Mitochondrial dysfunction and role in spreading depolarization and seizure

Abstract

The effect of pathological phenomena such as epileptic seizures and spreading depolarization (SD) on mitochondria and the potential feedback of mitochondrial dysfunction into the dynamics of those phenomena are complex and difficult to study experimentally due to the simultaneous changes in many variables governing neuronal behavior. By combining a model that accounts for a wide range of neuronal behaviors including seizures, normoxic SD, and hypoxic SD (HSD), together with a detailed model of mitochondrial function and intracellular Ca²⁺ dynamics, we investigate mitochondrial dysfunction and its potential role in recovery of the neuron from seizures, HSD, and SD. Our results demonstrate that HSD leads to the collapse of mitochondrial membrane potential and cellular ATP levels that recover only when normal oxygen supply is restored. Mitochondrial organic phosphate and pH gradients determine the strength of the depolarization block during HSD and SD, how quickly the cell enters the depolarization block when the oxygen supply is disrupted or potassium in the bath solution is raised beyond the physiological value, and how fast the cell recovers from SD and HSD when normal potassium concentration and oxygen supply are restored. Although not as dramatic as phosphate and pH gradients, mitochondrial Ca²⁺ uptake has a similar effect on neuronal behavior during these conditions.

Spontaneous synaptic drive in detrusor smooth muscle: computational investigation and implications for urinary bladder function

Abstract

The detrusor, a key component of the urinary bladder wall, is a densely innervated syncytial smooth muscle tissue. Random spontaneous release of neurotransmitter at neuromuscular junctions (NMJs) in the detrusor gives rise to spontaneous excitatory junction potentials (SEJPs). These sub-threshold passive signals not only offer insights into the syncytial nature of the tissue, their spatio-temporal integration is critical to the generation of spontaneous neurogenic action potentials which lead to focal contractions during the filling phase of the bladder. Given the structural complexity and the contractile nature of the tissue, electrophysiological investigations on spatio-temporal integration of SEJPs in the detrusor are technically challenging. Here we report a biophysically constrained computational model of a detrusor syncytium overlaid with spatially distributed innervation, using which we explored salient features of the integration of SEJPs in the tissue and the key factors that contribute to this integration. We validated our model against experimental data, ascertaining that observations were congruent with theoretical predictions. With the help of comparative studies, we propose that the amplitude of the spatio-temporally integrated SEJP is most sensitive to the inter-cellular coupling strength in the detrusor, while frequency of observed events depends more strongly on innervation density. An experimentally testable prediction arising from our study is that spontaneous release frequency of neurotransmitter may be implicated in the generation of detrusor overactivity. Set against histological observations, we also conjecture possible changes in the electrical activity of the detrusor during pathology involving patchy denervation. Our model thus provides a physiologically realistic, heuristic framework to investigate the spread and integration of passive potentials in an innervated syncytial tissue under normal conditions and in pathophysiology.

A novel neural computational model of generalized periodic discharges in acute hepatic encephalopathy

Abstract

Acute hepatic encephalopathy (AHE) due to acute liver failure is a common form of delirium, a state of confusion, impaired attention, and decreased arousal. The electroencephalogram (EEG) in AHE often exhibits a striking abnormal pattern of brain activity, which epileptiform discharges repeat in a regular repeating pattern. This pattern is known as generalized periodic discharges, or triphasic-waves (TPWs). While much is known about the neurophysiological mechanisms underlying AHE, how these mechanisms relate to TPWs is poorly understood. In order to develop hypotheses how TPWs arise, our work builds a computational model of AHE (AHE-CM), based on three modifications of the well-studied Liley model which emulate mechanisms believed central to brain dysfunction in AHE: increased neuronal excitability, impaired synaptic transmission, and enhanced postsynaptic inhibition. To relate our AHE-CM to clinical EEG data from patients with AHE, we design a model parameter optimization method based on particle filtering (PF-POM). Based on results from 7 AHE patients, we find that the proposed AHE-CM not only performs well in reproducing important aspects of the EEG, namely the periodicity of triphasic waves (TPWs), but is also helpful in suggesting mechanisms underlying variation in EEG patterns seen in AHE. In particular, our model helps explain what conditions lead to increased frequency of TPWs. In this way, our model represents a starting point for exploring the underlying mechanisms of brain dynamics in delirium by relating microscopic mechanisms to EEG patterns.

Reducing variability in motor cortex activity at a resting state by extracellular GABA for reliable perceptual decision-making

Abstract

Interaction between sensory and motor cortices is crucial for perceptual decision-making, in which intracortical inhibition might have an important role. We simulated a neural network model consisting of a sensory network (N_S) and a motor network (N_M) to elucidate the significance of their interaction in perceptual decision-making in association with the level of GABA in extracellular space: extracellular GABA concentration. Extracellular GABA molecules acted on extrasynaptic receptors embedded in membranes of pyramidal cells and suppressed them. A reduction in extracellular GABA concentration either in N_S or N_M increased the rate of errors in perceptual decision-making, for which an increase in ongoing-spontaneous fluctuations in subthreshold neuronal activity in N_M prior to sensory stimulation was responsible. Feedback (N_M-to-N_S) signaling enhanced selective neuronal responses in N_S, which in turn increased stimulus-evoked neuronal activity in N_M. We suggest that GABA in extracellular space contributes to reducing variability in motor cortex activity at a resting state and thereby the motor cortex can respond correctly to a subsequent sensory stimulus. Feedback signaling from the motor cortex improves the selective responsiveness of the sensory cortex, which ensures the fidelity of information transmission to the motor cortex, leading to reliable perceptual decision-making.

