A Codimension-2 Bifurcation Controlling Endogenous Bursting Activity and Pulse-Triggered Responses of a Neuron Model

The dynamics of individual neurons are crucial for producing functional activity in neuronal networks. An open question is how temporal characteristics can be controlled in bursting activity and in transient neuronal responses to synaptic input. Bifurcation theory provides a framework to discover generic mechanisms addressing this question. We present a family of mechanisms organized around a global codimension-2 bifurcation. The cornerstone bifurcation is located at the intersection of the border between bursting and spiking and the border between bursting and silence. These borders correspond to the blue sky catastrophe bifurcation and the saddle-node bifurcation on an invariant circle (SNIC) curves, respectively. The cornerstone bifurcation satisfies the conditions for both the blue sky catastrophe and SNIC. The burst duration and interburst interval increase as the inverse of the square root of the difference between the corresponding bifurcation parameter and its bifurcation value. For a given set of burst duration and interburst interval, one can find the parameter values supporting these temporal characteristics. The cornerstone bifurcation also determines the responses of silent and spiking neurons. In a silent neuron with parameters close to the SNIC, a pulse of current triggers a single burst. In a spiking neuron with parameters close to the blue sky catastrophe, a pulse of current temporarily silences the neuron. These responses are stereotypical: the durations of the transient intervals–the duration of the burst and the duration of latency to spiking–are governed by the inverse-square-root laws. The mechanisms described here could be used to coordinate neuromuscular control in central pattern generators. As proof of principle, we construct small networks that control metachronal-wave motor pattern exhibited in locomotion. This pattern is determined by the phase relations of bursting neurons in a simple central pattern generator modeled by a chain of oscillators

Six Types of Multistability in a Neuronal Model Based on Slow Calcium Current

Background: Multistability of oscillatory and silent regimes is a ubiquitous phenomenon exhibited by excitable systems such as neurons and cardiac cells. Multistability can play functional roles in short-term memory and maintaining posture. It seems to pose an evolutionary advantage for neurons which are part of multifunctional Central Pattern Generators to possess multistability. The mechanisms supporting multistability of bursting regimes are not well understood or classified. Methodology/Principal Findings: Our study is focused on determining the bio-physical mechanisms underlying different types of co-existence of the oscillatory and silent regimes observed in a neuronal model. We develop a low-dimensional model typifying the dynamics of a single leech heart interneuron. We carry out a bifurcation analysis of the model and show that it possesses six different types of multistability of dynamical regimes. These types are the co-existence of 1) bursting and silence, 2) tonic spiking and silence, 3) tonic spiking and subthreshold oscillations, 4) bursting and subthreshold oscillations, 5) bursting, subthreshold oscillations and silence, and 6) bursting and tonic spiking. These first five types of multistability occur due to the presence of a separating regime that is either a saddle periodic orbit or a saddle equilibrium. We found that the parameter range wherein multistability is observed is limited by the parameter values at which the separating regimes emerge and terminate. Conclusions: We developed a neuronal model which exhibits a rich variety of different types of multistability. We described a novel mechanism supporting the bistability of bursting and silence. This neuronal model provides a unique opportunity to study the dynamics of networks with neurons possessing different types of multistability

Acute Alterations of Somatodendritic Action Potential Dynamics in Hippocampal CA1 Pyramidal Cells after Kainate-Induced Status Epilepticus in Mice

Pathophysiological remodeling processes at an early stage of an acquired epilepsy are critical but not well understood. Therefore, we examined acute changes in action potential (AP) dynamics immediately following status epilepticus (SE) in mice. SE was induced by intraperitoneal (i.p.) injection of kainate, and behavioral manifestation of SE was monitored for 3–4 h. After this time interval CA1 pyramidal cells were studied ex vivo with whole-cell current-clamp and Ca2+ imaging techniques in a hippocampal slice preparation. Following acute SE both resting potential and firing threshold were modestly depolarized (2–5 mV). No changes were seen in input resistance or membrane time constant, but AP latency was prolonged and AP upstroke velocity reduced following acute SE. All cells showed an increase in AP halfwidth and regular (rather than burst) firing, and in a fraction of cells the notch, typically preceding spike afterdepolarization (ADP), was absent following acute SE. Notably, the typical attenuation of backpropagating action potential (b-AP)-induced Ca2+ signals along the apical dendrite was strengthened following acute SE. The effects of acute SE on the retrograde spread of excitation were mimicked by applying the Kv4 current potentiating drug NS5806. Our data unveil a reduced somatodendritic excitability in hippocampal CA1 pyramidal cells immediately after acute SE with a possible involvement of both Na+ and K+ current components

Exploring Neuronal Bistability at the Depolarization Block

Many neurons display bistability - coexistence of two firing modes such as bursting and tonic spiking or tonic spiking and silence. Bistability has been proposed to endow neurons with richer forms of information processing in general and to be involved in short-term memory in particular by allowing a brief signal to elicit long-lasting changes in firing. In this paper, we focus on bistability that allows for a choice between tonic spiking and depolarization block in a wide range of the depolarization levels. We consider the spike-producing currents in two neurons, models of which differ by the parameter values. Our dopaminergic neuron model displays bistability in a wide range of applied currents at the depolarization block. The Hodgkin-Huxley model of the squid giant axon shows no bistability. We varied parameter values for the model to analyze transitions between the two parameter sets. We show that bistability primarily characterizes the inactivation of the Na+ current. Our study suggests a connection between the amount of the Na+ window current and the length of the bistability range. For the dopaminergic neuron we hypothesize that bistability can be linked to a prolonged action of antipsychotic drugs.Comment: 26 pages, 8 figures, accepted to PLoS ON

Paw-shake Response and Locomotion: Can One CPG Generate Two Different Rhythmic Behaviors?

Using software AnimatLab we developed a 5-segment cat hindlimb model with 12 Hill-type muscle actuators controlled by (1) a half-center CPG activating flexor and extensor muscles (two-joint muscles received both flexion- and extension-related signals) and (2) proprioceptive input originated from the muscle spindle and Golgi tendon organ afferents