Modelling vesicular release at hippocampal synapses

A spatial model of autophosphorylation of Ca2+/calmodulin-dependent protein kinase II (CaMKII) predicts that the lifetime of phospho-CaMKII after induction of synaptic plasticity is greatly prolonged by CaM-trapping

Long-term potentiation (LTP) is a biochemical process that underlies learning in excitatory glutamatergic synapses in the Central Nervous System (CNS). The critical early driver of LTP is autophosphorylation of the abundant postsynaptic enzyme, Ca2+/calmodulin-dependent protein kinase II (CaMKII). Autophosphorylation is initiated by Ca2+ flowing through NMDA receptors activated by strong synaptic activity. Its lifetime is ultimately determined by the balance of the rates of autophosphorylation and of dephosphorylation by protein phosphatase 1 (PP1). Here we have modeled the autophosphorylation and dephosphorylation of CaMKII during synaptic activity in a spine synapse using MCell4, an open source computer program for creating particle-based stochastic, and spatially realistic models of cellular microchemistry. The model integrates four earlier detailed models of separate aspects of regulation of spine Ca2+ and CaMKII activity, each of which incorporate experimentally measured biochemical parameters and have been validated against experimental data. We validate the composite model by showing that it accurately predicts previous experimental measurements of effects of NMDA receptor activation, including high sensitivity of induction of LTP to phosphatase activity in vivo, and persistence of autophosphorylation for a period of minutes after the end of synaptic stimulation. We then use the model to probe aspects of the mechanism of regulation of autophosphorylation of CaMKII that are difficult to measure in vivo. We examine the effects of "CaM-trapping," a process in which the affinity for Ca2+/CaM increases several hundred-fold after autophosphorylation. We find that CaM-trapping does not increase the proportion of autophosphorylated subunits in holoenzymes after a complex stimulus, as previously hypothesized. Instead, CaM-trapping may dramatically prolong the lifetime of autophosphorylated CaMKII through steric hindrance of dephosphorylation by protein phosphatase 1. The results provide motivation for experimental measurement of the extent of suppression of dephosphorylation of CaMKII by bound Ca2+/CaM. The composite MCell4 model of biochemical effects of complex stimuli in synaptic spines is a powerful new tool for realistic, detailed dissection of mechanisms of synaptic plasticity.

Aβ-mediated synaptic glutamate dynamics and calcium dynamics in astrocytes associated with Alzheimer's disease

The accumulation of amyloid β peptide A β is assumed to be one of the main causes of Alzheimer's disease AD . There is increasing evidence that astrocytes are the primary targets of Aβ. Aβ can cause abnormal synaptic glutamate, aberrant extrasynaptic glutamate, and astrocytic calcium dysregulation through astrocyte glutamate transporters facing the synaptic cleft (GLT-syn), astrocyte glutamate transporters facing the extrasynaptic space (GLT-ess), metabotropic glutamate receptors in astrocytes (mGluR), N-methyl-D-aspartate receptors in astrocytes (NMDAR), and glutamatergic gliotransmitter release (Glio-Rel). However, it is difficult to experimentally identify the extent to which each pathway affects synaptic glutamate, extrasynaptic glutamate, and astrocytic calcium signaling. Motivated by these findings, this work established a concise mathematical model of astrocyteCa 2 + dynamics, including the above Aβ-mediated glutamate-related multiple pathways. The model results presented the extent to which five mechanisms acted upon by Aβ affect synaptic glutamate, extrasynaptic glutamate, and astrocytic intracellularCa 2 + signals. We found that GLT-syn is the main pathway through which Aβ affects synaptic glutamate. GLT-ess and Glio-Rel are the main pathways through which A β affects extrasynaptic glutamate. GLT-syn, mGluR, and NMDAR are the main pathways through which Aβ affects astrocytic intracellularCa 2 + signals. Additionally, we discovered a strong, monotonically increasing relationship between the mean glutamate concentration and the meanCa 2 + oscillation amplitude (or frequency). Our results may have therapeutic implications for slowing cell death induced by the combination of glutamate imbalance andCa 2 + dysregulation in AD.

Synaptotagmins 3 and 7 mediate the majority of asynchronous release from synapses in the cerebellum and hippocampus

Neurotransmitter release consists of rapid synchronous release followed by longer-lasting asynchronous release (AR). Although the presynaptic proteins that trigger synchronous release are well understood, the mechanisms for AR remain unclear. AR is sustained by low concentrations of intracellular Ca2+ and Sr2+, suggesting the involvement of sensors with high affinities for both ions. Synaptotagmin 7 (SYT7) partly mediates AR, but substantial AR persists in the absence of SYT7. The closely related SYT3 binds Ca2+ and Sr2+ with high affinity, making it a promising candidate to mediate AR. Here, we use knockout mice to study the contribution of SYT3 and SYT7 to AR at cerebellar and hippocampal synapses. AR is dramatically reduced when both isoforms are absent, which alters the number and timing of postsynaptic action potentials. Our results confirm the long-standing prediction that SYT3 mediates AR and show that SYT3 and SYT7 act as dominant mechanisms for AR at three central synapses.

Synapse-specific structural plasticity that protects and refines local circuits during LTP and LTD

Synapses form trillions of connections in the brain. Long-term potentiation (LTP) and long-term depression (LTD) are cellular mechanisms vital for learning that modify the strength and structure of synapses. Three-dimensional reconstruction from serial section electron microscopy reveals three distinct pre- to post-synaptic arrangements: strong active zones (AZs) with tightly docked vesicles, weak AZs with loose or non-docked vesicles, and nascent zones (NZs) with a postsynaptic density but no presynaptic vesicles. Importantly, LTP can be temporarily saturated preventing further increases in synaptic strength. At the onset of LTP, vesicles are recruited to NZs, converting them to AZs. During recovery of LTP from saturation (1-4 h), new NZs form, especially on spines where AZs are most enlarged by LTP. Sentinel spines contain smooth endoplasmic reticulum (SER), have the largest synapses and form clusters with smaller spines lacking SER after LTP recovers. We propose a model whereby NZ plasticity provides synapse-specific AZ expansion during LTP and loss of weak AZs that drive synapse shrinkage during LTD. Spine clusters become functionally engaged during LTP or disassembled during LTD. Saturation of LTP or LTD probably acts to protect recently formed memories from ongoing plasticity and may account for the advantage of spaced over massed learning. This article is part of a discussion meeting issue 'Long-term potentiation: 50 years on'.

MCell4 with BioNetGen: A Monte Carlo simulator of rule-based reaction-diffusion systems with Python interface

Biochemical signaling pathways in living cells are often highly organized into spatially segregated volumes, membranes, scaffolds, subcellular compartments, and organelles comprising small numbers of interacting molecules. At this level of granularity stochastic behavior dominates, well-mixed continuum approximations based on concentrations break down and a particle-based approach is more accurate and more efficient. We describe and validate a new version of the open-source MCell simulation program (MCell4), which supports generalized 3D Monte Carlo modeling of diffusion and chemical reaction of discrete molecules and macromolecular complexes in solution, on surfaces representing membranes, and combinations thereof. The main improvements in MCell4 compared to the previous versions, MCell3 and MCell3-R, include a Python interface and native BioNetGen reaction language (BNGL) support. MCell4's Python interface opens up completely new possibilities for interfacing with external simulators to allow creation of sophisticated event-driven multiscale/multiphysics simulations. The native BNGL support, implemented through a new open-source library libBNG (also introduced in this paper), provides the capability to run a given BNGL model spatially resolved in MCell4 and, with appropriate simplifying assumptions, also in the BioNetGen simulation environment, greatly accelerating and simplifying model validation and comparison.

Making time and space for calcium control of neuron activity

Calcium directly controls or indirectly regulates numerous functions that are critical for neuronal network activity. Intracellular calcium concentration is tightly regulated by numerous molecular mechanisms because spatial domains and temporal dynamics (not just peak amplitude) are critical for calcium control of synaptic plasticity and ion channel activation, which in turn determine neuron spiking activity. The computational models investigating calcium control are valuable because experiments achieving high spatial and temporal resolution simultaneously are technically unfeasible. Simulations of calcium nanodomains reveal that specific calcium sources can couple to specific calcium targets, providing a mechanism to determine the direction of synaptic plasticity. Cooperativity of calcium domains opposes specificity, suggesting that the dendritic branch might be the preferred computational unit of the neuron.

