Modeling and simulation of organophosphate-induced neurotoxicity: Prediction and validation by experimental studies.

Exposure to organophosphorus (OP) compounds, either pesticides or chemical warfare agents, represents a major health problem. As potent irreversible inhibitors of cholinesterase, OP may induce seizures, as in status epilepticus, and occasionally brain lesions. Although these compounds are extremely toxic agents, the search for novel antidotes remains extremely limited. In silico modeling constitutes a useful tool to identify pharmacological targets and to develop efficient therapeutic strategies. In the present work, we developed a new in silico simulator in order to predict the neurotoxicity of irreversible inhibitors of acetyl- and/or butyrylcholinesterase (ChE) as well as the potential neuroprotection provided by antagonists of cholinergic muscarinic and glutamate N-methyl-d-aspartate (NMDA) receptors. The simulator reproduced firing of CA1 hippocampal neurons triggered by exposure to paraoxon (POX), as found in patch-clamp recordings in in vitro mouse hippocampal slices. In the case of POX intoxication, it predicted a preventing action of the muscarinic receptor antagonist atropine sulfate, as well as a synergistic action with the non-competitive NMDA receptor antagonist memantine. These in silico predictions relative to beneficial effects of atropine sulfate combined with memantine were recapitulated experimentally in an in vivo model of POX in adult male Swiss mice using electroencephalic (EEG) recordings. Thus, our simulator is a new powerful tool to identify protective therapeutic strategies against OP central effects, by screening various combinations of muscarinic and NMDA receptor antagonists.

A fully parallel in time and space algorithm for simulating the electrical activity of a neural tissue.

BACKGROUND: The resolution of a model describing the electrical activity of neural tissue and its propagation within this tissue is highly consuming in term of computing time and requires strong computing power to achieve good results. NEW METHOD: In this study, we present a method to solve a model describing the electrical propagation in neuronal tissue, using parareal algorithm, coupling with parallelization space using CUDA in graphical processing unit (GPU). RESULTS: We applied the method of resolution to different dimensions of the geometry of our model (1-D, 2-D and 3-D). The GPU results are compared with simulations from a multi-core processor cluster, using message-passing interface (MPI), where the spatial scale was parallelized in order to reach a comparable calculation time than that of the presented method using GPU. A gain of a factor 100 in term of computational time between sequential results and those obtained using the GPU has been obtained, in the case of 3-D geometry. Given the structure of the GPU, this factor increases according to the fineness of the geometry used in the computation. COMPARISON WITH EXISTING METHOD(S): To the best of our knowledge, it is the first time such a method is used, even in the case of neuroscience. CONCLUSION: Parallelization time coupled with GPU parallelization space allows for drastically reducing computational time with a fine resolution of the model describing the propagation of the electrical signal in a neuronal tissue.

Synaptic Efficacy as a Function of Ionotropic Receptor Distribution: A Computational Study.

Glutamatergic synapses are the most prevalent functional elements of information processing in the brain. Changes in pre-synaptic activity and in the function of various post-synaptic elements contribute to generate a large variety of synaptic responses. Previous studies have explored postsynaptic factors responsible for regulating synaptic strength variations, but have given far less importance to synaptic geometry, and more specifically to the subcellular distribution of ionotropic receptors. We analyzed the functional effects resulting from changing the subsynaptic localization of ionotropic receptors by using a hippocampal synaptic computational framework. The present study was performed using the EONS (Elementary Objects of the Nervous System) synaptic modeling platform, which was specifically developed to explore the roles of subsynaptic elements as well as their interactions, and that of synaptic geometry. More specifically, we determined the effects of changing the localization of ionotropic receptors relative to the presynaptic glutamate release site, on synaptic efficacy and its variations following single pulse and paired-pulse stimulation protocols. The results indicate that changes in synaptic geometry do have consequences on synaptic efficacy and its dynamics.

Influence of ionotropic receptors localization on glutamatergic synaptic response to paired-pulse stimulation protocol.

Paired-pulse protocol is a stimulation pattern that is often used to characterize short-term changes in synaptic potency. Responses to such protocol often yield varying results, going from a depressing response to a facilitated one following the second pulse. Similarly, experimental results have shown that synaptic structures are dynamic and receptors move along the postsynaptic membrane. The present study provides insights on the impact of glutamatergic receptors localization with respect to the neurotransmitters release site on the postsynaptic currents measured; it also proposes an explanation on the diversity of responses observed experimentally. The platform we used is the EONS/RHENOMS modeling platform widely described in the literature, which encompasses a multitude of highly detailed subsynaptic elements to most faithfully replicate synaptic function.

A computational model to investigate astrocytic glutamate uptake influence on synaptic transmission and neuronal spiking.

