133 research outputs found
Depleting the signal: Analysis of chemotaxis-consumption models -- A survey
We give an overview of analytical results concerned with chemotaxis systems
where the signal is absorbed. We recall results on existence and properties of
solutions for the prototypical chemotaxis-consumption model and various
variants and review more recent findings on its ability to support the
emergence of spatial structures
Depleting the signal: Analysis of chemotaxis-consumption models—A survey
We give an overview of analytical results concerned with chemotaxis systems where the signal is absorbed. We recall results on existence and properties of solutions for the prototypical chemotaxis-consumption model and various variants and review more recent findings on its ability to support the emergence of spatial structures
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
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
Traveling Waves of a Mutualistic Model of Mistletoes and Birds
The existences of an asymptotic spreading speed and traveling wave solutions for a diffusive model which describes the interaction of mistletoe and bird populations with nonlocal diffusion and delay effect are proved by using monotone semiflow theory. The effects of different dispersal kernels on the asymptotic spreading speeds are investigated through concrete examples and simulations
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
Modeling random crawling, membrane deformation and intracellular polarity of motile amoeboid cells
Amoeboid movement is one of the most widespread forms of cell motility that plays a key
role in numerous biological contexts. While many aspects of this process are well investigated,
the large cell-to-cell variability in the motile characteristics of an otherwise uniform
population remains an open question that was largely ignored by previous models. In this
article, we present a mathematical model of amoeboid motility that combines noisy bistable
kinetics with a dynamic phase field for the cell shape. To capture cell-to-cell variability, we
introduce a single parameter for tuning the balance between polarity formation and intracellular
noise. We compare numerical simulations of our model to experiments with the social
amoeba Dictyostelium discoideum. Despite the simple structure of our model, we found
close agreement with the experimental results for the center-of-mass motion as well as for
the evolution of the cell shape and the overall intracellular patterns. We thus conjecture that
the building blocks of our model capture essential features of amoeboid motility and may
serve as a starting point for more detailed descriptions of cell motion in chemical gradients
and confined environments.Peer ReviewedPostprint (published version
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