Lattice gas automata for reactive systems

Boon, Jean‐Pierre; Dab, David; Kapral, Raymond; Ławniczak, Anna T.

doi:10.1016/0370-1573(95)00080-1

Cited by 143 publications

(90 citation statements)

References 119 publications

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“…Dormann provides a wonderful introduction to CA [34]. For details about CA models in physics see Chopard and Droz [19] and specifically for lattice-gas models see Wolf-Gladrow [162] and Boon et al [14]. In their biological applications LGCA treat cells as pointlike objects with an internal state but no spatial structure.…”

mentioning

confidence: 99%

On Cellular Automaton Approaches to Modeling Biological Cells

Alber

Kiskowski

Glazier

et al. 2003

Mathematical Systems Theory in Biology, Communications, Computation, and Finance

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Abstract. We discuss two different types of Cellular Automata (CA): lattice-gasbased cellular automata (LGCA) and the cellular Potts model (CPM), and describe their applications in biological modeling.LGCA were originally developed for modeling ideal gases and fluids. We describe several extensions of the classical LGCA model to self-driven biological cells. In particular, we review recent models for rippling in myxobacteria, cell aggregation, swarming, and limb bud formation. These LGCA-based models show the versatility of CA in modeling and their utility in addressing basic biological questions.The CPM is a more sophisticated CA, which describes individual cells as extended objects of variable shape. We review various extensions to the original Potts model and describe their application to morphogenesis; the development of a complex spatial structure by a collection of cells. We focus on three phenomena: cell sorting in aggregates of embryonic chicken cells, morphological development of the slime mold Dictyostelium discoideum and avascular tumor growth. These models include intercellular and extracellular interactions, as well as cell growth and death.

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mentioning

confidence: 99%

On Cellular Automaton Approaches to Modeling Biological Cells

Alber

Kiskowski

Glazier

et al. 2003

Mathematical Systems Theory in Biology, Communications, Computation, and Finance

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“…This suggests that when reduced to its essential constituents the system can be represented in space as a set of structured lattice points ͑cells͒ evolving in time according to well defined rules. Following these lines we recently developed 7 a simple cellular automaton 8,9 evolving in time through a two-step rule. Focusing on a cell at a particular time step, ͑i͒ we find out how a͒ Author to whom correspondence should be addressed.…”

Section: Introductionmentioning

confidence: 99%

Diffusion in tight confinement: A lattice-gas cellular automaton approach. I. Structural equilibrium properties

Demontis

Pazzona

Suffritti

2007

The Journal of Chemical Physics

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The thermodynamic and transport properties of diffusing species in microporous materials are strongly influenced by their interactions with the confining framework, which provide the energy landscape for the transport process. The simple topology and the cellular nature of the ␣ cages of a ZK4 zeolite suggest that it is appropriate to apply to the study of the problem of diffusion in tight confinement a time-space discrete model such as a lattice-gas cellular automaton ͑LGCA͒. In this paper we investigate the properties of an equilibrium LGCA constituted by a constant number of noninteracting identical particles, distributed among a fixed number of identical cells arranged in a three-dimensional cubic network and performing a synchronous random walk at constant temperature. Each cell of this network is characterized by a finite number of two types of adsorption sites: the exit sites available to particle transfer and the inner sites not available to such transfers. We represent the particle-framework interactions by assuming a differentiation in binding energy of the two types of sites. This leads to a strong dependence of equilibrium and transport properties on loading and temperature. The evolution rule of our LGCA model is constituted by two operations ͑randomization, in which the number of particles which will be able to try a jump to neighboring cells is determined, and propagation, in which the allowed jumps are performed͒, each one applied synchronously to all of the cells. The authors study the equilibrium distribution of states and the adsorption isotherm of the model under various conditions of loading and temperature. In connection with the differentiation in energy between exit and inner sites, the adsorption isotherm is described by a conventional Langmuir isotherm at high temperature and by a dual-site Langmuir isotherm at low temperature, while a first order diffuse phase transition takes place at very low temperature.

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“…the migration/proliferation dichotomy is not assumed. This model assumes therefore a "Go-and-Grow" behavior, which can generally be described macroscopically by a system of reaction-diffusion equations [2] and, in our specific case, as a Fisher-Kolmogorovlike equation with well-known properties [13].…”

Section: Numerical Investigationmentioning

confidence: 99%

Investigation of the Migration/Proliferation Dichotomy and its Impact on Avascular Glioma Invasion

Böttger

Hatzikirou

Chauvière

et al. 2012

Math. Model. Nat. Phenom.

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Abstract. Gliomas are highly invasive brain tumors that exhibit high and spatially heterogeneous cell proliferation and motility rates. The interplay of proliferation and migration dynamics plays an important role in the invasion of these malignant tumors. We analyze the regulation of proliferation and migration processes with a lattice-gas cellular automaton (LGCA). We study and characterize the influence of the migration/proliferation dichotomy (also known as the "Go-or-Grow" mechanism) on avascular glioma invasion, in terms of invasion speed and width of the infiltration zone. We show that the invasive behavior of the (macroscopic) tumor colony is a highly complex phenomenon that cannot be extrapolated by the sole knowledge of the (microscopic) individual cell phenotype.

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Lattice gas automata for reactive systems

Cited by 143 publications

References 119 publications

On Cellular Automaton Approaches to Modeling Biological Cells

On Cellular Automaton Approaches to Modeling Biological Cells

Diffusion in tight confinement: A lattice-gas cellular automaton approach. I. Structural equilibrium properties

Investigation of the Migration/Proliferation Dichotomy and its Impact on Avascular Glioma Invasion

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