Modelling and Simulation by Stochastic Interacting Particle Systems

Klauß, Tobias; Böhme, Anja Voß

doi:10.1007/978-0-8176-4556-4_31

Cited by 5 publications

(7 citation statements)

References 3 publications

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“…The trajectories of the resulting time-discrete Markov chain show the same longtime behavior as the continuous-time cell sorting model. See Klauss and Voss-Boehme [2008] for details.…”

Section: Applied Methods For the Model Analysismentioning

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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“…The trajectories of the resulting time-discrete Markov chain show the same longtime behavior as the continuous-time cell sorting model. See Klauss and Voss-Boehme [2008] for details.…”

Section: Applied Methods For the Model Analysismentioning

confidence: 99%

“…From our analytical viewpoint, continuous-time models are easier to handle and more natural. See Klauss and Voss-Boehme [2008] for the derivation of a according time-discrete model.…”

mentioning

confidence: 99%

The cellular basis of cell sorting kinetics

Voß-Böhme

Deutsch

2010

Journal of Theoretical Biology

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“…To sample from the trajectories of our stochastic model we employ the exact stochastic simulation algorithm by Gillespie [51] in an efficient implementation for IPS [46,47]. Three of six parameters are held fixed as described in section 2.2: γ = 1 by dedimensionalisation, s = (1, 0), s = 1.…”

Section: Simulationmentioning

confidence: 99%

“…Taken together, the model equations (2.1)-(2.4), (2.6) and (2.7) define the transition rates of a continuous time Markov chain (h(t)) t!0 or more specifically an IPS [41][42][43], which we call the dynamically diluted alignment model. See figure 2 for an illustration of the model dynamics.…”

Section: Mathematical Model Of Cell Polarity and Turnover 21 Model Definitionmentioning

confidence: 99%

A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns

Hoffmann

Voß-Böhme

Rink

et al. 2017

J. R. Soc. Interface.

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The polarization of cells and tissues is fundamental for tissue morphogenesis during biological development and regeneration. A deeper understanding of biological polarity pattern formation can be gained from the consideration of pattern reorganization in response to an opposing instructive cue, which we here consider using the example of experimentally inducible body axis inversions in planarian flatworms. We define a dynamically diluted alignment model linking three processes: entrainment of cell polarity by a global signal, local cell-cell coupling aligning polarity among neighbours, and cell turnover replacing polarized cells by initially unpolarized cells. We show that a persistent global orienting signal determines the final mean polarity orientation in this stochastic model. Combining numerical and analytical approaches, we find that neighbour coupling retards polarity pattern reorganization, whereas cell turnover accelerates it. We derive a formula for an effective neighbour coupling strength integrating both effects and find that the time of polarity reorganization depends linearly on this effective parameter and no abrupt transitions are observed. This allows us to determine neighbour coupling strengths from experimental observations. Our model is related to a dynamic 8-Potts model with annealed site-dilution and makes testable predictions regarding the polarization of dynamic systems, such as the planarian epithelium.

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“…1, i). In contrast, individual-based models simulate consequences of local interactions among individual members of a population [10], such as cooperators and cheaters. A cooperator pays a fitness cost to produce a benefit for another individual, whereas a cheater receives the benefit without paying the cost of cooperation.…”

Section: Artificial Systemsmentioning

confidence: 99%

Using artificial systems to explore the ecology and evolution of symbioses

Momeni

Chen

Hillesland

et al. 2011

Cell. Mol. Life Sci.

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The web of life is weaved from diverse symbiotic interactions between species. Symbioses vary from antagonistic interactions such as competition and predation to beneficial interactions such as mutualism. What are the bases for the origin and persistence of symbiosis? What affects the ecology and evolution of symbioses? How do symbiotic interactions generate ecological patterns? How do symbiotic partners evolve and coevolve? Many of these questions are difficult to address in natural systems. Artificial systems, from abstract to living, have been constructed to capture essential features of natural symbioses and to address these key questions. With reduced complexity and increased controllability, artificial systems can serve as useful models for natural systems. We review how artificial systems have contributed to our understanding of symbioses.

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Modelling and Simulation by Stochastic Interacting Particle Systems

Cited by 5 publications

References 3 publications

The cellular basis of cell sorting kinetics

The cellular basis of cell sorting kinetics

A dynamically diluted alignment model reveals the impact of cell turnover on the plasticity of tissue polarity patterns

Using artificial systems to explore the ecology and evolution of symbioses

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