Dictyostelium discoideum chemotaxis: threshold for directed motion

Decoding complex transport patterns in flow-induced autologous chemotaxis of multicellular systems

Cell migration via autologous chemotaxis in the presence of interstitial fluid flow is important in cancer metastasis and embryonic development. Despite significant recent progress, our understanding of flow-induced autologous chemotaxis of multicellular systems remains poor. The literature presents inconsistent findings regarding the effectiveness of collective autologous chemotaxis of densely packed cells under interstitial fluid flow. Here, we present a high-fidelity computational model to analyze the migration of multicellular systems performing autologous chemotaxis in the presence of interstitial fluid flow. Our simulations show that the details of the complex transport dynamics of the chemoattractant and fluid flow patterns that occur in the extracellular space, previously overlooked, are essential to understand this cell migration mechanism. We find that, although flow-induced autologous chemotaxis is a robust migration mechanism for individual cells, the cell-cell interactions that occur in multicellular systems render autologous chemotaxis an inefficient mechanism of collective cell migration. Our results offer new perspectives on the potential role of autologous chemotaxis in the tumor microenvironment, where fluid flow is an important modulator of transport.

Gradient sensing limit of an elongated cell with orientational control

Eukaryotic cells perform chemotaxis by determining the direction of chemical gradients based on stochastic sensing of concentrations at the cell surface. To examine the efficiency of this process, previous studies have investigated the limit of estimation accuracy for gradients. However, most studies have treated a circular cell shape, and the few considering elongated shapes assume the elongated direction as fixed. This leaves the question of how adaptive regulation of cell shape affects the estimation limit. Dynamics of cell shape during gradient sensing is biologically ubiquitous and can influence the estimation by altering the way the concentration is measured, and cells may strategically regulate their shape to improve estimation accuracy. To address this gap, we investigate the estimation limits in dynamic situations where elongated cells change their orientation adaptively depending on the sensed signal. We approach this problem by analyzing the stationary solution of the Bayesian nonlinear filtering equation. By applying diffusion approximation to the ligand-receptor binding process and the Laplace method for the posterior expectation under a high signal-to-noise ratio regime, we obtain an analytical expression for the estimation limit. This expression indicates that estimation accuracy can be improved by aligning the elongated direction perpendicular to the estimated direction, which is also confirmed by numerical simulations. Our analysis provides a basis for clarifying the interplay between estimation and control in gradient sensing and sheds light on how cells optimize their shape to enhance chemotactic efficiency.

Dynamic cluster field modeling of collective chemotaxis

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

Eukaryotic Chemotaxis under Periodic Stimulation Shows Temporal Gradient Dependence

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

Leveraging Tunable Nanoparticle Surface Functionalization to Alter Cellular Migration

Gold nanoparticles (AuNPs) are a promising platform for biomedical applications including therapeutics, imaging, and drug delivery. While much of the literature surrounding the introduction of AuNPs into cellular systems focuses on uptake and cytotoxicity, less is understood about how AuNPs can indirectly affect cells via interactions with the extracellular environment. Previous work has shown that the monocytic cell line THP-1's ability to undergo chemotaxis in response to a gradient of monocyte chemoattractant protein 1 (MCP-1) was compromised by extracellular polysulfonated AuNPs, presumably by binding to MCP-1 with some preference over other proteins in the media. The hypothesis to be explored in this work is that the degree of sulfonation of the surface would therefore be correlated with the ability of AuNPs to interrupt chemotaxis. Highly sulfonated poly(styrenesulfonate)-coated AuNPs caused strong inhibition of THP-1 chemotaxis; by reducing the degree of sulfonation on the AuNP surface with copolymers [poly(styrenesulfonate-co-maleate) of different compositions], it was found that medium and low sulfonation levels caused weak to no inhibition, respectively. Small, rigid molecular sulfonate surfaces were relatively ineffective at chemotaxis inhibition. Unusually, free poly(styrenesulfonate) caused a dose-dependent reversal of THP-1 cell migration: at low concentrations, free poly(styrenesulfonate) significantly inhibited MCP-1-induced chemotaxis. However, at high concentrations, free poly(styrenesulfonate) acted as a chemorepellent, causing a reversal in the cell migration direction.

