Approaching the molecular origins of collective dynamics in oscillating cell populations

Formation of recurring transient Ca2+-based intercellular communities during Drosophila hematopoiesis

Tissue development occurs through a complex interplay between many individual cells. Yet, the fundamental question of how collective tissue behavior emerges from heterogeneous and noisy information processing and transfer at the single-cell level remains unknown. Here, we reveal that tissue scale signaling regulation can arise from local gap-junction mediated cell-cell signaling through the spatiotemporal establishment of an intermediate-scale of transient multicellular communication communities over the course of tissue development. We demonstrated this intermediate scale of emergent signaling using Ca2+ signaling in the intact, ex vivo cultured, live developing Drosophila hematopoietic organ, the lymph gland. Recurrent activation of these transient signaling communities defined self-organized signaling "hotspots" that gradually formed over the course of larva development. These hotspots receive and transmit information to facilitate repetitive interactions with nonhotspot neighbors. Overall, this work bridges the scales between single-cell and emergent group behavior providing key mechanistic insight into how cells establish tissue-scale communication networks.

Cooperation in bioluminescence: understanding the role of autoinducers by a stochastic random resistor model

Quorum sensing is a communication mechanism adopted by different bacterial strains for the regulation of gene transcription. It takes place through the exchange of molecules called autoinducers. Bioluminescence is an emergent threshold phenomenon shown by some bacteria strains. Its precise relationship to quorum sensing is a debated topic, particularly regarding the role of the different autoinducers used by bacteria. In this paper, assuming a direct relationship between bioluminescence and quorum sensing, we investigate the role of multiple autoinducers in the bioluminescence response of Vibrio harveyi, considered as a model bioluminescent strain, due to its quorum sensing circuitry involving an array of three different autoinducers. Experiments on mutants of this bacterium, obtained by suppression of one or more autoinducers, reveal their relative non-trivial relevance and cooperative interaction patterns. The proposed analysis is implemented on a regular lattice, whose nodes represent microbial entities equipped with charges, which represent the ability to up/down regulate the gene expression. Quorum sensing results from a Coulomb-type field, produced by the charges. In analogy with random resistor network models, the lattice is permeated by an effective current which accounts for the amount and distribution of the charges. We propose that the presence of different autoinducers correspond to a different up/down regulation of gene expression, i.e., to a different way to account for the charges. Then, by introducing a modulation of the charge dependence into the current flowing within the network, we show that it is able to describe the bioluminescence exhibited by V. harveyi mutants. Furthermore, modulation of the charge dependence allows the interactions between the different autoinducers to be taken into account, providing a prediction regarding the data obtainable under specific growth conditions.

Microbial models of development: Inspiration for engineering self-assembled synthetic multicellularity

While the field of synthetic developmental biology has traditionally focused on the study of the rich developmental processes seen in metazoan systems, an attractive alternate source of inspiration comes from microbial developmental models. Microbes face unique lifestyle challenges when forming emergent multicellular collectives. As a result, the solutions they employ can inspire the design of novel multicellular systems. In this review, we dissect the strategies employed in multicellular development by two model microbial systems: the cellular slime mold Dictyostelium discoideum and the biofilm-forming bacterium Bacillus subtilis. Both microbes face similar challenges but often have different solutions, both from metazoan systems and from each other, to create emergent multicellularity. These challenges include assembling and sustaining a critical mass of participating individuals to support development, regulating entry into development, and assigning cell fates. The mechanisms these microbial systems exploit to robustly coordinate development under a wide range of conditions offer inspiration for a new toolbox of solutions to the synthetic development community. Additionally, recreating these phenomena synthetically offers a pathway to understanding the key principles underlying how these behaviors are coordinated naturally.

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.