Over the past decades, our view of astrocytes has switched from passive support cells to active processing elements in the brain. The current view is that astrocytes shape neuronal communication and also play an important role in many neurodegenerative diseases. Despite the growing awareness of the importance of astrocytes, the exact mechanisms underlying neuron-astrocyte communication and the physiological consequences of astrocytic-neuronal interactions remain largely unclear. In this work, we define a modeling framework that will permit to address unanswered questions regarding the role of astrocytes. Our computational model of a detailed glutamatergic synapse facilitates the analysis of neural system responses to various stimuli and conditions that are otherwise difficult to obtain experimentally, in particular the readouts at the sub-cellular level. In this paper, we extend a detailed glutamatergic synaptic model, to include astrocytic glutamate transporters. We demonstrate how these glial transporters, responsible for the majority of glutamate uptake, modulate synaptic transmission mediated by ionotropic AMPA and NMDA receptors at glutamatergic synapses. Furthermore, we investigate how these local signaling effects at the synaptic level are translated into varying spatio-temporal patterns of neuron firing. Paired pulse stimulation results reveal that the effect of astrocytic glutamate uptake is more apparent when the input inter-spike interval is sufficiently long to allow the receptors to recover from desensitization. These results suggest an important functional role of astrocytes in spike timing dependent processes and demand further investigation of the molecular basis of certain neurological diseases specifically related to alterations in astrocytic glutamate uptake, such as epilepsy.

Influence of ionotropic receptor location on their dynamics at glutamatergic synapses.

In this paper we study the effects of the location of ionotropic receptors, especially AMPA and NMDA receptors, on their function at excitatory glutamatergic synapses. As few computational models only allow to evaluate the influence of receptor location on state transition and receptor dynamics, we present an elaborate computational model of a glutamatergic synapse that takes into account detailed parametric models of ionotropic receptors along with glutamate diffusion within the synaptic cleft. Our simulation results underscore the importance of the wide spread distribution of AMPA receptors which is required to avoid massive desensitization of these receptors following a single glutamate release event while NMDA receptor location is potentially optimal relative to the glutamate release site thus, emphasizing the contribution of location dependent effects of the two major ionotropic receptors to synaptic efficacy.

Modeling of the nervous system: from modulation of glutamatergic and gabaergic molecular dynamics to neuron spiking activity.

One of the fundamental characteristics of the brain is its hierarchical and temporal organization: scales in both space and time must be considered to fully grasp the system's underlying mechanisms and their impact on brain function. Complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. These integrations across hierarchies of the nervous system are sufficiently complex to have impeded the development of routine multi-level modeling methodologies. The present study describes an example of our multiscale efforts to rise from the biomolecular level to the neuron level. We more specifically describe how we integrate biomolecular mechanisms taking place at glutamatergic and gabaergic synapses and integrate them to study the impact of these modifications on spiking activity of a CA1 pyramidal cell in the hippocampus.

Simulation of postsynaptic glutamate receptors reveals critical features of glutamatergic transmission.

Activation of several subtypes of glutamate receptors contributes to changes in postsynaptic calcium concentration at hippocampal synapses, resulting in various types of changes in synaptic strength. Thus, while activation of NMDA receptors has been shown to be critical for long-term potentiation (LTP) and long term depression (LTD) of synaptic transmission, activation of metabotropic glutamate receptors (mGluRs) has been linked to either LTP or LTD. While it is generally admitted that dynamic changes in postsynaptic calcium concentration represent the critical elements to determine the direction and amplitude of the changes in synaptic strength, it has been difficult to quantitatively estimate the relative contribution of the different types of glutamate receptors to these changes under different experimental conditions. Here we present a detailed model of a postsynaptic glutamatergic synapse that incorporates ionotropic and mGluR type I receptors, and we use this model to determine the role of the different receptors to the dynamics of postsynaptic calcium with different patterns of presynaptic activation. Our modeling framework includes glutamate vesicular release and diffusion in the cleft and a glutamate transporter that modulates extracellular glutamate concentration. Our results indicate that the contribution of mGluRs to changes in postsynaptic calcium concentration is minimal under basal stimulation conditions and becomes apparent only at high frequency of stimulation. Furthermore, the location of mGluRs in the postsynaptic membrane is also a critical factor, as activation of distant receptors contributes significantly less to calcium dynamics than more centrally located ones. These results confirm the important role of glutamate transporters and of the localization of mGluRs in postsynaptic sites in their signaling properties, and further strengthen the notion that mGluR activation significantly contributes to postsynaptic calcium dynamics only following high-frequency stimulation. They also provide a new tool to analyze the interactions between metabotropic and ionotropic glutamate receptors.

Integrated multiscale modeling of the nervous system: predicting changes in hippocampal network activity by a positive AMPA receptor modulator.

