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.
Strong evidence indicates that amyloid beta (Aβ) inflicts its toxicity in Alzheimer’s disease (AD) by promoting uncontrolled elevation of cytosolic Ca2+ in neurons. We have previously shown that synthetic Aβ42 oligomers stimulate abnormal intracellular Ca2+ release from the endoplasmic reticulum stores, suggesting that a similar mechanism of Ca2+ toxicity may be common to the endogenous Aβs oligomers. Here, we use human postmortem brain extracts from AD-affected patients and test their ability to trigger Ca2+ fluxes when injected intracellularly into Xenopus oocytes. Immunological characterization of the samples revealed the elevated content of soluble Aβ oligomers only in samples from AD patients. Intracellular injection of brain extracts from control patients failed to trigger detectable changes in intracellular Ca2+. Conversely, brain extracts from AD patients triggered Ca2+ events consisting of local and global Ca2+ fluorescent transients. Pre-incubation with either the conformation-specific OC antiserum or caffeine completely suppressed the brain extract’s ability to trigger cytosolic Ca2+ events. Computational modeling suggests that these Ca2+ fluxes may impair cells bioenergetic by affecting ATP and ROS production. These results support the hypothesis that Aβ oligomers contained in neurons of AD-affected brains may represent the toxic agents responsible for neuronal malfunctioning and death associated with the disruption of Ca2+ homeostasis.
Oxygen is an essential element for brain activity. The brain is a metabolic engine that requires 20% of the body’s metabolic energy, despite being only 2% of the human body mass [1]. Two thirds of brain’s metabolic energy is dedicated to supporting neural spiking activity. Much of the O2 dependent ATP metabolism in single neurons is used by energetic Na/K-ATPase pumps that transport 3Na+ outwards with 2K+ inward against their concentration gradients for each ATP hydrolyzed [2,3]. However, understanding the relationship between seizures and real-time oxygen dynamics has been restricted by current technical limitations. Computational models can offer insight to help understand the measurements from experiments.
We have performed experiments relating seizure activity at the cellular level with simultaneous real-time O2 microdomain measurements. In this paper, we build a mathematical neuron model that extends the Hodgkin-Huxley formalism containing leak currents for sodium, potassium and chloride ions, transient sodium currents, and delayed rectifier potassium currents. This neuron was embedded within an extracellular space and a simplified glia-endothelium system. The Na+ and K+ ion concentrations as well as extracellular oxygen density were continuously estimated. Hypoxia was modeled by reducing both neuron and glial Na/K-ATPase pump activities.
During seizure events, the extracellular K+ and intracellular Na+ were increased, which further activated the Na/K-ATPase pump activity. Energy (ATP) and O2 demand were simultaneously increased. Therefore, local available [O2] decreased substantially during seizure events, and the apparent O2 debt substantially outlasts the intense electrical activity of a seizure, as shown in Figure Figure1.1. This result is consistent with experimental data [4]. We also observed that hypoxia alone can induce seizure like events, which occurs only in a narrow range of bath oxygen pressure, reflecting experimental observations. Lastly, we reproduced the interplay between excitatory and inhibitory neurons seen in experiments. Our model accounts for the different [O2] levels that we have observed during seizures in pyramidal cell layers vs. inhibitory (oriens lacunosum moleculare) cell layers. Our work suggests the critical importance of modeling extracellular ion concentration and oxygen dynamics to properly understand the underlying mechanisms behind seizure and related phenomena.
Figure 1
Membrane potentials (top trace), extracellular potassium concentration (middle trace), and oxygen density (bottom trace) from a single model neuron during a seizure event. The time course of [O2] debt is qualitatively similar to that observed experimentally. ...
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