Methods and computational tools to study eukaryotic cell migration in vitro

Cellular movement is essential for many vital biological functions where it plays a pivotal role both at the single cell level, such as during division or differentiation, and at the macroscopic level within tissues, where coordinated migration is crucial for proper morphogenesis. It also has an impact on various pathological processes, one for all, cancer spreading. Cell migration is a complex phenomenon and diverse experimental methods have been developed aimed at dissecting and analysing its distinct facets independently. In parallel, corresponding analytical procedures and tools have been devised to gain deep insight and interpret experimental results. Here we review established experimental techniques designed to investigate specific aspects of cell migration and present a broad collection of historical as well as cutting-edge computational tools used in quantitative analysis of cell motion.

Exotic swarming dynamics of high-dimensional swarmalators

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized D-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.

Physical limits on galvanotaxis

Eukaryotic cells can polarize and migrate in response to electric fields via "galvanotaxis," which aids wound healing. Experimental evidence suggests cells sense electric fields via molecules on the cell's surface redistributing via electrophoresis and electroosmosis, though the sensing species has not yet been conclusively identified. We develop a model that links sensor redistribution and galvanotaxis using maximum likelihood estimation. Our model predicts a single universal curve for how galvanotactic directionality depends on field strength. We can collapse measurements of galvanotaxis in keratocytes, neural crest cells, and granulocytes to this curve, suggesting that stochasticity due to the finite number of sensors may limit galvanotactic accuracy. We find cells can achieve experimentally observed directionalities with either a few (∼100) highly polarized sensors or many (∼10^{4}) sensors with an ∼6-10% change in concentration across the cell. We also identify additional signatures of galvanotaxis via sensor redistribution, including the presence of a tradeoff between accuracy and variance in cells being controlled by rapidly switching fields. Our approach shows how the physics of noise at the molecular scale can limit cell-scale galvanotaxis, providing important constraints on sensor properties and allowing for new tests to determine the specific molecules underlying galvanotaxis.

Alignment interaction and band formation in assemblies of autochemorepulsive walkers

Chemotaxis refers to the motion of an organism induced by chemical stimuli and is a motility mode shared by many living species that has been developed by evolution to optimize certain biological processes such as foraging or immune response. In particular, autochemotaxis refers to chemotaxis mediated by a cue produced by the chemotactic particle itself. Here, we investigate the collective behavior of autochemotactic particles that are repelled by the cue and therefore migrate preferentially towards low-concentration regions. To this end, we introduce a lattice model inspired by the true self-avoiding walk which reduces to the Keller-Segel model in the continuous limit, for which we describe the rich phase behavior. We first rationalize the chemically mediated alignment interaction between walkers in the limit of stationary concentration fields, and then describe the various large-scale structures that can spontaneously form and the conditions for them to emerge, among which we find stable bands traveling at constant speed in the direction transverse to the band.

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

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

Universal energy-accuracy tradeoffs in nonequilibrium cellular sensing

We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two-state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg-Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)0006-349510.1016/S0006-3495(77)85544-6] on cellular sensing along multiple dimensions.

Short-time diffusive fluxes over membrane receptors yields the direction of a signalling source

An essential ability of many cell types is to detect stimuli in the form of shallow chemical gradients. Such cues may indicate the direction that new growth should occur, or the location of a mate. Amplification of these faint signals is due to intra-cellular mechanisms, while the cue itself is generated by the noisy arrival of signalling molecules to surface bound membrane receptors. We employ a new hybrid numerical-asymptotic technique coupling matched asymptotic analysis and numerical inverse Laplace transform to rapidly and accurately solve the parabolic exterior problem describing the dynamic diffusive fluxes to receptors. We observe that equilibration occurs on long timescales, potentially limiting the usefulness of steady-state quantities for localization at practical biological timescales. We demonstrate that directional information is encoded primarily in early arrivals to the receptors, while equilibrium quantities inform on source distance. We develop a new homogenization result showing that complex receptor configurations can be replaced by a uniform effective condition. In the extreme scenario where the cell adopts the angular direction of the first impact, we show this estimate to be surprisingly accurate.

