Buckling instability in ordered bacterial colonies

Bacterial colonies often exhibit complex spatio-temporal organization. This collective behavior is affected by a multitude of factors ranging from the properties of individual cells (shape, motility, membrane structure) to chemotaxis and other means of cell-cell communication. One of the important but often overlooked mechanisms of spatio-temporal organization is direct mechanical contact among cells in dense colonies such as biofilms. While in natural habitats all these different mechanisms and factors act in concert, one can use laboratory cell cultures to study certain mechanisms in isolation. Recent work demonstrated that growth and ensuing expansion flow of rod-like bacteria Escherichia coli in confined environments leads to orientation of cells along the flow direction and thus to ordering of cells. However, the cell orientational ordering remained imperfect. In this paper we study one mechanism responsible for the persistence of disorder in growing cell populations. We demonstrate experimentally that a growing colony of nematically ordered cells is prone to the buckling instability. Our theoretical analysis and discrete-element simulations suggest that the nature of this instability is related to the anisotropy of the stress tensor in the ordered cell colony.     

Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences

Differential movement of individual cells within tissues is an important yet poorly understood process in biological development. Here we present a computational study of cell sorting caused by a combination of cell adhesion and chemotaxis, where we assume that all cells respond equally to the chemotactic signal. To capture in our model mesoscopic properties of biological cells, such as their size and deformability, we use the Cellular Potts Model, a multiscale, cell-based Monte Carlo model. We demonstrate a rich array of cell-sorting phenomena, which depend on a combination of mescoscopic cell properties and tissue level constraints. Under the conditions studied, cell sorting is a fast process, which scales linearly with tissue size. We demonstrate the occurrence of “absolute negative mobility”, which means that cells may move in the direction opposite to the applied force (here chemotaxis). Moreover, during the sorting, cells may even reverse the direction of motion. Another interesting phenomenon is “minority sorting”, where the direction of movement does not depend on cell type, but on the frequency of the cell type in the tissue. A special case is the cAMP-wave-driven chemotaxis of Dictyostelium cells, which generates pressure waves that guide the sorting. The mechanisms we describe can easily be overlooked in studies of differential cell movement, hence certain experimental observations may be misinterpreted.     

Who's really in charge: Diverse follower cell behaviors in collective cell migration

Collective cell migrations drive morphogenesis, wound healing, and cancer dissemination. Cells located at the front are considered leaders while those behind them are defined topologically as followers. Leader cell behaviors, including chemotaxis and their coupling to followers, have been well-studied and reviewed. However, the contributions of follower cells to collective cell migration represent an emerging area of interest. In this perspective, we highlight recent research into the broadening array of follower cell behaviors found in moving collectives. We describe examples of follower cells that possess cryptic leadership potential and followers that lack that potential but contribute in diverse and sometimes surprising ways to collective movement, even steering from behind. We highlight collectives in which all cells both lead and follow, and a few passive passengers. The molecular mechanisms controlling follower cell function and behavior are just emerging and represent an exciting frontier in collective cell migration research.     

Cell traction in collective cell migration and morphogenesis: The chase and run mechanism

Directional collective cell migration plays an important role in development, physiology, and disease. An increasing number of studies revealed key aspects of how cells coordinate their movement through distances surpassing several cell diameters. While physical modeling and measurements of forces during collective cell movements helped to reveal key mechanisms, most of these studies focus on tightly connected epithelial cultures. Less is known about collective migration of mesenchymal cells. A typical example of such behavior is the migration of the neural crest cells, which migrate large distances as a group. A recent study revealed that this persistent migration is aided by the interaction between the neural crest and the neighboring placode cells, whereby neural crest chase the placodes via chemotaxis, but upon contact both populations undergo contact inhibition of locomotion and a rapid reorganization of cellular traction. The resulting asymmetric traction field of the placodes forces them to run away from the chasers. We argue that this chase and run interaction may not be specific only to the neural crest system, but could serve as the underlying mechanism for several morphogenetic processes involving collective cell migration.     

