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

Fatoyinbo, Hammed Olawale; Brown, Richard G.; Simpson, David J. W.; Brunt, Bruce van

doi:10.1007/s11538-020-00771-6

Cited by 13 publications

(20 citation statements)

References 62 publications

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“…We consider a nondimensionalised reaction-diffusion system to model the dynamics of a population of coupled SMCs through passive electrical coupling of adjacent cells. The reaction term in the model is based on our previous study on an isolated SMC [25]. The model equations are…”

Section: A Nondimensionalised Morris-lecar System With Diffusionmentioning

confidence: 99%

“…where v1 and v3 measure the potential at which potassium and calcium channels are halfopened, ψ is a time constant, and v2 and v4 are additional parameters. as listed in [25]: v1 = −0.2813, v2 = 0.3125, v3 = −0.1380, v4 = 0.1812, ψ = 0.1665, vL = −0.875, vK = −1.125, ḡL = 0.25, ḡK = 1.0, and ḡCa = 0.4997. In this paper we consider a one-dimensional spatial domain Ω = [−L, L] for the values of X.…”

Section: A Nondimensionalised Morris-lecar System With Diffusionmentioning

confidence: 99%

“…We study a spatially-extended two-variable nondimensionalised Morris-Lecar model with no applied current. As shown in our previous work [25], without diffusion the model is a reduced form of the three-dimensional ODE model of Gonzalez-Fernandez and Ermentrout ( [32]) for the dynamics of pacemaker vasomotion in SMCs of small arteries.…”

Section: Introductionmentioning

confidence: 99%

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Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Fatoyinbo¹,

Brown²,

Simpson³

et al. 2021

Preprint

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Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that spatiotemporal patterns in electrically-coupled smooth muscle cells occur even in the absence of forcing. We study a reaction-diffusion system with the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling -in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and use travelling wave coordinates to analyse travelling waves.

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Section: A Nondimensionalised Morris-lecar System With Diffusionmentioning

confidence: 99%

Section: A Nondimensionalised Morris-lecar System With Diffusionmentioning

confidence: 99%

See 1 more Smart Citation

Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Fatoyinbo¹,

Brown²,

Simpson³

et al. 2021

Preprint

Self Cite

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“…Due to both types of excitability are very important, the dynamics or bifurcations related to type I excitability and type II excitability, and the dynamics or bifurcations for the transition between excitability types have attracted much attention in both theoretical studies [59][60][61][62][63][64][65] and biological experiments [27][28][29][30][31][32][33][34][35][36][37]. In the biological experiments, the switch between type I excitability and type II excitability was identified and induced by multiple modulations such as the M-type potassium current, A-type current, optogenetic stimulation, and in vitro or in vivo-like conditions, and so on [28-30, 35, 57, 58, 64].…”

Section: Introductionmentioning

confidence: 99%

“…In some Refs. [5,62,65], the codimension-2 bifurcation point, Saddle-Node Homoclinic orbit (SNHO) bifurcation which is related to SNIC, SN, and BHom, is thought to be related to the transition between type I and II excitabilities. Therefore, the roles of codimension-2 bifurcations such as BT or SNHO bifurcations in the transition between type I and II excitabilities should be further identified.…”

Section: Introductionmentioning

confidence: 99%

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Wang

et al. 2021

Preprint

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Neuron exhibits nonlinear dynamics such as excitability transition and post-inhibitory rebound (PIR) spike related to bifurcations, which are associated with information processing, locomotor modulation, or brain disease. PIR spike is evoked by inhibitory stimulation instead of excitatory stimulation, which presents a challenge to the threshold concept. In the present paper, 7 codimension-2 or degenerate bifurcations related to 10 codimension-1 bifurcations are acquired in a neuronal model, which presents the bifurcations underlying the excitability transition and PIR spike. Type I excitability corresponds to saddle-node bifurcation on an invariant cycle (SNIC) bifurcation, and type II excitability to saddle-node (SN) bifurcation or sub-critical Hopf (SubH) bifurcation or sup-critical Hopf (SupH) bifurcation. The excitability transition from type I to II corresponds to the codimension-2 bifurcation, Saddle-Node Homoclinic orbit (SNHO) bifurcation, via which SNIC bifurcation terminates and meanwhile big homoclinic orbit (BHom) bifurcation and SN bifurcation emerge. A degenerate bifurcation via which BHom bifurcation terminates and fold limit cycle (LPC) bifurcation emerges is responsible for spiking transition from type I to II, and the roles of other codimension-2 bifurcations (Cusp, Bogdanov-Takens, and Bautin) are discussed. In addition, different from the widely accepted viewpoint that PIR spike is mainly evoked near Hopf bifurcation rather than SNIC bifurcation, PIR spike is identified to be induced near SNIC or BHom or LPC bifurcations, and threshold curves resemble that of Hopf bifurcation. The complex bifurcations present comprehensive and deep understandings of excitability transition and PIR spike, which are helpful for the modulation to neural firing activities and physiological functions.

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Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

et al. 2022

Self Cite

View full text Add to dashboard Cite

Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris–Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling — in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

show abstract

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

Cited by 13 publications

References 62 publications

Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Multiple and Complex Codimension-2 Bifurcations underlying Post-inhibitory Rebound Spike and Excitability Transition

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

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