Chemotaxis-based spatial self-organization algorithms

Self-organization is a process that increases the order of a system as a result of local interactions among low-level, simple components, without the guidance of an outside source. Spatial self-organization is a process in which shapes and structures emerge at a global level from collective movements of low level shape primitives. Spatial self-organization is a stochastic process, and the outcome of the aggregation cannot necessarily be guaranteed. Despite the inherent ambiguity, self-organizing complex systems arise everywhere in nature. Motivated by the ability of living cells to form specific shapes and structures, we develop two self-organizing systems towards the ultimate goal of directing the spatial self-organizing process. We first develop a self-sorting system composed of a mixture of cells. The system consistently produces a sorted structure. We then extend the sorting system to a general shape formation system. To do so, we introduce morphogenetic primitives (MP), defined as software agents, which enable self-organizing shape formation of user-defined structures through a chemotaxis paradigm. One challenge that arises from the shape formation process is that the process may form two or more stable final configurations. In order to direct the self-organizing process, we find a way to characterize the macroscopic configuration of the MP swarm. We demonstrate that statistical moments of the primitives' locations can successfully capture the macroscopic structure of the aggregated shape. We do so by predicting the final configurations produced by our spatial self-organization system at an early stage in the process using features based on the statistical moments. At the next stage, we focus on developing a technique to control the outcome of bifurcating aggregations. We identify thresholds of the moments and generate biased initial conditions whose statistical moments meet the thresholds. By starting simulations with biased, random initial configurations, we successfully control the aggregation for a number of swarms produced by the agent-based shape formation system. This thesis demonstrates that chemotaxis can be used as a paradigm to create an agent- based spatial self-organization system. Furthermore, statistical moments of the swarm can be used to robustly predict and control the outcomes of the aggregation process.Ph.D., Computer Science -- Drexel University, 201

Mathematical models for cell migration: A non-local perspective

We provide a review of recent advancements in non-local continuous models for migration, mainly from the perspective of its involvement in embryonal development and cancer invasion. Particular emphasis is placed on spatial non-locality occurring in advection terms, used to characterize a cell's motility bias according to its interactions with other cellular and acellular components in its vicinity (e.g. cell-cell and cell-tissue adhesions, non-local chemotaxis), but we also briefly address spatially non-local source terms. Following a short introduction and description of applications, we give a systematic classification of available PDE models with respect to the type of featured non-localities and review some of the mathematical challenges arising from such models, with a focus on analytical aspects. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'

Individual and collective dynamics of chemotaxing cells

The study of the dynamics of interacting self-propelled entities is a growing area of physics research. This dissertation investigates individual and collective motion of the eukaryote Dictyostelium discoideum, a system amenable to signal manipulation, mathematical modeling, and quantitative analysis. In the wild, Dictyostelium survive adverse conditions through collective behaviors caused by secreting and responding to chemical signals. We explore this collective behavior on size scales ranging from subcellular biochemistry up to dynamics of thousands of communicating cells. To study how individual cells respond to multiple signals, we perform stability analysis on a previously-developed computational model of signal sensing. Polarized cells are linearly stable to perturbations, with a least stable region at about 60 degrees off the polarization axis. This finding is confirmed through simulations of the model response to additional chemical signals. The off-axis sensitivity suggests a mechanism for previously observed zig-zag motion of real cells randomly migrating or chemotaxing in a linear gradient. Moving up in scale, we experimentally investigate the rules of cell motion and interaction in the context of thousands of cells. Migrating Dictyostelium discoideum cells communicate by sensing and secreting directional signals, and we find that this process leads to an initial signal having an increased spatial range of an order of magnitude. While this process steers cells, measurements indicate that intrinsic cell motility remains unaffected. Additionally, migration of individual cells is unaffected by changing cell-surface adhesion energy by nine orders of magnitude, showing that individual motility is a robust process. In contrast, we find that collective dynamics depend on cell-surface adhesion, with greater adhesion causing cells to form smaller collective structures. Overall, this work suggests that the underlying migration ability of individual Dictyostelium cells operates largely independent of environmental conditions. Our gradient-sensing model shows that polarized cells are stable to small perturbations, and our experiments demonstrate that the motility apparatus is robust to considerable changes in cell-surface adhesion or complex signaling fields. However, we find that environmental factors can dramatically affect the collective behavior of cells, emphasizing that the laws governing cell-cell interaction can change migration patterns without altering intrinsic cell motility

Simulating Brain Tumor Heterogeneity with a Multiscale Agent-Based Model: Linking Molecular Signatures, Phenotypes and Expansion Rate

We have extended our previously developed 3D multi-scale agent-based brain tumor model to simulate cancer heterogeneity and to analyze its impact across the scales of interest. While our algorithm continues to employ an epidermal growth factor receptor (EGFR) gene-protein interaction network to determine the cells' phenotype, it now adds an explicit treatment of tumor cell adhesion related to the model's biochemical microenvironment. We simulate a simplified tumor progression pathway that leads to the emergence of five distinct glioma cell clones with different EGFR density and cell 'search precisions'. The in silico results show that microscopic tumor heterogeneity can impact the tumor system's multicellular growth patterns. Our findings further confirm that EGFR density results in the more aggressive clonal populations switching earlier from proliferation-dominated to a more migratory phenotype. Moreover, analyzing the dynamic molecular profile that triggers the phenotypic switch between proliferation and migration, our in silico oncogenomics data display spatial and temporal diversity in documenting the regional impact of tumorigenesis, and thus support the added value of multi-site and repeated assessments in vitro and in vivo. Potential implications from this in silico work for experimental and computational studies are discussed.Comment: 37 pages, 10 figure

