Dynamic transition of neuronal firing induced by abnormal astrocytic glutamate oscillation

The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence

Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.

A computational model to uncover the biophysical underpinnings of neural firing heterogeneity in dissociated hippocampal cultures

Calcium (Ca2+ ) imaging reveals a variety of correlated firing in cultures of dissociated hippocampal neurons, pinpointing the non-synaptic paracrine release of glutamate as a possible mediator for such firing patterns, although the biophysical underpinnings remain unknown. An intriguing possibility is that extracellular glutamate could bind metabotropic receptors linked with inositol trisphosphate (IP3 ) mediated release of Ca2+ from the endoplasmic reticulum of individual neurons, thereby modulating neural activity in combination with sarco/endoplasmic reticulum Ca2+ transport ATPase (SERCA) and voltage-gated Ca2+ channels (VGCC). However, the possibility that such release may occur in different neuronal compartments and can be inherently stochastic poses challenges in the characterization of such interplay between various Ca2+ channels. Here we deploy biophysical modeling in association with Monte Carlo parameter sampling to characterize such interplay and successfully predict experimentally observed Ca2+ patterns. The results show that the neurotransmitter level at the plasma membrane is the extrinsic source of heterogeneity in somatic Ca2+ transients. Our analysis, in particular, identifies the origin of such heterogeneity to an intrinsic differentiation of hippocampal neurons in terms of multiple cellular properties pertaining to intracellular Ca2+ signaling, such as VGCC, IP3 receptor, and SERCA expression. In the future, the biophysical model and parameter estimation approach used in this study can be upgraded to predict the response of a system of interconnected neurons.

Astrocytic modulation of neuronal signalling

Neuronal signalling is a key element in neuronal communication and is essential for the proper functioning of the CNS. Astrocytes, the most prominent glia in the brain play a key role in modulating neuronal signalling at the molecular, synaptic, cellular, and network levels. Over the past few decades, our knowledge about astrocytes and their functioning has evolved from considering them as merely a brain glue that provides structural support to neurons, to key communication elements. Astrocytes can regulate the activity of neurons by controlling the concentrations of ions and neurotransmitters in the extracellular milieu, as well as releasing chemicals and gliotransmitters that modulate neuronal activity. The aim of this review is to summarise the main processes through which astrocytes are modulating brain function. We will systematically distinguish between direct and indirect pathways in which astrocytes affect neuronal signalling at all levels. Lastly, we will summarize pathological conditions that arise once these signalling pathways are impaired focusing on neurodegeneration.

Transition behavior of the seizure dynamics modulated by the astrocyte inositol triphosphate noise

Epilepsy is a neurological disorder with recurrent seizures, which convey complex dynamical characteristics including chaos and randomness. Until now, the underlying mechanism has not been fully elucidated, especially the bistable property beneath the epileptic random induction phenomena in certain conditions. Inspired by the recent finding that astrocyte GTPase-activating protein (G-protein)-coupled receptors could be involved in stochastic epileptic seizures, we proposed a neuron-astrocyte network model, incorporating the noise of the astrocytic second messenger, inositol triphosphate (IP3) that is modulated by G-protein-coupled receptor activation. Based on this model, we have statistically analyzed the transitions of epileptic seizures by performing repeatable simulation trials. Our simulation results show that the increase in the IP3 noise intensity induces depolarization-block epileptic seizures together with an increase in neuronal firing frequency, consistent with corresponding experiments. Meanwhile, the bistable states of the seizure dynamics were present under certain noise intensities, during which the neuronal firing pattern switches between regular sparse spiking and epileptic seizure states. This random presence of epileptic seizures is absent when the noise intensity continues to increase, accompanying with an increase in the epileptic depolarization block duration. The simulation results also shed light on the fact that calcium signals in astrocytes play significant roles in the pattern formations of the epileptic seizure. Our results provide a potential pathway for understanding the epileptic randomness in certain conditions.

