Variability-sustained pattern formation in subexcitable media

Glatt, Erik; Gassel, Martin; Kaiser, F.

doi:10.1103/physreve.75.026206

Cited by 34 publications

(24 citation statements)

References 18 publications

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“…One method of incorporating variability into Dictyostelium models is the use of agent-based models, with applications to processes such as cell sorting [ 45 ]. The role of coupling strength was investigated in [ 46 ] and [ 47 ]; effects such as target-spiral competition were shown in [ 48 ].…”

Section: Introductionmentioning

confidence: 99%

Regulation of Spatiotemporal Patterns by Biological Variability: General Principles and Applications to Dictyostelium discoideum

Grace

Hütt

2015

PLoS Comput Biol

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Spatiotemporal patterns often emerge from local interactions in a self-organizing fashion. In biology, the resulting patterns are also subject to the influence of the systematic differences between the system’s constituents (biological variability). This regulation of spatiotemporal patterns by biological variability is the topic of our review. We discuss several examples of correlations between cell properties and the self-organized spatiotemporal patterns, together with their relevance for biology. Our guiding, illustrative example will be spiral waves of cAMP in a colony of Dictyostelium discoideum cells. Analogous processes take place in diverse situations (such as cardiac tissue, where spiral waves occur in potentially fatal ventricular fibrillation) so a deeper understanding of this additional layer of self-organized pattern formation would be beneficial to a wide range of applications. One of the most striking differences between pattern-forming systems in physics or chemistry and those in biology is the potential importance of variability. In the former, system components are essentially identical with random fluctuations determining the details of the self-organization process and the resulting patterns. In biology, due to variability, the properties of potentially very few cells can have a driving influence on the resulting asymptotic collective state of the colony. Variability is one means of implementing a few-element control on the collective mode. Regulatory architectures, parameters of signaling cascades, and properties of structure formation processes can be "reverse-engineered" from observed spatiotemporal patterns, as different types of regulation and forms of interactions between the constituents can lead to markedly different correlations. The power of this biology-inspired view of pattern formation lies in building a bridge between two scales: the patterns as a collective state of a very large number of cells on the one hand, and the internal parameters of the single cells on the other.

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Section: Introductionmentioning

confidence: 99%

Regulation of Spatiotemporal Patterns by Biological Variability: General Principles and Applications to Dictyostelium discoideum

Grace

Hütt

2015

PLoS Comput Biol

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“…For example, Gosak [65] investigated the role of cellular variability on the occurrence of Ca wave propagation in a net of diffusively coupled cells, and confirmed a resonance-like response due to the cellular variability by analyzing the spatial profile via the autocorrelation function. Glatt et al [66] studied the pattern formation in subexcitable net of FitzHugh-Nagumo elements with parameter variability (diversity) being considered, an intermediate variability strength induced similar spatiotemporal stochastic resonance generated by additive noise in subexcitable media and transition induced by variability in coupling intensity is also observed. Surely, a local periodic forcing is also effective to generate a target-like wave in the network as well.…”

Section: Introductionmentioning

confidence: 99%

Selection of Multiarmed Spiral Waves in a Regular Network of Neurons

Tang

2013

PLoS ONE

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Formation and selection of multiarmed spiral wave due to spontaneous symmetry breaking are investigated in a regular network of Hodgkin-Huxley neuron by changing the excitability and imposing spatial forcing currents on the neurons in the network. The arm number of the multiarmed spiral wave is dependent on the distribution of spatial forcing currents and excitability diversity in the network, and the selection criterion for supporting multiarmed spiral waves is discussed. A broken spiral segment is measured by a short polygonal line connected by three adjacent points (controlled nodes), and a double-spiral wave can be developed from the spiral segment. Multiarmed spiral wave is formed when a group of double-spiral waves rotate in the same direction in the network. In the numerical studies, a group of controlled nodes are selected and spatial forcing currents are imposed on these nodes, and our results show that l-arm stable spiral wave (l = 2, 3, 4,...8) can be induced to occupy the network completely. It is also confirmed that low excitability is critical to induce multiarmed spiral waves while high excitability is important to propagate the multiarmed spiral wave outside so that distinct multiarmed spiral wave can occupy the network completely. Our results confirm that symmetry breaking of target wave in the media accounts for emergence of multiarmed spiral wave, which can be developed from a group of spiral waves with single arm under appropriate condition, thus the potential formation mechanism of multiarmed spiral wave in the media is explained.

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“…Recently, there are several reports about the effect of diversity on spatially extended systems. It was found that parameter variability is able to induce pattern formation [31] and resonance-like behavior [32] in an excitable square lattice. For spatially extended chaotic systems, it was also found that parameter variability has the ability to induce coherence resonance [33].…”

Section: Discussionmentioning

confidence: 98%