Role of boundary conditions in an experimental model of epithelial wound healing

Coordinated cell movements in epithelial layers are essential for proper tissue morphogenesis and homeostasis, but our understanding of the mechanisms that coordinate the behavior of multiple cells in these processes is far from complete. Recent experiments with Madin-Darby canine kidney epithelial monolayers revealed a wave-like pattern of injury-induced MAPK activation and showed that it is essential for collective cell migration after wounding. To investigate the effects of the different aspects of wounding on cell sheet migration, we engineered a system that allowed us to dissect the classic wound healing assay. We studied Madin-Darby canine kidney sheet migration under three different conditions: 1) the classic wound healing assay, 2) empty space induction, where a confluent monolayer is grown adjacent to a slab of polydimethylsiloxane and the monolayer is not injured but allowed to migrate upon removal of the slab, and 3) injury via polydimethylsiloxane membrane peel-off, where an injured monolayer migrates onto plain tissue culture surface, as in the case of empty space induction allowing for direct comparison. By tracking the motion of individual cells within the sheet under these three conditions, we show how the dynamics of the individual cells' motion is responsible for the coordinated migration of the sheet and is coordinated with the activation of ERK1/2 MAPK. In addition, we demonstrate that the propagation of the waves of MAPK activation depends on the generation of reactive oxygen species at the wound edge.     

Anchor cell invasion into the vulval epithelium in C. elegans

An understanding of cell-invasive behavior has been limited by the lack of in vivo models where this activity can be clearly visualized and manipulated. We show that a single cell in the Caenorhabditis elegans gonad, the anchor cell (AC), initiates uterine-vulval contact through a cell invasion event. Using genetic analysis, laser ablations, and cell-specific markers, we demonstrate that AC invasion is predominantly stimulated by the 1 degrees vulval lineage cells, which generate a diffusible signal that promotes AC invasive behavior toward these cells and further targets invasive processes between the two central 1 degrees vulval lineage cells. We also show that AC invasion is regulated by the AC response to this cue, as well as a vulval-independent mechanism that weakly drives invasion. These studies dissect the regulatory mechanisms that underlie a simple cell-invasive behavior in vivo, and introduce AC invasion as a model for understanding key checkpoints controlling cell invasion.     

Self-organization of collective escape in pigeon flocks

Bird flocks under predation demonstrate complex patterns of collective escape. These patterns may emerge by self-organization from local interactions among group-members. Computational models have been shown to be valuable for identifying what behavioral rules may govern such interactions among individuals during collective motion. However, our knowledge of such rules for collective escape is limited by the lack of quantitative data on bird flocks under predation in the field. In the present study, we analyze the first GPS trajectories of pigeons in airborne flocks attacked by a robotic falcon in order to build a species-specific model of collective escape. We use our model to examine a recently identified distance-dependent pattern of collective behavior: the closer the prey is to the predator, the higher the frequency with which flock members turn away from it. We first extract from the empirical data of pigeon flocks the characteristics of their shape and internal structure (bearing angle and distance to nearest neighbors). Combining these with information on their coordination from the literature, we build an agent-based model adjusted to pigeons’ collective escape. We show that the pattern of turning away from the predator with increased frequency when the predator is closer arises without prey prioritizing escape when the predator is near. Instead, it emerges through self-organization from a behavioral rule to avoid the predator independently of their distance to it. During this self-organization process, we show how flock members increase their consensus over which direction to escape and turn collectively as the predator gets closer. Our results suggest that coordination among flock members, combined with simple escape rules, reduces the cognitive costs of tracking the predator while flocking. Such escape rules that are independent of the distance to the predator can now be investigated in other species. Our study showcases the important role of computational models in the interpretation of empirical findings of collective behavior.     

Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred.     

Collective Signal Processing in Cluster Chemotaxis: Roles of Adaptation,Amplification, and Co-attraction in Collective Guidance

Single eukaryotic cells commonly sense and follow chemical gradients, performing chemotaxis. Recent experiments and theories, however, show that even when single cells do not chemotax, clusters of cells may, if their interactions are regulated by the chemoattractant. We study this general mechanism of “collective guidance” computationally with models that integrate stochastic dynamics for individual cells with biochemical reactions within the cells, and diffusion of chemical signals between the cells. We show that if clusters of cells use the well-known local excitation, global inhibition (LEGI) mechanism to sense chemoattractant gradients, the speed of the cell cluster becomes non-monotonic in the cluster’s size—clusters either larger or smaller than an optimal size will have lower speed. We argue that the cell cluster speed is a crucial readout of how the cluster processes chemotactic signals; both amplification and adaptation will alter the behavior of cluster speed as a function of size. We also show that, contrary to the assumptions of earlier theories, collective guidance does not require persistent cell-cell contacts and strong short range adhesion. If cell-cell adhesion is absent, and the cluster cohesion is instead provided by a co-attraction mechanism, e.g. chemotaxis toward a secreted molecule, collective guidance may still function. However, new behaviors, such as cluster rotation, may also appear in this case. Co-attraction and adaptation allow for collective guidance that is robust to varying chemoattractant concentrations while not requiring strong cell-cell adhesion.     

