Mathematical Modeling of PI3K/Akt Pathway in Microglia.

The motility of microglia involves intracellular signaling pathways that are predominantly controlled by changes in cytosolic Ca2+ and activation of PI3K/Akt (phosphoinositide-3-kinase/protein kinase B). In this letter, we develop a novel biophysical model for cytosolic Ca2+ activation of the PI3K/Akt pathway in microglia where Ca2+ influx is mediated by both P2Y purinergic receptors (P2YR) and P2X purinergic receptors (P2XR). The model parameters are estimated by employing optimization techniques to fit the model to phosphorylated Akt (pAkt) experimental modeling/in vitro data. The integrated model supports the hypothesis that Ca2+ influx via P2YR and P2XR can explain the experimentally reported biphasic transient responses in measuring pAkt levels. Our predictions reveal new quantitative insights into P2Rs on how they regulate Ca2+ and Akt in terms of physiological interactions and transient responses. It is shown that the upregulation of P2X receptors through a repetitive application of agonist results in a continual increase in the baseline [Ca2+], which causes the biphasic response to become a monophasic response which prolongs elevated levels of pAkt.

Mathematical modelling of human P2X-mediated plasma membrane electrophysiology and calcium dynamics in microglia.

Regulation of cytosolic calcium (Ca2+) dynamics is fundamental to microglial function. Temporal and spatial Ca2+ fluxes are induced from a complicated signal transduction pathway linked to brain ionic homeostasis. In this paper, we develop a novel biophysical model of Ca2+ and sodium (Na+) dynamics in human microglia and evaluate the contribution of purinergic receptors (P2XRs) to both intracellular Ca2+ and Na+ levels in response to agonist/ATP binding. This is the first comprehensive model that integrates P2XRs to predict intricate Ca2+ and Na+ transient responses in microglia. Specifically, a novel compact biophysical model is proposed for the capture of whole-cell patch-clamp currents associated with P2X4 and P2X7 receptors, which is composed of only four state variables. The entire model shows that intricate intracellular ion dynamics arise from the coupled interaction between P2X4 and P2X7 receptors, the Na+/Ca2+ exchanger (NCX), Ca2+ extrusion by the plasma membrane Ca2+ ATPase (PMCA), and Ca2+ and Na+ leak channels. Both P2XRs are modelled as two separate adenosine triphosphate (ATP) gated Ca2+ and Na+ conductance channels, where the stoichiometry is the removal of one Ca2+ for the hydrolysis of one ATP molecule. Two unique sets of model parameters were determined using an evolutionary algorithm to optimise fitting to experimental data for each of the receptors. This allows the proposed model to capture both human P2X7 and P2X4 data (hP2X7 and hP2X4). The model architecture enables a high degree of simplicity, accuracy and predictability of Ca2+ and Na+ dynamics thus providing quantitative insights into different behaviours of intracellular Na+ and Ca2+ which will guide future experimental research. Understanding the interactions between these receptors and other membrane-bound transporters provides a step forward in resolving the qualitative link between purinergic receptors and microglial physiology and their contribution to brain pathology.

Image-based computer modeling assessment of microwave ablation for treatment of adrenal tumors.

PURPOSE: To assess the feasibility of delivering microwave ablation for targeted treatment of aldosterone producing adenomas using image-based computational models. METHODS: We curated an anonymized dataset of diagnostic 11C-metomidate PET/CT images of 14 patients with aldosterone producing adenomas (APA). A semi-automated approach was developed to segment the APA, adrenal gland, and adjacent organs within 2 cm of the APA boundary. The segmented volumes were used to implement patient-specific 3D electromagnetic-bioheat transfer models of microwave ablation with a 2.45 GHz directional microwave ablation applicator. Ablation profiles were quantitatively assessed based on the extent of the APA target encompassed by an ablative thermal dose, while limiting thermal damage to the adjacent normal adrenal tissue and sensitive critical structures. RESULTS: Across the 14 patients, adrenal tumor volumes ranged between 393 mm3 and 2,395 mm3. On average, 70% of the adrenal tumor volumes received an ablative thermal dose of 240CEM43, while limiting thermal damage to non-target structures, and thermally sparing 83.5-96.4% of normal adrenal gland. Average ablation duration was 293 s (range: 60-600 s). Simulations indicated coverage of the APA with an ablative dose was limited when the axis of the ablation applicator was not well aligned with the major axis of the targeted APA. CONCLUSIONS: Image-based computational models demonstrate the potential for delivering microwave ablation to APA targets within the adrenal gland, while limiting thermal damage to surrounding non-target structures.