MACC1-induced migration in tumors: Current state and perspective

Malignant tumors are still a global, heavy health burden. Many tumor types cannot be treated curatively, underlining the need for new treatment targets. In recent years, metastasis associated in colon cancer 1 (MACC1) was identified as a promising biomarker and drug target, as it is promoting tumor migration, initiation, proliferation, and others in a multitude of solid cancers. Here, we will summarize the current knowledge about MACC1-induced tumor cell migration with a special focus on the cytoskeletal and adhesive systems. In addition, a brief overview of several in vitro models used for the analysis of cell migration is given. In this context, we will point to issues with the currently most prevalent models used to study MACC1-dependent migration. Lastly, open questions about MACC1-dependent effects on tumor cell migration will be addressed.

Controlling periodic long-range signalling to drive a morphogenetic transition

Cells use signal relay to transmit information across tissue scales. However, the production of information carried by signal relay remains poorly characterised. To determine how the coding features of signal relay are generated, we used the classic system for long-range signalling: the periodic cAMP waves that drive Dictyostelium collective migration. Combining imaging and optogenetic perturbation of cell signalling states, we find that migration is triggered by an increase in wave frequency generated at the signalling centre. Wave frequency is regulated by cAMP wave circulation, which organises the long-range signal. To determine the mechanisms modulating wave circulation, we combined mathematical modelling, the general theory of excitable media, and mechanical perturbations to test competing models. Models in which cell density and spatial patterning modulate the wave frequency cannot explain the temporal evolution of signalling waves. Instead, our evidence leads to a model where wave circulation increases the ability for cells to relay the signal, causing further increase in the circulation rate. This positive feedback between cell state and signalling pattern regulates the long-range signal coding that drives morphogenesis.

Diverse behaviors in non-uniform chiral and non-chiral swarmalators

We study the emergent behaviors of a population of swarming coupled oscillators, dubbed swarmalators. Previous work considered the simplest, idealized case: identical swarmalators with global coupling. Here we expand this work by adding more realistic features: local coupling, non-identical natural frequencies, and chirality. This more realistic model generates a variety of new behaviors including lattices of vortices, beating clusters, and interacting phase waves. Similar behaviors are found across natural and artificial micro-scale collective systems, including social slime mold, spermatozoa vortex arrays, and Quincke rollers. Our results indicate a wide range of future use cases, both to aid characterization and understanding of natural swarms, and to design complex interactions in collective systems from soft and active matter to micro-robotics.

Multi-scale organization in communicating active matter

The emergence of collective motion among interacting, self-propelled agents is a central paradigm in non-equilibrium physics. Examples of such active matter range from swimming bacteria and cytoskeletal motility assays to synthetic self-propelled colloids and swarming microrobots. Remarkably, the aggregation capabilities of many of these systems rely on a theme as fundamental as it is ubiquitous in nature: communication. Despite its eminent importance, the role of communication in the collective organization of active systems is not yet fully understood. Here we report on the multi-scale self-organization of interacting self-propelled agents that locally process information transmitted by chemical signals. We show that this communication capacity dramatically expands their ability to form complex structures, allowing them to self-organize through a series of collective dynamical states at multiple hierarchical levels. Our findings provide insights into the role of self-sustained signal processing for self-organization in biological systems and open routes to applications using chemically driven colloids or microrobots.