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.     

The dopamine circuit as a reward-taxis navigation system

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs ‘reward-taxis’ where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.     

Directed assembly of a bacterial quorum

Many reports have elucidated the mechanisms and consequences of bacterial quorum sensing (QS), a molecular communication system by which bacterial cells enumerate their cell density and organize collective behavior. In few cases, however, the numbers of bacteria exhibiting this collective behavior have been reported, either as a number concentration or a fraction of the whole. Not all cells in the population, for example, take on the collective phenotype. Thus, the specific attribution of the postulated benefit can remain obscure. This is partly due to our inability to independently assemble a defined quorum, for natural and most artificial systems the quorum itself is a consequence of the biological context (niche and signaling mechanisms). Here, we describe the intentional assembly of quantized quorums. These are made possible by independently engineering the autoinducer signal transduction cascade of Escherichia coli (E. coli) and the sensitivity of detector cells so that upon encountering a particular autoinducer level, a discretized sub-population of cells emerges with the desired phenotype. In our case, the emergent cells all express an equivalent amount of marker protein, DsRed, as an indicator of a specific QS-mediated activity. The process is robust, as detector cells are engineered to target both large and small quorums. The process takes about 6 h, irrespective of quorum level. We demonstrate sensitive detection of autoinducer-2 (AI-2) as an application stemming from quantized quorums. We then demonstrate sub-population partitioning in that AI-2-secreting cells can ‘call'' groups neighboring cells that ‘travel'' and establish a QS-mediated phenotype upon reaching the new locale.     

Do Pioneer Cells Exist?

Most mathematical models of collective cell spreading make the standard assumption that the cell diffusivity and cell proliferation rate are constants that do not vary across the cell population. Here we present a combined experimental and mathematical modeling study which aims to investigate how differences in the cell diffusivity and cell proliferation rate amongst a population of cells can impact the collective behavior of the population. We present data from a three-dimensional transwell migration assay that suggests that the cell diffusivity of some groups of cells within the population can be as much as three times higher than the cell diffusivity of other groups of cells within the population. Using this information, we explore the consequences of explicitly representing this variability in a mathematical model of a scratch assay where we treat the total population of cells as two, possibly distinct, subpopulations. Our results show that when we make the standard assumption that all cells within the population behave identically we observe the formation of moving fronts of cells where both subpopulations are well-mixed and indistinguishable. In contrast, when we consider the same system where the two subpopulations are distinct, we observe a very different outcome where the spreading population becomes spatially organized with the more motile subpopulation dominating at the leading edge while the less motile subpopulation is practically absent from the leading edge. These modeling predictions are consistent with previous experimental observations and suggest that standard mathematical approaches, where we treat the cell diffusivity and cell proliferation rate as constants, might not be appropriate.     

Collective motion of cells mediates segregation and pattern formation in co-cultures

Pattern formation by segregation of cell types is an important process during embryonic development. We show that an experimentally yet unexplored mechanism based on collective motility of segregating cells enhances the effects of known pattern formation mechanisms such as differential adhesion, mechanochemical interactions or cell migration directed by morphogens. To study in vitro cell segregation we use time-lapse videomicroscopy and quantitative analysis of the main features of the motion of individual cells or groups. Our observations have been extensive, typically involving the investigation of the development of patterns containing up to 200,000 cells. By either comparing keratocyte types with different collective motility characteristics or increasing cells' directional persistence by the inhibition of Rac1 GTP-ase we demonstrate that enhanced collective cell motility results in faster cell segregation leading to the formation of more extensive patterns. The growth of the characteristic scale of patterns generally follows an algebraic scaling law with exponent values up to 0.74 in the presence of collective motion, compared to significantly smaller exponents in case of diffusive motion.     