Case Study-Spiking Neural Network Hardware System for Structural Health Monitoring.

This case study provides feasibility analysis of adapting Spiking Neural Networks (SNN) based Structural Health Monitoring (SHM) system to explore low-cost solution for inspection of structural health of damaged buildings which survived after natural disaster that is, earthquakes or similar activities. Various techniques are used to detect the structural health status of a building for performance benchmarking, including different feature extraction methods and classification techniques (e.g., SNN, K-means and artificial neural network etc.). The SNN is utilized to process the sensory data generated from full-scale seven-story reinforced concrete building to verify the classification performances. Results show that the proposed SNN hardware has high classification accuracy, reliability, longevity and low hardware area overhead.

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.

Potassium and sodium microdomains in thin astroglial processes: A computational model study.

A biophysical model that captures molecular homeostatic control of ions at the perisynaptic cradle (PsC) is of fundamental importance for understanding the interplay between astroglial and neuronal compartments. In this paper, we develop a multi-compartmental mathematical model which proposes a novel mechanism whereby the flow of cations in thin processes is restricted due to negatively charged membrane lipids which result in the formation of deep potential wells near the dipole heads. These wells restrict the flow of cations to "hopping" between adjacent wells as they transverse the process, and this surface retention of cations will be shown to give rise to the formation of potassium (K+) and sodium (Na+) microdomains at the PsC. We further propose that a K+ microdomain formed at the PsC, provides the driving force for the return of K+ to the extracellular space for uptake by the neurone, thereby preventing K+ undershoot. A slow decay of Na+ was also observed in our simulation after a period of glutamate stimulation which is in strong agreement with experimental observations. The pathological implications of microdomain formation during neuronal excitation are also discussed.

The influence of astrocytic leaflet motility on ionic signalling and homeostasis at active synapses.

Astrocytes display a highly complex, spongiform morphology, with their fine terminal processes (leaflets) exercising dynamic degrees of synaptic coverage, from touching and surrounding the synapse to being retracted from the synaptic region. In this paper, a computational model is used to reveal the effect of the astrocyte-synapse spatial relationship on ionic homeostasis. Specifically, our model predicts that varying degrees of astrocyte leaflet coverage influences concentrations of K+, Na+ and Ca2+, and results show that leaflet motility strongly influences Ca2+ uptake, as well as glutamate and K+ to a lesser extent. Furthermore, this paper highlights that an astrocytic leaflet that is in proximity to the synaptic cleft loses the ability to form a Ca2+ microdomain, whereas when the leaflet is remote from the synaptic cleft, a Ca2+ microdomain can form. This may have implications for Ca2+-dependent leaflet motility.

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.

Exploring Self-Repair in a Coupled Spiking Astrocyte Neural Network.