The release of inhibition model reproduces kinetics and plasticity of neurotransmitter release in central synapses

Calcium-evoked release of neurotransmitters from synaptic vesicles (SVs) is catalysed by SNARE proteins. The predominant view is that, at rest, complete assembly of SNARE complexes is inhibited ('clamped') by synaptotagmin and complexin molecules. Calcium binding by synaptotagmins releases this fusion clamp and triggers fast SV exocytosis. However, this model has not been quantitatively tested over physiological timescales. Here we describe an experimentally constrained computational modelling framework to quantitatively assess how the molecular architecture of the fusion clamp affects SV exocytosis. Our results argue that the 'release-of-inhibition' model can indeed account for fast calcium-activated SV fusion, and that dual binding of synaptotagmin-1 and synaptotagmin-7 to the same SNARE complex enables synergistic regulation of the kinetics and plasticity of neurotransmitter release. The developed framework provides a powerful and adaptable tool to link the molecular biochemistry of presynaptic proteins to physiological data and efficiently test the plausibility of calcium-activated neurotransmitter release models.

Crosstalk between biochemical signalling network architecture and trafficking governs AMPAR dynamics in synaptic plasticity

Synaptic plasticity involves modification of both biochemical and structural components of neurons. Many studies have revealed that the change in the number density of the glutamatergic receptor AMPAR at the synapse is proportional to synaptic weight update; an increase in AMPAR corresponds to strengthening of synapses while a decrease in AMPAR density weakens synaptic connections. The dynamics of AMPAR are thought to be regulated by upstream signalling, primarily the calcium-CaMKII pathway, trafficking to and from the synapse, and influx from extrasynaptic sources. Previous work in the field of deterministic modelling of CaMKII dynamics has assumed bistable kinetics, while experiments and rule-based modelling have revealed that CaMKII dynamics can be either monostable or ultrasensitive. This raises the following question: how does the choice of model assumptions involving CaMKII dynamics influence AMPAR dynamics at the synapse? To answer this question, we have developed a set of models using compartmental ordinary differential equations to systematically investigate contributions of different signalling and trafficking variations, along with their coupled effects, on AMPAR dynamics at the synaptic site. We find that the properties of the model including network architecture describing different stability features of CaMKII and parameters that capture the endocytosis and exocytosis of AMPAR significantly affect the integration of fast upstream species by slower downstream species. Furthermore, we predict that the model outcome, as determined by bound AMPAR at the synaptic site, depends on (1) the choice of signalling model (bistable CaMKII or monostable CaMKII dynamics), (2) trafficking versus influx contributions and (3) frequency of stimulus. KEY POINTS: The density of AMPA receptors (AMPARs) at the postsynaptic density of the synapse provides a readout of synaptic plasticity, which involves crosstalk between complex biochemical signalling networks including CaMKII dynamics and trafficking pathways including exocytosis and endocytosis. Here we build a model that integrates CaMKII dynamics and AMPAR trafficking to explore this crosstalk. We compare different models of CaMKII that result in monostable or bistable kinetics and their impact on AMPAR dynamics. Our results show that AMPAR density depends on the coupling between aspects of biochemical signalling and trafficking. Specifically, assumptions regarding CaMKII dynamics and its stability features can alter AMPAR density at the synapse. Our model also predicts that the kinetics of trafficking versus influx of AMPAR from the extrasynaptic space can further impact AMPAR density. Thus, the contributions of both signalling and trafficking should be considered in computational models.

Upregulated Ca2+ Release from the Endoplasmic Reticulum Leads to Impaired Presynaptic Function in Familial Alzheimer's Disease

Neurotransmitter release from presynaptic terminals is primarily regulated by rapid Ca2+ influx through membrane-resident voltage-gated Ca2+ channels (VGCCs). Moreover, accumulating evidence indicates that the endoplasmic reticulum (ER) is extensively present in axonal terminals of neurons and plays a modulatory role in synaptic transmission by regulating Ca2+ levels. Familial Alzheimer's disease (FAD) is marked by enhanced Ca2+ release from the ER and downregulation of Ca2+ buffering proteins. However, the precise consequence of impaired Ca2+ signaling within the vicinity of VGCCs (active zone (AZ)) on exocytosis is poorly understood. Here, we perform in silico experiments of intracellular Ca2+ signaling and exocytosis in a detailed biophysical model of hippocampal synapses to investigate the effect of aberrant Ca2+ signaling on neurotransmitter release in FAD. Our model predicts that enhanced Ca2+ release from the ER increases the probability of neurotransmitter release in FAD. Moreover, over very short timescales (30-60 ms), the model exhibits activity-dependent and enhanced short-term plasticity in FAD, indicating neuronal hyperactivity-a hallmark of the disease. Similar to previous observations in AD animal models, our model reveals that during prolonged stimulation (~450 ms), pathological Ca2+ signaling increases depression and desynchronization with stimulus, causing affected synapses to operate unreliably. Overall, our work provides direct evidence in support of a crucial role played by altered Ca2+ homeostasis mediated by intracellular stores in FAD.

Multiscale modeling of presynaptic dynamics from molecular to mesoscale

Chemical synapses exhibit a diverse array of internal mechanisms that affect the dynamics of transmission efficacy. Many of these processes, such as release of neurotransmitter and vesicle recycling, depend strongly on activity-dependent influx and accumulation of Ca²⁺. To model how each of these processes may affect the processing of information in neural circuits, and how their dysfunction may lead to disease states, requires a computationally efficient modelling framework, capable of generating accurate phenomenology without incurring a heavy computational cost per synapse. Constructing a phenomenologically realistic model requires the precise characterization of the timing and probability of neurotransmitter release. Difficulties arise in that functional forms of instantaneous release rate can be difficult to extract from noisy data without running many thousands of trials, and in biophysical synapses, facilitation of per-vesicle release probability is confounded by depletion. To overcome this, we obtained traces of free Ca²⁺ concentration in response to various action potential stimulus trains from a molecular MCell model of a hippocampal Schaffer collateral axon. Ca²⁺ sensors were placed at varying distance from a voltage-dependent calcium channel (VDCC) cluster, and Ca²⁺ was buffered by calbindin. Then, using the calcium traces to drive deterministic state vector models of synaptotagmin 1 and 7 (Syt-1/7), which respectively mediate synchronous and asynchronous release in excitatory hippocampal synapses, we obtained high-resolution profiles of instantaneous release rate, to which we applied functional fits. Synchronous vesicle release occurred predominantly within half a micron of the source of spike-evoked Ca²⁺ influx, while asynchronous release occurred more consistently at all distances. Both fast and slow mechanisms exhibited multi-exponential release rate curves, whose magnitudes decayed exponentially with distance from the Ca²⁺ source. Profile parameters facilitate on different time scales according to a single, general facilitation function. These functional descriptions lay the groundwork for efficient mesoscale modelling of vesicular release dynamics.

Most information transmission between neurons in the brain occurs via release of neurotransmitter from synaptic vesicles. In response to a presynaptic spike, calcium influx at the active zone of a synapse can trigger the release of neurotransmitter with a certain probability. These stochastic release events may occur immediately after a spike or with some delay. As calcium accumulates from one spike to the next, the probability of release may increase (facilitate) for subsequent spikes. This process, known as short-term plasticity, transforms the spiking code to a release code, underlying much of the brain’s information processing. In this paper, we use an accurate, detailed model of presynaptic molecular physiology to characterize these processes at high precision in response to various spike trains. We then apply model reduction to the results to obtain a phenomenological model of release timing, probability, and facilitation, which can perform as accurately as the molecular model but with far less computational cost. This mesoscale model of spike-evoked release and facilitation helps to bridge the gap between microscale molecular dynamics and macroscale information processing in neural circuits. It can thus benefit large scale modelling of neural circuits, biologically inspired machine learning models, and the design of neuromorphic chips.