Understanding the Cell's Response to Chemical Signals: Utilisation of Microfluidic Technology in Studies of Cellular and Dictyostelium discoideum Chemotaxis

Cellular chemotaxis has been the subject of a variety of studies due to its relevance in physiological processes, disease pathogenesis, and systems biology, among others. The migration of cells towards a chemical source remains a closely studied topic, with the Boyden chamber being one of the earlier techniques that has successfully studied cell chemotaxis. Despite its success, diffusion chambers such as these presented a number of problems, such as the quantification of many aspects of cell behaviour, the reproducibility of procedures, and measurement accuracy. The advent of microfluidic technology prompted more advanced studies of cell chemotaxis, usually involving the social amoeba Dictyostelium discoideum (D. discoideum) as a model organism because of its tendency to aggregate towards chemotactic agents and its similarities to higher eukaryotes. Microfluidic technology has made it possible for studies to look at chemotactic properties that would have been difficult to observe using classic diffusion chambers. Its flexibility and its ability to generate consistent concentration gradients remain some of its defining aspects, which will surely lead to an even better understanding of cell migratory behaviour and therefore many of its related biological processes. This paper first dives into a brief introduction of D. discoideum as a social organism and classical chemotaxis studies. It then moves to discuss early microfluidic devices, before diving into more recent and advanced microfluidic devices and their use with D. discoideum. The paper then closes with brief opinions about research progress in the field and where it will possibly lead in the future.

Collective gradient sensing with limited positional information

Eukaryotic cells sense chemical gradients to decide where and when to move. Clusters of cells can sense gradients more accurately than individual cells by integrating measurements of the concentration made across the cluster. Is this gradient-sensing accuracy impeded when cells have limited knowledge of their position within the cluster, i.e., limited positional information? We apply maximum likelihood estimation to study gradient-sensing accuracy of a cluster of cells with finite positional information. If cells must estimate their location within the cluster, this lowers the accuracy of collective gradient sensing. We compare our results with a tug-of-war model where cells respond to the gradient by polarizing away from their neighbors without relying on their positional information. As the cell positional uncertainty increases, there is a trade-off where the tug-of-war model responds more accurately to the chemical gradient. However, for sufficiently large cell clusters or sufficiently shallow chemical gradients, the tug-of-war model will always be suboptimal to one that integrates information from all cells, even if positional uncertainty is high.

Limitations on concentration measurements and gradient discerning times in cellular systems

This work reports on two results. At first we revisit the Berg and Purcell calculation that provides a lower bound to the error in concentration measurement by cells by considering the realistic case when the cell starts measuring the moment it comes in contact with the chemoattractants, instead of measuring after equilibrating with the chemotactic concentration as done in the classic Berg and Purcell paper. We find that the error in concentration measurement is still the same as evaluated by Berg and Purcell. We next derive a lower bound on measurement time below which it is not possible for the cell to discern extracellular chemotactic gradients through spatial sensing mechanisms. This bound is independent of diffusion rate and concentration of the chemoattracts and is instead set by detachment rate of ligands from the cell receptors. The result could help explain experimental observations.

Cellular inertia

It has been experimentally reported that chemotactic cells exhibit cellular memory, that is, a tendency to maintain the migration direction despite changes in the chemoattractant gradient. In this study, we analyzed a phenomenological model assuming the presence of cellular inertia, as well as a response time in motility, resulting in the reproduction of the cellular memory observed in the previous experiments. According to the analysis, the cellular motion is described by the superposition of multiple oscillative functions induced by the multiplication of the oscillative polarity and motility. The cellular intertia generates cellular memory by regulating phase differences between those oscillative functions. By applying the theory to the experimental data, the cellular inertia was estimated at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m=3-6$$\end{document}m=3-6 min. In addition, physiological parameters, such as response time in motility and intracellular processing speed, were also evaluated. The agreement between the experiemental data and theory suggests the possibility of the presence of the response time in motility, which has never been biologically verified and should be explored in the future.

