Modeling of slow glutamate diffusion and AMPA receptor activation in the cerebellar glomerulus

Computational models of neurotransmission at cerebellar synapses unveil the impact on network computation

The neuroscientific field benefits from the conjoint evolution of experimental and computational techniques, allowing for the reconstruction and simulation of complex models of neurons and synapses. Chemical synapses are characterized by presynaptic vesicle cycling, neurotransmitter diffusion, and postsynaptic receptor activation, which eventually lead to postsynaptic currents and subsequent membrane potential changes. These mechanisms have been accurately modeled for different synapses and receptor types (AMPA, NMDA, and GABA) of the cerebellar cortical network, allowing simulation of their impact on computation. Of special relevance is short-term synaptic plasticity, which generates spatiotemporal filtering in local microcircuits and controls burst transmission and information flow through the network. Here, we present how data-driven computational models recapitulate the properties of neurotransmission at cerebellar synapses. The simulation of microcircuit models is starting to reveal how diverse synaptic mechanisms shape the spatiotemporal profiles of circuit activity and computation.

The glutamatergic synapse: a complex machinery for information processing

Being the most abundant synaptic type, the glutamatergic synapse is responsible for the larger part of the brain's information processing. Despite the conceptual simplicity of the basic mechanism of synaptic transmission, the glutamatergic synapse shows a large variation in the response to the presynaptic release of the neurotransmitter. This variability is observed not only among different synapses but also in the same single synapse. The synaptic response variability is due to several mechanisms of control of the information transferred among the neurons and suggests that the glutamatergic synapse is not a simple bridge for the transfer of information but plays an important role in its elaboration and management. The control of the synaptic information is operated at pre, post, and extrasynaptic sites in a sort of cooperation between the pre and postsynaptic neurons which also involves the activity of other neurons. The interaction between the different mechanisms of control is extremely complicated and its complete functionality is far from being fully understood. The present review, although not exhaustively, is intended to outline the most important of these mechanisms and their complexity, the understanding of which will be among the most intriguing challenges of future neuroscience.

Deciphering in silico the Role of Mutated Na V 1.1 Sodium Channels in Enhancing Trigeminal Nociception in Familial Hemiplegic Migraine Type 3

Familial hemiplegic migraine type 3 (FHM3) is caused by gain-of-function mutations in the SCN1A gene that encodes the α1 subunit of voltage-gated Na_V1.1 sodium channels. The high level of expression of Na_V1.1 channels in peripheral trigeminal neurons may lead to abnormal nociceptive signaling thus contributing to migraine pain. Na_V1.1 dysfunction is relevant also for other neurological disorders, foremost epilepsy and stroke that are comorbid with migraine. Here we used computer modeling to test the functional role of FHM3-mutated Na_V1.1 channels in mechanisms of trigeminal pain. The activation of Aδ-fibers was studied for two algogens, ATP and 5-HT, operating through P2X3 and 5-HT3 receptors, respectively, at trigeminal nerve terminals. In WT Aδ-fibers of meningeal afferents, Na_V1.1 channels efficiently participate in spike generation induced by ATP and 5-HT supported by Na_V1.6 channels. Of the various FHM3 mutations tested, the L263V missense mutation, with a longer activation state and lower activation voltage, resulted in the most pronounced spiking activity. In contrast, mutations that result in a loss of Na_V1.1 function largely reduced firing of trigeminal nerve fibers. The combined activation of P2X3 and 5-HT3 receptors and branching of nerve fibers resulted in very prolonged and high-frequency spiking activity in the mutants compared to WT. We identified, in silico, key determinants of long-lasting nociceptive activity in FHM3-mutated Aδ-fibers that naturally express P2X3 and 5-HT3 receptors and suggest mutant-specific correction options. Modeled trigeminal nerve firing was significantly higher for FHM3 mutations, compared to WT, suggesting that pronounced nociceptive signaling may contribute to migraine pain.

