Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

González-Miranda, J. M.

doi:10.1063/1.3687017

Cited by 24 publications

(6 citation statements)

References 46 publications

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“…The three-dimensional Sherman model, which shares most of the properties of the Chay model, has a bifurcation process similar to that of the Chay model, as investigated in a previous study [11]. Recently, the dynamics of the Chay model have been investigated in multiple two-dimensional parameter spaces [55], [56]. So far, no chaotic firing pattern lying between period-1 and period-2 firing patterns has been reported in the Chay model or the Sherman model.…”

Section: Discussionmentioning

confidence: 85%

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

2013

PLoS ONE

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An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern.

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Section: Discussionmentioning

confidence: 85%

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

2013

PLoS ONE

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“…In the CCD model that is also a pathological pain model, changes of firing frequency as well as the firing patterns were observed when riluzole that is a block of the persistent sodium current was used, which means that changes of the neuropathic pain information (Xie et al 2011). Mathematical models, such as the Hodgkin-Huxley model, the FitzHugh-Nagmo model, the Hindmarsh-Rose (HR) model, and the Chay model have been widely studied to identify the different firing patterns and bifurcations of neural firing patterns (Hindmarsh and Rose 1984;Fan and Holden 1992;Chay 1985;González-Miranda 2012;Innocenti et al 2007;Duan et al 2008;Shilnikov and Kolomiets 2008;Innocenti and Genesio 2009;Rech 2011).…”

Section: Introductionmentioning

confidence: 99%

“…Many complex or novel nonlinear behaviors related to chaos or bifurcations have been investigated in the theoretical models, which are helpful for the progresses of nonlinear dynamics in neuroscience (González-Miranda 2005, 2012; Barrio and Shilnikov 2011;Barrio et al 2015Barrio et al , 2014Zheng and Tonnelier 2009;Yamada and Kashimori 2013;Wei et al 2014;Ma and Tang 2015).…”

Section: Introductionmentioning

confidence: 99%

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Jia

Xue

2017

Cogn Neurodyn

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Two different bifurcation scenarios of firing patterns with decreasing extracellular calcium concentrations were observed in identical sciatic nerve fibers of a chronic constriction injury (CCI) model when the extracellular 4-aminopyridine concentrations were fixed at two different levels. Both processes proceeded from period-1 bursting to period-1 spiking via complex or simple processes. Multiple typical experimental examples manifested dynamics closely matching those simulated in a recently proposed 4-dimensional model to describe the nonlinear dynamics of the CCI model, which included most cases of the bifurcation scenarios. As the extracellular 4-aminopyridine concentrations is increased, the structure of the bifurcation scenario becomes more complex. The results provide a basic framework for identifying the relationships between different neural firing patterns and different bifurcation scenarios and for revealing the complex nonlinear dynamics of neural firing patterns. The potential roles of the basic bifurcation structures in identifying the information process mechanism are discussed.

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“…See also 40 for a similar twoparameter bifurcation analysis of the Chay neuronal model. retical 40,41 and computational 42 . The importance of the leak channel in the pacemaker dynamics of the full Morris-Lecar model has been studied by González-Miranda 43 .…”

Section: Introductionmentioning

confidence: 99%

Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells

Fatoyinbo,

Brown,

Simpson

et al. 2020

Preprint

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Evidence from experimental studies shows that oscillations due to electro-mechanical coupling can be generated spontaneously in smooth muscle cells. Such cellular dynamics are known as pacemaker dynamics. In this article we address pacemaker dynamics associated with the interaction of Ca 2+ and K + fluxes in the cell membrane of a smooth muscle cell.First we reduce a pacemaker model to a two-dimensional system equivalent to the reduced Morris-Lecar model and then perform a detailed numerical bifurcation analysis of the reduced model. Existing bifurcation analyses of the Morris-Lecar model concentrate on external applied current whereas we focus on parameters that model the response of the cell to changes in transmural pressure. We reveal a transition between Type I and Type II excitabilities with no external current required. We also compute a two-parameter bifurcation diagram and show how the transition is explained by the bifurcation structure.

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Nonlinear dynamics of the membrane potential of a bursting pacemaker cell

Cited by 24 publications

References 46 publications

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

A basic bifurcation structure from bursting to spiking of injured nerve fibers in a two-dimensional parameter space

Numerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells

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