Using Live-Cell Imaging and Synthetic Biology to Probe Directed Migration in Dictyostelium

For decades, the social amoeba Dictyostelium discoideum has been an invaluable tool for dissecting the biology of eukaryotic cells. Its short growth cycle and genetic tractability make it ideal for a variety of biochemical, cell biological, and biophysical assays. Dictyostelium have been widely used as a model of eukaryotic cell motility because the signaling and mechanical networks which they use to steer and produce forward motion are highly conserved. Because these migration networks consist of hundreds of interconnected proteins, perturbing individual molecules can have subtle effects or alter cell morphology and signaling in major unpredictable ways. Therefore, to fully understand this network, we must be able to quantitatively assess the consequences of abrupt modifications. This ability will allow us better control cell migration, which is critical for development and disease, in vivo. Here, we review recent advances in imaging, synthetic biology, and computational analysis which enable researchers to tune the activity of individual molecules in single living cells and precisely measure the effects on cellular motility and signaling. We also provide practical advice and resources to assist in applying these approaches in Dictyostelium.

Different Heterotrimeric G Protein Dynamics for Wide-Range Chemotaxis in Eukaryotic Cells

Chemotaxis describes directional motility along ambient chemical gradients and has important roles in human physiology and pathology. Typical chemotactic cells, such as neutrophils and Dictyostelium cells, can detect spatial differences in chemical gradients over a background concentration of a 10⁵ scale. Studies of Dictyostelium cells have elucidated the molecular mechanisms of gradient sensing involving G protein coupled receptor (GPCR) signaling. GPCR transduces spatial information through its cognate heterotrimeric G protein as a guanine nucleotide change factor (GEF). More recently, studies have revealed unconventional regulation of heterotrimeric G protein in the gradient sensing. In this review, we explain how multiple mechanisms of GPCR signaling ensure the broad range sensing of chemical gradients in Dictyostelium cells as a model for eukaryotic chemotaxis.

Cell dispersal by localized degradation of a chemoattractant

Chemotaxis, the guided motion of cells by chemical gradients, plays a crucial role in many biological processes. In the social amoeba Dictyostelium discoideum, chemotaxis is critical for the formation of cell aggregates during starvation. The cells in these aggregates generate a pulse of the chemoattractant, cyclic adenosine 3',5'-monophosphate (cAMP), every 6 min to 10 min, resulting in surrounding cells moving toward the aggregate. In addition to periodic pulses of cAMP, the cells also secrete phosphodiesterase (PDE), which degrades cAMP and prevents the accumulation of the chemoattractant. Here we show that small aggregates of Dictyostelium can disperse, with cells moving away from instead of toward the aggregate. This surprising behavior often exhibited oscillatory cycles of motion toward and away from the aggregate. Furthermore, the onset of outward cell motion was associated with a doubling of the cAMP signaling period. Computational modeling suggests that this dispersal arises from a competition between secreted cAMP and PDE, creating a cAMP gradient that is directed away from the aggregate, resulting in outward cell motion. The model was able to predict the effect of PDE inhibition as well as global addition of exogenous PDE, and these predictions were subsequently verified in experiments. These results suggest that localized degradation of a chemoattractant is a mechanism for morphogenesis.

Pleiotropy enables specific and accurate signaling in the presence of ligand cross talk

Living cells sense their environment through the binding of extracellular molecular ligands to cell surface receptors. Puzzlingly, vast numbers of signaling pathways exhibit a high degree of cross talk between different signals whereby different ligands act through the same receptor or shared components downstream. It remains unclear how a cell can accurately process information from the environment in such cross-wired pathways. We show that a feature which commonly accompanies cross talk-signaling pleiotropy (the ability of a receptor to produce multiple outputs)-offers a solution to the cross-talk problem. In a minimal model we show that a single pleiotropic receptor can simultaneously identify and accurately sense the concentrations of arbitrary unknown ligands present individually or in a mixture. We calculate the fundamental limits of the signaling specificity and accuracy of such signaling schemes. The model serves as an elementary "building block" toward understanding more complex cross-wired receptor-ligand signaling networks.