Modeling cortical spreading depression induced by the hyperactivity of interneurons

Abstract

Cortical spreading depression (CSD) is a wave of transient intense neuronal firing leading to a long lasting depolarizing block of neuronal activity. It is a proposed pathological mechanism of migraine with aura. Some forms of migraine are associated with a genetic mutation of the Na_v1.1 channel, resulting in its gain of function and implying hyperexcitability of interneurons. This leads to the counterintuitive hypothesis that intense firing of interneurons can cause CSD ignition. To test this hypothesis in silico, we developed a computational model of an E-I pair (a pyramidal cell and an interneuron), in which the coupling between the cells in not just synaptic, but takes into account also the effects of the accumulation of extracellular potassium caused by the activity of the neurons and of the synapses. In the context of this model, we show that the intense firing of the interneuron can lead to CSD. We have investigated the effect of various biophysical parameters on the transition to CSD, including the levels of glutamate or GABA, frequency of the interneuron firing and the efficacy of the KCC2 co-transporter. The key element for CSD ignition in our model was the frequency of interneuron firing and the related accumulation of extracellular potassium, which induced a depolarizing block of the pyramidal cell. This constitutes a new mechanism of CSD ignition.

Reduced order models of myelinated axonal compartments

Abstract

The paper presents a hierarchical series of computational models for myelinated axonal compartments. Three classes of models are considered, either with distributed parameters (2.5D EQS–ElectroQuasi Static, 1D TL-Transmission Lines) or with lumped parameters (0D). They are systematically analyzed with both analytical and numerical approaches, the main goal being to identify the best procedure for order reduction of each case. An appropriate error estimator is proposed in order to assess the accuracy of the models. This is the foundation of a procedure able to find the simplest reduced model having an imposed precision. The most computationally efficient model from the three geometries proved to be the analytical 1D one, which is able to have accuracy less than 0.1%. By order reduction with vector fitting, a finite model is generated with a relative difference of 10^− 4 for order 5. The dynamical models thus extracted allow an efficient simulation of neurons and, consequently, of neuronal circuits. In such situations, the linear models of the myelinated compartments coupled with the dynamical, non-linear models of the Ranvier nodes, neuronal body (soma) and dendritic tree give global reduced models. In order to ease the simulation of large-scale neuronal systems, the sub-models at each level, including those of myelinated compartments should have the lowest possible order. The presented procedure is a first step in achieving simulations of neural systems with accuracy control.

Analyzing dynamic decision-making models using Chapman-Kolmogorov equations

Abstract

Decision-making in dynamic environments typically requires adaptive evidence accumulation that weights new evidence more heavily than old observations. Recent experimental studies of dynamic decision tasks require subjects to make decisions for which the correct choice switches stochastically throughout a single trial. In such cases, an ideal observer’s belief is described by an evolution equation that is doubly stochastic, reflecting stochasticity in the both observations and environmental changes. In these contexts, we show that the probability density of the belief can be represented using differential Chapman-Kolmogorov equations, allowing efficient computation of ensemble statistics. This allows us to reliably compare normative models to near-normative approximations using, as model performance metrics, decision response accuracy and Kullback-Leibler divergence of the belief distributions. Such belief distributions could be obtained empirically from subjects by asking them to report their decision confidence. We also study how response accuracy is affected by additional internal noise, showing optimality requires longer integration timescales as more noise is added. Lastly, we demonstrate that our method can be applied to tasks in which evidence arrives in a discrete, pulsatile fashion, rather than continuously.

Introducing double bouquet cells into a modular cortical associative memory model

Abstract

We present an electrophysiological model of double bouquet cells and integrate them into an established cortical columnar microcircuit model that has previously been used as a spiking attractor model for memory. Learning in that model relies on a Hebbian-Bayesian learning rule to condition recurrent connectivity between pyramidal cells. We here demonstrate that the inclusion of a biophysically plausible double bouquet cell model can solve earlier concerns about learning rules that simultaneously learn excitation and inhibition and might thus violate Dale’s principle. We show that learning ability and resulting effective connectivity between functional columns of previous network models is preserved when pyramidal synapses onto double bouquet cells are plastic under the same Hebbian-Bayesian learning rule. The proposed architecture draws on experimental evidence on double bouquet cells and effectively solves the problem of duplexed learning of inhibition and excitation by replacing recurrent inhibition between pyramidal cells in functional columns of different stimulus selectivity with a plastic disynaptic pathway. We thus show that the resulting change to the microcircuit architecture improves the model’s biological plausibility without otherwise impacting the model’s spiking activity, basic operation, and learning abilities.

Modeling grid fields instead of modeling grid cells

Abstract

A neuron’s firing correlates are defined as the features of the external world to which its activity is correlated. In many parts of the brain, neurons have quite simple such firing correlates. A striking example are grid cells in the rodent medial entorhinal cortex: their activity correlates with the animal’s position in space, defining ‘grid fields’ arranged with a remarkable periodicity. Here, we show that the organization and evolution of grid fields relate very simply to physical space. To do so, we use an effective model and consider grid fields as point objects (particles) moving around in space under the influence of forces. We reproduce several observations on the geometry of grid patterns. This particle-like behavior is particularly salient in a recent experiment in which two separate grid patterns merge. We discuss pattern formation in the light of known results from physics of two-dimensional colloidal systems. Notably, we study the limitations of the widely used ‘gridness score’ and show how physics of 2d systems could be a source of inspiration, both for data analysis and computational modeling. Finally, we draw the relationship between our ‘macroscopic’ model for grid fields and existing ‘microscopic’ models of grid cell activity and discuss how a description at the level of grid fields allows to put constraints on the underlying grid cell network.