Collective Chemotaxis through Noisy Multicellular Gradient Sensing

Decoding physical principles of cell migration under controlled environment using microfluidics

Living cells can perform incredible tasks that man-made micro/nano-sized robots have not yet been able to accomplish. One example is that white blood cells can sense and move to the site of pathogen attack within minutes. The robustness and precision of cellular functions have been perfected through billions of years of evolution. In this context, we ask the question whether cells follow a set of physical principles to sense, adapt, and migrate. Microfluidics has emerged as an enabling technology for recreating well-defined cellular environment for cell migration studies, and its ability to follow single cell dynamics allows for the results to be amenable for theoretical modeling. In this review, we focus on the development of microfluidic platforms for recreating cellular biophysical (e.g., mechanical stress) and biochemical (e.g., nutrients and cytokines) environments for cell migration studies in 3D. We summarize the basic principles that cells (including bacteria, algal, and mammalian cells) use to respond to chemical gradients learned from microfluidic systems. We also discuss about novel biological insights gained from studies of cell migration under biophysical cues and the need for further quantitative studies of cell function under well-controlled biophysical environments in the future.

Galvanotactic directionality of cell groups depends on group size

Motile cells migrate directionally in the electric field in a process known as galvanotaxis, important and under-investigated phenomenon in wound healing and development. We previously reported that individual fish keratocyte cells migrate to the cathode in electric fields, that inhibition of PI3 kinase reverses single cells to the anode, and that large cohesive groups of either unperturbed or PI3K-inhibited cells migrate to the cathode. Here we find that small uninhibited cell groups move to the cathode, while small groups of PI3K-inhibited cells move to the anode. Small groups move faster than large groups, and groups of unperturbed cells move faster than PI3K-inhibited cell groups of comparable sizes. Shapes and sizes of large groups change little when they start migrating, while size and shapes of small groups change significantly, lamellipodia disappear from the rear edges of these groups, and their shapes start to resemble giant single cells. Our results are consistent with the computational model, according to which cells inside and at the edge of the groups pool their propulsive forces to move but interpret directional signals differently. Namely, cells in the group interior are directed to the cathode independently of their chemical state. Meanwhile, the edge cells behave like individual cells: they are directed to the cathode/anode in uninhibited/PI3K-inhibited groups, respectively. As a result, all cells drive uninhibited groups to the cathode, while larger PI3K-inhibited groups are directed by cell majority in the group interior to the cathode, while majority of the edge cells in small groups win the tug-of-war driving these groups to the anode.

Collective effects in flow-driven cell migration

Autologous chemotaxis is the process in which cells secrete and detect molecules to determine the direction of fluid flow. Experiments and theory suggest that autologous chemotaxis fails at high cell densities because molecules from other cells interfere with a given cell's signal. We investigate autologous chemotaxis using a three-dimensional Monte Carlo-based motility simulation that couples spatial and temporal gradient sensing with cell-cell repulsion. Surprisingly, we find that when temporal gradient sensing dominates, high-density clusters chemotax faster than individual cells. To explain this observation, we propose a mechanism by which temporal gradient sensing allows cells to form a collective sensory unit. We demonstrate using computational fluid mechanics that that this mechanism indeed allows a cluster of cells to outperform single cells in terms of the detected anisotropy of the signal, a finding that we demonstrate with analytic scaling arguments. Our work suggests that collective autologous chemotaxis at high cell densities is possible and requires only known, ubiquitous cell capabilities.

Collective directional migration drives the formation of heteroclonal cancer cell clusters

Metastasisation occurs through the acquisition of invasive and survival capabilities that allow tumour cells to colonise distant sites. While the role of multicellular aggregates in cancer dissemination is acknowledged, the mechanisms that drive the formation of multiclonal cell aggregates are not fully elucidated. Here, we show that cancer cells of different tissue of origins can perform collective directional migration and can actively form heteroclonal aggregates in 3D, through a proliferation-independent mechanism. Coalescence of distant cell clusters is mediated by subcellular actin-rich protrusions and multicellular outgrowths that extend towards neighbouring aggregates. Coherently, perturbation of cytoskeletal dynamics impairs collective migration while myosin II activation is necessary for multicellular movements. We put forward the hypothesis that cluster attraction is mediated by secreted soluble factors. Such a hypothesis is consistent with the abrogation of aggregation by inhibition of PI3K/AKT/mTOR and MEK/ERK, the chemoattracting activity of conditioned culture media and with a wide screening of secreted proteins. Our results present a novel collective migration model and shed light on the mechanisms of formation of heteroclonal aggregates in cancer.