Acceleration of lipid reproduction by emergence of microscopic motion

Self-reproducing molecules abound in nature where they support growth and motion of living systems. In artificial settings, chemical reactions can also show complex kinetics of reproduction, however integrating self-reproducing molecules into larger chemical systems remains a challenge towards achieving higher order functionality. Here, we show that self-reproducing lipids can initiate, sustain and accelerate the movement of octanol droplets in water. Reciprocally, the chemotactic movement of the octanol droplets increases the rate of lipid reproduction substantially. Reciprocal coupling between bond-forming chemistry and droplet motility is thus established as an effect of the interplay between molecular-scale events (the self-reproduction of lipid molecules) and microscopic events (the chemotactic movement of the droplets). This coupling between molecular chemistry and microscopic motility offers alternative means of performing work and catalysis in micro-heterogeneous environments.

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.

Analysis of barotactic and chemotactic guidance cues on directional decision-making of Dictyostelium discoideum cells in confined environments

Neutrophils and dendritic cells when migrating in confined environments have been shown to actuate a directional choice toward paths of least hydraulic resistance (barotaxis), in some cases overriding chemotactic responses. Here, we investigate whether this barotactic response is conserved in the more primitive model organism Dictyostelium discoideum using a microfluidic chip design. This design allowed us to monitor the behavior of single cells via live imaging when confronted with bifurcating microchannels, presenting different combinations of hydraulic and chemical stimuli. Under the conditions employed we find no evidence in support of a barotactic response; the cells base their directional choices on the chemotactic cues. When the cells are confronted by a microchannel bifurcation, they often split their leading edge and start moving into both channels, before a decision is made to move into one and retract from the other channel. Analysis of this decision-making process has shown that cells in steeper nonhydrolyzable adenosine- 3', 5'- cyclic monophosphorothioate, Sp- isomer (cAMPS) gradients move faster and split more readily. Furthermore, there exists a highly significant strong correlation between the velocity of the pseudopod moving up the cAMPS gradient to the total velocity of the pseudopods moving up and down the gradient over a large range of velocities. This suggests a role for a critical cortical tension gradient in the directional decision-making process.

Receptor Organization Determines the Limits of Single-Cell Source Location Detection

Many types of cells require the ability to pinpoint the location of an external stimulus from the arrival of diffusing signaling molecules at cell-surface receptors. How does the organization (number and spatial configuration) of these receptors shape the limit of a cell's ability to infer the source location? In the idealized scenario of a spherical cell, we apply asymptotic analysis to compute splitting probabilities between individual receptors and formulate an information-theoretic framework to quantify the role of receptor organization. Clustered configurations of receptors provide an advantage in detecting sources aligned with the clusters, suggesting a possible multiscale mechanism for single-cell source inference.

Autoselective transport of mammalian cells with a chemotactic droplet

Liquid chemical droplets, as models of artificial life, when pushed away from equilibrium possess some life-like behaviors such as fission, fusion, movement and chemotaxis. Chemotaxis, directed motion in response to external gradients, is typically an important process in living systems, but certain artificial systems are also capable of this activity. Previously it was shown that droplet-based chemotactic systems when interfaced with biological systems can act as transporters to move cargo such as hydrogel alginate capsules containing living cells. Here the effectiveness of our system to transport different mammalian cell lines (H460, H1299, A549, HEK293T and HS68) was tested. It was discovered that some lung cancer cell lines release surfactants only when placed in the hydrogel capsules. These surfactants establish the interface between the encapsulated cells and the droplet and also support the chemotaxis of the droplet. Because of this, the droplet-mediated transport system is selective for living cells that produce biosurfactants. This is an example of how the integration of artificial life and biological life could be designed where the systems augment each other and function together as a unit. In this case the living system produces the surfactants that the droplet needs for cargo transport and the artificial system provides the transport for the otherwise sessile mammalian cells. Future applications of droplet-based cell handling that is able to distinguish between cells based not only on viability but cell type, developmental stage or other quantifiable traits are considered.