From non-excitable single-cell to multicellular bioelectrical states supported by ion channels and gap junction proteins: Electrical potentials as distributed controllers

Endogenous bioelectric patterns within tissues are an important driver of morphogenesis and a tractable component of a number of disease states. Developing system-level understanding of the dynamics by which non-neural bioelectric circuits regulate complex downstream cascades is a key step towards both, an evolutionary understanding of ion channel genes, and novel strategies in regenerative medicine. An important capability gap is deriving rational modulation strategies targeting individual cells' bioelectric states to achieve global (tissue- or organ-level) outcomes. Here, we develop an ion channel-based model that describes multicellular states on the basis of spatio-temporal patterns of electrical potentials in aggregates of non-excitable cells. The model is of biological interest because modern techniques allow to associate bioelectrical signals with specific ion channel proteins in the cell membrane that are central to embryogenesis, regeneration, and tumorigenesis. As a complementary approach to the usual biochemical description, we have studied four biophysical questions: (i) how can single-cell bioelectrical states be established; (ii) how can a change in the cell potential caused by a transient perturbation of the cell state be maintained after the stimulus is gone (bioelectrical memory); (iii) how can a single-cell contribute to the control of multicellular ensembles based on the spatio-temporal pattern of electrical potentials; and (iv) how can oscillatory patterns arise from the single-cell bioelectrical dynamics. Experimentally, endogenous bioelectric gradients have emerged as instructive agents for morphogenetic processes. In this context, the simulations can guide new procedures that may allow a distributed control of the multicellular ensemble.

Synchronization of Bioelectric Oscillations in Networks of Nonexcitable Cells: From Single-Cell to Multicellular States

Biological networks use collective oscillations for information processing tasks. In particular, oscillatory membrane potentials have been observed in nonexcitable cells and bacterial communities where specific ion channel proteins contribute to the bioelectric coordination of large populations. We aim at describing theoretically the oscillatory spatiotemporal patterns that emerge at the multicellular level from the single-cell bioelectric dynamics. To this end, we focus on two key questions: (i) What single-cell properties are relevant to multicellular behavior? (ii) What properties defined at the multicellular level can allow an external control of the bioelectric dynamics? In particular, we explore the interplay between transcriptional and translational dynamics and membrane potential dynamics in a model multicellular ensemble, describe the spatiotemporal patterns that arise when the average electric potential allows groups of cells to act as a coordinated multicellular patch, and characterize the resulting synchronization phenomena. The simulations concern bioelectric networks and collective communication across different scales based on oscillatory and synchronization phenomena, thus shedding light on the physiological dynamics of a wide range of endogenous contexts across embryogenesis and regeneration.

Modeling of Nanomachine/Micromachine Crowds: Interplay between the Internal State and Surroundings

The activity of biological cells is primarily based on chemical reactions and typically modeled as a reaction-diffusion system. Cells are, however, highly crowded with macromolecules, including a variety of molecular machines such as enzymes. The working cycles of these machines are often coupled with their internal motion (conformational changes). In the crowded environment of a cell, motion interference between neighboring molecules is not negligible, and this interference can affect the reaction dynamics through machine operation. To simulate such a situation, we propose a reaction-diffusion model consisting of particles whose shape depends on an internal state variable, for crowds of nano- to micromachines. The interference between nearby particles is naturally introduced through excluded volume repulsion. In the simulations, we observed segregation and flow-like patterns enhanced by crowding out of relevant molecules, as well as molecular synchronization waves and phase transitions. The presented model is simple and extensible for diverse molecular machinery and may serve as a framework to study the interplay between the mechanical stress/strain network and the chemical reaction network in the cell. Applications to more macroscopic systems, e.g., crowds of cells, are also discussed.

Excitable Dynamics and Yap-Dependent Mechanical Cues Drive the Segmentation Clock

The periodic segmentation of the vertebrate body axis into somites, and later vertebrae, relies on a genetic oscillator (the segmentation clock) driving the rhythmic activity of signaling pathways in the presomitic mesoderm (PSM). To understand whether oscillations are an intrinsic property of individual cells or represent a population-level phenomenon, we established culture conditions for stable oscillations at the cellular level. This system was used to demonstrate that oscillations are a collective property of PSM cells that can be actively triggered in vitro by a dynamical quorum sensing signal involving Yap and Notch signaling. Manipulation of Yap-dependent mechanical cues is sufficient to predictably switch isolated PSM cells from a quiescent to an oscillatory state in vitro, a behavior reminiscent of excitability in other systems. Together, our work argues that the segmentation clock behaves as an excitable system, introducing a broader paradigm to study such dynamics in vertebrate morphogenesis.

Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

Understanding how biochemical networks lead to large-scale nonequilibrium self-organization and pattern formation in life is a major challenge, with important implications for the design of programmable synthetic systems. Here, we assembled cell-free genetic oscillators in a spatially distributed system of on-chip DNA compartments as artificial cells, and measured reaction-diffusion dynamics at the single-cell level up to the multicell scale. Using a cell-free gene network we programmed molecular interactions that control the frequency of oscillations, population variability, and dynamical stability. We observed frequency entrainment, synchronized oscillatory reactions and pattern formation in space, as manifestation of collective behavior. The transition to synchrony occurs as the local coupling between compartments strengthens. Spatiotemporal oscillations are induced either by a concentration gradient of a diffusible signal, or by spontaneous symmetry breaking close to a transition from oscillatory to nonoscillatory dynamics. This work offers design principles for programmable biochemical reactions with potential applications to autonomous sensing, distributed computing, and biomedical diagnostics.

Communication shapes sensory response in multicellular networks

Collective sensing by interacting cells is observed in a variety of biological systems, and yet, a quantitative understanding of how sensory information is collectively encoded is lacking. Here, we investigate the ATP-induced calcium dynamics of monolayers of fibroblast cells that communicate via gap junctions. Combining experiments and stochastic modeling, we find that increasing the ATP stimulus increases the propensity for calcium oscillations, despite large cell-to-cell variability. The model further predicts that the oscillation propensity increases with not only the stimulus, but also the cell density due to increased communication. Experiments confirm this prediction, showing that cell density modulates the collective sensory response. We further implicate cell-cell communication by coculturing the fibroblasts with cancer cells, which we show act as "defects" in the communication network, thereby reducing the oscillation propensity. These results suggest that multicellular networks sit at a point in parameter space where cell-cell communication has a significant effect on the sensory response, allowing cells to simultaneously respond to a sensory input and the presence of neighbors.

Molecular-Level Tuning of Cellular Autonomy Controls the Collective Behaviors of Cell Populations

A rigorous understanding of how multicellular behaviors arise from the actions of single cells requires quantitative frameworks that bridge the gap between genetic circuits, the arrangement of cells in space, and population-level behaviors. Here, we provide such a framework for a ubiquitous class of multicellular systems-namely, "secrete-and-sense cells" that communicate by secreting and sensing a signaling molecule. By using formal, mathematical arguments and introducing the concept of a phenotype diagram, we show how these cells tune their degrees of autonomous and collective behavior to realize distinct single-cell and population-level phenotypes; these phenomena have biological analogs, such as quorum sensing or paracrine signaling. We also define the "entropy of population," a measurement of the number of arrangements that a population of cells can assume, and demonstrate how a decrease in the entropy of population accompanies the formation of ordered spatial patterns. Our conceptual framework ties together diverse systems, including tissues and microbes, with common principles.

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

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

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

Modeling oscillations and spiral waves in Dictyostelium populations

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

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

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

Secreting and sensing the same molecule allows cells to achieve versatile social behaviors

Cells that secrete and sense the same signaling molecule are ubiquitous. To uncover the functional capabilities of the core "secrete-and-sense" circuit motif shared by these cells, we engineered yeast to secrete and sense the mating pheromone. Perturbing each circuit element revealed parameters that control the degree to which the cell communicated with itself versus with its neighbors. This tunable interplay of self-communication and neighbor communication enables cells to span a diverse repertoire of cellular behaviors. These include a cell being asocial by responding only to itself and social through quorum sensing, and an isogenic population of cells splitting into social and asocial subpopulations. A mathematical model explained these behaviors. The versatility of the secrete-and-sense circuit motif may explain its recurrence across species.

