The pathological phenomena of seizures and spreading depression have long been considered separate physiological events in the brain. By incorporating conservation of particles and charge, and accounting for the energy required to restore ionic gradients, we extend the classic Hodgkin-Huxley formalism to uncover a unification of neuronal membrane dynamics. By examining the dynamics as a function of potassium and oxygen, we now account for a wide range of neuronal activities, from spikes to seizures, spreading depression (whether high potassium or hypoxia induced), mixed seizure and spreading depression states, and the terminal anoxic "wave of death." Such a unified framework demonstrates that all of these dynamics lie along a continuum of the repertoire of the neuron membrane. Our results demonstrate that unified frameworks for neuronal dynamics are feasible, can be achieved using existing biological structures and universal physical conservation principles, and may be of substantial importance in enabling our understanding of brain activity and in the control of pathological states.

recordings show intense neuronal firing during epileptic seizures leading to enhanced energy consumption. However, the relationship between oxygen metabolism and seizure patterns has not been well studied. Recent studies have developed fast and quantitative techniques to measure oxygen microdomain concentration during seizure events. In this article, we develop a biophysical model that accounts for these experimental observations. The model is an extension of the Hodgkin-Huxley formalism and includes the neuronal microenvironment dynamics of sodium, potassium, and oxygen concentrations. Our model accounts for metabolic energy consumption during and following seizure events. We can further account for the experimental observation that hypoxia can induce seizures, with seizures occurring only within a narrow range of tissue oxygen pressure. We also reproduce the interplay between excitatory and inhibitory neurons seen in experiments, accounting for the different oxygen levels observed during seizures in excitatory vs. inhibitory cell layers. Our findings offer a more comprehensive understanding of the complex interrelationship among seizures, ion dynamics, and energy metabolism.hippocampus; hypoxia; bifurcation; epilepsy; potassium THE BRAIN CONSUMES 20% OF the body's metabolic energy with muscles and digestive system at rest, despite being only 2% of the human body mass (Attwell and Laughlin 2001). The majority of the brain's metabolic energy is dedicated to supporting neural spiking activity, most of which is used by Na ϩ -K ϩ

Sleep is critical for regulation of synaptic efficacy, memories, and learning. However, the underlying mechanisms of how sleep rhythms contribute to consolidating memories acquired during wakefulness remain unclear. Here we studied the role of slow oscillations, 0.2-1 Hz rhythmic transitions between Up and Down states during stage 3/4 sleep, on dynamics of synaptic connectivity in the thalamocortical network model implementing spike-timing-dependent synaptic plasticity. We found that the spatiotemporal pattern of Up-state propagation determines the changes of synaptic strengths between neurons. Furthermore, an external input, mimicking hippocampal ripples, delivered to the cortical network results in input-specific changes of synaptic weights, which persisted after stimulation was removed. These synaptic changes promoted replay of specific firing sequences of the cortical neurons. Our study proposes a neuronal mechanism on how an interaction between hippocampal input, such as mediated by sharp wave-ripple events, cortical slow oscillations, and synaptic plasticity, may lead to consolidation of memories through preferential replay of cortical cell spike sequences during slow-wave sleep.

Sleep plays an important role in consolidation of recent memories. However, the mechanisms of consolidation remain poorly understood. In this study, using a realistic computational model of the thalamocortical network, we demonstrated that sleep spindles (the hallmark of N2 stage sleep) and slow oscillations (the hallmark of N3 stage sleep) both facilitate spike sequence replay as necessary for consolidation. When multiple memories were trained, the local nature of spike sequence replay during spindles allowed replay of the memories independently, while during slow oscillations replay of the weak memory was competing to the strong memory replay. This led to the weak memory extinction unless when sleep spindles (N2 sleep) preceded slow oscillations (N3 sleep), as observed during natural sleep. Our study presents a mechanistic explanation for the role of sleep rhythms in memory consolidation and proposes a testable hypothesis how the natural structure of sleep stages provides an optimal environment to consolidate memories.peer-reviewed) is the author/funder. All rights reserved. No reuse allowed without permission.The copyright holder for this preprint (which was not . http://dx.doi.org/10.1101/153007 doi: bioRxiv preprint first posted online 3 Significant StatementNumerous studies suggest importance of NREM sleep rhythms -spindles and slow oscillations -in sleep related memory consolidation. However, synaptic mechanisms behind the role of these rhythms in memory and learning are still unknown. Our new study predicts that sleep replay -the neuronal substrate of memory consolidation -is organized within the sleep spindles and coordinated by the Down to Up state transitions of the slow oscillation. For multiple competing memories, slow oscillations facilitated only strongest memory replay, while sleep spindles allowed a consolidation of the multiple competing memories independently. Our study predicts how the basic structure of the natural sleep stages provides an optimal environment for consolidation of multiple memories.peer-reviewed)

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynamics. By incorporating cell swelling together with dynamic ion concentrations and oxygen supply into Hodgkin-Huxley type spiking dynamics, we demonstrate the spontaneous transition between epileptic seizure and spreading depression states as the cell swells and contracts in response to changes in osmotic pressure. Our use of volume as an order parameter further revealed a dynamical definition for the experimentally described physiological ceiling that separates seizure from spreading depression, as well as predicted a second ceiling that demarcates spreading depression from anoxic depolarization. Our model highlights the neuroprotective role of glial K buffering against seizures and spreading depression, and provides novel insights into anoxic depolarization and the relevant cell swelling during ischemia. We argue that the dynamics of seizures, spreading depression, and anoxic depolarization lie along a continuum of the repertoire of the neuron membrane that can be understood only when the dynamic ion concentrations, oxygen homeostasis,and cell swelling in response to osmotic pressure are taken into consideration. Our results demonstrate the feasibility of a unified framework for a wide range of neuronal behaviors that may be of substantial importance in the understanding of and potentially developing universal intervention strategies for these pathological states.