Consequences of molecular-level Ca2+ channel and synaptic vesicle colocalization for the Ca2+ microdomain and neurotransmitter exocytosis: a monte carlo study

Close agreement between deterministic versus stochastic modeling of first-passage time to vesicle fusion

Ca2+-dependent cell processes, such as neurotransmitter or endocrine vesicle fusion, are inherently stochastic due to large fluctuations in Ca2+ channel gating, Ca2+ diffusion, and Ca2+ binding to buffers and target sensors. However, previous studies revealed closer-than-expected agreement between deterministic and stochastic simulations of Ca2+ diffusion, buffering, and sensing if Ca2+ channel gating is not Ca2+ dependent. To understand this result more fully, we present a comparative study complementing previous work, focusing on Ca2+ dynamics downstream of Ca2+ channel gating. Specifically, we compare deterministic (mean-field/mass-action) and stochastic simulations of vesicle exocytosis latency, quantified by the probability density of the first-passage time (FPT) to the Ca2+-bound state of a vesicle fusion sensor, following a brief Ca2+ current pulse. We show that under physiological constraints, the discrepancy between FPT densities obtained using the two approaches remains small even if as few as ∼50 Ca2+ ions enter per single channel-vesicle release unit. Using a reduced two-compartment model for ease of analysis, we illustrate how this close agreement arises from the smallness of correlations between fluctuations of the reactant molecule numbers, despite the large magnitude of fluctuation amplitudes. This holds if all relevant reactions are heteroreaction between molecules of different species, as is the case for bimolecular Ca2+ binding to buffers and downstream sensor targets. In this case, diffusion and buffering effectively decorrelate the state of the Ca2+ sensor from local Ca2+ fluctuations. Thus, fluctuations in the Ca2+ sensor's state underlying the FPT distribution are only weakly affected by the fluctuations in the local Ca2+ concentration around its average, deterministically computable value.

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.

A first-passage approach to diffusion-influenced reversible binding and its insights into nanoscale signaling at the presynapse

Synaptic transmission between neurons is governed by a cascade of stochastic calcium ion reaction–diffusion events within nerve terminals leading to vesicular release of neurotransmitter. Since experimental measurements of such systems are challenging due to their nanometer and sub-millisecond scale, numerical simulations remain the principal tool for studying calcium-dependent neurotransmitter release driven by electrical impulses, despite the limitations of time-consuming calculations. In this paper, we develop an analytical solution to rapidly explore dynamical stochastic reaction–diffusion problems based on first-passage times. This is the first analytical model that accounts simultaneously for relevant statistical features of calcium ion diffusion, buffering, and its binding/unbinding reaction with a calcium sensor for synaptic vesicle fusion. In particular, unbinding kinetics are shown to have a major impact on submillisecond sensor occupancy probability and therefore cannot be neglected. Using Monte Carlo simulations we validated our analytical solution for instantaneous calcium influx and that through voltage-gated calcium channels. We present a fast and rigorous analytical tool that permits a systematic exploration of the influence of various biophysical parameters on molecular interactions within cells, and which can serve as a building block for more general cell signaling simulators.

Quantitation and Simulation of Single Action Potential-Evoked Ca2+ Signals in CA1 Pyramidal Neuron Presynaptic Terminals

Presynaptic Ca²⁺ evokes exocytosis, endocytosis, and synaptic plasticity. However, Ca²⁺ flux and interactions at presynaptic molecular targets are difficult to quantify because fluorescence imaging has limited resolution. In rats of either sex, we measured single varicosity presynaptic Ca²⁺ using Ca²⁺ dyes as buffers, and constructed models of Ca²⁺ dispersal. Action potentials evoked Ca²⁺ transients with little variation when measured with low-affinity dye (peak amplitude 789 ± 39 nM, within 2 ms of stimulation; decay times, 119 ± 10 ms). Endogenous Ca²⁺ buffering capacity, action potential-evoked free [Ca²⁺]_i, and total Ca²⁺ amounts entering terminals were determined using Ca²⁺ dyes as buffers. These data constrained Monte Carlo (MCell) simulations of Ca²⁺ entry, buffering, and removal. Simulations of experimentally-determined Ca²⁺ fluxes, buffered by simulated calbindin_28K well fit data, and were consistent with clustered Ca²⁺ entry followed within 4 ms by diffusion throughout the varicosity. Repetitive stimulation caused free varicosity Ca²⁺ to sum. However, simulated in nanometer domains, its removal by pumps and buffering was negligible, while local diffusion dominated. Thus, Ca²⁺ within tens of nanometers of entry, did not accumulate. A model of synaptotagmin1 (syt1)-Ca²⁺ binding indicates that even with 10 µM free varicosity evoked Ca²⁺, syt1 must be within tens of nanometers of channels to ensure occupation of all its Ca²⁺-binding sites. Repetitive stimulation, evoking short-term synaptic enhancement, does not modify probabilities of Ca²⁺ fully occupying syt1’s C2 domains, suggesting that enhancement is not mediated by Ca²⁺-syt1 interactions. We conclude that at spatiotemporal scales of fusion machines, Ca²⁺ necessary for their activation is diffusion dominated.