Influence of T-Bar on Calcium Concentration Impacting Release Probability

The relation of form and function, namely the impact of the synaptic anatomy on calcium dynamics in the presynaptic bouton, is a major challenge of present (computational) neuroscience at a cellular level. The Drosophila larval neuromuscular junction (NMJ) is a simple model system, which allows studying basic effects in a rather simple way. This synapse harbors several special structures. In particular, in opposite to standard vertebrate synapses, the presynaptic boutons are rather large, and they have several presynaptic zones. In these zones, different types of anatomical structures are present. Some of the zones bear a so-called T-bar, a particular anatomical structure. The geometric form of the T-bar resembles the shape of the letter “T” or a table with one leg. When an action potential arises, calcium influx is triggered. The probability of vesicle docking and neurotransmitter release is superlinearly proportional to the concentration of calcium close to the vesicular release site. It is tempting to assume that the T-bar causes some sort of calcium accumulation and hence triggers a higher release probability and thus enhances neurotransmitter exocytosis. In order to study this influence in a quantitative manner, we constructed a typical T-bar geometry and compared the calcium concentration close to the active zones (AZs). We compared the case of synapses with and without T-bars. Indeed, we found a substantial influence of the T-bar structure on the presynaptic calcium concentrations close to the AZs, indicating that this anatomical structure increases vesicle release probability. Therefore, our study reveals how the T-bar zone implies a strong relation between form and function. Our study answers the question of experimental studies (namely “Wichmann and Sigrist, Journal of neurogenetics 2010”) concerning the sense of the anatomical structure of the T-bar.

Markov Chain Abstractions of Electrochemical Reaction-Diffusion in Synaptic Transmission for Neuromorphic Computing

Progress in computational neuroscience toward understanding brain function is challenged both by the complexity of molecular-scale electrochemical interactions at the level of individual neurons and synapses and the dimensionality of network dynamics across the brain covering a vast range of spatial and temporal scales. Our work abstracts an existing highly detailed, biophysically realistic 3D reaction-diffusion model of a chemical synapse to a compact internal state space representation that maps onto parallel neuromorphic hardware for efficient emulation at a very large scale and offers near-equivalence in input-output dynamics while preserving biologically interpretable tunable parameters.

Presynaptic endoplasmic reticulum regulates short-term plasticity in hippocampal synapses

Short-term plasticity preserves a brief history of synaptic activity that is communicated to the postsynaptic neuron. This is primarily regulated by a calcium signal initiated by voltage dependent calcium channels in the presynaptic terminal. Imaging studies of CA3-CA1 synapses reveal the presence of another source of calcium, the endoplasmic reticulum (ER) in all presynaptic terminals. However, the precise role of the ER in modifying STP remains unexplored. We performed in-silico experiments in synaptic geometries based on reconstructions of the rat CA3-CA1 synapses to investigate the contribution of ER. Our model predicts that presynaptic ER is critical in generating the observed short-term plasticity profile of CA3-CA1 synapses and allows synapses with low release probability to operate more reliably. Blocking the ER lowers facilitation in a manner similar to what has been previously characterized in animal models of Alzheimer's disease and underscores the important role played by presynaptic stores in normal function.

Local Design Principles at Hippocampal Synapses Revealed by an Energy-Information Trade-Off

Synapses across different brain regions display distinct structure-function relationships. We investigated the interplay of fundamental design constraints that shape the transmission properties of the excitatory CA3-CA1 pyramidal cell connection, a prototypic synapse for studying the mechanisms of learning in the mammalian hippocampus. This small synapse is characterized by probabilistic release of transmitter, which is markedly facilitated in response to naturally occurring trains of action potentials. Based on a physiologically motivated computational model of the rat CA3 presynaptic terminal, we show how unreliability and short-term dynamics of vesicular release work together to regulate the trade-off of information transfer versus energy use. We propose that individual CA3-CA1 synapses are designed to operate near the maximum possible capacity of information transmission in an efficient manner. Experimental measurements reveal a wide range of vesicular release probabilities at hippocampal synapses, which may be a necessary consequence of long-term plasticity and homeostatic mechanisms that manifest as presynaptic modifications of the release probability. We show that the timescales and magnitude of short-term plasticity (STP) render synaptic information transfer nearly independent of differences in release probability. Thus, individual synapses transmit optimally while maintaining a heterogeneous distribution of presynaptic strengths indicative of synaptically-encoded memory representations. Our results support the view that organizing principles that are evident on higher scales of neural organization percolate down to the design of an individual synapse.

Estimating the Readily-Releasable Vesicle Pool Size at Synaptic Connections in the Neocortex

Previous studies based on the 'Quantal Model' for synaptic transmission suggest that neurotransmitter release is mediated by a single release site at individual synaptic contacts in the neocortex. However, recent studies seem to contradict this hypothesis and indicate that multi-vesicular release (MVR) could better explain the synaptic response variability observed in vitro. In this study we present a novel method to estimate the number of release sites per synapse, also known as the size of the readily releasable pool (N_RRP), from paired whole-cell recordings of connections between layer 5 thick tufted pyramidal cell (L5_TTPC) in the juvenile rat somatosensory cortex. Our approach extends the work of Loebel et al. (2009) by leveraging a recently published data-driven biophysical model of neocortical tissue. Using this approach, we estimated N_RRP to be between two to three for synaptic connections between L5_TTPCs. To constrain N_RRP values for other connections in the microcircuit, we developed and validated a generalization approach using published data on the coefficient of variation (CV) of the amplitudes of post-synaptic potentials (PSPs) from literature and comparing them against in silico experiments. Our study predicts that transmitter release at synaptic connections in the neocortex could be mediated by MVR and provides a data-driven approach to constrain the MVR model parameters in the microcircuit.

Considerable differences between auditory medulla, auditory midbrain, and hippocampal synapses during sustained high-frequency stimulation: Exceptional vesicle replenishment restricted to sound localization circuit

Reliable synaptic transmission is essential for interneuronal communication. Synaptic inputs to auditory brainstem neurons, particularly those involved in sound localization, are characterized by resilience during sustained activity and temporal precision in the sub-millisecond range. Both features are obtained by synchronous release of a high number of synaptic vesicles following a single action potential. Here, we compare transmission behavior of three heterogeneous types of inputs in the auditory midbrain and medulla. The first terminate in the central inferior colliculus (ICc) and are glutamatergic (activated from the lateral lemniscus, LL). The medullary inputs terminate in the lateral superior olive (LSO) and are glutamatergic (from the cochlear nuclear complex, CN) or glycinergic (from the medial nucleus of the trapezoid body, MNTB). LSO neurons are the first to integrate binaural information and compute interaural level differences, whereas ICc neurons receive information from almost all auditory brainstem nuclei and construct an initial auditory image used for reflexive behavior. We hypothesized that CN-LSO and MNTB-LSO inputs are more resilient to synaptic fatigue during sustained stimulation than LL-ICc inputs. To test the hypothesis, we performed whole-cell patch-clamp recordings in acute brainstem slices of juvenile mice. We investigated the synaptic performance during prolonged periods of high-frequency stimulation (60 s, up to 200 Hz) and assessed several features, e.g. depression, recovery, latency, temporal precision, quantal size and content, readily releasable pool size, release probability, and replenishment rate. Overall, LL-ICc inputs performed less robustly and temporally precisely than CN-LSO and MNTB-LSO inputs. When stimulated at ≥50 Hz, the former depressed completely within a few seconds. In contrast, CN-LSO and MNTB-LSO inputs transmitted faithfully up to 200 Hz, indicative of very efficient replenishment mechanisms. LSO inputs also displayed considerably lower latency jitter than LL-ICc inputs. The latter behaved similarly to two types of input in the hippocampus for which we performed a meta-analysis. Mechanistically, the high-fidelity behavior of LSO inputs, particularly MNTB-LSO synapses, is based on exceptional release properties not present at auditory midbrain or hippocampal inputs. We conclude that robustness and temporal precision are hallmarks of auditory synapses in the medullary brainstem. These key features are less eminent at higher stations, such as the ICc, and they are also absent outside the central auditory system, namely the hippocampal formation.

The Small and Dynamic Pre-primed Pool at the Release Site; A Useful Concept to Understand Release Probability and Short-Term Synaptic Plasticity?