Eco-evolutionary significance of "loners"

Loners—individuals out of sync with a coordinated majority—occur frequently in nature. Are loners incidental byproducts of large-scale coordination attempts, or are they part of a mosaic of life-history strategies? Here, we provide empirical evidence of naturally occurring heritable variation in loner behavior in the model social amoeba Dictyostelium discoideum. We propose that Dictyostelium loners—cells that do not join the multicellular life stage—arise from a dynamic population-partitioning process, the result of each cell making a stochastic, signal-based decision. We find evidence that this imperfectly synchronized multicellular development is affected by both abiotic (environmental porosity) and biotic (signaling) factors. Finally, we predict theoretically that when a pair of strains differing in their partitioning behavior coaggregate, cross-signaling impacts slime-mold diversity across spatiotemporal scales. Our findings suggest that loners could be critical to understanding collective and social behaviors, multicellular development, and ecological dynamics in D. discoideum. More broadly, across taxa, imperfect coordination of collective behaviors might be adaptive by enabling diversification of life-history strategies.

Loners (individuals out of sync with a coordinated majority) occur frequently in nature and are generally assumed to be incidental by-products of imperfect coordination attempts. Experimental and theoretical work on the slime mold Dictyostelium discoideum suggests that "lonerism" might actually be an alternative life-history strategy.

Harnessing Motile Amoeboid Cells as Trucks for Microtransport and -Assembly

Cell-driven microtransport is one of the most prominent applications in the emerging field of biohybrid systems. While bacterial cells have been successfully employed to drive the swimming motion of micrometer-sized cargo particles, the transport capacities of motile adherent cells remain largely unexplored. Here, it is demonstrated that motile amoeboid cells can act as efficient and versatile trucks to transport microcargo. When incubated together with microparticles, cells of the social amoeba Dictyostelium discoideum readily pick up and move the cargo particles. Relying on the unspecific adhesive properties of the amoeba, a wide range of different cargo materials can be used. The cell-driven transport can be directionally guided based on the chemotactic responses of amoeba to chemoattractant gradients. On the one hand, the cargo can be assembled into clusters in a self-organized fashion, relying on the developmentally induced chemotactic aggregation of cells. On the other hand, chemoattractant gradients can be externally imposed to guide the cellular microtrucks to a desired location. Finally, larger cargo particles of different shapes that exceed the size of a single cell by more than an order of magnitude, can also be transported by the collective effort of large numbers of motile cells.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells

Amoeboid movement is one of the most widespread forms of cell motility that plays a key role in numerous biological contexts. While many aspects of this process are well investigated, the large cell-to-cell variability in the motile characteristics of an otherwise uniform population remains an open question that was largely ignored by previous models. In this article, we present a mathematical model of amoeboid motility that combines noisy bistable kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we introduce a single parameter for tuning the balance between polarity formation and intracellular noise. We compare numerical simulations of our model to experiments with the social amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found close agreement with the experimental results for the center-of-mass motion as well as for the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that the building blocks of our model capture essential features of amoeboid motility and may serve as a starting point for more detailed descriptions of cell motion in chemical gradients and confined environments.

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.

Collective gradient sensing and chemotaxis: modeling and recent developments

Cells measure a vast variety of signals, from their environment's stiffness to chemical concentrations and gradients; physical principles strongly limit how accurately they can do this. However, when many cells work together, they can cooperate to exceed the accuracy of any single cell. In this topical review, I will discuss the experimental evidence showing that cells collectively sense gradients of many signal types, and the models and physical principles involved. I also propose new routes by which experiments and theory can expand our understanding of these problems.

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.

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.