Modeling a Nociceptive Neuro-Immune Synapse Activated by ATP and 5-HT in Meninges: Novel Clues on Transduction of Chemical Signals Into Persistent or Rhythmic Neuronal Firing

Extracellular ATP and serotonin (5-HT) are powerful triggers of nociceptive firing in the meninges, a process supporting headache and whose cellular mechanisms are incompletely understood. The current study aimed to develop, with the neurosimulator NEURON, a novel approach to explore in silico the molecular determinants of the long-lasting, pulsatile nature of migraine attacks. The present model included ATP and 5-HT release, ATP diffusion and hydrolysis, 5-HT uptake, differential activation of ATP P2X or 5-HT3 receptors, and receptor subtype-specific desensitization. The model also tested the role of branched meningeal fibers with multiple release sites. Spike generation and propagation were simulated using variable contribution by potassium and sodium channels in a multi-compartment fiber environment. Multiple factors appeared important to ensure prolonged nociceptive firing potentially relevant to long-lasting pain. Crucial roles were observed in: (i) co-expression of ATP P2X2 and P2X3 receptor subunits; (ii) intrinsic activation/inactivation properties of sodium Nav1.8 channels; and (iii) temporal and spatial distribution of ATP/5-HT release sites along the branches of trigeminal nerve fibers. Based on these factors we could obtain either persistent activation of nociceptive firing or its periodic bursting mimicking the pulsating nature of pain. In summary, our model proposes a novel tool for the exploration of peripheral nociception to test the contribution of clinically relevant factors to headache including migraine pain.

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

Receptor recharge time drastically reduces the number of captured particles

Many diverse biological systems are described by randomly moving particles that can be captured by traps in their environment. Examples include neurotransmitters diffusing in the synaptic cleft before binding to receptors and prey roaming an environment before capture by predators. In most cases, the traps cannot capture particles continuously. Rather, each trap must wait a transitory “recharge” time after capturing a particle before additional captures. This recharge time is often overlooked. In the case of instant recharge, the average number of particles captured before they escape grows linearly in the total number of particles. In stark contrast, we prove that for any nonzero recharge time, the average number of captured particles grows at most logarithmically in the total particle number. This is a fundamental effect of recharge, as it holds under very general assumptions on particle motion and spatial domain. Furthermore, we characterize the parameter regime in which a given recharge time will dramatically affect a system, allowing researchers to easily verify if they need to account for recharge in their specific system. Finally, we consider a few examples, including a neural system in which recharge reduces neurotransmitter bindings by several orders of magnitude.

Consider particles that are released into an environment (think diffusing molecules or plankton), and suppose that there are traps in the environment. How many particles will be captured by the traps before they escape? In a standard model, the number of captured particles is proportional to the initial number released. In this paper, we show that for a more realistic model of a trap (one in which traps must recharge after every capture), the number of captures is proportional to the logarithm of the initial number released. That means that if 10⁶ particles are released, only about 6 will be captured. We prove this result mathematically, and then consider a number of applications, including neuronal synapses and ambush predators.

Stochastic, structural and functional factors influencing AMPA and NMDA synaptic response variability: a review

Synaptic transmission is the basic mechanism of information transfer between neurons not only in the brain, but along all the nervous system. In this review we will briefly summarize some of the main parameters that produce stochastic variability in the synaptic response. This variability produces different effects on important brain phenomena, like learning and memory, and, alterations of its basic factors can cause brain malfunctioning.

Anomalous extracellular diffusion in rat cerebellum

Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures.

GLT-1 Transport Stoichiometry Is Constant at Low and High Glutamate Concentrations when Chloride Is Substituted by Gluconate

