Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates

Upadhyaya, Arpita; Rieu, Jean-Paul; Glazier, James A.; Sawada, Yasuji

doi:10.1016/s0378-4371(01)00009-7

Cited by 243 publications

(267 citation statements)

References 23 publications

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“…The intuition that individual cell mobility is lower the more a cell adheres to its neighbors seems to be plausible but shall be discussed explicitly. Our assumption is supported by the findings in Upadhyaya et al [2001]. There Upadhyaya and coworkers monitored and analyzed the motion of single endodermal cells within homotypic endodermal and ectodermal cell aggregates.…”

Section: Biological Foundation Of the Modeling Assumptionssupporting

confidence: 79%

“…Cell mobility is a prerequisite for active tissue rearrangement and is thereby essential for the process of sorting. It is widely agreed, that the cells in a tissues are able to change their spatial positions [Upadhyaya, Rieu, Glazier and Sawada, 2001]. Regarding intercellular adhesion, it is accepted [Wolpert, 2007], that there is a complex system of attraction and repulsion mechanisms operating between cells of various types.…”

Section: Introductionmentioning

confidence: 99%

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The cellular basis of cell sorting kinetics

Voß-Böhme

Deutsch

2010

Journal of Theoretical Biology

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Cell sorting is a dynamical cooperative phenomenon that is fundamental for tissue morphogenesis and tissue homeostasis. According to Steinberg's differential adhesion hypothesis, the structure of sorted cell aggregates is determined by physical characteristics of the respective tissues, the tissue surface tensions. Steinberg postulated that tissue surface tensions result from quantitative differences in intercellular adhesion. Several experiments in cell cultures as well as in developing organisms support this hypothesis.The question of how tissue surface tension might result from differential adhesion was addressed in some theoretical models. These models describe the cellular interdependence structure once the temporal evolution has stabilized. In general, these models are capable of reproducing sorted patterns. However the model dynamics at the cellular scale are defined implicitly and are not welljustified. The precise mechanism describing how differential adhesion generates the observed sorting kinetics at the tissue level is still unclear.It is necessary to formulate the concepts of cell level kinetics explicitly. Only then it is possible to understand the temporal development at the cellular and tissue scales. Here we argue that individual cell mobility is reduced the more the cells stick to their neighbors. We translate this assumption into a precise mathematical model which belongs to the class of stochastic interacting particle systems. Analyzing this model, we are able to predict the emergent sorting behavior at the population level. We describe qualitatively the geometry of cell segregation depending on the intercellular adhesion parameters. Furthermore, we derive a functional relationship between intercellular adhesion and surface tension and highlight the role of cell mobility in the process of sorting. We show that the interaction between the cells and the boundary of a confining vessel has a major impact on the sorting geometry.Keywords: differential adhesion hypothesis, tissue surface tension, phase segregation, stochastic lattice gas, interacting particle system 2000 MSC: 92C15, 92C17, 92C37 * Corresponding author Email addresses: anja.voss-boehme@tu-dresden.de (A. Voß-Böhme), andreas.deutsch@tu-dresden.de (A. Deutsch) Preprint submitted to Elsevier 4th December 2009A c c e p t e d m a n u s c r i p t

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Section: Biological Foundation Of the Modeling Assumptionssupporting

confidence: 79%

Section: Introductionmentioning

confidence: 99%

The cellular basis of cell sorting kinetics

Voß-Böhme

Deutsch

2010

Journal of Theoretical Biology

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“…In summary, by statistical analysis of experimental data we have shown that the equilibrium migration of the biological cells under consideration is anomalous. Related anomalies have also been observed for other types of migrating cells [84,85,86,87,88]. These experimental results are coherently reproduced by a mathematical model in form of a stochastic fractional equation.…”

supporting

confidence: 73%

“…On the other hand, according to Einstein's theory of Brownian motion a Brownian particle is passively driven by collisions from the surrounding fluid molecules, whereas biological cells move actively by themselves converting chemical into kinetic energy. This raises the question whether the random-looking paths of crawling biological cells can really be understood in terms of simple Brownian motion [82,83] or whether more advanced concepts of dynamical modeling have to be applied [84,85,86,87,88]. …”

Section: Cell Migration In Equilibriummentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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Abstract. We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: Lévy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.

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“…In particular, a natural arena for this statistical mechanics appears to be the so called complex systems [9]. We shall briefly review here four recent applications, namely fully developed turbulence [10][11][12], hadronic jets produced by electron-positron annihilation [13], motion of Hydra viridissima [14], and quantitative linguistics [15].…”

Section: Applications In and Out From Equilibriummentioning

confidence: 99%

Nonextensive statistical mechanics: a brief review of its present status

Tsallis

2002

An. Acad. Bras. Ciênc.

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We briefly review the present status of nonextensive statistical mechanics. We focus on (i) the central equations of the formalism, (ii) the most recent applications in physics and other sciences, (iii) the a priori determination (from microscopic dynamics) of the entropic index q for two important classes of physical systems, namely low-dimensional maps (both dissipative and conservative) and long-range interacting many-body hamiltonian classical systems.

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Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates

Cited by 243 publications

References 23 publications

The cellular basis of cell sorting kinetics

The cellular basis of cell sorting kinetics

Anomalous Fluctuation Relations

Nonextensive statistical mechanics: a brief review of its present status

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