles, suggesting that cells may specialize to leader and follower roles. We use a minimal mathematical model to understand when this specialization is advantageous. In our model, leader cells sense the gradient with an accuracy that depends on the kinetics of ligand-receptor binding, while follower cells follow the cluster's direction with a finite error. Intuitively, specialization into leaders and followers should be optimal when a few cells have more information than the rest of the cluster, such as in the presence of a sharp transition in chemoattractant concentration. We do find this-but also find that high levels of specialization can be optimal in the opposite limit of very shallow gradients. We also predict that the best location for leaders may not be at the front of the cluster. In following leaders, clusters may have to choose between speed and flexibility. Clusters with only a few leaders can take orders of magnitude more time to reorient than all-leader clusters.

Chemotaxis Model for Breast Cancer Cells Based on Signal/Noise Ratio

Chemotaxis, a biased migration of cells under a chemical gradient, plays a significant role in diverse biological phenomena including cancer metastasis. Stromal cells release signaling proteins to induce chemotaxis, which leads to organ-specific metastasis. Epidermal growth factor (EGF) is an example of the chemical attractants, and its gradient stimulates metastasis of breast cancer cells. Hence, the interactions between EGF and breast cancer cells have long been a subject of interest for oncologists and clinicians. However, most current approaches do not systematically separate the effects of gradient and absolute concentration of EGF on chemotaxis of breast cancer cells. In this work, we develop a theoretical model based on signal/noise ratio to represent stochastic properties and report our microfluidic experiments to verify the analytical predictions from the model. The results demonstrate that even under the same EGF concentration gradients (0-50 or 0-150 ng/mL), breast cancer cells reveal a more evident chemotaxis pattern when the absolute EGF concentrations are low. Moreover, we found that reducing the number of EGF receptors (EGFRs) with addition of EGFR antibody (1 ng/mL) can promote chemotaxis at an EGF gradient of 0-1 ng/mL as shown by chemotaxis index (0.121 ± 0.037, reduced EGFRs vs. 0.003 ± 0.041, control). This counterintuitive finding suggests that EGFR-targeted therapy may stimulate metastasis of breast cancer because the partial suppression of the receptors makes the number of receptors close to the optimal one for chemotaxis. This analysis should be considered in anticancer drug design.

Decision making improves sperm chemotaxis in the presence of noise

To navigate their surroundings, cells rely on sensory input that is corrupted by noise. In cells performing chemotaxis, such noise arises from the stochastic binding of signalling molecules at low chemoattractant concentrations. We reveal a fundamental relationship between the speed of chemotactic steering and the strength of directional fluctuations that result from the amplification of noise in a chemical input signal. This relation implies a trade-off between steering that is slow and reliable, and steering that is fast but less reliable. We show that dynamic switching between these two modes of steering can substantially increase the probability to find a target, such as an egg to be found by sperm cells. This decision making confers no advantage in the absence of noise, but is beneficial when chemical signals are detectable, yet characterized by low signal-to-noise ratios. The latter applies at intermediate distances from a target, where signalling molecules are diluted, thus defining a ‘noise zone’ that cells have to cross. Our results explain decision making observed in recent experiments on sea urchin sperm chemotaxis. More generally, our theory demonstrates how decision making enables chemotactic agents to cope with high levels of noise in gradient sensing by dynamically adjusting the persistence length of a biased random walk.

Many cells can navigate upwards a concentration gradient of signalling molecules, a process called chemotaxis. Chemotaxis is used e.g. by sperm cells to find the egg. To measure and compare concentrations, cells count stochastic binding events of signalling molecules that diffuse to cellular receptors. Efficient chemotaxis strategies must be adapted to this molecular shot noise of concentration measurements. We reveal a fundamental relationship between the speed of chemotactic steering and the strength of directional fluctuations that result from the amplification of noise. This implies a trade-off between steering fast and steering reliable. Inspired by recent experiments on chemotaxis of sperm cells of marine invertebrates, we develop a theory that allows to efficiently compute optimal chemotaxis strategies. We show that dynamic switching between either fast or reliable steering can substantially increase the probability for a sperm cell to find the egg. Furthermore, the optimal strategy requires only minimal computational capacities of the chemotactic agent, a key constraint for biological cells. More generally, our work demonstrates a benefit of decision making for chemotaxis in the presence of noise, which could inspire optimal control designs for artificial microswimmers.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?