It is now known that astrocytes modulate the activity at the tripartite synapses where indirect signaling via the retrograde messengers, endocannabinoids, leads to a localized self-repairing capability. In this paper, a self-repairing spiking astrocyte neural network (SANN) is proposed to demonstrate a distributed self-repairing capability at the network level. The SANN uses a novel learning rule that combines the spike-timing-dependent plasticity (STDP) and Bienenstock, Cooper, and Munro (BCM) learning rules (hereafter referred to as the BSTDP rule). In this learning rule, the synaptic weight potentiation is not only driven by the temporal difference between the presynaptic and postsynaptic neuron firing times but also by the postsynaptic neuron activity. We will show in this paper that the BSTDP modulates the height of the plasticity window to establish an input-output mapping (in the learning phase) and also maintains this mapping (via self-repair) if synaptic pathways become dysfunctional. It is the functional dependence of postsynaptic neuron firing activity on the height of the plasticity window that underpins how the proposed SANN self-repairs on the fly. The SANN also uses the coupling between the tripartite synapses and γ -GABAergic interneurons. This interaction gives rise to a presynaptic neuron frequency filtering capability that serves to route information, represented as spike trains, to different neurons in the subsequent layers of the SANN. The proposed SANN follows a feedforward architecture with multiple interneuron pathways and astrocytes modulate synaptic activity at the hidden and output neuronal layers. The self-repairing capability will be demonstrated in a robotic obstacle avoidance application, and the simulation results will show that the SANN can maintain learned maneuvers at synaptic fault densities of up to 80% regardless of the fault locations.

Calcium Microdomain Formation at the Perisynaptic Cradle Due to NCX Reversal: A Computational Study.

It has recently been proposed using a multi-compartmental mathematical model that negatively fixed charged membrane-associated sites constrain the flow of cations in perisynaptic astroglial processes. This restricted movement of ions between the perisynaptic cradle (PsC), principal astroglial processes and the astrocyte soma gives rise to potassium (K+) and sodium (Na+) microdomains at the PsC. The present paper extends the above model to demonstrate that the formation of an Na+ microdomain can reverse the Na+/Ca2+ exchanger (NCX) thus providing an additional source of calcium (Ca2+) at the PsC. Results presented clearly show that reversal of the Na+/Ca2+ exchanger is instigated by a glutamate transporter coupled increase in concentration of cytoplasmic [Na+]i at the PsC, which and instigates Ca2+ influx through the NCX. As the flow of Ca2+ along the astrocyte process and away from the PsC is also constrained by Ca2+ binding proteins, then a Ca2+ microdomain forms at the PsC. The paper also serves to demonstrate that the EAAT, NKA, and NCX represent the minimal requirement necessary and sufficient for the development of a Ca2+ microdomain and that these mechanisms directly link neuronal activity and glutamate release to the formation of localized Na+ and Ca2+ microdomains signals at the PsC. This local source of Ca2+ can provide a previously underexplored form of astroglial Ca2+ signaling.

GABA Regulation of Burst Firing in Hippocampal Astrocyte Neural Circuit: A Biophysical Model.

It is now widely accepted that glia cells and gamma-aminobutyric acidergic (GABA) interneurons dynamically regulate synaptic transmission and neuronal activity in time and space. This paper presents a biophysical model that captures the interaction between an astrocyte cell, a GABA interneuron and pre/postsynaptic neurons. Specifically, GABA released from a GABA interneuron triggers in astrocytes the release of calcium (Ca 2+) from the endoplasmic reticulum via the inositol 1, 4, 5-trisphosphate (IP 3) pathway. This results in gliotransmission which elevates the presynaptic transmission probability rate (PR) causing weight potentiation and a gradual increase in postsynaptic neuronal firing, that eventually stabilizes. However, by capturing the complex interactions between IP 3, generated from both GABA and the 2-arachidonyl glycerol (2-AG) pathway, and PR, this paper shows that this interaction not only gives rise to an initial weight potentiation phase but also this phase is followed by postsynaptic bursting behavior. Moreover, the model will show that there is a presynaptic frequency range over which burst firing can occur. The proposed model offers a novel cellular level mechanism that may underpin both seizure-like activity and neuronal synchrony across different brain regions.

SPANNER: A Self-Repairing Spiking Neural Network Hardware Architecture.

