Kunichika Tsumoto

Bifurcations in Morris-Lecar neuron model

The Morris-Lecar (M-L) equations are an important neuron model that exhibits classes I and II excitabilities when system parameters are set appropriately. Although many papers have clarified characteristic behaviors of the model, the detailed transition between two classes is unclear from the viewpoint of bifurcation analyses. In this paper, we investigate bifurcations of invariant sets in a five-dimensional parameter space, and identify an essential parameter of the half-activated potential of the potassium activation curve that contributes to the alternation of the membrane properties of the M-L neuron. We also show that the membrane property can be controlled by varying the value of the single parameter.

Synchronization of Firing in Cortical Fast-Spiking Interneurons at Gamma Frequencies: A Phase-Resetting Analysis

Fast-spiking (FS) cells in the neocortex are interconnected both by inhibitory chemical synapses and by electrical synapses, or gap-junctions. Synchronized firing of FS neurons is important in the generation of gamma oscillations, at frequencies between 30 and 80 Hz. To understand how these synaptic interactions control synchronization, artificial synaptic conductances were injected in FS cells, and the synaptic phase-resetting function (SPRF), describing how the compound synaptic input perturbs the phase of gamma-frequency spiking as a function of the phase at which it is applied, was measured. GABAergic and gap junctional conductances made distinct contributions to the SPRF, which had a surprisingly simple piecewise linear form, with a sharp midcycle break between phase delay and advance. Analysis of the SPRF showed how the intrinsic biophysical properties of FS neurons and their interconnections allow entrainment of firing over a wide gamma frequency band, whose upper and lower frequency limits are controlled by electrical synapses and GABAergic inhibition respectively.

Bifurcations in synaptically coupled BVP neurons

We investigate bifurcations of periodic solutions in model equations of two and three Bonhoffer–van der Pol (BVP) neurons coupled through the characteristics of synaptic transmissions with a time delay. Bifurcations of the coupled BVP neurons are compared with bifurcations of synaptically coupled Hodgkin–Huxley neurons. We obtained a parameter set of the BVP system, such that the two systems are qualitatively very similar from a bifurcational point of view. This study is a base for the analysis of synaptically coupled neurons with a large number of coupling strategies.

Roles of Subcellular Na+ Channel Distributions in the Mechanism of Cardiac Conduction

The gap junction and voltage-gated Na(+) channel play an important role in the action potential propagation. The purpose of this study was to elucidate the roles of subcellular Na(+) channel distribution in action potential propagation. To achieve this, we constructed the myocardial strand model, which can calculate the current via intercellular cleft (electric-field mechanism) together with gap-junctional current (gap-junctional mechanism). We conducted simulations of action potential propagation in a myofiber model where cardiomyocytes were electrically coupled with gap junctions alone or with both the gap junctions and the electric field mechanism. Then we found that the action potential propagation was greatly affected by the subcellular distribution of Na(+) channels in the presence of the electric field mechanism. The presence of Na(+) channels in the lateral membrane was important to ensure the stability of propagation under conditions of reduced gap-junctional coupling. In the poorly coupled tissue with sufficient Na(+) channels in the lateral membrane, the slowing of action potential propagation resulted from the periodic and intermittent dysfunction of the electric field mechanism. The changes in the subcellular Na(+) channel distribution might be in part responsible for the homeostatic excitation propagation in the diseased heart.

Modeling Light Adaptation in Circadian Clock: Prediction of the Response That Stabilizes Entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature.

Ischemia-related subcellular redistribution of sodium channels enhances the proarrhythmic effect of class I antiarrhythmic drugs: a simulation study.

Background Cardiomyocytes located at the ischemic border zone of infarcted ventricle are accompanied by redistribution of gap junctions, which mediate electrical transmission between cardiomyocytes. This ischemic border zone provides an arrhythmogenic substrate. It was also shown that sodium (Na+) channels are redistributed within myocytes located in the ischemic border zone. However, the roles of the subcellular redistribution of Na+ channels in the arrhythmogenicity under ischemia remain unclear. Methods Computer simulations of excitation conduction were performed in a myofiber model incorporating both subcellular Na+ channel redistribution and the electric field mechanism, taking into account the intercellular cleft potentials. Results We found in the myofiber model that the subcellular redistribution of the Na+ channels under myocardial ischemia, decreasing in Na+ channel expression of the lateral cell membrane of each myocyte, decreased the tissue excitability, resulting in conduction slowing even without any ischemia-related electrophysiological change. The conventional model (i.e., without the electric field mechanism) did not reproduce the conduction slowing caused by the subcellular Na+ channel redistribution. Furthermore, Na+ channel blockade with the coexistence of a non-ischemic zone with an ischemic border zone expanded the vulnerable period for reentrant tachyarrhythmias compared to the model without the ischemic border zone. Na+ channel blockade tended to cause unidirectional conduction block at sites near the ischemic border zone. Thus, such a unidirectional conduction block induced by a premature stimulus at sites near the ischemic border zone is associated with the initiation of reentrant tachyarrhythmias. Conclusions Proarrhythmia of Na+ channel blockade in patients with old myocardial infarction might be partly attributable to the ischemia-related subcellular Na+ channel redistribution.