Advanced imaging techniques have revealed that synapses contain nanomodules in which pre- and post-synaptic molecules are brought together to form an integrated subsynaptic component for vesicle release and transmitter reception. Based on data from an electrophysiological study of ours in which release from synapses containing a single nanomodule was induced by brief 50 Hz trains using minimal stimulation, and on data from such imaging studies, we present a possible modus operandi of such a nanomodule. We will describe the techniques and tools used to obtain and analyze the electrophysiological data from single CA3–CA1 hippocampal synapses from the neonatal rat brain. This analysis leads to the proposal that a nanomodule, despite containing a number of release locations, operates as a single release site, releasing at most a single vesicle at a time. In this nanomodule there appears to be two separate sets of release locations, one set that is responsible for release in response to the first few action potentials and another set that produces the release thereafter. The data also suggest that vesicles at the first set of release locations are primed by synaptic inactivity lasting seconds, this synaptic inactivity also resulting in a large heterogeneity in the values for vesicle release probability among the synapses. The number of vesicles being primed at this set of release locations prior to the arrival of an action potential is small (0–3) and varies from train to train. Following the first action potential, this heterogeneity in vesicle release probability largely vanishes in a release-independent manner, shaping a variation in paired-pulse plasticity among the synapses. After the first few action potentials release is produced from the second set of release locations, and is given by vesicles that have been recruited after the onset of synaptic activity. This release depends on the number of such release locations and the recruitment to such a location. The initial heterogeneity in vesicle release probability, its disappearance after a single action potential, and variation in the recruitment to the second set of release locations are instrumental in producing the heterogeneity in short-term synaptic plasticity among these synapses, and can be seen as means to create differential dynamics within a synapse population.

Spatially dispersed synapses yield sharply-tuned place cell responses through dendritic spike initiation

KEY POINTS

The generation of dendritic spikes and the consequent sharp tuning of neuronal responses are together attainable even when iso-feature synapses are randomly dispersed across the dendritic arbor. Disparate combinations of channel conductances with distinct configurations of randomly dispersed place field synapses concomitantly yield similar sharp tuning profiles and similar functional maps of several intrinsic properties. Targeted synaptic plasticity converts silent cells to place cells for specific place fields in models with disparate channel combinations that receive dispersed synaptic inputs from multiple place field locations. Dispersed localization of iso-feature synapses is a strong candidate for achieving sharp feature selectivity in neurons across sensory-perceptual systems, with several degrees of freedom in relation to synaptic locations. Quantitative evidence for the possibility that degeneracy (i.e. the ability of disparate structural components to yield similar functional outcomes) could act as a broad framework that effectively accomplishes the twin goals of input-feature encoding and homeostasis of intrinsic properties without cross interferences.

ABSTRACT

A prominent hypothesis spanning several sensory-perceptual systems implicates spatially clustered synapses in the generation of dendritic spikes that mediate sharply-tuned neuronal responses to input features. In this conductance-based morphologically-precise computational study, we tested this hypothesis by systematically analysing the impact of distinct synaptic and channel localization profiles on sharpness of spatial tuning in hippocampal pyramidal neurons. We found that the generation of dendritic spikes, the emergence of an excitatory ramp in somatic voltage responses, the expression of several intrinsic somatodendritic functional maps and sharp tuning of place-cell responses were all attainable even when iso-feature synapses are randomly dispersed across the dendritic arbor of models with disparate channel combinations. Strikingly, the generation and propagation of dendritic spikes, reliant on dendritic sodium channels and N-methyl-d-asparate receptors, mediated the sharpness of spatial tuning achieved with dispersed synaptic localization. To ensure that our results were not artefacts of narrow parametric choices, we confirmed these conclusions with independent multiparametric stochastic search algorithms spanning thousands of unique models for each synaptic localization scenario. Next, employing virtual knockout models, we demonstrated a vital role for dendritically expressed voltage-gated ion channels, especially the transient potassium channels, in maintaining sharpness of place-cell tuning. Importantly, we established that synaptic potentiation targeted to afferents from one specific place field was sufficient to impart place field selectivity even when intrinsically disparate neurons received randomly dispersed afferents from multiple place field locations. Our results provide quantitative evidence for disparate combinations of channel and synaptic localization profiles to concomitantly yield similar tuning and similar intrinsic properties.

The First 100 nm Inside the Pre-synaptic Terminal Where Calcium Diffusion Triggers Vesicular Release

Calcium diffusion in the thin 100 nm layer located between the plasma membrane and docked vesicles in the pre-synaptic terminal of neuronal cells mediates vesicular fusion and synaptic transmission. Accounting for the narrow-cusp geometry located underneath the vesicle is a key ingredient that defines the probability and the time scale of calcium diffusion to bind calcium sensors for the initiation of vesicular release. We review here the time scale, the calcium binding dynamics and the consequences for asynchronous versus synchronous release. To conclude, three-dimensional modeling approaches and the associated coarse-grained simulations can now account efficiently for the precise co-organization of vesicles and Voltage-Gated-Calcium-Channel (VGCC). This co-organization is a key determinant of short-term plasticity and it shapes asynchronous release. Moreover, changing the location of VGCC from few nanometers underneath the vesicle modifies significantly the release probability. Finally, by modifying the calcium buffer concentration, a single synapse can switch from facilitation to depression.

Importance of vesicle release stochasticity in neuro-spike communication

Aim of this paper is proposing a stochastic model for vesicle release process, a part of neuro-spike communication. Hence, we study biological events occurring in this process and use microphysiological simulations to observe functionality of these events. Since the most important source of variability in vesicle release probability is opening of voltage dependent calcium channels (VDCCs) followed by influx of calcium ions through these channels, we propose a stochastic model for this event, while using a deterministic model for other variability sources. To capture the stochasticity of calcium influx to pre-synaptic neuron in our model, we study its statistics and find that it can be modeled by a distribution defined based on Normal and Logistic distributions.

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.

Degeneracy in the regulation of short-term plasticity and synaptic filtering by presynaptic mechanisms

KEY POINTS

We develop a new biophysically rooted, physiologically constrained conductance-based synaptic model to mechanistically account for short-term facilitation and depression, respectively through residual calcium and transmitter depletion kinetics. We address the specific question of how presynaptic components (including voltage-gated ion channels, pumps, buffers and release-handling mechanisms) and interactions among them define synaptic filtering and short-term plasticity profiles. Employing global sensitivity analyses (GSAs), we show that near-identical synaptic filters and short-term plasticity profiles could emerge from disparate presynaptic parametric combinations with weak pairwise correlations. Using virtual knockout models, a technique to address the question of channel-specific contributions within the GSA framework, we unveil the differential and variable impact of each ion channel on synaptic physiology. Our conclusions strengthen the argument that parametric and interactional complexity in biological systems should not be viewed from the limited curse-of-dimensionality standpoint, but from the evolutionarily advantageous perspective of providing functional robustness through degeneracy.

ABSTRACT

Information processing in neurons is known to emerge as a gestalt of pre- and post-synaptic filtering. However, the impact of presynaptic mechanisms on synaptic filters has not been quantitatively assessed. Here, we developed a biophysically rooted, conductance-based model synapse that was endowed with six different voltage-gated ion channels, calcium pumps, calcium buffer and neurotransmitter-replenishment mechanisms in the presynaptic terminal. We tuned our model to match the short-term plasticity profile and band-pass structure of Schaffer collateral synapses, and performed sensitivity analyses to demonstrate that presynaptic voltage-gated ion channels regulated synaptic filters through changes in excitability and associated calcium influx. These sensitivity analyses also revealed that calcium- and release-control mechanisms were effective regulators of synaptic filters, but accomplished this without changes in terminal excitability or calcium influx. Next, to perform global sensitivity analysis, we generated 7000 randomized models spanning 15 presynaptic parameters, and computed eight different physiological measurements in each of these models. We validated these models by applying experimentally obtained bounds on their measurements, and found 104 (∼1.5%) models to match the validation criteria for all eight measurements. Analysing these valid models, we demonstrate that analogous synaptic filters emerge from disparate combinations of presynaptic parameters exhibiting weak pairwise correlations. Finally, using virtual knockout models, we establish the variable and differential impact of different presynaptic channels on synaptic filters, underlining the critical importance of interactions among different presynaptic components in defining synaptic physiology. Our results have significant implications for protein-localization strategies required for physiological robustness and for degeneracy in long-term synaptic plasticity profiles.