Chemotaxis of Dictyostelium discoideum: collective oscillation of cellular contacts

Chemotactic responses of Dictyostelium discoideum cells to periodic self-generated signals of extracellular cAMP comprise a large number of intricate morphological changes on different length scales. Here, we scrutinized chemotaxis of single Dictyostelium discoideum cells under conditions of starvation using a variety of optical, electrical and acoustic methods. Amebas were seeded on gold electrodes displaying impedance oscillations that were simultaneously analyzed by optical video microscopy to relate synchronous changes in cell density, morphology, and distance from the surface to the transient impedance signal. We found that starved amebas periodically reduce their overall distance from the surface producing a larger impedance and higher total fluorescence intensity in total internal reflection fluorescence microscopy. Therefore, we propose that the dominant sources of the observed impedance oscillations observed on electric cell-substrate impedance sensing electrodes are periodic changes of the overall cell-substrate distance of a cell. These synchronous changes of the cell-electrode distance were also observed in the oscillating signal of acoustic resonators covered with amebas. We also found that periodic cell-cell aggregation into transient clusters correlates with changes in the cell-substrate distance and might also contribute to the impedance signal. It turned out that cell-cell contacts as well as cell-substrate contacts form synchronously during chemotaxis of Dictyostelium discoideum cells.

Kuramoto model with coupling through an external medium

Synchronization of coupled oscillators is often described using the Kuramoto model. Here, we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model exhibits interesting new phenomena such as bistability between synchronization and incoherence and a qualitatively new form of synchronization where the external medium exhibits small-amplitude oscillations. We conclude by discussing the relationship of the model to other variations of the Kuramoto model including the Kuramoto model with a bimodal frequency distribution and the Millennium bridge problem.

Dynamical quorum-sensing in oscillators coupled through an external medium

Many biological and physical systems exhibit population-density dependent transitions to synchronized oscillations in a process often termed "dynamical quorum sensing". Synchronization frequently arises through chemical communication via signaling molecules distributed through an external medium. We study a simple theoretical model for dynamical quorum sensing: a heterogenous population of limit-cycle oscillators diffusively coupled through a common medium. We show that this model exhibits a rich phase diagram with four qualitatively distinct physical mechanisms that can lead to a loss of coherent population-level oscillations, including a novel mechanism arising from effective time-delays introduced by the external medium. We derive a single pair of analytic equations that allow us to calculate phase boundaries as a function of population density and show that the model reproduces many of the qualitative features of recent experiments on BZ catalytic particles as well as synthetically engineered bacteria.

Information processing and integration with intracellular dynamics near critical point

Recent experimental observations suggest that cells can show relatively precise and reliable responses to external signals even though substantial noise is inevitably involved in the signals. An intriguing question is the way how cells can manage to do it. One possible way to realize such response for a cell is to evolutionary develop and optimize its intracellular signaling pathways so as to extract relevant information from the noisy signal. We recently demonstrated that certain intracellular signaling reactions could actually conduct statistically optimal information processing. In this paper, we clarify that such optimal reaction operates near bifurcation point. This result suggests that critical-like phenomena in the single-cell level may be linked to efficient information processing inside a cell. In addition, improving the performance of response in the single-cell level is not the only way for cells to realize reliable response. Another possible strategy is to integrate information of individual cells by cell-to-cell interaction such as quorum sensing. Since cell-to-cell interaction is a common phenomenon, it is equally important to investigate how cells can integrate their information by cell-to-cell interaction to realize efficient information processing in the population level. In this paper, we consider roles and benefits of cell-to-cell interaction by considering integrations of obtained information of individuals with the other cells from the viewpoint of information processing. We also demonstrate that, by introducing cell movement, spatial organizations can spontaneously emerge as a result of efficient responses of the population to external signals.

Understanding microbial cooperation

The field of microbial cooperation has grown enormously over the last decade, leading to improved experimental techniques and a growing awareness of collective behavior in microbes. Unfortunately, many of our theoretical tools and concepts for understanding cooperation fail to take into account the peculiarities of the microbial world, namely strong selection strengths, unique population structure, and non-linear dynamics. Worse yet, common verbal arguments are often far removed from the math involved, leading to confusion and mistakes. Here, we review the general mathematical forms of Price's equation, Hamilton's rule, and multilevel selection as they are applied to microbes and provide some intuition on these otherwise abstract formulas. However, these sometimes overly general equations can lack specificity and predictive power, ultimately forcing us to advocate for more direct modeling techniques.