Astrocytic modulation on neuronal electric mode selection induced by magnetic field effect

Astrocytes as well as electromagnetic induction have been primarily considered as main factors in regulating neuronal firing patterns in the recent decade. In this work, an improved neuron-astrocyte model in consideration of the modulation of astrocytes and the electromagnetic induction is employed to explore the extend to which both of the factors affect the firing modes of the neurons. The "alternation mode", defined as the alternative of neural normal spiking mode with the high-frequency bursting-like mode, clearly shows the functions of astrocytes on neurons. Moreover, the firing pattern of the neuron becomes more abnormal when astrocytes are hyper-excitable, the reason why the abnormal coupling of the astrocyte leads to the "alternation mode" of the neuron have been studied. In addition, the effect of electromagnetic induction manifests nonlinear characteristic towards neurons, complex firing modes of neurons are observed in the weaker field and a switching mode consists with quiescent and spiking mode appears when there is a higher stronger field. This approved model can reveal the normal or abnormal electric activities of neuron considered electromagnetic induction induced by the degree of excitability of the astrocyte. These results can provide potential understanding about the effects of astrocyte on neuronal activity when the coupling of electromagnetic field is considered.

A Computational Study of Astrocytic GABA Release at the Glutamatergic Synapse: EAAT-2 and GAT-3 Coupled Dynamics

Neurotransmitter dynamics within neuronal synapses can be controlled by astrocytes and reflect key contributors to neuronal activity. In particular, Glutamate (Glu) released by activated neurons is predominantly removed from the synaptic space by perisynaptic astrocytic transporters EAAT-2 (GLT-1). In previous work, we showed that the time course of Glu transport is affected by ionic concentration gradients either side of the astrocytic membrane and has the propensity for influencing postsynaptic neuronal excitability. Experimental findings co-localize GABA transporters GAT-3 with EAAT-2 on the perisynaptic astrocytic membrane. While these transporters are unlikely to facilitate the uptake of synaptic GABA, this paper presents simulation results which demonstrate the coupling of EAAT-2 and GAT-3, giving rise to the ionic-dependent reversed transport of GAT-3. The resulting efflux of GABA from the astrocyte to the synaptic space reflects an important astrocytic mechanism for modulation of hyperexcitability. Key results also illustrate an astrocytic-mediated modulation of synaptic neuronal excitation by released GABA at the glutamatergic synapse.

Dysregulation of Ambient Glutamate and Glutamate Receptors in Epilepsy: An Astrocytic Perspective

Given the important functions that glutamate serves in excitatory neurotransmission, understanding the regulation of glutamate in physiological and pathological states is critical to devising novel therapies to treat epilepsy. Exclusive expression of pyruvate carboxylase and glutamine synthetase in astrocytes positions astrocytes as essential regulators of glutamate in the central nervous system (CNS). Additionally, astrocytes can significantly alter the volume of the extracellular space (ECS) in the CNS due to their expression of the bi-directional water channel, aquaporin-4, which are enriched at perivascular endfeet. Rapid ECS shrinkage has been observed following epileptiform activity and can inherently concentrate ions and neurotransmitters including glutamate. This review highlights our emerging knowledge on the various potential contributions of astrocytes to epilepsy, particularly supporting the notion that astrocytes may be involved in seizure initiation via failure of homeostatic responses that lead to increased ambient glutamate. We also review the mechanisms whereby ambient glutamate can influence neuronal excitability, including via generation of the glutamate receptor subunit GluN2B-mediated slow inward currents, as well as indirectly affect neuronal excitability via actions on metabotropic glutamate receptors that can potentiate GluN2B currents and influence neuronal glutamate release probabilities. Additionally, we discuss evidence for upregulation of System x c - , a cystine/glutamate antiporter expressed on astrocytes, in epileptic tissue and changes in expression patterns of glutamate receptors.