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

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

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.

Tumor spheroid invasion in epidermal growth factor gradients revealed by a 3D microfluidic device

Epidermal growth factor (EGF), a potent cytokine, is known to promote tumor invasion bothin vivoandin vitro. Previously, we observed that single breast tumor cells (MDA-MB-231 cell line) embedded within a 3D collagen matrix displayed enhanced motility but no discernible chemotaxis in the presence of linear EGF gradients using a microfluidic platform. Inspired by a recent theoretical development that clustered mammalian cells respond differently to chemical gradients than single cells, we studied tumor spheroid invasion within a 3D extracellular matrix (ECM) in the presence of EGF gradients. We found that EGF gradients promoted tumor cell detachment from the spheroid core, and the position of the tumor spheroid core showed a mild chemotactic response towards the EGF gradients. For those tumor cells detached from the spheroids, they showed an enhanced motility response in contrast to previous experimental results using single cells embedded within an ECM. No discernible chemotactic response towards the EGF gradients was found for the cells outside the spheroid core. This work demonstrates that a cluster of tumor cells responds differently than single tumor cells towards EGF gradients and highlights the importance of a tumor spheroid platform for tumor invasion studies.

The role of cell geometry and cell-cell communication in gradient sensing

Cells can measure shallow gradients of external signals to initiate and accomplish a migration or a morphogenetic process. Recently, starting from mathematical models like the local-excitation global-inhibition (LEGI) model and with the support of empirical evidence, it has been proposed that cellular communication improves the measurement of an external gradient. However, the mathematical models that have been used have over-simplified geometries (e.g., they are uni-dimensional) or assumptions about cellular communication, which limit the possibility to analyze the gradient sensing ability of more complex cellular systems. Here, we generalize the existing models to study the effects on gradient sensing of cell number, geometry and of long- versus short-range cellular communication in 2D systems representing epithelial tissues. We find that increasing the cell number can be detrimental for gradient sensing when the communication is weak and limited to nearest neighbour cells, while it is beneficial when there is long-range communication. We also find that, with long-range communication, the gradient sensing ability improves for tissues with more disordered geometries; on the other hand, an ordered structure with mostly hexagonal cells is advantageous with nearest neighbour communication. Our results considerably extend the current models of gradient sensing by epithelial tissues, making a step further toward predicting the mechanism of communication and its putative mediator in many biological processes.

Theoretical Constraints Imposed by Gradient Detection and Dispersal on Microbial Size in Astrobiological Environments

The capacity to sense gradients efficiently and acquire information about the ambient environment confers many advantages such as facilitating movement toward nutrient sources or away from toxic chemicals. The amplified dispersal evinced by organisms endowed with motility is possibly beneficial in related contexts. Hence, the connections between information acquisition, motility, and microbial size are explored from an explicitly astrobiological standpoint. By using prior theoretical models, the constraints on organism size imposed by gradient detection and motility are elucidated in the form of simple heuristic scaling relations. It is argued that environments such as alkaline hydrothermal vents, which are distinguished by the presence of steep gradients, might be conducive to the existence of "small" microbes (with radii of ≳0.1 μm) in principle, when only the above two factors are considered; other biological functions (e.g., metabolism and genetic exchange) could, however, regulate the lower bound on microbial size and elevate it. The derived expressions are potentially applicable to a diverse array of settings, including those entailing solvents other than water; for example, the lakes and seas of Titan. The article concludes with a brief exposition of how this formalism may be of practical and theoretical value to astrobiology.