Glutamate is the major excitatory neurotransmitter, but prolonged exposure even at micromolar concentrations causes neuronal death. Extracellular glutamate is maintained at nanomolar level by glutamate transporters, which, however, may reverse transport and release glutamate. If and when the reverse occurs depends on glutamate transport stoichiometry (GTS). Previously we found that in the presence of chloride, the coupled GLT-1 glutamate transporter current and its relationship to radiolabeled glutamate flux significantly decreased when extracellular glutamate concentration increased above 0.2 mM, which implies a change in GTS. Such high concentrations are feasible near GLT-1 expressed close to synaptic release site during excitatory neurotransmission. The aim of this study was to determine GLT-1 GTS at both low (19–75 μM) and high (300–1200 μM) glutamate concentration ranges. GTS experiments were conducted in the absence of chloride to avoid contributions by the GLT-1 uncoupled chloride conductance. Mathematical analysis of the transporter thermodynamic equilibrium allowed us to derive equations revealing the number of a particular type of ion transported per elementary charge based on the measurements of the transporter reversal potential. We found that GLT-1a expressed in COS-7 cells co-transports 1.5 Na⁺, 0.5 Glu^-, 0.5 H⁺ and counter-transports 0.6 K⁺ per elementary charge in both glutamate concentration ranges, and at both 37°C and 26°C temperatures. The thermodynamic parameter Q₁₀ = 2.4 for GLT-1 turnover rate of 19 s^-1 (37°C, -50 mV) remained constant in the 10 μM–10 mM glutamate concentration range. Importantly, the previously reported decrease in the current/flux ratio at high glutamate concentration was not seen in the absence of chloride in both COS-7 cells and cultured rat neurons. Therefore, only in the absence of chloride, GLT-1 GTS remains constant at all glutamate concentrations. Possible explanations for why apparent GTS might vary in the presence of chloride are discussed.

Computational modeling of diffusion in the cerebellum

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.

Role of perisynaptic parameters in neurotransmitter homeostasis--computational study of a general synapse

Extracellular neurotransmitter concentrations vary over a wide range depending on the type of neurotransmitter and location in the brain. Neurotransmitter homeostasis near a synapse is achieved by a balance of several mechanisms including vesicular release from the presynapse, diffusion, uptake by transporters, nonsynaptic production, and regulation of release by autoreceptors. These mechanisms are also affected by the glia surrounding the synapse. However, the role of these mechanisms in achieving neurotransmitter homeostasis is not well understood. A biophysical modeling framework was proposed, based on a cortico-accumbens synapse example case, to reverse engineer glial configurations and parameters related to homeostasis for synapses that support a range of neurotransmitter gradients. Model experiments reveal that synapses with extracellular neurotransmitter concentrations in the micromolar range require nonsynaptic neurotransmitter sources and tight synaptic isolation by extracellular glial formations. The model was used to identify the role of perisynaptic parameters on neurotransmitter homeostasis and to propose glial configurations that could support different levels of extracellular neurotransmitter concentrations. Ranking the parameters based on their effect on neurotransmitter homeostasis, nonsynaptic sources were found to be the most important followed by transporter concentration and diffusion coefficient.

Synaptic glutamate spillover increases NMDA receptor reliability at the cerebellar glomerulus

Glutamate spillover in the mossy fiber to granule cell cerebellar glomeruli has been hypothesized to increase neurotransmission reliability. In this study, we evaluate this hypothesis using an experimentally based quantitative model of glutamate spillover on the N-methyl-d-aspartate receptors (NMDA-Rs) at the cerebellar glomerulus. The transient and steady-state responses of NMDA-Rs were examined over a physiological range of firing rates. Examined cases included direct glutamate release activation, glutamate spillover activation, and a combination of direct and spillover activation. Our results illustrate that the effects of spillover alone are equivalent to direct release and, notably, combined spillover and direct release effects on NMDA-Rs are not additive. Our results show that spillover does in fact provide a high degree of reliability given that the synaptic vesicle release rate must fall to approximately 15-25% of what is considered the normal baseline level in order to substantially alter neurotransmission across the examined range of frequencies. We suggest that the high reliability provided by activation due to glutamate spillover could be used to conserve energy by reducing the required overall glutamate load at higher frequencies.