Extracellular Processing of Molecular Gradients by Eukaryotic Cells Can Improve Gradient Detection Accuracy

Eukaryotic cells sense molecular gradients by measuring spatial concentration variation through the difference in the number of occupied receptors to which molecules can bind. They also secrete enzymes that degrade these molecules, and it is presently not well understood how this affects the local gradient perceived by cells. Numerical and analytical results show that these enzymes can substantially increase the signal-to-noise ratio of the receptor difference and allow cells to respond to a much broader range of molecular concentrations and gradients than they would without these enzymes.

Modelling of Dictyostelium discoideum movement in a linear gradient of chemoattractant

Chemotaxis is a ubiquitous biological phenomenon in which cells detect a spatial gradient of chemoattractant, and then move towards the source. Here we present a position-dependent advection-diffusion model that quantitatively describes the statistical features of the chemotactic motion of the social amoeba Dictyostelium discoideum in a linear gradient of cAMP (cyclic adenosine monophosphate). We fit the model to experimental trajectories that are recorded in a microfluidic setup with stationary cAMP gradients and extract the diffusion and drift coefficients in the gradient direction. Our analysis shows that for the majority of gradients, both coefficients decrease over time and become negative as the cells crawl up the gradient. The extracted model parameters also show that besides the expected drift in the direction of the chemoattractant gradient, we observe a nonlinear dependency of the corresponding variance on time, which can be explained by the model. Furthermore, the results of the model show that the non-linear term in the mean squared displacement of the cell trajectories can dominate the linear term on large time scales.

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.

Chemotaxis and autochemotaxis of self-propelling droplet swimmers

Chemotaxis and autochemotaxis play an important role in many essential biological processes. We present a self-propelling artificial swimmer system that exhibits chemotaxis as well as negative autochemotaxis. Oil droplets in an aqueous surfactant solution are driven by interfacial Marangoni flows induced by micellar solubilization of the oil phase. We demonstrate that chemotaxis along micellar surfactant gradients can guide these swimmers through a microfluidic maze. Similarly, a depletion of empty micelles in the wake of a droplet swimmer causes negative autochemotaxis and thereby trail avoidance. We studied autochemotaxis quantitatively in a microfluidic device of bifurcating channels: Branch choices of consecutive swimmers are anticorrelated, an effect decaying over time due to trail dispersion. We modeled this process by a simple one-dimensional diffusion process and stochastic Langevin dynamics. Our results are consistent with a linear surfactant gradient force and diffusion constants appropriate for micellar diffusion and provide a measure of autochemotactic feedback strength vs. stochastic forces. This assay is readily adaptable for quantitative studies of both artificial and biological autochemotactic systems.

Dendritic Cells Interpret Haptotactic Chemokine Gradients in a Manner Governed by Signal-to-Noise Ratio and Dependent on GRK6

Navigation of cells along gradients of guidance cues is a determining step in many developmental and immunological processes. Gradients can either be soluble or immobilized to tissues as demonstrated for the haptotactic migration of dendritic cells (DCs) toward higher concentrations of immobilized chemokine CCL21. To elucidate how gradient characteristics govern cellular response patterns, we here introduce an in vitro system allowing to track migratory responses of DCs to precisely controlled immobilized gradients of CCL21. We find that haptotactic sensing depends on the absolute CCL21 concentration and local steepness of the gradient, consistent with a scenario where DC directionality is governed by the signal-to-noise ratio of CCL21 binding to the receptor CCR7. We find that the conditions for optimal DC guidance are perfectly provided by the CCL21 gradients we measure in vivo. Furthermore, we find that CCR7 signal termination by the G-protein-coupled receptor kinase 6 (GRK6) is crucial for haptotactic but dispensable for chemotactic CCL21 gradient sensing in vitro and confirm those observations in vivo. These findings suggest that stable, tissue-bound CCL21 gradients as sustainable "roads" ensure optimal guidance in vivo.