Dynamic Transitions in Neuronal Network Firing Sustained by Abnormal Astrocyte Feedback

Astrocytes play a crucial role in neuronal firing activity. Their abnormal state may lead to the pathological transition of neuronal firing patterns and even induce seizures. However, there is still little evidence explaining how the astrocyte network modulates seizures caused by structural abnormalities, such as gliosis. To explore the role of gliosis of the astrocyte network in epileptic seizures, we first established a direct astrocyte feedback neuronal network model on the basis of the hippocampal CA3 neuron-astrocyte model to simulate the condition of gliosis when astrocyte processes swell and the feedback to neurons increases in an abnormal state. We analyzed the firing pattern transitions of the neuronal network when astrocyte feedback starts to change via increases in both astrocyte feedback intensity and the connection probability of astrocytes to neurons in the network. The results show that as the connection probability and astrocyte feedback intensity increase, neuronal firing transforms from a nonepileptic synchronous firing state to an asynchronous firing state, and when astrocyte feedback starts to become abnormal, seizure-like firing becomes more severe and synchronized; meanwhile, the synchronization area continues to expand and eventually transforms into long-term seizure-like synchronous firing. Therefore, our results prove that astrocyte feedback can regulate the firing of the neuronal network, and when the astrocyte network develops gliosis, there will be an increase in the induction rate of epileptic seizures.

Dynamic Transitions of Epilepsy Waveforms Induced by Astrocyte Dysfunction and Electrical Stimulation

Experimental studies have shown that astrocytes participate in epilepsy through inducing the release of glutamate. Meanwhile, considering the disinhibition circuit among inhibitory neuronal populations with different time scales and the feedforward inhibition connection from thalamic relay nucleus to cortical inhibitory neuronal population, here, we propose a modified thalamocortical field model to systematically investigate the mechanism of epilepsy. Firstly, our results show that rich firing activities can be induced by astrocyte dysfunction, including high or low saturated state, high- or low-frequency clonic, spike-wave discharge (SWD), and tonic. More importantly, with the enhancement of feedforward inhibition connection, SWD and tonic oscillations will disappear. In other words, all these pathological waveforms can be suppressed or eliminated. Then, we explore the control effects after different external stimulations applying to thalamic neuronal population. We find that single-pulse stimulation can not only suppress but also induce pathological firing patterns, such as SWD, tonic, and clonic oscillations. And we further verify that deep brain stimulation can control absence epilepsy by regulating the amplitude and pulse width of stimulation. In addition, based on our modified model, 3 : 2 coordinated reset stimulation strategies with different intensities are compared and a more effective and safer stimulation mode is proposed. Our conclusions are expected to give more theoretical insights into the treatment of epilepsy.

A Computational Model to Investigate GABA-Activated Astrocyte Modulation of Neuronal Excitation

Gamma-aminobutyric acid (GABA) is critical for proper neural network function and can activate astrocytes to induce neuronal excitability; however, the mechanism by which astrocytes transform inhibitory signaling to excitatory enhancement remains unclear. Computational modeling can be a powerful tool to provide further understanding of how GABA-activated astrocytes modulate neuronal excitation. In the present study, we implemented a biophysical neuronal network model to investigate the effects of astrocytes on excitatory pre- and postsynaptic terminals following exposure to increasing concentrations of external GABA. The model completely describes the effects of GABA on astrocytes and excitatory presynaptic terminals within the framework of glutamatergic gliotransmission according to neurophysiological findings. Utilizing this model, our results show that astrocytes can rapidly respond to incoming GABA by inducing Ca²⁺ oscillations and subsequent gliotransmitter glutamate release. Elevation in GABA concentrations not only naturally decreases neuronal spikes but also enhances astrocytic glutamate release, which leads to an increase in astrocyte-mediated presynaptic release and postsynaptic slow inward currents. Neuronal excitation induced by GABA-activated astrocytes partly counteracts the inhibitory effect of GABA. Overall, the model helps to increase knowledge regarding the involvement of astrocytes in neuronal regulation using simulated bath perfusion of GABA, which may be useful for exploring the effects of GABA-type antiepileptic drugs.

Winfree loop sustained oscillation in two-dimensional excitable lattices: Prediction and realization

The problem of self-sustained oscillations in excitable complex networks is the central issue under investigation, among which the prediction and the realization of self-sustained oscillations in different kinds of excitable networks are the challenging tasks. In this paper, we extensively investigate the prediction and the realization of a Winfree loop sustained oscillation (WLSO) in two-dimensional (2D) excitable lattices. By analyzing the network structure, the fundamental oscillation source structure (FOSS) of WLSO in a 2D excitable lattice is exposed explicitly. For the suitable combinations of system parameters, the Winfree loop can self-organize on the FOSS to form an oscillation source sustaining the oscillation, and these suitable parameter combinations are predicted by calculating the minimum Winfree loop length and have been further confirmed in numerical simulations. However, the FOSS cannot spontaneously offer the WLSO in 2D excitable lattices in usual cases due to the coupling bidirectionality and the symmetry properties of the lattice. A targeted protection scheme of the oscillation source is proposed by overcoming these two drawbacks. Finally, the WLSO is realized in the 2D excitable lattice successfully.