Computational investigation of the changing patterns of subtype specific NMDA receptor activation during physiological glutamatergic neurotransmission

NMDA receptors (NMDARs) are the major mediator of the postsynaptic response during synaptic neurotransmission. The diversity of roles for NMDARs in influencing synaptic plasticity and neuronal survival is often linked to selective activation of multiple NMDAR subtypes (NR1/NR2A-NMDARs, NR1/NR2B-NMDARs, and triheteromeric NR1/NR2A/NR2B-NMDARs). However, the lack of available pharmacological tools to block specific NMDAR populations leads to debates on the potential role for each NMDAR subtype in physiological signaling, including different models of synaptic plasticity. Here, we developed a computational model of glutamatergic signaling at a prototypical dendritic spine to examine the patterns of NMDAR subtype activation at temporal and spatial resolutions that are difficult to obtain experimentally. We demonstrate that NMDAR subtypes have different dynamic ranges of activation, with NR1/NR2A-NMDAR activation sensitive at univesicular glutamate release conditions, and NR2B containing NMDARs contributing at conditions of multivesicular release. We further show that NR1/NR2A-NMDAR signaling dominates in conditions simulating long-term depression (LTD), while the contribution of NR2B containing NMDAR significantly increases for stimulation frequencies that approximate long-term potentiation (LTP). Finally, we show that NR1/NR2A-NMDAR content significantly enhances response magnitude and fidelity at single synapses during chemical LTP and spike timed dependent plasticity induction, pointing out an important developmental switch in synaptic maturation. Together, our model suggests that NMDAR subtypes are differentially activated during different types of physiological glutamatergic signaling, enhancing the ability for individual spines to produce unique responses to these different inputs.

Release of glutamate from one neuron onto glutamate receptors on adjacent neurons serves as the primary basis for neuronal communication. Further, different types of glutamate signals produce unique responses within the neuronal network, providing the ability for glutamate receptors to discriminate between alternative types of signaling. The NMDA receptor (NMDAR) is a glutamate receptor that mediates a variety of physiological functions, including the molecular basis for learning and memory. These receptors exist as a variety of subtypes, and this molecular heterogeneity is used to explain the diversity in signaling initiated by NMDARs. However, the lack of reliable experimental tools to control the activation of each subtype has led to debate over the subtype specific roles of the NMDAR. We have developed a stochastic model of glutamate receptor activation at a single synapse and find that NMDAR subtypes detect different types of glutamate signals. Moreover, the presence of multiple populations of NMDAR subtypes on a given neuron allows for differential patterns of NMDAR activation in response to varied glutamate inputs. This model demonstrates how NMDAR subtypes enable effective and reliable communication within neuronal networks and can be used as a tool to examine specific roles of NMDAR subtypes in neuronal function.

Molecular diffusion model of neurotransmitter homeostasis around synapses supporting gradients

Neurotransmitter homeostasis in and around a synapse involves complex random processes such as diffusion, molecular binding, and uptake by glial transporters. A three-dimensional stochastic diffusion model of a synapse was developed to provide molecular-level details of neurotransmitter homeostasis not predicted by alternative models based on continuum approaches. The development was illustrated through an example case cortico-accumbens synapse that successfully integrated neuroadaptations observed after chronic cocaine. By incorporating cystine-glutamate exchanger as a nonsynaptic release site for glutamate, the stochastic model was used to quantify the relative contributions of synaptic and nonsynaptic sources to extracellular concentration and to estimate molecular influx rates into the perisynapse. A perturbation analysis showed that among the parameters considered, variation in surface density of glial transporters had the largest effect on glutamate concentrations. The stochastic diffusion model of the example synapse was further generalized to characterize glial morphology by studying the role of diffusion path length in supporting neurotransmitter gradients and isolating the synapse. For the same set of parameters, diffusion path length was found to be proportional to the gradient supported.

Increased accuracy of ligand sensing by receptor diffusion on cell surface

The physical limit with which a cell senses external ligand concentration corresponds to the perfect absorber, where all ligand particles are absorbed and overcounting of same ligand particles does not occur. Here, we analyze how the lateral diffusion of receptors on the cell membrane affects the accuracy of sensing ligand concentration. Specifically, we connect our modeling to neurotransmission in neural synapses where the diffusion of glutamate receptors is already known to refresh synaptic connections. We find that receptor diffusion indeed increases the accuracy of sensing for both the glutamate α-Amino-3-hydroxy-5-Methyl-4-isoxazolePropionic Acid (AMPA) and N-Methyl-D-aspartic Acid (NMDA) receptor, although the NMDA receptor is overall much noisier. We propose that the difference in accuracy of sensing of the two receptors can be linked to their different roles in neurotransmission. Specifically, the high accuracy in sensing glutamate is essential for the AMPA receptor to start membrane depolarization, while the NMDA receptor is believed to work in a second stage as a coincidence detector, involved in long-term potentiation and memory.

Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density

One mechanism of information storage in neurons is believed to be determined by the strength of synaptic contacts. The strength of an excitatory synapse is partially due to the concentration of a particular type of ionotropic glutamate receptor (AMPAR) in the post-synaptic density (PSD). AMPAR concentration in the PSD has to be plastic, to allow the storage of new memories; but it also has to be stable to preserve important information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which AMPAR can enter, leave and remain in the synapse are unclear. We used Monte Carlo simulations to determine the influence of PSD structure and activity in maintaining homeostatic concentrations of AMPARs in the synapse. We found that, the high concentration and excluded volume caused by PSD molecules result in molecular crowding. Diffusion of AMPAR in the PSD under such conditions is anomalous. Anomalous diffusion of AMPAR results in retention of these receptors inside the PSD for periods ranging from minutes to several hours in the absence of strong binding of receptors to PSD molecules. Trapping of receptors in the PSD by crowding effects was very sensitive to the concentration of PSD molecules, showing a switch-like behavior for retention of receptors. Non-covalent binding of AMPAR to anchored PSD molecules allowed the synapse to become well-mixed, resulting in normal diffusion of AMPAR. Binding also allowed the exchange of receptors in and out of the PSD. We propose that molecular crowding is an important biophysical mechanism to maintain homeostatic synaptic concentrations of AMPARs in the PSD without the need of energetically expensive biochemical reactions. In this context, binding of AMPAR with PSD molecules could collaborate with crowding to maintain synaptic homeostasis but could also allow synaptic plasticity by increasing the exchange of these receptors with the surrounding extra-synaptic membrane.

One of the most accepted theories of information storage in neurons is that it is partially localized in the strength of synaptic contacts. Evidence suggests that at the cellular level, in combination with other cellular mechanisms, this is implemented by increasing or decreasing the concentration of a particular type of membrane molecules. Two opposing mechanisms have to coexist in synapses to allow them to store information. On one hand, synapses have to be flexible, to allow the storage of new memories. On the other hand, synapses have to be stable to preserve previously learned information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which molecules can enter, leave and remain in the synapse are unclear. Our modeling work uses fundamental biophysical principles to quantify the effects of molecular collisions and biochemical reactions. Our results show that molecular collisions alone, between the diffusing proteins with anchored molecules in the synapse, can replicate known experimental results. Molecular collision in combination with biochemical binding can be fundamental biophysical principles used by synapses for the formation and preservation of memories.

Astrocytic dysfunction in epileptogenesis: consequence of altered potassium and glutamate homeostasis?

Focal epilepsy often develops following traumatic, ischemic, or infectious brain injury. While the electrical activity of the epileptic brain is well characterized, the mechanisms underlying epileptogenesis are poorly understood. We have recently shown that in the rat neocortex, long-lasting breakdown of the blood-brain barrier (BBB) or direct exposure of the neocortex to serum-derived albumin leads to rapid upregulation of the astrocytic marker GFAP (glial fibrillary acidic protein), followed by delayed (within 4-7 d) development of an epileptic focus. We investigated the role of astrocytes in epileptogenesis in the BBB-breakdown and albumin models of epileptogenesis. We found similar, robust changes in astrocytic gene expression in the neocortex within hours following treatment with deoxycholic acid (BBB breakdown) or albumin. These changes predict reduced clearance capacity for both extracellular glutamate and potassium. Electrophysiological recordings in vitro confirmed the reduced clearance of activity-dependent accumulation of both potassium and glutamate 24 h following exposure to albumin. We used a NEURON model to simulate the consequences of reduced astrocytic uptake of potassium and glutamate on EPSPs. The model predicted that the accumulation of glutamate is associated with frequency-dependent (>100 Hz) decreased facilitation of EPSPs, while potassium accumulation leads to frequency-dependent (10-50 Hz) and NMDA-dependent synaptic facilitation. In vitro electrophysiological recordings during epileptogenesis confirmed frequency-dependent synaptic facilitation leading to seizure-like activity. Our data indicate a transcription-mediated astrocytic transformation early during epileptogenesis. We suggest that the resulting reduction in the clearance of extracellular potassium underlies frequency-dependent neuronal hyperexcitability and network synchronization.