Recent research has shown that a glial cell of astrocyte underpins a self-repair mechanism in the human brain, where spiking neurons provide direct and indirect feedbacks to presynaptic terminals. These feedbacks modulate the synaptic transmission probability of release (PR). When synaptic faults occur, the neuron becomes silent or near silent due to the low PR of synapses; whereby the PRs of remaining healthy synapses are then increased by the indirect feedback from the astrocyte cell. In this paper, a novel hardware architecture of Self-rePAiring spiking Neural NEtwoRk (SPANNER) is proposed, which mimics this self-repairing capability in the human brain. This paper demonstrates that the hardware can self-detect and self-repair synaptic faults without the conventional components for the fault detection and fault repairing. Experimental results show that SPANNER can maintain the system performance with fault densities of up to 40%, and more importantly SPANNER has only a 20% performance degradation when the self-repairing architecture is significantly damaged at a fault density of 80%.

Low Cost Interconnected Architecture for the Hardware Spiking Neural Networks.

A novel low cost interconnected architecture (LCIA) is proposed in this paper, which is an efficient solution for the neuron interconnections for the hardware spiking neural networks (SNNs). It is based on an all-to-all connection that takes each paired input and output nodes of multi-layer SNNs as the source and destination of connections. The aim is to maintain an efficient routing performance under low hardware overhead. A Networks-on-Chip (NoC) router is proposed as the fundamental component of the LCIA, where an effective scheduler is designed to address the traffic challenge due to irregular spikes. The router can find requests rapidly, make the arbitration decision promptly, and provide equal services to different network traffic requests. Experimental results show that the LCIA can manage the intercommunication of the multi-layer neural networks efficiently and have a low hardware overhead which can maintain the scalability of hardware SNNs.

ARDebug: An Augmented Reality Tool for Analysing and Debugging Swarm Robotic Systems.

Despite growing interest in collective robotics over the past few years, analysing and debugging the behaviour of swarm robotic systems remains a challenge due to the lack of appropriate tools. We present a solution to this problem-ARDebug: an open-source, cross-platform, and modular tool that allows the user to visualise the internal state of a robot swarm using graphical augmented reality techniques. In this paper we describe the key features of the software, the hardware required to support it, its implementation, and usage examples. ARDebug is specifically designed with adoption by other institutions in mind, and aims to provide an extensible tool that other researchers can easily integrate with their own experimental infrastructure.

On the role of astroglial syncytia in self-repairing spiking neural networks.

It has been shown that brain-like self-repair can arise from the interactions between neurons and astrocytes where endocannabinoids are synthesized and released from active neurons. This retrograde messenger feeds back to local synapses directly and indirectly to distant synapses via astrocytes. This direct/indirect feedback of the endocannabinoid retrograde messenger results in the modulation of the probability of release (PR) at synaptic sites. When synapses fail, there is a corresponding falloff in the firing activity of the associated neurons, and hence the strength of the direct feedback messenger diminishes. This triggers an increase in PR of healthy synapses, due to the indirect messenger from other active neurons, which is the catalyst for the repair process. In this paper, the repair process is implemented by developing a new learning rule that captures the spike-timing-dependent plasticity and Bienenstock, Cooper, and Munro learning rules. The rule is activated by the increase in PR and results in a potentiation of the weight values, which reestablishes the firing activity of neurons. In addition, this self-repairing mechanism is extended to network-level repair where astrocyte to astrocyte communications are implemented using a linear gap junction model. This facilitates the implementation of an astroglial syncytium involving multiple astrocytes, which relays the indirect feedback messenger to distant neurons: each astrocyte is bidirectionally coupled to neurons. A detailed and comprehensive set of results with analysis is presented demonstrating repair at both cellular and network levels.

Biologically Inspired SNN for Robot Control.

This paper proposes a spiking-neural-network-based robot controller inspired by the control structures of biological systems. Information is routed through the network using facilitating dynamic synapses with short-term plasticity. Learning occurs through long-term synaptic plasticity which is implemented using the temporal difference learning rule to enable the robot to learn to associate the correct movement with the appropriate input conditions. The network self-organizes to provide memories of environments that the robot encounters. A Pioneer robot simulator with laser and sonar proximity sensors is used to verify the performance of the network with a wall-following task, and the results are presented.