Multi-State Transition Kinetics of Intracellular Signaling Molecules by Single-Molecule Imaging Analysis

The chemotactic signaling of eukaryotic cells is based on a chain of interactions between signaling molecules diffusing on the cell membrane and those shuttling between the membrane and cytoplasm. In this chapter, we describe methods to quantify lateral diffusion and reaction kinetics on the cell membrane. By the direct visualization and statistic analyses of molecular Brownian movement achieved by single-molecule imaging techniques, multiple states of membrane-bound molecules are successfully revealed with state transition kinetics. Using PTEN, a phosphatidylinositol-3,4,5-trisphosphate (PI(3,4,5)P3) 3'-phosphatase, in Dictyostelium discoideum undergoing chemotaxis as a model, each process of the analysis is described in detail. The identified multiple state kinetics provides an essential clue to elucidating the molecular mechanism of chemoattractant-induced dynamic redistribution of the signaling molecule asymmetrically on the cell membrane. Quantitative parameters for molecular reactions and diffusion complement a conventional view of the chemotactic signaling system, where changing a static network of molecules connected by causal relationships into a spatiotemporally dynamic one permits a mathematical description of stochastic migration of the cell along a shallow chemoattractant gradient.

A dynamic model of chemoattractant-induced cell migration

Cell migration refers to a directional cell movement in response to chemoattractant stimulation. In this work, we developed a cell-migration model by mimicking in vivo migration using optically manipulated chemoattractant-loaded microsources. The model facilitates a quantitative characterization of the relationship among the protrusion force, cell motility, and chemoattractant gradient for the first time (to our knowledge). We verified the correctness of the model using migrating leukemia cancer Jurkat cells. The results show that one can achieve the ideal migrating capacity by choosing the appropriate chemoattractant gradient and concentration at the leading edge of the cell.

Distinct cell shapes determine accurate chemotaxis

The behaviour of an organism often reflects a strategy for coping with its environment. Such behaviour in higher organisms can often be reduced to a few stereotyped modes of movement due to physiological limitations, but finding such modes in amoeboid cells is more difficult as they lack these constraints. Here, we examine cell shape and movement in starved Dictyostelium amoebae during migration toward a chemoattractant in a microfluidic chamber. We show that the incredible variety in amoeboid shape across a population can be reduced to a few modes of variation. Interestingly, cells use distinct modes depending on the applied chemical gradient, with specific cell shapes associated with shallow, difficult-to-sense gradients. Modelling and drug treatment reveals that these behaviours are intrinsically linked with accurate sensing at the physical limit. Since similar behaviours are observed in a diverse range of cell types, we propose that cell shape and behaviour are conserved traits.

Active Brownian agents with concentration-dependent chemotactic sensitivity

We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.

High fidelity information processing in folic acid chemotaxis of Dictyostelium amoebae

Living cells depend upon the detection of chemical signals for their existence. Eukaryotic cells can sense a concentration difference as low as a few per cent across their bodies. This process was previously suggested to be limited by the receptor-ligand binding fluctuations. Here, we first determine the chemotaxis response of Dictyostelium cells to static folic acid gradients and show that they can significantly exceed this sensitivity, responding to gradients as shallow as 0.2% across the cell body. Second, using a previously developed information theory framework, we compare the total information gained about the gradient (based on the cell response) to its upper limit: the information gained at the receptor-ligand binding step. We find that the model originally applied to cAMP sensing fails as demonstrated by the violation of the data processing inequality, i.e. the total information exceeds the information at the receptor-ligand binding step. We propose an extended model with multiple known receptor types and with cells allowed to perform several independent measurements of receptor occupancy. This does not violate the data processing inequality and implies the receptor-ligand binding noise dominates both for low- and high-chemoattractant concentrations. We also speculate that the interplay between exploration and exploitation is used as a strategy for accurate sensing of otherwise unmeasurable levels of a chemoattractant.

Recent developments in microfluidics-based chemotaxis studies

Microfluidic devices can better control cellular microenvironments compared to conventional cell migration assays. Over the past few years, microfluidics-based chemotaxis studies showed a rapid growth. New strategies were developed to explore cell migration in manipulated chemical gradients. In addition to expanding the use of microfluidic devices for a broader range of cell types, microfluidic devices were used to study cell migration and chemotaxis in complex environments. Furthermore, high-throughput microfluidic chemotaxis devices and integrated microfluidic chemotaxis systems were developed for medical and commercial applications. In this article, we review recent developments in microfluidics-based chemotaxis studies and discuss the new trends in this field observed over the past few years.

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.

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

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

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