Protease activated-receptor 2 is necessary for neutrophil chemorepulsion induced by trypsin, tryptase, or dipeptidyl peptidase IV

Compared to neutrophil chemoattractants, relatively little is known about the mechanism neutrophils use to respond to chemorepellents. We previously found that the soluble extracellular protein dipeptidyl peptidase IV (DPPIV) is a neutrophil chemorepellent. In this report, we show that an inhibitor of the protease activated receptor 2 (PAR2) blocks DPPIV-induced human neutrophil chemorepulsion, and that PAR2 agonists such as trypsin, tryptase, 2f-LIGRL, SLIGKV, and AC55541 induce human neutrophil chemorepulsion. Several PAR2 agonists in turn block the ability of the chemoattractant fMLP to attract neutrophils. Compared to neutrophils from male and female C57BL/6 mice, neutrophils from male and female mice lacking PAR2 are insensitive to the chemorepulsive effects of DPPIV or PAR2 agonists. Acute respiratory distress syndrome (ARDS) involves an insult-mediated influx of neutrophils into the lungs. In a mouse model of ARDS, aspiration of PAR2 agonists starting 24 h after an insult reduce neutrophil numbers in the bronchoalveolar lavage (BAL) fluid, as well as the post-BAL lung tissue. Together, these results indicate that the PAR2 receptor mediates DPPIV-induced chemorepulsion, and that PAR2 agonists might be useful to induce neutrophil chemorepulsion.

Modelling the collective response of heterogeneous cell populations to stationary gradients and chemical signal relay

The directed motion of cell aggregates toward a chemical source occurs in many relevant biological processes. Understanding the mechanisms that control this complex behavior is of great relevance for our understanding of developmental biological processes and many diseases. In this paper, we consider a self-propelled particle model for the movement of heterogeneous subpopulations of chemically interacting cells towards an imposed stable chemical gradient. Our simulations show explicitly how self-organisation of cell populations (which could lead to engulfment or complete cell segregation) can arise from the heterogeneity of chemotactic responses alone. This new result complements current theoretical and experimental studies that emphasise the role of differential cell-cell adhesion on self-organisation and spatial structure of cellular aggregates. We also investigate how the speed of individual cell aggregations increases with the chemotactic sensitivity of the cells, and decreases with the number of cells inside the aggregates.

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.

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.

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.

Collective Chemotaxis through Noisy Multicellular Gradient Sensing

Collective cell migration in response to a chemical cue occurs in many biological processes such as morphogenesis and cancer metastasis. Clusters of migratory cells in these systems are capable of responding to gradients of <1% difference in chemical concentration across a cell length. Multicellular systems are extremely sensitive to their environment, and although the limits to multicellular sensing are becoming known, how this information leads to coherent migration remains poorly understood. We develop a computational model of multicellular sensing and migration in which groups of cells collectively measure noisy chemical gradients. The output of the sensing process is coupled to the polarization of individual cells to model migratory behavior. Through the use of numerical simulations, we find that larger clusters of cells detect the gradient direction with higher precision and thus achieve stronger polarization bias, but larger clusters also induce more drag on collective motion. The trade-off between these two effects leads to an optimal cluster size for most efficient migration. We discuss how our model could be validated using simple, phenomenological experiments.

A Haptotaxis Assay for Neutrophils using Optical Patterning and a High-content Approach

Neutrophil recruitment guided by chemotactic cues is a central event in host defense against infection and tissue injury. While the mechanisms underlying neutrophil chemotaxis have been extensively studied, these are just recently being addressed by using high-content approaches or surface-bound chemotactic gradients (haptotaxis) in vitro. Here, we report a haptotaxis assay, based on the classic under-agarose assay, which combines an optical patterning technique to generate surface-bound formyl peptide gradients as well as an automated imaging and analysis of a large number of migration trajectories. We show that human neutrophils migrate on covalently-bound formyl-peptide gradients, which influence the speed and frequency of neutrophil penetration under the agarose. Analysis revealed that neutrophils migrating on surface-bound patterns accumulate in the region of the highest peptide concentration, thereby mimicking in vivo events. We propose the use of a chemotactic precision index, gyration tensors and neutrophil penetration rate for characterizing haptotaxis. This high-content assay provides a simple approach that can be applied for studying molecular mechanisms underlying haptotaxis on user-defined gradient shape.

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.