One of the fundamental characteristics of the brain is its hierarchical organization. Scales in both space and time that must be considered when integrating across hierarchies of the nervous system are sufficiently great as to have impeded the development of routine multilevel modeling methodologies. Complex molecular interactions at the level of receptors and channels regulate activity at the level of neurons; interactions between multiple populations of neurons ultimately give rise to complex neural systems function and behavior. This spatial complexity takes place in the context of a composite temporal integration of multiple, different events unfolding at the millisecond, second, minute, hour, and longer time scales. In this study, we present a multiscale modeling methodology that integrates synaptic models into single neuron, and multineuron, network models. We have applied this approach to the specific problem of how changes at the level of kinetic parameters of a receptor-channel model are translated into changes in the temporal firing pattern of a single neuron, and ultimately, changes in the spatiotemporal activity of a network of neurons. These results demonstrate how this powerful methodology can be applied to understand the effects of a given local process within multiple hierarchical levels of the nervous system.

Modeling of the nervous system: from molecular dynamics and synaptic modulation to neuron spiking activity.

The brain is a perfect example of an integrated multi-scale system, as the complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. In the present study we illustrate our approach to model and simulate the spatio-temporal complexity of the nervous system by developing a multi-scale model integrating synaptic models into the neuronal and ultimately network levels. We apply this approach to a concrete example and demonstrate how changes at the level of kinetic parameters of a receptor model are translated into significant changes in the firing of a pyramidal neuron. These results illustrate the abilities of our modeling approach and support its direct application to the evaluation of the effects of drugs, from functional target to integrated system.

Paired-pulse stimulation at glutamatergic synapses - pre- and postsynaptic components.

Paired-pulse stimulation is a standard protocol that has been used for decades to characterize dynamic systems: the differences in responses to two sequential identical stimuli as a function of inter-stimulus interval provide quantitative information on the dynamics of the system. In neuroscience, the paired-pulse protocol is also widely used at multiple levels of analysis, from behavioral conditioning to synaptic plasticity, and in particular to define the biomolecular mechanism of learning and memory. In a system as small and complex as synapses, it is extremely challenging - if not impossible - to experimentally gain access to the multitude of possible readouts. In the present study, we first introduce a computational synaptic modeling platform that we developed and calibrated based on experimental data from both our laboratories and a variety of publications. We then show how this platform allows not only to replicate experimental data, but also to go beyond technological boundaries and investigate the main parameters responsible for regulation of synaptic transmission and plasticity. The results provide critical information regarding the respective role of various subsynaptic processes and of their interactions. Additionally, this approach can strengthen our understanding of potential dysfunctions (pathologies) and suggest potential approaches to re-establish normal function.

Computational studies of NMDA receptors: differential effects of neuronal activity on efficacy of competitive and non-competitive antagonists.

N-Methyl-D-Aspartate receptors (NMDARs) play important physiological as well as pathological roles in the central nervous system (CNS). While NMDAR competitive antagonists, such as D-2-Amino-5-Phosphopentanoic acid (AP5) have been shown to impair learning and memory, the non-competitive antagonist, memantine, is paradoxically beneficial in mild to moderate Alzheimer's disease (AD) patients. It has been proposed that differences in kinetic properties could account for antagonist functional differences. Here we present a new elaborated kinetic model of NMDARs that incorporates binding sites for the agonist (glutamate) and co-agonist (glycine), channel blockers, such as memantine and magnesium (Mg(2+)), as well as competitive antagonists. We first validated and optimized the parameters used in the model by comparing simulated results with a wide range of experimental data from the literature. We then evaluated the effects of stimulation frequency and membrane potential (Vm) on the characteristics of AP5 and memantine inhibition of NMDARs. Our results indicated that the inhibitory effects of AP5 were independent of Vm but decreased with increasing stimulation frequency. In contrast, memantine inhibitory effects decreased with both increasing Vm and stimulation frequency. They support the idea that memantine could provide tonic blockade of NMDARs under basal stimulation conditions without blocking their activation during learning. Moreover they underline the necessity of considering receptor kinetics and the value of the biosimulation approach to better understand mechanisms of drug action and to identify new ways of regulating receptor function.

Modeling glutamatergic synapses: insights into mechanisms regulating synaptic efficacy.

The hippocampal formation is critically involved for the long-term storage of various forms of information, and it is widely believed that the phenomenon of long-term potentiation (LTP) of synaptic transmission is a molecular/cellular mechanism participating in memory formation. Although several high level models of hippocampal function have been developed, they do not incorporate detailed molecular information of the type necessary to understand the contribution of individual molecular events to the mechanisms underlying LTP and learning and memory. We are therefore developing new technological tools based on mathematical modeling and computer simulation of the molecular processes taking place in realistic biological networks to reach such an understanding. This article briefly summarizes the approach we are using and illustrates it by presenting data regarding the effects of changing the number of AMPA receptors on various features of glutamatergic transmission, including NMDA receptor-mediated responses and paired-pulse facilitation. We conclude by discussing the significance of these results and providing some ideas for future directions with this approach.