Bifurcation analysis and diverse firing activities of a modified excitable neuron model

Electrical activities of excitable cells produce diverse spiking-bursting patterns. The dynamics of the neuronal responses can be changed due to the variations of ionic concentrations between outside and inside the cell membrane. We investigate such type of spiking-bursting patterns under the effect of an electromagnetic induction on an excitable neuron model. The effect of electromagnetic induction across the membrane potential can be considered to analyze the collective behavior for signal processing. The paper addresses the issue of the electromagnetic flow on a modified Hindmarsh-Rose model (H-R) which preserves biophysical neurocomputational properties of a class of neuron models. The different types of firing activities such as square wave bursting, chattering, fast spiking, periodic spiking, mixed-mode oscillations etc. can be observed using different injected current stimulus. The improved version of the model includes more parameter sets and the multiple electrical activities are exhibited in different parameter regimes. We perform the bifurcation analysis analytically and numerically with respect to the key parameters which reveals the properties of the fast-slow system for neuronal responses. The firing activities can be suppressed/enhanced using the different external stimulus current and by allowing a noise induced current. To study the electrical activities of neural computation, the improved neuron model is suitable for further investigation.

Assessing the Effects of Opioids on Pathological Memory by a Computational Model

Introduction:

Opioids hijack learning and memory formation mechanisms of brain and induce a pathological memory in the hippocampus. This effect is mainly mediated by modifications in glutamatergic system. Speaking more precisely, Opioids presence in a synapse inhibits blockage of N-Methyl-D-Aspartate Receptor (NMDAR) by Mg²⁺, enhances conductance of NMDAR and thus, induces false Long-Term Potentiation (LTP).

Methods:

Based on experimental observations of different researchers, we developed a mathematical model for a pyramidal neuron of the hippocampus to study this false LTP. The model contains a spine of the pyramidal neuron with NMDAR, α-Amino-3-hydroxy-5-Methyl-4-isoxazole Propionic Acid Receptors (AMPARs), and Voltage-Gated Calcium Channels (VGCCs). The model also describes Calmodulin-dependent protein Kinase II (CaMKII) and AMPAR phosphorylation processes which are assumed to be the indicators of LTP induction in the synapse.

Results:

Simulation results indicate that the effect of inhibition of blockage of NMDARs by Mg²⁺ on the false LTP is not as crucial as the effect of NMDAR’s conductance modification by opioids. We also observed that activation of VGCCs has a dominant role in inducing pathological LTP.

Conclusion:

Our results confirm that preventing this pathological LTP is possible by three different mechanisms: 1. By decreasing NMDAR’s conductance; and 2. By attenuating VGCC’s mediated current; and 3. By enhancing glutamate clearance rate from the synapse.

A computational study of astrocytic glutamate influence on post-synaptic neuronal excitability

The ability of astrocytes to rapidly clear synaptic glutamate and purposefully release the excitatory transmitter is critical in the functioning of synapses and neuronal circuits. Dysfunctions of these homeostatic functions have been implicated in the pathology of brain disorders such as mesial temporal lobe epilepsy. However, the reasons for these dysfunctions are not clear from experimental data and computational models have been developed to provide further understanding of the implications of glutamate clearance from the extracellular space, as a result of EAAT2 downregulation: although they only partially account for the glutamate clearance process. In this work, we develop an explicit model of the astrocytic glutamate transporters, providing a more complete description of the glutamate chemical potential across the astrocytic membrane and its contribution to glutamate transporter driving force based on thermodynamic principles and experimental data. Analysis of our model demonstrates that increased astrocytic glutamate content due to glutamine synthetase downregulation also results in increased postsynaptic quantal size due to gliotransmission. Moreover, the proposed model demonstrates that increased astrocytic glutamate could prolong the time course of glutamate in the synaptic cleft and enhances astrocyte-induced slow inward currents, causing a disruption to the clarity of synaptic signalling and the occurrence of intervals of higher frequency postsynaptic firing. Overall, our work distilled the necessity of a low astrocytic glutamate concentration for reliable synaptic transmission of information and the possible implications of enhanced glutamate levels as in epilepsy.