Dynamical mechanisms of phase-2 early afterdepolarizations in human ventricular myocytes: insights from bifurcation analyses of two mathematical models

Early afterdepolarization (EAD) is known as a cause of ventricular arrhythmias in long QT syndromes. We theoretically investigated how the rapid (IKr) and slow (IKs) components of delayed-rectifier K+ channel currents, L-type Ca2+ channel current (ICaL), Na+/Ca2+ exchanger current (INCX), Na+-K+ pump current (INaK), intracellular Ca2+ (Cai) handling via sarcoplasmic reticulum (SR), and intracellular Na+ concentration (Nai) contribute to initiation, termination, and modulation of phase-2 EADs, using two human ventricular myocyte models. Bifurcation structures of dynamical behaviors in model cells were explored by calculating equilibrium points, limit cycles (LCs), and bifurcation points as functions of parameters. EADs were reproduced by numerical simulations. The results are summarized as follows: 1) decreasing IKs and/or IKr or increasing ICaL led to EAD generation, to which mid-myocardial cell models were especially susceptible; the parameter regions of EADs overlapped the regions of stable LCs. 2) Two types of EADs (termination mechanisms), IKs activation-dependent and ICaL inactivation-dependent EADs, were detected; IKs was not necessarily required for EAD formation. 3) Inhibiting INCX suppressed EADs via facilitating Ca2+-dependent ICaL inactivation. 4) Cai dynamics (SR Ca2+ handling) and Nai strongly affected bifurcations and EAD generation in model cells via modulating ICaL, INCX, and INaK Parameter regions of EADs, often overlapping those of stable LCs, shifted depending on Cai and Nai in stationary and dynamic states. 5) Bradycardia-related induction of EADs was mainly due to decreases in Nai at lower pacing rates. This study demonstrates that bifurcation analysis allows us to understand the dynamical mechanisms of EAD formation more profoundly. NEW & NOTEWORTHY We investigated mechanisms of phase-2 early afterdepolarization (EAD) by bifurcation analyses of human ventricular myocyte (HVM) models. EAD formation in paced HVMs basically depended on bifurcation phenomena in non-paced HVMs, but was strongly affected by intracellular ion concentrations in stationary and dynamic states. EAD generation did not necessarily require IKs.

Nonlinear dynamics and bifurcations of a coupled oscillator model for calling behavior of Japanese tree frogs (Hyla japonica)

Synchronization has been observed in various systems, including living beings. In a previous study, we reported a new phenomenon with antisynchronization in calling behavior of two interacting Japanese tree frogs. In this paper, we theoretically analyse nonlinear dynamics in a system of three coupled oscillators, which models three interacting frogs, where the oscillators of each pair have the property of antisynchronization; in particular, we perform bifurcation analysis and Lyapunov function analysis.

Phase-Resetting Analysis of Gamma-Frequency Synchronization of Cortical Fast-Spiking Interneurons Using Synaptic-like Conductance Injection

Synchronous firing of cortical fast-spiking (FS) interneurons is important in generating gamma frequency (30–80 Hz) oscillations. These cells connect with each other, both through inhibitory chemical synapses and through gap junctions. To understand how these synaptic interactions control synchronization, we injected artificial synaptic conductances in FS cells, and measured the phase resetting produced by synaptic inputs, the synaptic phase-resetting function (SPRF), during gamma-frequency firing. We found that artificial GABAA receptor and gap junctional conductances made distinct contributions to the SPRF, which had a remarkably simple, piecewise linear form, with a sharp break between regions of phase delay and advance. Analysing the SPRF shows how the intrinsic properties of FS neurons and their synaptic connections allow synchronization of firing over a wide gamma frequency band, and upper and lower frequency limits of this band are shown to be controlled by gap junctions and GABAergic inhibition, respectively. This phase-resetting model gives insight into how FS cells synchronize so effectively at gamma oscillations, and can be a building block in large-scale simulations of the FS cell networks, in order to understand the onset and stability of patterns of gamma oscillation in the cortex.

Facilitation of hERG channels by blockers: a mechanism predicted to reduce lethal cardiac arrhythmias

Fatal cardiac arrhythmias are caused by some, but not all, drugs that inhibit the cardiac rapid delayed-rectifier current (IKr) by blocking hERG channels. Here, we propose a novel mechanism that could make certain hERG blockers less proarrhythmic. Several drugs that block hERG channels, yet have favorable cardiac safety profiles, also evoke another effect; they increase the current amplitude upon low-voltage depolarization (facilitation). Voltage-clamp recordings of hERG block and facilitation by nifekalant, a Class III antiarrhythmic agent, constrained a model of human cardiac IKr. In human ventricular action potential simulations, nifekalant showed its therapeutic ability to suppress ectopic excitations, with or without facilitation. Without facilitation, excessive IKr block evoked early afterdepolarizations, which cause lethal arrhythmias. Facilitation prevented early afterdepolarizations at the same degree of block by increasing IKr during repolarization phase of action potentials. Thus, facilitation is proposed to reduce the arrhythmogenic risk of hERG blockers. Abbreviations AP: action potential; APD: action potential duration; APD90: action potential duration measured at 90% repolarization; EAD: early afterdepolarization; hERG: human ether-ago-go-related gene; ICaL: L-type Ca2+ channel current; Inet: net ionic current; IK1: inward-rectifier potassium current; IKr: rapid component of the delayed-rectifier potassium current; INa: sodium current; ORd: O’Hara-Rudy dynamic