Surface dynamics of voltage-gated ion channels

Neurons encode information in fast changes of the membrane potential, and thus electrical membrane properties are critically important for the integration and processing of synaptic inputs by a neuron. These electrical properties are largely determined by ion channels embedded in the membrane. The distribution of most ion channels in the membrane is not spatially uniform: they undergo activity-driven changes in the range of minutes to days. Even in the range of milliseconds, the composition and topology of ion channels are not static but engage in highly dynamic processes including stochastic or activity-dependent transient association of the pore-forming and auxiliary subunits, lateral diffusion, as well as clustering of different channels. In this review we briefly discuss the potential impact of mobile sodium, calcium and potassium ion channels and the functional significance of this for individual neurons and neuronal networks.

Time-coded neurotransmitter release at excitatory and inhibitory synapses

Communication between neurons at chemical synapses is regulated by hundreds of different proteins that control the release of neurotransmitter that is packaged in vesicles, transported to an active zone, and released when an input spike occurs. Neurotransmitter can also be released asynchronously, that is, after a delay following the spike, or spontaneously in the absence of a stimulus. The mechanisms underlying asynchronous and spontaneous neurotransmitter release remain elusive. Here, we describe a model of the exocytotic cycle of vesicles at excitatory and inhibitory synapses that accounts for all modes of vesicle release as well as short-term synaptic plasticity (STSP). For asynchronous release, the model predicts a delayed inertial protein unbinding associated with the SNARE complex assembly immediately after vesicle priming. Experiments are proposed to test the model's molecular predictions for differential exocytosis. The simplicity of the model will also facilitate large-scale simulations of neural circuits.

A Phenomenological Synapse Model for Asynchronous Neurotransmitter Release

Neurons communicate with each other via synapses. Action potentials cause release of neurotransmitters at the axon terminal. Typically, this neurotransmitter release is tightly time-locked to the arrival of an action potential and is thus called synchronous release. However, neurotransmitter release is stochastic and the rate of release of small quanta of neurotransmitters can be considerably elevated even long after the ceasing of spiking activity, leading to asynchronous release of neurotransmitters. Such asynchronous release varies for tissue and neuron types and has been shown recently to be pronounced in fast-spiking neurons. Notably, it was found that asynchronous release is enhanced in human epileptic tissue implicating a possibly important role in generating abnormal neural activity. Current neural network models for simulating and studying neural activity virtually only consider synchronous release and ignore asynchronous transmitter release. Here, we develop a phenomenological model for asynchronous neurotransmitter release, which, on one hand, captures the fundamental features of the asynchronous release process, and, on the other hand, is simple enough to be incorporated in large-size network simulations. Our proposed model is based on the well-known equations for short-term dynamical synaptic interactions and includes an additional stochastic term for modeling asynchronous release. We use experimental data obtained from inhibitory fast-spiking synapses of human epileptic tissue to fit the model parameters, and demonstrate that our model reproduces the characteristics of realistic asynchronous transmitter release.

The volterra functional series is a viable alternative to kinetic models for synaptic modeling--calibration and benchmarking

Synaptic transmission is governed by a series of complex and highly nonlinear mechanisms and pathways in which the dynamics have a profound influence on the overall signal sent to the postsynaptic cell. In simulation, these mechanisms are often represented through kinetic models governed by state variables and rate law equations. Calculations of such ordinary differential equations (ODEs) in kinetic models can be computationally intensive, and although algorithms have been optimally developed to handle ODEs efficiently, simulation of numerous, large and complex kinetic models requires a prohibitively large amount of computational power. Here we present an alternative representation of ionotropic glutamatergic receptors AMPAr and NMDAr kinetic models consisting of input-output surrogates of the receptor models which can capture the nonlinear dynamics seen in the kinetic models. We benchmark this Input-Output (IO) synapse model and compare it with kinetic receptor models to evaluate the simulation time required when using either synapse model, as well as the number of time steps each model needs for simulation. While remaining faithful to the original dynamics of the model, our results indicate that the IO synapse model requires less simulation time than the kinetic models under conditions which elicit normal physiological responses, thereby improving computational efficiency while preserving the complex non-linear dynamics of the receptors. These IO surrogates therefore constitute an appealing alternative to kinetic models in large scale networks simulations.

Microdomain [Ca(2+)] Fluctuations Alter Temporal Dynamics in Models of Ca(2+)-Dependent Signaling Cascades and Synaptic Vesicle Release

Ca(2+)-dependent signaling is often localized in spatially restricted microdomains and may involve only 1 to 100 Ca(2+) ions. Fluctuations in the microdomain Ca(2+) concentration (Ca(2+)) can arise from a wide range of elementary processes, including diffusion, Ca(2+) influx, and association/dissociation with Ca(2+) binding proteins or buffers. However, it is unclear to what extent these fluctuations alter Ca(2+)-dependent signaling. We construct Markov models of a general Ca(2+)-dependent signaling cascade and Ca(2+)-triggered synaptic vesicle release. We compare the hitting (release) time distribution and statistics for models that account for [Ca(2+)] fluctuations with the corresponding models that neglect these fluctuations. In general, when Ca(2+) fluctuations are much faster than the characteristic time for the signaling event, the hitting time distributions and statistics for the models with and without Ca(2+) fluctuation are similar. However, when the timescale of Ca(2+) fluctuations is on the same order as the signaling cascade or slower, the hitting time mean and variability are typically increased, in particular when the average number of microdomain Ca(2+) ions is small, a consequence of a long-tailed hitting time distribution. In a model of Ca(2+)-triggered synaptic vesicle release, we demonstrate the conditions for which [Ca(2+)] fluctuations do and do not alter the distribution, mean, and variability of release timing. We find that both the release time mean and variability can be increased, demonstrating that Ca(2+) fluctuations are an important aspect of microdomain Ca(2+) signaling and further suggesting that Ca(2+) fluctuations in the presynaptic terminal may contribute to variability in synaptic vesicle release and thus variability in neuronal spiking.

Nanoconnectomic upper bound on the variability of synaptic plasticity

Information in a computer is quantified by the number of bits that can be stored and recovered. An important question about the brain is how much information can be stored at a synapse through synaptic plasticity, which depends on the history of probabilistic synaptic activity. The strong correlation between size and efficacy of a synapse allowed us to estimate the variability of synaptic plasticity. In an EM reconstruction of hippocampal neuropil we found single axons making two or more synaptic contacts onto the same dendrites, having shared histories of presynaptic and postsynaptic activity. The spine heads and neck diameters, but not neck lengths, of these pairs were nearly identical in size. We found that there is a minimum of 26 distinguishable synaptic strengths, corresponding to storing 4.7 bits of information at each synapse. Because of stochastic variability of synaptic activation the observed precision requires averaging activity over several minutes.

DOI:http://dx.doi.org/10.7554/eLife.10778.001

What is the memory capacity of a human brain? The storage capacity in a computer memory is measured in bits, each of which can have a value of 0 or 1. In the brain, information is stored in the form of synaptic strength, a measure of how strongly activity in one neuron influences another neuron to which it is connected. The number of different strengths can be measured in bits. The total storage capacity of the brain therefore depends on both the number of synapses and the number of distinguishable synaptic strengths.

Structurally, neurons consist of a cell body that influences other neurons through a cable-like axon. The cell body bears numerous short branches called dendrites, which are covered in tiny protrusions, or “spines”. Most excitatory synapses are formed between the axon of one neuron and a dendritic spine on another. When two neurons on either side of a synapse are active simultaneously, that synapse becomes stronger, a form of memory. The dendritic spine also becomes larger to accommodate the extra molecular machinery needed to support a stronger synapse.

Some axons form two or more synapses with the same dendrite, but on different dendritic spines. These synapses should be the same strength because they will have experienced the same history of neural activity. Bartol et al. used a technique called serial section electron microscopy to create a 3D reconstruction of part of the brain that allowed the sizes of the dendritic spines these synapses form on to be compared. This revealed that the synaptic areas and volumes of the spine heads were nearly identical. This remarkable similarity can be used to estimate the number of bits of information that a single synapse can store, since the size of dendritic spines and their synapses can be used as proxies for synaptic strength.