The role of astrocytes in the excitability and hyperexcitability of neurons is a subject which has gained a lot of attention, particularly in the pathology of neurological disorders including epilepsy. Although not completely understood, the control of glutamate homeostasis is believed to play a role in paroxysmal neuronal hyperexcitability known to precede seizure activity. We have developed a computational model which explores two of the astrocytic homeostatic mechanisms, namely glutamate clearance and gliotransmission, and connect them with a common controlling factor, astrocytic cytoplasmic glutamate concentration. In our model simulations we demonstrate both a slower clearance rate of synaptic glutamate and enhanced astrocytic glutamate release where cytoplasmic glutamate is elevated, both of which contribute to high frequency neuronal firing and conditions for seizure generation. We also describe a viable role for astrocytes as a “high pass” filter, where astrocytic activation in the form of intracellular calcium oscillations is possible for only a certain range of presynaptic neuronal firing rates, the lower bound of the range being reduced where astrocytic glutamate is elevated. In physiological terms this perhaps indicates not only neuronal but also astrocytic glutamate-mediated excitation in the neural-astrocytic network.

Computational Models for Calcium-Mediated Astrocyte Functions

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

Minimum Winfree loop determines self-sustained oscillations in excitable Erdös-Rényi random networks

The investigation of self-sustained oscillations in excitable complex networks is very important in understanding various activities in brain systems, among which the exploration of the key determinants of oscillations is a challenging task. In this paper, by investigating the influence of system parameters on self-sustained oscillations in excitable Erdös-Rényi random networks (EERRNs), the minimum Winfree loop (MWL) is revealed to be the key factor in determining the emergence of collective oscillations. Specifically, the one-to-one correspondence between the optimal connection probability (OCP) and the MWL length is exposed. Moreover, many important quantities such as the lower critical connection probability (LCCP), the OCP, and the upper critical connection probability (UCCP) are determined by the MWL. Most importantly, they can be approximately predicted by the network structure analysis, which have been verified in numerical simulations. Our results will be of great importance to help us in understanding the key factors in determining persistent activities in biological systems.

DPP4 regulates the inflammatory response in a rat model of febrile seizures

Febrile seizures (FS) are the most common seizure disorders in children aged 6 months to 5 years. Children suffering from complex FS have a high risk of developing subsequent temporal lobe epilepsy (TLE). Neuroinflammation is involved in the pathogenesis of FS although the mechanism remains unknown. Our previous study using the Whole Rat Genome Oligo Microarray determined that Dipeptidyl peptidase IV (DPP4) is potentially a related gene in FS rats. In this study, we demonstrated that DPP4 expression was significantly increased at both the protein and mRNA levels after hyperthermia induction. Sitagliptin, a specific enzyme inhibitor of DPP4, remarkably attenuated the severity of seizures in FS rats, and hyperthermia-induced astrocytosis was suppressed after DPP4 inhibition. Furthermore, sitagliptin significantly decreased the levels of the inflammatory cytokines IL-1β, TNF-α, and IL-6 but not IL-10. In addition, sitagliptin prevented NF-κB activation by decreasing phosphorylation of the p65 subunit. Taken together, our findings demonstrate that DPP4 functions as a critical regulator of neuroinflammation in hyperthermia-induced seizures and the DPP4 inhibitor may be a viable option for FS therapeutics.