Pathology dynamics predict spinal cord injury therapeutic success

Secondary injury, the complex cascade of cellular events following spinal cord injury (SCI), is a major source of post-insult neuron death. Experimental work has focused on the details of individual factors or mechanisms that contribute to secondary injury, but little is known about the interactions among factors leading to the overall pathology dynamics that underlie its propagation. Prior hypotheses suggest that the pathology is dominated by interactions, with therapeutic success lying in combinations of neuroprotective treatments. In this study, we provide the first comprehensive, system-level characterization of the entire secondary injury process using a novel relational model methodology that aggregates the findings of approximately 250 experimental studies. Our quantitative examination of the overall pathology dynamics suggests that, while the pathology is initially dominated by "fire-like", rate-dependent interactions, it quickly switches to a "flood-like", accumulation-dependent process with contributing factors being largely independent. Our evaluation of approximately 20,000 potential single and combinatorial treatments indicates this flood-like pathology results in few highly influential factors at clinically realistic treatment time frames, with multi-factor treatments being merely additive rather than synergistic in reducing neuron death. Our findings give new fundamental insight into the understanding of the secondary injury pathology as a whole, provide direction for alternative therapeutic strategies, and suggest that ultimate success in treating SCI lies in the pursuit of pathology dynamics in addition to individually involved factors.

Computational model of extracellular glutamate in the nucleus accumbens incorporates neuroadaptations by chronic cocaine

Chronic cocaine administration causes instability in extracellular glutamate in the nucleus accumbens that is thought to contribute to the vulnerability to relapse. A computational framework was developed to model glutamate in the extracellular space, including synaptic and nonsynaptic glutamate release, glutamate elimination by glutamate transporters and diffusion, and negative feedback on synaptic release via metabotropic glutamate receptors (mGluR2/3). This framework was used to optimize the geometry of the glial sheath surrounding excitatory synapses, and by inserting physiological values, accounted for known stable extracellular, extrasynaptic concentrations of glutamate measured by microdialysis and glutamatergic tone on mGluR2/3. By using experimental values for cocaine-induced reductions in cystine-glutamate exchange and mGluR2/3 signaling, and by predicting the down-regulation of glutamate transporters, the computational model successfully represented the experimentally observed increase in glutamate that is seen in rats during cocaine-seeking. This model provides a mathematical framework for describing how pharmacological or pathological conditions influence glutamate transmission measured by microdialysis.

Output-based comparison of alternative kinetic schemes for the NMDA receptor within a glutamate spillover model

Recent experimental and theoretical work continues to explore the mechanisms and implications of neurotransmitter spillover. Here we examine N-methyl-D-aspartate receptor (NMDA-R) kinetics to determine their implication(s) in glutamate spillover by comparing two mechanistically different NMDA-R models, the 5-state Lester and Jahr (LJ) model and the 8-state Banke and Traynelis (BT) model, within the context of a glutamate spillover model. We employ a search-survey-and-summarize strategy to analyze the relationships within model behavior (model relational analysis) and form a model output landscape. Our results indicate that model relational analysis can reveal differences in models whose outputs would be considered the same. The analysis reveals that the BT model, with its more complex kinetics, is less reliant on diffusion compared to the LJ version, resulting in differences in the relationships between open probability and glutamate concentration despite the fact that both model versions were able to produce the same target output values. Additionally, model relational analysis is able to distinguish between the BT and LJ NMDA-R model versions even though factor analysis indicates that the overall model output space dimensions are the same for both NMDA-R models. Furthermore, the work presented here suggests that model relational analysis may be broadly applicable as a means to examine the complex interactions hidden within overall model behavior.