Measurements in a small cube of brain tissue revealed 26 different dendritic spine sizes, each associated with a distinct synaptic strength. This number translates into a storage capacity of roughly 4.7 bits of information per synapse. This estimate is markedly higher than previous suggestions. It implies that the total memory capacity of the brain – with its many trillions of synapses – may have been underestimated by an order of magnitude. Additional measurements in the same and other brain regions are needed to confirm this possibility.

DOI:http://dx.doi.org/10.7554/eLife.10778.002

Inhibitory and excitatory axon terminals share a common nano-architecture of their Cav2.1 (P/Q-type) Ca(2+) channels

Tuning of the time course and strength of inhibitory and excitatory neurotransmitter release is fundamental for the precise operation of cortical network activity and is controlled by Ca²⁺ influx into presynaptic terminals through the high voltage-activated P/Q-type Ca²⁺ (Ca_v2.1) channels. Proper channel-mediated Ca²⁺-signaling critically depends on the topographical arrangement of the channels in the presynaptic membrane. Here, we used high-resolution SDS-digested freeze-fracture replica immunoelectron microscopy together with automatized computational analysis of Ca_v2.1 immunogold labeling to determine the precise subcellular organization of Ca_v2.1 channels in both inhibitory and excitatory terminals. Immunoparticles labeling the pore-forming α1 subunit of Ca_v2.1 channels were enriched over the active zone of the boutons with the number of channels (3–62) correlated with the area of the synaptic membrane. Detailed analysis showed that Ca_v2.1 channels are non-uniformly distributed over the presynaptic membrane specialization where they are arranged in clusters of an average five channels per cluster covering a mean area with a diameter of about 70 nm. Importantly, clustered arrangement and cluster properties did not show any significant difference between GABAergic and glutamatergic terminals. Our data demonstrate a common nano-architecture of Ca_v2.1 channels in inhibitory and excitatory boutons in stratum radiatum of the hippocampal CA1 area suggesting that the cluster arrangement is crucial for the precise release of transmitters from the axonal boutons.

Cellular biomechanics of central nervous system injury

With a growing interest in how the brain responds and remodels itself following a traumatic injury, this chapter outlines the major organizing principles of how to study these injuries in the laboratory and extend these findings back into the clinic. A new repertoire of models is available to examine the response of isolated circuits of the brain in vitro, and to study precisely how mechanical forces applied to even small regions of these circuits can disrupt the entire circuit dysfunction. We review the existing knowledge garnered from these models and our current understanding of mechanically sensitive receptors and channels activated immediately following trauma. In turn, we point to the emergence of in silico models of network function that will lead to an improved understanding of the principles for the remodeling of circuit structure after traumatic, possibly pointing out new biological rules for circuit reassembly that would help guide new therapies for reconstructing brain circuits after trauma.

Nanoscale distribution of presynaptic Ca(2+) channels and its impact on vesicular release during development

Synaptic efficacy and precision are influenced by the coupling of voltage-gated Ca²⁺ channels (VGCCs) to vesicles. But because the topography of VGCCs and their proximity to vesicles is unknown, a quantitative understanding of the determinants of vesicular release at nanometer scale is lacking. To investigate this, we combined freeze-fracture replica immunogold labeling of Ca_v2.1 channels, local [Ca²⁺] imaging, and patch pipette perfusion of EGTA at the calyx of Held. Between postnatal day 7 and 21, VGCCs formed variable sized clusters and vesicular release became less sensitive to EGTA, whereas fixed Ca²⁺ buffer properties remained constant. Experimentally constrained reaction-diffusion simulations suggest that Ca²⁺ sensors for vesicular release are located at the perimeter of VGCC clusters (<30 nm) and predict that VGCC number per cluster determines vesicular release probability without altering release time course. This “perimeter release model” provides a unifying framework accounting for developmental changes in both synaptic efficacy and time course.

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Ca²⁺ channels form clusters with highly variable numbers of channels

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EGTA sensitivity suggests that synaptic vesicles are tightly coupled to clusters

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Ca²⁺ channel number per cluster alters synaptic efficacy, but not precision

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A perimeter model accounts for synaptic efficacy and precision during development

Maximum likelihood estimation of biophysical parameters of synaptic receptors from macroscopic currents

Dendritic integration and neuronal firing patterns strongly depend on biophysical properties of synaptic ligand-gated channels. However, precise estimation of biophysical parameters of these channels in their intrinsic environment is complicated and still unresolved problem. Here we describe a novel method based on a maximum likelihood approach that allows to estimate not only the unitary current of synaptic receptor channels but also their multiple conductance levels, kinetic constants, the number of receptors bound with a neurotransmitter, and the peak open probability from experimentally feasible number of postsynaptic currents. The new method also improves the accuracy of evaluation of unitary current as compared to the peak-scaled non-stationary fluctuation analysis, leading to a possibility to precisely estimate this important parameter from a few postsynaptic currents recorded in steady-state conditions. Estimation of unitary current with this method is robust even if postsynaptic currents are generated by receptors having different kinetic parameters, the case when peak-scaled non-stationary fluctuation analysis is not applicable. Thus, with the new method, routinely recorded postsynaptic currents could be used to study the properties of synaptic receptors in their native biochemical environment.

New insights into short-term synaptic facilitation at the frog neuromuscular junction

Short-term synaptic facilitation occurs during high-frequency stimulation, is known to be dependent on presynaptic calcium ions, and persists for tens of milliseconds after a presynaptic action potential. We have used the frog neuromuscular junction as a model synapse for both experimental and computer simulation studies aimed at testing various mechanistic hypotheses proposed to underlie short-term synaptic facilitation. Building off our recently reported excess-calcium-binding-site model of synaptic vesicle release at the frog neuromuscular junction (Dittrich M, Pattillo JM, King JD, Cho S, Stiles JR, Meriney SD. Biophys J 104: 2751-2763, 2013), we have investigated several mechanisms of short-term facilitation at the frog neuromuscular junction. Our studies place constraints on previously proposed facilitation mechanisms and conclude that the presence of a second class of calcium sensor proteins distinct from synaptotagmin can explain known properties of facilitation observed at the frog neuromuscular junction. We were further able to identify a novel facilitation mechanism, which relied on the persistent binding of calcium-bound synaptotagmin molecules to lipids of the presynaptic membrane. In a real physiological context, both mechanisms identified in our study (and perhaps others) may act simultaneously to cause the experimentally observed facilitation. In summary, using a combination of computer simulations and physiological recordings, we have developed a stochastic computer model of synaptic transmission at the frog neuromuscular junction, which sheds light on the facilitation mechanisms in this model synapse.

Biophysical properties of presynaptic short-term plasticity in hippocampal neurons: insights from electrophysiology, imaging and mechanistic models

Hippocampal neurons show different types of short-term plasticity (STP). Some exhibit facilitation of their synaptic responses and others depression. In this review we discuss presynaptic biophysical properties behind heterogeneity in STP in hippocampal neurons such as alterations in vesicle priming and docking, fusion, neurotransmitter filling and vesicle replenishment. We look into what types of information electrophysiology, imaging and mechanistic models have given about the time scales and relative impact of the different properties on STP with an emphasis on the use of mechanistic models as complementary tools to experimental procedures. Taken together this tells us that it is possible for a multitude of different mechanisms to underlie the same STP pattern, even though some are more important in specific cases, and that mechanistic models can be used to integrate the biophysical properties to see which mechanisms are more important in specific cases of STP.