Combined Effects of Feedforward Inhibition and Excitation in Thalamocortical Circuit on the Transitions of Epileptic Seizures

The mechanisms underlying electrophysiologically observed two-way transitions between absence and tonic-clonic epileptic seizures in cerebral cortex remain unknown. The interplay within thalamocortical network is believed to give rise to these epileptic multiple modes of activity and transitions between them. In particular, it is thought that in some areas of cortex there exists feedforward inhibition from specific relay nucleus of thalamus (TC) to inhibitory neuronal population (IN) which has even more stronger functions on cortical activities than the known feedforward excitation from TC to excitatory neuronal population (EX). Inspired by this, we proposed a modified computational model by introducing feedforward inhibitory connectivity within thalamocortical circuit, to systematically investigate the combined effects of feedforward inhibition and excitation on transitions of epileptic seizures. We first found that the feedforward excitation can induce the transition from tonic oscillation to spike and wave discharges (SWD) in cortex, i.e., the epileptic tonic-absence seizures, with the fixed weak feedforward inhibition. Thereinto, the phase of absence seizures corresponding to strong feedforward excitation can be further transformed into the clonic oscillations with the increasing of feedforward inhibition, representing the epileptic absence-clonic seizures. We also observed the other fascinating dynamical states, such as periodic 2/3/4-spike and wave discharges, reversed SWD and clonic oscillations, as well as saturated firings. More importantly, we can identify the stable parameter regions representing the tonic-clonic oscillations and SWD discharges of epileptic seizures on the 2-D plane composed of feedforward inhibition and excitation, where the physiologically plausible transition pathways between tonic-clonic and absence seizures can be figured out. These results indicate the functional role of feedforward pathways in controlling epileptic seizures and the modified thalamocortical model may provide a guide for future efforts to mechanistically link feedforward pathways in the pathogenesis of epileptic seizures.

Action potential initiation in a two-compartment model of pyramidal neuron mediated by dendritic Ca2+ spike

Dendritic Ca²⁺ spike endows cortical pyramidal cell with powerful ability of synaptic integration, which is critical for neuronal computation. Here we propose a two-compartment conductance-based model to investigate how the Ca²⁺ activity of apical dendrite participates in the action potential (AP) initiation to affect the firing properties of pyramidal neurons. We have shown that the apical input with sufficient intensity triggers a dendritic Ca²⁺ spike, which significantly boosts dendritic inputs as it propagates to soma. Such event instantaneously shifts the limit cycle attractor of the neuron and results in a burst of APs, which makes its firing rate reach a plateau steady-state level. Delivering current to two chambers simultaneously increases the level of neuronal excitability and decreases the threshold of input-output relation. Here the back-propagating APs facilitate the initiation of dendritic Ca²⁺ spike and evoke BAC firing. These findings indicate that the proposed model is capable of reproducing in vitro experimental observations. By determining spike initiating dynamics, we have provided a fundamental link between dendritic Ca²⁺ spike and output APs, which could contribute to mechanically interpreting how dendritic Ca²⁺ activity participates in the simple computations of pyramidal neuron.

Metabolic Energy of Action Potentials Modulated by Spike Frequency Adaptation

Spike frequency adaptation (SFA) exists in many types of neurons, which has been demonstrated to improve their abilities to process incoming information by synapses. The major carrier used by a neuron to convey synaptic signals is the sequences of action potentials (APs), which have to consume substantial metabolic energies to initiate and propagate. Here we use conductance-based models to investigate how SFA modulates the AP-related energy of neurons. The SFA is attributed to either calcium-activated K⁺ (I_AHP) or voltage-activated K⁺ (I_M) current. We observe that the activation of I_AHP or I_M increases the Na⁺ load used for depolarizing membrane, while produces few effects on the falling phase of AP. Then, the metabolic energy involved in Na⁺ current significantly increases from one AP to the next, while for K⁺ current it is less affected. As a consequence, the total energy cost by each AP gets larger as firing rate decays down. It is also shown that the minimum Na⁺ charge needed for the depolarization of each AP is unaffected during the course of SFA. This indicates that the activation of either adaptation current makes APs become less efficient to use Na⁺ influx for their depolarization. Further, our simulations demonstrate that the different biophysical properties of I_M and I_AHP result in distinct modulations of metabolic energy usage for APs. These investigations provide a fundamental link between adaptation currents and neuronal energetics, which could facilitate to interpret how SFA participates in neuronal information processing.