Silicon-based dynamic synapse with depressing response.

A compact implementation of a dynamic charge transfer synapse cell, capable of implementing synaptic depression, is presented. The cell is combined with a simple current mirror summing node to produce biologically plausible postsynaptic potentials (PSPs). A single charge packet is effectively transferred from the synapse to the summing node, whenever a presynaptic pulse is applied to one of its terminals. The charge packet is "weighted" by a voltage applied to the second terminal of the synapse. A voltage applied to the third terminal determines the charge recovery time in the synapse, which can be adjusted over several orders of magnitude. This voltage determines the paired pulse ratio for the synapse. The fall time of the PSP is also adjustable and is set by the gate voltage of a metal-oxide-semiconductor field-effect transistor operating in subthreshold. Results extracted from chips fabricated in a 0.35-µm complementary metal-oxide-semiconductor process, alongside theoretical and simulation results, confirm the ability of the cell to produce PSPs that are characteristic of real synapses. The concept addresses a key requirement for scalable hardware neural networks.

Synchrony: a spiking-based mechanism for processing sensory stimuli.

Synchronous behaviour of neurons is both beneficial and detrimental to the neural code. On the one extreme, synchronous firing activity is well known to be a symptom of epileptic seizures, whilst on the other synchrony provides a mechanism for coordinating brain activity. This paper briefly reviews some current thinking with regard to synchrony, and outlines some experiments with LIF neurons that harness near-synchronous states for processing biologically-realistic sensory stimuli. Inspired by the topology of neurons in the cochlear nucleus, laterally connected leaky integrate and fire neurons, operating in near-synchronous states, are investigated for their ability to reduce noisy spikes and increase spectral contrast of auditory stimuli. Two connectivity parameters, referred to as connection length and neighbourhood radius, are introduced to configure lateral inhibitory connectivity to generate this neural behaviour. Information-theoretic principles are then employed to quantify the information retained by the coding, and then this is compared to the information retained by the various output topologies.

Self-repair in a bidirectionally coupled astrocyte-neuron (AN) system based on retrograde signaling.

In this paper we demonstrate that retrograde signaling via astrocytes may underpin self-repair in the brain. Faults manifest themselves in silent or near silent neurons caused by low transmission probability (PR) synapses; the enhancement of the transmission PR of a healthy neighboring synapse by retrograde signaling can enhance the transmission PR of the "faulty" synapse (repair). Our model of self-repair is based on recent research showing that retrograde signaling via astrocytes can increase the PR of neurotransmitter release at damaged or low transmission PR synapses. The model demonstrates that astrocytes are capable of bidirectional communication with neurons which leads to modulation of synaptic activity, and that indirect signaling through retrograde messengers such as endocannabinoids leads to modulation of synaptic transmission PR. Although our model operates at the level of cells, it provides a new research direction on brain-like self-repair which can be extended to networks of astrocytes and neurons. It also provides a biologically inspired basis for developing highly adaptive, distributed computing systems that can, at fine levels of granularity, fault detect, diagnose and self-repair autonomously, without the traditional constraint of a central fault detect/repair unit.

Spiking neural network model of sound localization using the interaural intensity difference.

In this paper, a spiking neural network (SNN) architecture to simulate the sound localization ability of the mammalian auditory pathways using the interaural intensity difference cue is presented. The lateral superior olive was the inspiration for the architecture, which required the integration of an auditory periphery (cochlea) model and a model of the medial nucleus of the trapezoid body. The SNN uses leaky integrate-and-fire excitatory and inhibitory spiking neurons, facilitating synapses and receptive fields. Experimentally derived head-related transfer function (HRTF) acoustical data from adult domestic cats were employed to train and validate the localization ability of the architecture, training used the supervised learning algorithm called the remote supervision method to determine the azimuthal angles. The experimental results demonstrate that the architecture performs best when it is localizing high-frequency sound data in agreement with the biology, and also shows a high degree of robustness when the HRTF acoustical data is corrupted by noise.