Computational modeling of spike generation in serotonergic neurons of the dorsal raphe nucleus

Serotonergic neurons of the dorsal raphe nucleus, with their extensive innervation of limbic and higher brain regions and interactions with the endocrine system have important modulatory or regulatory effects on many cognitive, emotional and physiological processes. They have been strongly implicated in responses to stress and in the occurrence of major depressive disorder and other psychiatric disorders. In order to quantify some of these effects, detailed mathematical models of the activity of such cells are required which describe their complex neurochemistry and neurophysiology. We consider here a single-compartment model of these neurons which is capable of describing many of the known features of spike generation, particularly the slow rhythmic pacemaking activity often observed in these cells in a variety of species. Included in the model are 11 kinds of ion channels: a fast sodium current INa, a delayed rectifier potassium current IKDR, a transient potassium current IA, a slow non-inactivating potassium current IM, a low-threshold calcium current IT, two high threshold calcium currents IL and IN, small and large conductance potassium currents ISK and IBK, a hyperpolarization-activated cation current IH and a leak current ILeak. In Sections 3-8, each current type is considered in detail and parameters estimated from voltage clamp data where possible. Three kinds of model are considered for the BK current and two for the leak current. Intracellular calcium ion concentration Cai is an additional component and calcium dynamics along with buffering and pumping is discussed in Section 9. The remainder of the article contains descriptions of computed solutions which reveal both spontaneous and driven spiking with several parameter sets. Attention is focused on the properties usually associated with these neurons, particularly long duration of action potential, steep upslope on the leading edge of spikes, pacemaker-like spiking, long-lasting afterhyperpolarization and the ramp-like return to threshold after a spike. In some cases the membrane potential trajectories display doublets or have humps or notches as have been reported in some experimental studies. The computed time courses of IA and IT during the interspike interval support the generally held view of a competition between them in influencing the frequency of spiking. Spontaneous activity was facilitated by the presence of IH which has been found in these neurons by some investigators. For reasonable sets of parameters spike frequencies between about 0.6Hz and 1.2Hz are obtained, but frequencies as high as 6Hz could be obtained with special parameter choices. Topics investigated and compared with experiment include shoulders, notches, anodal break phenomena, the effects of noradrenergic input, frequency versus current curves, depolarization block, effects of cell size and the effects of IM. The inhibitory effects of activating 5-HT1A autoreceptors are also investigated. There is a considerable discussion of in vitro versus in vivo firing behavior, with focus on the roles of noradrenergic input, corticotropin-releasing factor and orexinergic inputs. Location of cells within the nucleus is probably a major factor, along with the state of the animal.

Multiscale modeling and synaptic plasticity

Synaptic plasticity is a major convergence point for theory and computation, and the process of plasticity engages physiology, cell, and molecular biology. In its many manifestations, plasticity is at the hub of basic neuroscience questions about memory and development, as well as more medically themed questions of neural damage and recovery. As an important cellular locus of memory, synaptic plasticity has received a huge amount of experimental and theoretical attention. If computational models have tended to pick specific aspects of plasticity, such as STDP, and reduce them to an equation, some experimental studies are equally guilty of oversimplification each time they identify a new molecule and declare it to be the last word in plasticity and learning. Multiscale modeling begins with the acknowledgment that synaptic function spans many levels of signaling, and these are so tightly coupled that we risk losing essential features of plasticity if we focus exclusively on any one level. Despite the technical challenges and gaps in data for model specification, an increasing number of multiscale modeling studies have taken on key questions in plasticity. These have provided new insights, but importantly, they have opened new avenues for questioning. This review discusses a wide range of multiscale models in plasticity, including their technical landscape and their implications.

A sequential vesicle pool model with a single release sensor and a Ca(2+)-dependent priming catalyst effectively explains Ca(2+)-dependent properties of neurosecretion

Neurotransmitter release depends on the fusion of secretory vesicles with the plasma membrane and the release of their contents. The final fusion step displays higher-order Ca²⁺ dependence, but also upstream steps depend on Ca²⁺. After deletion of the Ca²⁺ sensor for fast release – synaptotagmin-1 – slower Ca²⁺-dependent release components persist. These findings have provoked working models involving parallel releasable vesicle pools (Parallel Pool Models, PPM) driven by alternative Ca²⁺ sensors for release, but no slow release sensor acting on a parallel vesicle pool has been identified. We here propose a Sequential Pool Model (SPM), assuming a novel Ca²⁺-dependent action: a Ca²⁺-dependent catalyst that accelerates both forward and reverse priming reactions. While both models account for fast fusion from the Readily-Releasable Pool (RRP) under control of synaptotagmin-1, the origins of slow release differ. In the SPM the slow release component is attributed to the Ca²⁺-dependent refilling of the RRP from a Non-Releasable upstream Pool (NRP), whereas the PPM attributes slow release to a separate slowly-releasable vesicle pool. Using numerical integration we compared model predictions to data from mouse chromaffin cells. Like the PPM, the SPM explains biphasic release, Ca²⁺-dependence and pool sizes in mouse chromaffin cells. In addition, the SPM accounts for the rapid recovery of the fast component after strong stimulation, where the PPM fails. The SPM also predicts the simultaneous changes in release rate and amplitude seen when mutating the SNARE-complex. Finally, it can account for the loss of fast- and the persistence of slow release in the synaptotagmin-1 knockout by assuming that the RRP is depleted, leading to slow and Ca²⁺-dependent fusion from the NRP. We conclude that the elusive ‘alternative Ca²⁺ sensor’ for slow release might be the upstream priming catalyst, and that a sequential model effectively explains Ca²⁺-dependent properties of secretion without assuming parallel pools or sensors.

The release of neurotransmitter involves the rapid Ca²⁺-dependent fusion of vesicles with the plasma membrane. Kinetic heterogeneity is ubiquitous in secretory systems, with fast phases of release on the millisecond time scale being followed by slower phases. In the absence of synaptotagmin-1 – the Ca²⁺sensor for fast fusion – the fast phase of release is absent, while slower phases remain. To account for this, mathematical models incorporated several releasable vesicle pools with separate Ca²⁺ sensors. However, there is no clear evidence for parallel release pathways. We suggest a sequential model for Ca²⁺-dependent neurotransmitter release in adrenal chromaffin cells. We assume only a single releasable vesicle pool, and a Ca²⁺-dependent catalytic refilling process from a limited upstream vesicle pool. This model can produce kinetic heterogeneity and does better than the previous Parallel Pool Model in predicting the Ca²⁺-dependence of releasable pool refilling and the consequences of SNARE-protein mutation. It further accounts for the release in the absence of synaptotagmin-1 by assuming that the releasable vesicle pool is depleted, leading to slow and Ca²⁺-dependent fusion from the upstream pool, but through the same release pathway. Thus, we suggest that the elusive ‘alternative Ca²⁺ sensor’ is an upstream priming protein, rather than a parallel Ca²⁺ sensor.

The number and organization of Ca2+ channels in the active zone shapes neurotransmitter release from Schaffer collateral synapses

Fast synaptic transmission requires tight colocalization of Ca(2+) channels and neurotransmitter vesicles. It is generally thought that Ca(2+) channels are expressed abundantly in presynaptic active zones, that vesicles within the same active zone have similar release properties, and that significant vesicle depletion only occurs at synapses with high release probability. Here we show, at excitatory CA3→CA1 synapses in mouse hippocampus, that release from individual vesicles is generally triggered by only one Ca(2+) channel and that only few functional Ca(2+) channels may be spread in the active zone at variable distances to neighboring neurotransmitter vesicles. Using morphologically realistic Monte Carlo simulations, we show that this arrangement leads to a widely heterogeneous distribution of release probability across the vesicles docked at the active zone, and that depletion of the vesicles closest to Ca(2+) channels can account for the Ca(2+) dependence of short-term plasticity at these synapses. These findings challenge the prevailing view that efficient synaptic transmission requires numerous presynaptic Ca(2+) channels in the active zone, and indicate that the relative arrangement of Ca(2+) channels and vesicles contributes to the heterogeneity of release probability within and across synapses and to vesicle depletion at small central synapses with low average release probability.

Short-term plasticity constrains spatial organization of a hippocampal presynaptic terminal

Although the CA3-CA1 synapse is critically important for learning and memory, experimental limitations have to date prevented direct determination of the structural features that determine the response plasticity. Specifically, the local calcium influx responsible for vesicular release and short-term synaptic facilitation strongly depends on the distance between the voltage-dependent calcium channels (VDCCs) and the presynaptic active zone. Estimates for this distance range over two orders of magnitude. Here, we use a biophysically detailed computational model of the presynaptic bouton and demonstrate that available experimental data provide sufficient constraints to uniquely reconstruct the presynaptic architecture. We predict that for a typical CA3-CA1 synapse, there are ~70 VDCCs located 300 nm from the active zone. This result is surprising, because structural studies on other synapses in the hippocampus report much tighter spatial coupling. We demonstrate that the unusual structure of this synapse reflects its functional role in short-term plasticity (STP).

