Multistability in a neuron model with extracellular potassium dynamics

Spiking patterns of a neuron model to stimulus: Rich dynamics and oxygen's role

Neuronal spiking patterns, which are of fundamental importance for the understanding of information processing in neural systems, can be generated in response to different stimuli. We here investigate in detail the stimulus-induced spiking patterns in a biologically plausible neuron model in which the oxygen concentration and the dynamical concentrations of potassium, sodium, and chloride are considered. Various types of spiking patterns can be induced by the different external potassium accumulations in response to the stimulus, including two different types of epileptic seizure (SZ) and spreading depression (SD) states, two different mixed states of SD and SZ, SZ state with multi-burst, and tonic firing behaviors. Interestingly, we show that these rich spiking patterns can also be induced by the current stimulus with a low oxygen concentration. Furthermore, we reveal that the stimulus can induce two different phase transitions from the SD state to the SZ state according to the phase transition theory, which results in the different electrical activities. All these findings may provide insight into information processing in neural systems.

Subthalamic Nucleus Deep Brain Stimulation: Basic Concepts and Novel Perspectives

Over the last decades, extensive basic and clinical knowledge has been acquired on the use of subthalamic nucleus (STN) deep brain stimulation (DBS) for Parkinson's disease (PD). It is now clear that mechanisms involved in the effects of this therapy are far more complex than previously anticipated. At frequencies commonly used in clinical practice, neural elements may be excited or inhibited and novel dynamic states of equilibrium are reached. Electrode contacts used for chronic DBS in PD are placed near the dorsal border of the nucleus, a highly cellular region. DBS may thus exert its effects by modulating these cells, hyperdirect projections from motor cortical areas, afferent and efferent fibers to the motor STN. Advancements in neuroimaging techniques may allow us to identify these structures optimizing surgical targeting. In this review, we provide an update on mechanisms and the neural elements modulated by STN DBS.

Deep Brain Stimulation

High-frequency deep brain stimulation (DBS) is an effective treatment for some movement disorders. Though mechanisms underlying DBS are still unclear, commonly accepted theories include a “functional inhibition” of neuronal cell bodies and the excitation of axonal projections near the electrodes. It is becoming clear, however, that the paradoxical dissociation “local inhibition” and “distant excitation” is far more complex than initially thought. Despite an initial increase in neuronal activity following stimulation, cells are often unable to maintain normal ionic concentrations, particularly those of sodium and potassium. Based on currently available evidence, we proposed an alternative hypothesis. Increased extracellular concentrations of potassium during DBS may change the dynamics of both cells and axons, contributing not only to the intermittent excitation and inhibition of these elements but also to interrupt abnormal pathological activity. In this article, we review mechanisms through which high extracellular potassium may mediate some of the effects of DBS.

Effects of extracellular potassium diffusion on electrically coupled neuron networks

Potassium accumulation and diffusion during neuronal epileptiform activity have been observed experimentally, and potassium lateral diffusion has been suggested to play an important role in nonsynaptic neuron networks. We adopt a hippocampal CA1 pyramidal neuron network in a zero-calcium condition to better understand the influence of extracellular potassium dynamics on the stimulus-induced activity. The potassium concentration in the interstitial space for each neuron is regulated by potassium currents, Na(+)-K(+) pumps, glial buffering, and ion diffusion. In addition to potassium diffusion, nearby neurons are also coupled through gap junctions. Our results reveal that the latency of the first spike responding to stimulus monotonically decreases with increasing gap-junction conductance but is insensitive to potassium diffusive coupling. The duration of network oscillations shows a bell-like shape with increasing potassium diffusive coupling at weak gap-junction coupling. For modest electrical coupling, there is an optimal K(+) diffusion strength, at which the flow of potassium ions among the network neurons appropriately modulates interstitial potassium concentrations in a degree that provides the most favorable environment for the generation and continuance of the action potential waves in the network.

Enhanced multiple vibrational resonances by Na+ and K+ dynamics in a neuron model

Some neuronal receptors perceive external input in the form of hybrid periodic signals. The signal detection may be based on the mechanism of vibrational resonance, in which a system's response to the low frequency signal can become optimal by an appropriate choice of the vibration amplitude of HFS. The vibrational resonance effect is investigated in a neuron model in which the intra- and extra-cellular potassium and sodium concentrations are allowed to evolve temporally, depending on ion currents, Na⁺-K⁺ pumps, glial buffering, and ion diffusion. Our results reveal that, compared to the vibrational resonances in the model with constant ion concentrations, the significantly enhanced vibrational multi-resonances can be observed for the single neuron system where the potassium and sodium ion concentrations vary temporally. Thus, in contradiction to a popular view that ion concentrations dynamics play little role in signal detection, we indicate that the neuron's response to an external subthreshold signal can be largely improved by sodium and potassium dynamics.

Synchronization of chemical noise-sustained structures in asymmetrically coupled differential-flow reactors

The differential-flow-induced chemical instability is investigated in the context of two coupled reactors with cubic autocatalytic kinetics (the Gray-Scott model). Previous results for master-slave arrangement [Izús, Deza, and Sánchez, J. Chem. Phys. 132, 234112 (2010)] are extended in this study to include bidirectional coupling between reactions. Numerical simulations in the convectively unstable regime show that synchronized noise-sustained structures are developed in both reactors due to the selective amplification of noise. A theoretical analysis shows that the nature of the synchronization and the stability of the synchronized manifold are related with the properties of the critical modes.