Collective motion enhances chemotaxis in a two-dimensional bacterial swarm

In a dilute liquid environment in which cell-cell interaction is negligible, flagellated bacteria, such as Escherichia coli, perform chemotaxis by biased random walks alternating between run-and-tumble. In a two-dimensional crowded environment, such as a bacterial swarm, the typical behavior of run-and-tumble is absent, and this raises the question whether and how bacteria can perform chemotaxis in a swarm. Here, by examining the chemotactic behavior as a function of the cell density, we showed that chemotaxis is surprisingly enhanced because of cell crowding in a bacterial swarm, and this enhancement is correlated with increase in the degree of cell body alignment. Cells tend to form clusters that move collectively in a swarm with increased effective run length, and we showed analytically that this resulted in increased drift velocity toward attractants. We also explained the enhancement by stochastically simulating bacterial chemotaxis in a swarm. We found that cell crowding in a swarm enhances chemotaxis if the cell-cell interactions used in the simulation induce cell-cell alignment, but it impedes chemotaxis if the interactions are collisions that randomize cell moving direction. Therefore, collective motion in a bacterial swarm enhances chemotaxis.     

Comparison of Deterministic and Stochastic Models of the lac Operon Genetic Network

The lac operon has been a paradigm for genetic regulation with positive feedback, and several modeling studies have described its dynamics at various levels of detail. However, it has not yet been analyzed how stochasticity can enrich the system's behavior, creating effects that are not observed in the deterministic case. To address this problem we use a comparative approach. We develop a reaction network for the dynamics of the lac operon genetic switch and derive corresponding deterministic and stochastic models that incorporate biological details. We then analyze the effects of key biomolecular mechanisms, such as promoter strength and binding affinities, on the behavior of the models. No assumptions or approximations are made when building the models other than those utilized in the reaction network. Thus, we are able to carry out a meaningful comparison between the predictions of the two models to demonstrate genuine effects of stochasticity. Such a comparison reveals that in the presence of stochasticity, certain biomolecular mechanisms can profoundly influence the region where the system exhibits bistability, a key characteristic of the lac operon dynamics. For these cases, the temporal asymptotic behavior of the deterministic model remains unchanged, indicating a role of stochasticity in modulating the behavior of the system.     

Collective dynamics of cancer cells confined in a confluent monolayer of normal cells

Tumorigenesis often involves specific changes in cell motility and intercellular adhesion. Understanding the collective cancer cell behavior associated with these specific changes could facilitate the detection of malignant characteristics during tumor growth and invasion. In this study, a cellular vertex model is developed to investigate the collective dynamics of a disk-like aggregate of cancer cells confined in a confluent monolayer of normal cells. The effects of intercellular adhesion and cell motility on tumor progression are examined. It is found that the stresses in both the cancer cells and the normal cells increase with tumor growth, resulting in a crowded environment and enhanced cell apoptosis. The intercellular adhesion between cancer cells and normal cells is revealed to promote tumor growth and invasion. The tumor invasion dynamics hinges on the motility of cancer cells. The cancer cells could orchestrate into different collective migration modes, e.g., directional migration and rotational oscillations, dictated by the competition between cell persistence and local coordination. Phase diagrams are established to reveal the competitive mechanisms. This work highlights the role of mechanics in regulating tumor growth and invasion.     

The neutrophil's eye-view: inference and visualisation of the chemoattractant field driving cell chemotaxis in vivo

As we begin to understand the signals that drive chemotaxis in vivo, it is becoming clear that there is a complex interplay of chemotactic factors, which changes over time as the inflammatory response evolves. New animal models such as transgenic lines of zebrafish, which are near transparent and where the neutrophils express a green fluorescent protein, have the potential to greatly increase our understanding of the chemotactic process under conditions of wounding and infection from video microscopy data. Measurement of the chemoattractants over space (and their evolution over time) is a key objective for understanding the signals driving neutrophil chemotaxis. However, it is not possible to measure and visualise the most important contributors to in vivo chemotaxis, and in fact the understanding of the main contributors at any particular time is incomplete. The key insight that we make in this investigation is that the neutrophils themselves are sensing the underlying field that is driving their action and we can use the observations of neutrophil movement to infer the hidden net chemoattractant field by use of a novel computational framework. We apply the methodology to multiple in vivo neutrophil recruitment data sets to demonstrate this new technique and find that the method provides consistent estimates of the chemoattractant field across the majority of experiments. The framework that we derive represents an important new methodology for cell biologists investigating the signalling processes driving cell chemotaxis, which we label the neutrophils eye-view of the chemoattractant field.