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Basque Center for Applied Mathematics
"Predicting excitotoxicity at the onset of Alzheimer’s disease by a model of Aβ-dependent trafficking of astrocytic glutamate transporters"
At Alzheimer’s disease (AD) onset, extracellular accumulation of oligomeric amyloid-β (Aβ) correlates with excitotoxicity and the alteration of glutamate uptake by astrocytic transporters (GLT1). Experiments suggest that glutamate, Aβ, or a combination thereof, may dynamically regulate trafficking and expression of those transporters between perisynaptic and intracellular astrocytic compartments . There is no understanding however, whether and how such mechanisms could ultimately link with the emergence of excitotoxicity which hallmarks early stages of AD. With this regard, we consider a simplified description of astrocytic transporter trafficking based on a Markov process for transporter movements between the cytoplasm and the plasma membrane, and vice versa, and we use this model to identify potential ensembles of Aβ-dependent pathways of trafficking that could account for experimental observations. Next, we consider the mean-field rate description ensuing from the Markov model in the Finite Element Method (FEM) framework of a 3D model of glutamate diffusion at synaptic terminals and their surroundings. Changing extracellular Aβ concentration, we accordingly look at the time course of extracellular glutamate, and the conditions for its accumulation in the extrasynaptic space. Since extracellular glutamate alters synaptic activity, we estimate conditions for excitotoxicity linking neural network firing activity with extracellular glutamate. Consistent with experiments, our model predicts that GLT1 surface expression decreases when extracellular Aβ increases beyond a threshold concentration. This, in turn, favors extracellular glutamate accumulation, promoting a positive feedback loop that induce further synaptic glutamate release, and thereby excitotoxicity. Because the rate of glutamate accumulation depends on the uptake capacity by astrocytic transporters, which is a function of extracellular Aβ, local gradients of Aβ may dramatically affect synaptic environment, both locally and extra-synaptically. These results provide theoretical support to the possibility of looking at Aβ-dependent astrocytic GLT1 expression as a clinical marker for early diagnosis Alzheimer’s disease.
Universdad de la Republica
"Small-worldness favours network inference in synthetic neural networks"
A main goal in the analysis of a complex system is to infer its underlying network structure from time-series observations of its behaviour. The inference process is often done by using bi-variate similarity measures, such as the cross-correlation (CC) or mutual information (MI), however, the main factors favouring or hindering its success are still puzzling. Here, we use synthetic neuron models in order to reveal the main topological properties that frustrate or facilitate inferring the underlying network from CC measurements. Specifically, we use pulse-coupled Izhikevich neurons connected as in the Caenorhabditis elegans neural networks as well as in networks with similar randomness and small-worldness. We analyse the effectiveness and robustness of the inference process under different observations and collective dynamics, contrasting the results obtained from using membrane potentials and inter-spike interval time-series. We find that overall, small-worldness favours network inference and degree heterogeneity hinders it. In particular, success rates in C. elegans networks – that combine small-world properties with degree heterogeneity – are closer to success rates in Erdös-Rényi network models rather than those in Watts-Strogatz network models. These results are relevant to understand better the relationship between topological properties and function in different neural networks. Reference: García, R.A., Martí, A.C., Cabeza, C. et al. Small-worldness favours network inference in synthetic neural networks. Sci Rep 10, 2296 (2020).
"The data-based inference method reveals the network structure of the SCN"
The suprachiasmatic nucleus (SCN) is the central circadian pacemaker in mammals. Even though SCN is composed of thousands of heterogeneous self-oscillating cells, the SCN can synchronize its component oscillators through the SCN neuronal network. To understand the SCN network structure, previous studies used the time series data to infer the network structure. However, because the SCN is synchronized, previous methods falsely inferred the network as if all the SCN cells were coupled with each other. To circumvent this, we develop a novel data-based method, which can successfully infer the SCN network from the time series data. In particular, our method accurately infers the SCN network with single-cell resolution bioluminescence data from 2,000 mice SCN cells. Furthermore, our method can infer the directionality of the coupling between SCN cells.
Zeinab Tajik Mansoury
University of Tehran
"Opioid Addiction Affects Neuronal Synchronization in the Hippocampus: A Computational Model"
Drug addiction can affect the limbic system. Many computational models for drug addiction have been proposed, but most are for the reward system and behavioral models (Redish et al.,2004 and Gutkin et al.,2006). There are a few cellular mathematical models for drug addiction in the hippocampus that are very detailed (Borjkhani et al.,2018). We study a functional model for the synapses in the hippocampus to investigate the effect of opioid (Morphine) addiction on neuronal synchronization. We consider Pankratova et al.,2019 computational model. The model considers an astrocyte in synapses of two postsynaptic neurons in the hippocampus and studies the synchronization of the two neurons. In the model, we consider that Morphine addiction affects this tripartite synapses. The model consists of six differential equations for each neuron. One of the equations expresses the dynamics of the mean-field amount of released neurotransmitters based on presynaptic Poisson spike train and the astrocytic released glutamates in the synaptic cleft. Also, there is one differential equation for the mean-field amount of excitatory postsynaptic currents(EPSCs) based on presynaptic Poisson spike train and the D serine released from astrocyte. The four other equations indicate the Hodgkin-Huxley model (one of them for membrane voltage and the three other for gating variables), which its synaptic current input has been created by integrating EPSCs. Two differential equations describe the function of the astrocyte existed in synapses of the two neurons. One equation indicates the dynamics of the mean-field amount of astrocytic released glutamates based on the mean-field amount of the neurotransmitters of both neurons. The other equation expresses the dynamics of the mean-field amount of astrocytic released D serine based on the mean-field amount of the neurotransmitters of both neurons. Morphine addiction can affect three positions in synapses: presynaptic, astrocytic, and postsynaptic cells. It can cause an increase in neurotransmitters' concentration due to the disinhibitory mechanism of opioid receptors on presynaptic inhibitory neurons. Also, it can decrease the activity of astrocytic transporters causing fewer neurotransmitters reuptake by astrocyte. Morphine activates the opioid receptors on the postsynaptic neuron that increase NMDA's currents. In the model, we consider that Morphine influences the frequency of the Poisson spike train, the steady-state amount of neurotransmitters, and the gain of astrocytic glutamates. The amplitude of the EPCSs is also affected due to the Morphine addiction. The coefﬁcient of synchronization is the ratio of synchronous spikes to the total spike number of both neurons. The results indicate that morphine addiction increases the synchrony of neurons. Thus, it can represent memory formation. In future works, we will study the withdrawal state in this model to analyze the neuronal synchronization and how the cues can result in relapse and how to control it.
Hosted by eSMB2020 Follow
Virtual conference of the Society for Mathematical Biology, 2020.