The influence of ion concentrations on the dynamic behavior of the Hodgkin-Huxley model-based cortical network

Dynamics and conditions for inhibitory synaptic current to induce bursting and spreading depolarization in pyramidal neurons

Enhanced activity of inhibitory neurons, which is often used to suppress behaviors of pyramidal neurons to treat brain diseases, whereas can enhance spiking to a mixed-mode bursting (MMB) in recent experiments on migraine and seizure. The MMB contains a phase with high level of membrane potential/extracellular potassium concentration ([K+]o), which can propagate to form spreading depolarization (SD) wave. Different from the common view that the MMB/SD is often induced by enhanced positive effect or [K+]o, in the present paper, dynamics and conditions for the uncommon MMB/SD evoked by enhanced inhibitory synaptic current are obtained in a theoretical model. Firstly, in addition to the well-known positive threshold across which the common MMB is induced by positive effect, a spiking pyramidal neuron exhibits a novel negative threshold with a low level of [K+]o for the MMB. A long and strong inhibitory stimulation suppresses the spiking to silence phase via a saddle-node bifurcation on an invariant circle at first and then run across the negative threshold, triggering positive feedback to enhance membrane potential and [K+]o to levels high enough, then resulting in the uncommon MMB. Secondly, in a coupling model, enhanced inhibitory effect for enhanced spiking activity of interneuron and conductance of inhibitory synapse, and enhanced spiking activity of pyramidal neuron, are favorable for the uncommon MMB. Then, reducing these activities or parameters present potential measures to prevent the MMB. Finally, in network model, the uncommon MMB of a pyramidal neuron can induce SD wave. The results present a novel theoretical explanation to the uncommon MMB/SD, counterintuitive function of the inhibitory interneuron, and potential measures to treat the diseases.

Explaining neuronal membrane potentials: The Goldman equation vs. Lee's TELC hypothesis

In two recent papers (Curr Trends Neurol 17: 83-98, 2023; J Neurophysiol 124: 1029-1044, 2020), James Lee has argued that his Transmembrane Electrostatically-Localized Cations (TELC) hypothesis offers a model of neuron transmembrane potentials that is superior to Hodgkin-Huxley classic cable theory and the Goldman-Hodgkin-Katz (GHK) equation. Here we examine critically the arguments in these papers, finding key weaknesses and fallacies. We also examine closely the literature cited by Lee, and find (i) strong support for the GHK equation; (ii) published measurements that contradict TELC predictions; and (iii) no convincing support for the TELC hypothesis.

Analyses of Pore-Size-Dependent Ionic Transport in Nanopores in the Presence of Concentration and Temperature Gradients

Mass transport through nanopores occurs in various natural systems, including the human body. For example, ion transport across nerve cell membranes plays a significant role in neural signal transmission, which can be significantly affected by the electrolyte and temperature conditions. To better understand and control the underlying nanoscopic transport, it is necessary to develop multiphysical transport models as well as validate them using enhanced experimental methods for facile nanopore fabrication and precise nanoscale transport characterization. Here, we report a nanopore-integrated microfluidic platform to characterize ion transport in the presence of electrolyte and temperature gradients; we employ our previous self-assembled particle membrane (SAPM)-integrated microfluidic platform to produce various nanopores with different pore sizes. Subsequently, we quantify pore-size-dependent ionic transport by measuring the short circuit current (SCC) and open circuit voltage (OCV) across various nanopores by manipulating the electrolyte and temperature gradients. We establish three simple theoretical models that heavily depend on pore size, electrolyte concentration, and temperature and subsequently validate them with the experimental results. Finally, we anticipate that the results of this study would help clarify ion transport phenomena at low-temperature conditions, not only providing a fundamental understanding but also enabling practical applications of cryo-anesthesia in the near future.

Chaotic Dynamics Mediate Brain State Transitions, Driven by Changes in Extracellular Ion Concentrations

Previous studies have suggested that changes in extracellular ion concentrations initiate the transition from an activity state that characterizes sleep in cortical neurons to states that characterize wakefulness. However, because neuronal activity and extracellular ion concentrations are interdependent, isolating their unique roles during sleep-wake transitions is not possible in vivo. Here, we extend the Averaged-Neuron model and demonstrate that, although changes in extracellular ion concentrations occur concurrently, decreasing the conductance of calcium-dependent potassium channels initiates the transition from sleep to wakefulness. We find that sleep is governed by stable, self-sustained oscillations in neuronal firing patterns, whereas the quiet awake state and active awake state are both governed by irregular oscillations and chaotic dynamics; transitions between these separable awake states are prompted by ionic changes. Although waking is indicative of a shift from stable to chaotic neuronal firing patterns, we illustrate that the properties of chaotic dynamics ensure that the transition between states is smooth and robust to noise.

Neutral impulsive shunting inhibitory cellular neural networks with time-varying coefficients and leakage delays

In this article, we consider a class of neutral impulsive shunting inhibitory cellular neural networks with time varying coefficients and leakage delays. We study the existence and the exponential stability of the piecewise differentiable pseudo almost-periodic solutions and establish sufficient conditions for the existence and exponential stability of such solutions. An example is provided to illustrate the theory developed in this work.

Effect of different glucose supply conditions on neuronal energy metabolism

The glucose-excited neurons in brain can sense blood glucose levels and reflect different firing states, which are mainly associated with regulation of blood glucose and energy demand in the brain. In this paper, a new model of glucose-excited neuron in hypothalamus is proposed. The firing properties and energy consumption of this type of neuron under conditions of different glucose levels are simulated and analyzed. The results show that the firing rate and firing duration of the neuron both increase with increasing extracellular glucose levels, but the maximum energy power for an AP is reduced. Further study suggests that the neuron firstly absorbs energy substrates (e.g. glucose) from the blood to prepare for the high energy demand of high-frequency spikes.

A new work mechanism on neuronal activity

By re-examining the neuronal activity energy model, we show the inadequacies in the current understanding of the energy consumption associated with neuron activity. Specifically, we show computationally that a neuron first absorbs and then consumes energy during firing action potential, and this result cannot be produced from any current neuron models or biological neural networks. Based on this finding, we provide an explanation for the observation that when neurons are excited in the brain, blood flow increases significantly while the incremental oxygen consumption is very small. We can also explain why external stimulation and perception emergence are synchronized. We also show that negative energy presence in neurons at the sub-threshold state is an essential reason that leads to blood flow incremental response time in the brain rather than neural excitation to delay.