Assimilating Seizure Dynamics

Observability of a dynamical system requires an understanding of its state—the collective values of its variables. However, existing techniques are too limited to measure all but a small fraction of the physical variables and parameters of neuronal networks. We constructed models of the biophysical properties of neuronal membrane, synaptic, and microenvironment dynamics, and incorporated them into a model-based predictor-controller framework from modern control theory. We demonstrate that it is now possible to meaningfully estimate the dynamics of small neuronal networks using as few as a single measured variable. Specifically, we assimilate noisy membrane potential measurements from individual hippocampal neurons to reconstruct the dynamics of networks of these cells, their extracellular microenvironment, and the activities of different neuronal types during seizures. We use reconstruction to account for unmeasured parts of the neuronal system, relating micro-domain metabolic processes to cellular excitability, and validate the reconstruction of cellular dynamical interactions against actual measurements. Data assimilation, the fusing of measurement with computational models, has significant potential to improve the way we observe and understand brain dynamics

Simplification of Reversible Markov Chains by Removal of States With Low Equilibrium Occupancy

We present a practical method for simplifying Markov chains on a potentially large state space when detailed balance holds. A simple and transparent technique is introduced to remove states with low equilibrium occupancy. The resulting system has fewer parameters. The resulting effective rates between the remaining nodes give dynamics identical to the original system’s except on very fast timescales. This procedure amounts to using separation of timescales to neglect small capacitance nodes in a network of resistors and capacitors. We illustrate the technique by simplifying various reaction networks, including transforming an acyclic four-node network to a three-node cyclic network. For a reaction step in which a ligand binds, the law of mass action implies a forward rate proportional to ligand concentration. The effective rates in the simplified network are found to be rational functions of ligand concentratio

Questioning Glutamate Excitotoxicity in Acute Brain Damage: The Importance of Spreading Depolarization

Background Within 2 min of severe ischemia, spreading depolarization (SD) propagates like a wave through compromised gray matter of the higher brain. More SDs arise over hours in adjacent tissue, expanding the neuronal damage. This period represents a therapeutic window to inhibit SD and so reduce impending tissue injury. Yet most neuroscientists assume that the course of early brain injury can be explained by glutamate excitotoxicity, the concept that immediate glutamate release promotes early and downstream brain injury. There are many problems with glutamate release being the unseen culprit, the most practical being that the concept has yielded zero therapeutics over the past 30 years. But the basic science is also flawed, arising from dubious foundational observations beginning in the 1950s Methods Literature pertaining to excitotoxicity and to SD over the past 60 years is critiqued. Results Excitotoxicity theory centers on the immediate and excessive release of glutamate with resulting neuronal hyperexcitation. This instigates poststroke cascades with subsequent secondary neuronal injury. By contrast, SD theory argues that although SD evokes some brief glutamate release, acute neuronal damage and the subsequent cascade of injury to neurons are elicited by the metabolic stress of SD, not by excessive glutamate release. The challenge we present here is to find new clinical targets based on more informed basic science. This is motivated by the continuing failure by neuroscientists and by industry to develop drugs that can reduce brain injury following ischemic stroke, traumatic brain injury, or sudden cardiac arrest. One important step is to recognize that SD plays a central role in promoting early neuronal damage. We argue that uncovering the molecular biology of SD initiation and propagation is essential because ischemic neurons are usually not acutely injured unless SD propagates through them. The role of glutamate excitotoxicity theory and how it has shaped SD research is then addressed, followed by a critique of its fading relevance to the study of brain injury. Conclusions Spreading depolarizations better account for the acute neuronal injury arising from brain ischemia than does the early and excessive release of glutamate

The Critical Role of Spreading Depolarizations in Early Brain Injury: Consensus and Contention