Computational models of neuron-astrocyte interaction in epilepsy

Astrocytes actively shape the dynamics of neurons and neuronal ensembles by affecting several aspects critical to neuronal function, such as regulating synaptic plasticity, modulating neuronal excitability, and maintaining extracellular ion balance. These pathways for astrocyte-neuron interaction can also enhance the information-processing capabilities of brains, but in other circumstances may lead the brain on the road to pathological ruin. In this article, we review the existing computational models of astrocytic involvement in epileptogenesis, focusing on their relevance to existing physiological data.

Toward the virtual cell: automated approaches to building models of subcellular organization "learned" from microscopy images

We review state-of-the-art computational methods for constructing, from image data, generative statistical models of cellular and nuclear shapes and the arrangement of subcellular structures and proteins within them. These automated approaches allow consistent analysis of images of cells for the purposes of learning the range of possible phenotypes, discriminating between them, and informing further investigation. Such models can also provide realistic geometry and initial protein locations to simulations in order to better understand cellular and subcellular processes. To determine the structures of cellular components and how proteins and other molecules are distributed among them, the generative modeling approach described here can be coupled with high throughput imaging technology to infer and represent subcellular organization from data with few a priori assumptions. We also discuss potential improvements to these methods and future directions for research.

Downregulation of parvalbumin at cortical GABA synapses reduces network gamma oscillatory activity

Postmortem and functional imaging studies of patients with psychiatric disorders, including schizophrenia, are consistent with a dysfunction of interneurons leading to compromised inhibitory control of network activity. Parvalbumin (PV)-expressing, fast-spiking interneurons interacting with pyramidal neurons generate cortical gamma oscillations (30-80 Hz) that synchronize cortical activity during cognitive processing. In postmortem studies of schizophrenia patients, these interneurons show reduced PV and glutamic acid decarboxylase 67 (GAD67), an enzyme that synthesizes GABA, but the consequences of this downregulation are unclear. We developed a biophysically realistic and detailed computational model of a cortical circuit including asynchronous release from GABAergic interneurons to investigate how reductions in PV and GABA affect gamma oscillations induced by sensory stimuli. Networks with reduced GABA were disinhibited and had altered gamma oscillations in response to stimulation; PV-deficient GABA synapses had increased asynchronous release of GABA, which decreased the level of excitation and reduced gamma-band activity. Combined reductions of PV and GABA resulted in a diminished gamma-band oscillatory activity in response to stimuli, similar to that observed in schizophrenia patients. Our results suggest a mechanism by which reduced GAD67 and PV in fast-spiking interneurons may contribute to cortical dysfunction in schizophrenia and related psychiatric disorders.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Bidirectional coupling between astrocytes and neurons mediates learning and dynamic coordination in the brain: a multiple modeling approach

In recent years research suggests that astrocyte networks, in addition to nutrient and waste processing functions, regulate both structural and synaptic plasticity. To understand the biological mechanisms that underpin such plasticity requires the development of cell level models that capture the mutual interaction between astrocytes and neurons. This paper presents a detailed model of bidirectional signaling between astrocytes and neurons (the astrocyte-neuron model or AN model) which yields new insights into the computational role of astrocyte-neuronal coupling. From a set of modeling studies we demonstrate two significant findings. Firstly, that spatial signaling via astrocytes can relay a "learning signal" to remote synaptic sites. Results show that slow inward currents cause synchronized postsynaptic activity in remote neurons and subsequently allow Spike-Timing-Dependent Plasticity based learning to occur at the associated synapses. Secondly, that bidirectional communication between neurons and astrocytes underpins dynamic coordination between neuron clusters. Although our composite AN model is presently applied to simplified neural structures and limited to coordination between localized neurons, the principle (which embodies structural, functional and dynamic complexity), and the modeling strategy may be extended to coordination among remote neuron clusters.

A tale of two stories: astrocyte regulation of synaptic depression and facilitation

Short-term presynaptic plasticity designates variations of the amplitude of synaptic information transfer whereby the amount of neurotransmitter released upon presynaptic stimulation changes over seconds as a function of the neuronal firing activity. While a consensus has emerged that the resulting decrease (depression) and/or increase (facilitation) of the synapse strength are crucial to neuronal computations, their modes of expression in vivo remain unclear. Recent experimental studies have reported that glial cells, particularly astrocytes in the hippocampus, are able to modulate short-term plasticity but the mechanism of such a modulation is poorly understood. Here, we investigate the characteristics of short-term plasticity modulation by astrocytes using a biophysically realistic computational model. Mean-field analysis of the model, supported by intensive numerical simulations, unravels that astrocytes may mediate counterintuitive effects. Depending on the expressed presynaptic signaling pathways, astrocytes may globally inhibit or potentiate the synapse: the amount of released neurotransmitter in the presence of the astrocyte is transiently smaller or larger than in its absence. But this global effect usually coexists with the opposite local effect on paired pulses: with release-decreasing astrocytes most paired pulses become facilitated, namely the amount of neurotransmitter released upon spike i+1 is larger than that at spike i, while paired-pulse depression becomes prominent under release-increasing astrocytes. Moreover, we show that the frequency of astrocytic intracellular Ca(2+) oscillations controls the effects of the astrocyte on short-term synaptic plasticity. Our model explains several experimental observations yet unsolved, and uncovers astrocytic gliotransmission as a possible transient switch between short-term paired-pulse depression and facilitation. This possibility has deep implications on the processing of neuronal spikes and resulting information transfer at synapses.

Synaptic scaling stabilizes persistent activity driven by asynchronous neurotransmitter release

Small networks of cultured hippocampal neurons respond to transient stimulation with rhythmic network activity (reverberation) that persists for several seconds, constituting an in vitro model of synchrony, working memory, and seizure. This mode of activity has been shown theoretically and experimentally to depend on asynchronous neurotransmitter release (an essential feature of the developing hippocampus) and is supported by a variety of developing neuronal networks despite variability in the size of populations (10-200 neurons) and in patterns of synaptic connectivity. It has previously been reported in computational models that "small-world" connection topology is ideal for the propagation of similar modes of network activity, although this has been shown only for neurons utilizing synchronous (phasic) synaptic transmission. We investigated how topological constraints on synaptic connectivity could shape the stability of reverberations in small networks that also use asynchronous synaptic transmission. We found that reverberation duration in such networks was resistant to changes in topology and scaled poorly with network size. However, normalization of synaptic drive, by reducing the variance of synaptic input across neurons, stabilized reverberation in such networks. Our results thus suggest that the stability of both normal and pathological states in developing networks might be shaped by variance-normalizing constraints on synaptic drive. We offer an experimental prediction for the consequences of such regulation on the behavior of small networks.

Chondroitin sulfate A-adhering Plasmodium falciparum-infected erythrocytes express functionally important antibody epitopes shared by multiple variants

Acquired protection from Plasmodium falciparum placental malaria, a major cause of maternal, fetal, and infant morbidity, is mediated by IgG specific for the P. falciparum erythrocyte membrane protein 1 variant VAR2CSA. This protein enables adhesion of P. falciparum-infected erythrocytes to chondroitin sulfate A in the intervillous space. Although interclonal variation of the var2csa gene is lower than that among var genes in general, VAR2CSA-specific Abs appear to target mainly polymorphic epitopes. This has raised doubts about the feasibility of VAR2CSA-based vaccines. We used eight human monoclonal IgG Abs from affinity-matured memory B cells of P. falciparum-exposed women to study interclonal variation and functional importance of Ab epitopes among placental and peripheral parasites from East and West Africa. Most placental P. falciparum isolates were labeled by several mAbs, whereas peripheral isolates from children were essentially nonreactive. The mAb reactivity of peripheral isolates from pregnant women indicated that some were placental, whereas others had alternative sequestration foci. Most of the mAbs were comparable in their reactivity with bound infected erythrocytes (IEs) and recombinant VAR2CSA and interfered with IE and/or VAR2CSA binding to chondroitin sulfate A. Pair-wise mAb combinations were more inhibitory than single mAbs, and all of the mAbs together was the most efficient combination. Each mAb could opsonize IEs for phagocytosis, and a combination of the eight mAbs caused phagocytosis similar to that of plasma IgG-opsonized IEs. We conclude that functionally important Ab epitopes are shared by the majority of polymorphic VAR2CSA variants, which supports the feasibility of VAR2CSA-based vaccines against placental malaria.