An analysis of glutamate spillover on the N-methyl-D-aspartate receptors at the cerebellar glomerulus

Glutamate spillover is thought to play a significant role in increasing neural transmission at the mossy fiber/granule cell cerebellar glomerulus. Glutamate spillover has been shown to activate AMPA receptors at the glomerulus, and here we complete the characterization of spillover at the glomerulus by investigating the role of glutamate spillover in N-methyl-D-aspartate receptor (NMDA-R) activation. We present a quantitative model of glutamate spillover combining recent models of glutamate diffusion and NMDA-R binding to determine the open probabilities of NMDA-Rs over time at a neighbor synapse. Simulation results from a baseline set of physiologically realistic parameters show that glutamate spillover onto a single neighbor synapse, created by glutamate that diffuses from a point source into a restricted fractional 2D-3D space and the glutamate concentration created by neighboring glutamate release sites, is sufficient to elicit an NMDA-R peak open probability of 0.23, approximately 79% of that obtained by a direct release (peak open probability of 0.29). Thus, it would appear that glutamate spillover at the glomerulus at NMDA receptors is even more substantial than that seen at AMPA receptors.

LTP regulates burst initiation and frequency at mossy fiber-granule cell synapses of rat cerebellum: experimental observations and theoretical predictions

Long-term potentiation (LTP) is a synaptic change supposed to provide the cellular basis for learning and memory in brain neuronal circuits. Although specific LTP expression mechanisms could be critical to determine the dynamics of repetitive neurotransmission, this important issue remained largely unexplored. In this paper, we have performed whole cell patch-clamp recordings of mossy fiber-granule cell LTP in acute rat cerebellar slices and studied its computational implications with a mathematical model. During LTP, stimulation with short impulse trains at 100 Hz revealed earlier initiation of granule cell spike bursts and a smaller nonsignificant spike frequency increase. In voltage-clamp recordings, short AMPA excitatory postsynaptic current (EPSC) trains showed short-term facilitation and depression and a sustained component probably generated by spillover. During LTP, facilitation disappeared, depression accelerated, and the sustained current increased. The N-methyl-d-aspartate (NMDA) current also increased. In agreement with a presynaptic expression caused by increased release probability, similar changes were observed by raising extracellular [Ca(2+)]. A mathematical model of mossy fiber-granule cell neurotransmission showed that increasing release probability efficiently modulated the first-spike delay. Glutamate spillover, by causing tonic NMDA and AMPA receptor activation, accelerated excitatory postsynaptic potential (EPSP) temporal summation and maintained a sustained spike discharge. The effect of increasing neurotransmitter release could not be replicated by increasing receptor conductance, which, like postsynaptic manipulations enhancing intrinsic excitability, proved very effective in raising granule cell output frequency. Independent regulation of spike burst initiation and frequency during LTP may provide mechanisms for temporal recoding and gain control of afferent signals at the input stage of cerebellar cortex.

Changes in synaptic structure underlie the developmental speeding of AMPA receptor–mediated EPSCs

At many excitatory and inhibitory synapses throughout the nervous system, postsynaptic currents become faster as the synapse matures, primarily owing to changes in receptor subunit composition. The origin of the developmental acceleration of AMPA receptor (AMPAR)-mediated excitatory postsynaptic currents (EPSCs) remains elusive. We used patch-clamp recordings, electron microscopic immunogold localization of AMPARs, partial three-dimensional reconstruction of the neuropil and numerical simulations of glutamate diffusion and AMPAR activation to examine the factors underlying the developmental speeding of miniature EPSCs in mouse cerebellar granule cells. We found that the main developmental change that permits submillisecond transmission at mature synapses is an alteration in the glutamate concentration waveform as experienced by AMPARs. This can be accounted for by changes in the synaptic structure and surrounding neuropil, rather than by a change in AMPAR properties. Our findings raise the possibility that structural alterations could be a general mechanism underlying the change in the time course of AMPAR-mediated synaptic transmission.