Intermediate adhesion maximizes migration velocity of multicellular clusters

Collections of cells exhibit coherent migration during morphogenesis, cancer metastasis, and wound healing. In many cases, bigger clusters split, smaller subclusters collide and reassemble, and gaps continually emerge. The connections between cell-level adhesion and cluster-level dynamics, as well as the resulting consequences for cluster properties such as migration velocity, remain poorly understood. Here we investigate collective migration of one- and two-dimensional cell clusters that collectively track chemical gradients using a mechanism based on contact inhibition of locomotion. We develop both a minimal description based on the lattice gas model of statistical physics and a more realistic framework based on the cellular Potts model which captures cell shape changes and cluster rearrangement. In both cases, we find that cells have an optimal adhesion strength that maximizes cluster migration speed. The optimum negotiates a tradeoff between maintaining cell-cell contact and maintaining configurational freedom, and we identify maximal variability in the cluster aspect ratio as a revealing signature. Our results suggest a collective benefit for intermediate cell-cell adhesion.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

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.

Physical constraints on accuracy and persistence during breast cancer cell chemotaxis

Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of cell motion, but whether any of these quantities is physically constrained by the others is poorly understood. Using a combination of theory, simulations, and 3D chemotaxis assays on single metastatic breast cancer cells, we investigate the links among these different aspects of chemotactic performance. In particular, we observe in both experiments and simulations that the chemotactic accuracy, but not the persistence or speed, increases with the gradient strength. We use a random walk model to explain this result and to propose that cells’ chemotactic accuracy and persistence are mutually constrained. Our results suggest that key aspects of chemotactic performance are inherently limited regardless of how favorable the environmental conditions are.

One of the most ubiquitous and important cell behaviors is chemotaxis: the ability to move in the direction of a chemical gradient. Due to its importance, key aspects of chemotaxis have been quantified for a variety of cells, including the accuracy, persistence, and speed of cell motion. However, whether these aspects are mutually constrained is poorly understood. Can a cell be accurate but not persistent, or vice versa? Here we use theory, simulations, and experiments on cancer cells to uncover mutual constraints on the properties of chemotaxis. Our results suggest that accuracy and persistence are mutually constrained.

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.

The pivotal role of angiogenesis in a multi-scale modeling of tumor growth exhibiting the avascular and vascular phases

The mechanisms involved in tumor growth mainly occur at the microenvironment, where the interactions between the intracellular, intercellular and extracellular scales mediate the dynamics of tumor. In this work, we present a multi-scale model of solid tumor dynamics to simulate the avascular and vascular growth as well as tumor-induced angiogenesis. The extracellular and intercellular scales are modeled using partial differential equations and cellular Potts model, respectively. Also, few biochemical and biophysical rules control the dynamics of intracellular level. On the other hand, the growth of melanoma tumors is modeled in an animal in-vivo study to evaluate the simulation. The simulation shows that the model successfully reproduces a completed image of processes involved in tumor growth such as avascular and vascular growth as well as angiogenesis. The model incorporates the phenotypes of cancerous cells including proliferating, quiescent and necrotic cells, as well as endothelial cells during angiogenesis. The results clearly demonstrate the pivotal effect of angiogenesis on the progression of cancerous cells. Also, the model exhibits important events in tumor-induced angiogenesis like anastomosis. Moreover, the computational trend of tumor growth closely follows the observations in the experimental study.

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.

Emergent versus Individual-Based Multicellular Chemotaxis

Multicellular chemotaxis can occur via individually chemotaxing cells that are mechanically coupled. Alternatively, it can emerge collectively, from cells chemotaxing differently in a group than they would individually. Here we consider collective movement that emerges from cells on the exterior of the collective responding to chemotactic signals, whereas bulk cells remain uninvolved in sensing and directing the collective. We find that the precision of this type of emergent chemotaxis is higher than that of individual-based chemotaxis for one-dimensional cell chains and two-dimensional cell sheets, but not three-dimensional cell clusters. We describe the physical origins of these results, discuss their biological implications, and show how they can be tested using common experimental measures such as the chemotactic index.

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.