Background: When a patient arrives in the emergency department following a stroke, a traumatic brain injury, or sudden cardiac arrest, there is no therapeutic drug available to help protect their jeopardized neurons. One crucial reason is that we have not identified the molecular mechanisms leading to electrical failure, neuronal swelling, and blood vessel constriction in newly injured gray matter. All three result from a process termed spreading depolarization (SD). Because we only partially understand SD, we lack molecular targets and biomarkers to help neurons survive after losing their blood flow and then undergoing recurrent SD. Methods: In this review, we introduce SD as a single or recurring event, generated in gray matter following lost blood flow, which compromises the Na+/K+ pump. Electrical recovery from each SD event requires so much energy that neurons often die over minutes and hours following initial injury, independent of extracellular glutamate. Results: We discuss how SD has been investigated with various pitfalls in numerous experimental preparations, how overtaxing the Na+/K+ ATPase elicits SD. Elevated K+ or glutamate are unlikely natural activators of SD. We then turn to the properties of SD itself, focusing on its initiation and propagation as well as on computer modeling. Conclusions: Finally, we summarize points of consensus and contention among the authors as well as where SD research may be heading. In an accompanying review, we critique the role of the glutamate excitotoxicity theory, how it has shaped SD research, and its questionable importance to the study of early brain injury as compared with SD theory. © 2022, The Author(s)

Reduced Cooperativity of Voltage-gated Sodium Channels in the Hippocampal Interneurons of an Aged Mouse Model of Alzheimer’s Disease

Beta amyloid (Aβ role= presentation style= box-sizing: inherit; display: inline; line-height: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative; \u3eββ ) associated with Alzheimer’s disease (AD) leads to abnormal behavior in inhibitory neurons, resulting in hyperactive neuronal networks, epileptiform behavior, disrupted gamma rhythms, and aberrant synaptic plasticity. Previously, we used a dual modeling-experimental approach to explain several observations, including failure to reliably produce action potentials (APs), smaller AP amplitudes, higher resting membrane potential, and higher membrane depolarization in response to a range of stimuli in hippocampal inhibitory neurons from 12- to 16-month-old female AP Pswe/PSEN1DeltaE9 (APdE9) AD mice as compared to age-matched non-transgenic (NTG) mice. Our experimental results also showed that AP initiation in interneurons from APdE9 mice are significantly different from that of NTG mice. APs in interneurons from NTG mice are characterized by abrupt onset and an upstroke that is much steeper and occurs with larger variability as compared to cells from APdE9 mice. The phase plot (the rate of change of membrane potential versus the instantaneous membrane potential) of APs produced by interneurons from APdE9 mice shows a biphasic behavior, whereas that from NTG mice shows a monophasic behavior. Here we show that using the classic Hodgkin–Huxley (HH) formalism for the gating of voltage-gated sodium channels (VGSCs) in a single-compartment neuron, we cannot reproduce these features, and a model that takes into account a cooperative activation of VGSCs is needed. We also argue that considering a realistic multi-compartment neuron where the kinetics of VGSC is modeled by HH formalism, as done in the past, would not explain our observations when APs from both NTG and APdE9 mice are considered simultaneously. We further show that VGSCs in interneurons from APdE9 mice exhibit significantly lower cooperativity in their activation as compared to those from NTG mice

Anions Govern Cell Volume: A Case Study of Relative Astrocytic and Neuronal Swelling in Spreading Depolarization

Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little about the dynamics of cell and tissue swelling, and the differential changes in the volumes of neurons and glia during pathological states such as spreading depolarizations (SD) under ischemic and non–ischemic conditions, and epileptic seizures. By combining the Hodgkin–Huxley type spiking dynamics, dynamic ion concentrations, and simultaneous neuronal and astroglial volume changes into a comprehensive model, we elucidate why glial cells swell more than neurons in SD and the special case of anoxic depolarization (AD), and explore the relative contributions of the two cell types to tissue swelling. Our results demonstrate that anion channels, particularly Cl−, are intrinsically connected to cell swelling and blocking these currents prevents changes in cell volume. The model is based on a simple and physiologically realistic description. We introduce model extensions that are either derived purely from first physical principles of electroneutrality, osmosis, and conservation of particles, or by a phenomenological combination of these principles and known physiological facts. This work provides insights into numerous studies related to neuronal and glial volume changes in SD that otherwise seem contradictory, and is broadly applicable to swelling in other cell types and conditions