Branching instability in expanding bacterial colonies

International audienceSelf-organization in developing living organisms relies on the capability of cells to duplicate and perform a collective motion inside the surrounding environment. Chemical and mechanical interactions coordinate such a cooperative behaviour, driving the dynamical evolution of the macroscopic system. In this work, we perform an analytical and computational analysis to study pattern formation during the spreading of an initially circular bacterial colony on a Petri dish. The continuous mathematical model addresses the growth and the chemotactic migration of the living monolayer, together with the diffusion and consumption of nutrients in the agar. The governing equations contain four dimensionless parameters, accounting for the interplay among the chemotactic response, the bacteria-substrate interaction and the experimental geometry. The spreading colony is found to be always linearly unstable to perturbations of the interface, whereas branching instability arises in finite-element numerical simulations. The typical length scales of such fingers, which align in the radial direction and later undergo further branching, are controlled by the size parameters of the problem, whereas the emergence of branching is favoured if the diffusion is dominant on the chemotaxis. The model is able to predict the experimental morphologies, confirming that compact (resp. branched) patterns arise for fast (resp. slow) expanding colonies. Such results, while providing new insights into pattern selection in bacterial colonies, may finally have important applications for designing controlled patterns

Doctor of Philosophy

dissertationChapter 1 introduces a classic question from optimal foraging theory regarding space-use strategies of a forager, and gives context for addressing similar questions in groups of foraging ants. Chapter 2 generalizes the marginal value theorem (MVT) model by describing a rate-maximizing forager searching for pointwise resources with a specific searching distribution around previous resource finds, and giving-up value (GUV) strategy at resources. The model shows that the optimal ARS breadth increases, and the optimal GUV decreases, with increased dispersion of the resource distribution. Chapter 3 builds an agent-based model (ABM) and corresponding PDE model derived from an isotropic diffusion limit. The model links individual movement biases in the presence of pheromone to the colony-wide searching distribution. Parameterized with movement data obtained from Tetramorium caespitum (the pavement ant), the model predicts bistability in pheromonal recruitment at resource distances of 3 - 6 m; the onset-distance of bistability increases with colony size. Data collected from the field are used to estimate parameters of the PDE model for T. caespitum in Chapter 4. The ability of T. caespitum to find autocorrelated resources during recruitment is analyzed using a Cox proportional hazards model, the results of which are compared to those predicted by the PDE model developed in Chapter 3. Finally, Chapter 5 develops a simulation to assess the effect of individual trail fidelity on the ability of a colony to capitalize on autocorrelated resources in different resource scenarios; the results suggest that T. caespitum is tuned to exploit large, nonautocorrelated resource distributions

Durotaxis: The Hard Path from In Vitro to In Vivo

Durotaxis, the process by which cells follow gradients of extracellular mechanical stiffness, has been proposed as a mechanism driving directed migration. Despite the lack of evidence for its existence in vivo, durotaxis has become an active field of research, focusing on the mechanism by which cells respond to mechanical stimuli from the environment. In this review, we describe the technical and conceptual advances in the study of durotaxis in vitro, discuss to what extent the evidence suggests durotaxis may occur in vivo, and emphasize the urgent need for in vivo demonstration of durotaxis

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way

Dynamics and Structure of Cellular Aggregation

This work provides new insights into the dynamics and structure of cellular aggregation. Starting from cell motility which is necessary to get the cells into close proximity it presents new tools for visualization, analysis and modeling of aggregation processes. While a lot of work has been done in the field of microbial and amoeboid motility, there is a lack in theoretical understanding of mammalian cell motion, especially concerning directed migration stirred by external cues. To close this gap I developed a two-dimensional generic model based on mechanical cell-substrate interactions. This model facilitates the discrete nature of the motion cycle of mammalian cells by a randomized growth of protrusions and their retraction depending on the strength of an external cue. This model is capable of reproducing most experimental observations, especially the behavior at sharp changes in strength of the external cues, and provides an explanation for the attachment of the lagging cell pole as it increases the efficiency of gradient sensing. Furthermore, I introduce new experimental methods to visualize and analytical toolkits to analyze the structure of the highly irregular cell aggregates. These approaches were tested in two example cases: the two dimensional aggregation of mouse embryonic fibroblast (MEF)cells and the flocculation of S. cerevisiae mediated by the sugar-dependent adhesion protein Flo5. While it was possible to achieve temporal information of the MEF cell aggregation, the flocculation of S. cerevisiae is not accessible in this way. The time-lapse microscopy series indicate a subdivision of MEF cell aggregation into a spreading and a contraction phase. In addition, the data shows that there is a dependency of the aggregate’s structure on its size with a sharp transition from a linear dependency to a constant structure. The three-dimensional imaging of immobilized flocs using a confocal laser scanning microscope provided information about the structural properties of yeast flocs. The most important findings are that the flocs are self similar fractal structures and that cheater cells, i.e. cells that do not produce the necessary binding proteins but benefit from the altruistic behavior of producing cells, are largely underprivileged in the process. This indicates that, even though flo5 does not qualify as a “green beard gene” by definition, the benefits of the resulting altruistic behavior are strongly shifted in favor of the producing cells by the aggregation mechanism