A stochastic model of active zone material mediated synaptic vesicle docking and priming at resting active zones

Synaptic vesicles (SVs) fuse with the presynaptic membrane (PM) at specialized regions called active zones for synaptic transmission. SVs are associated with dense aggregates of macromolecules called active zone material (AZM) that has been thought to be involved in SV release. However, its role has recently begun to be elucidated. Several morphological studies proposed distinctively different AZM mediated SV docking and priming models: sequential and concurrent SV docking/priming. To explore ways to reconcile the contradictory models we develop a stochastic AZM mediated SV docking and priming model. We assume that the position of each connection site of the AZM macromolecules on their SV, directly linking the SV with the PM, varies by random shortening and lengthening of the macromolecules at resting active zones. We also perform computer simulations of SVs near the PM at resting active zones, and the results show that the distribution of the AZM connection sites can significantly affect the SV's docking efficiency and distribution of its contact area with the PM, thus priming and that the area correlates with the shape of the SVs providing a way to account for seemingly irreconcilable observations reported about the spatial relationship of SVs with the PM at active zones.

Recent advances in mathematical modeling and statistical analysis of exocytosis in endocrine cells

Most endocrine cells secrete hormones as a result of Ca²⁺-regulated exocytosis, i.e., fusion of the membranes of hormone-containing secretory granules with the cell membrane, which allows the hormone molecules to escape to the extracellular space. As in neurons, electrical activity and cell depolarization open voltage-sensitive Ca²⁺ channels, and the resulting Ca²⁺ influx elevate the intracellular Ca²⁺ concentration, which in turn causes exocytosis. Whereas the main molecular components involved in exocytosis are increasingly well understood, quantitative understanding of the dynamical aspects of exocytosis is still lacking. Due to the nontrivial spatiotemporal Ca²⁺ dynamics, which depends on the particular pattern of electrical activity as well as Ca²⁺ channel kinetics, exocytosis is dependent on the spatial arrangement of Ca²⁺ channels and secretory granules. For example, the creation of local Ca²⁺ microdomains, where the Ca²⁺ concentration reaches tens of µM, are believed to be important for triggering exocytosis. Spatiotemporal simulations of buffered Ca²⁺ diffusion have provided important insight into the interplay between electrical activity, Ca²⁺ channel kinetics, and the location of granules and Ca²⁺ channels. By confronting simulations with statistical time-to-event (or survival) regression analysis of single granule exocytosis monitored with TIRF microscopy, a direct connection between location and rate of exocytosis can be obtained at the local, single-granule level. To get insight into whole-cell secretion, simplifications of the full spatiotemporal dynamics have shown to be highly helpful. Here, we provide an overview of recent approaches and results for quantitative analysis of Ca²⁺ regulated exocytosis of hormone-containing granules.

Single calcium channel domain gating of synaptic vesicle fusion at fast synapses; analysis by graphic modeling

At fast-transmitting presynaptic terminals Ca²⁺ enter through voltage gated calcium channels (CaVs) and bind to a synaptic vesicle (SV) -associated calcium sensor (SV-sensor) to gate fusion and discharge. An open CaV generates a high-concentration plume, or nanodomain of Ca²⁺ that dissipates precipitously with distance from the pore. At most fast synapses, such as the frog neuromuscular junction (NMJ), the SV sensors are located sufficiently close to individual CaVs to be gated by single nanodomains. However, at others, such as the mature rodent calyx of Held (calyx of Held), the physiology is more complex with evidence that CaVs that are both close and distant from the SV sensor and it is argued that release is gated primarily by the overlapping Ca²⁺ nanodomains from many CaVs. We devised a 'graphic modeling' method to sum Ca²⁺ from individual CaVs located at varying distances from the SV-sensor to determine the SV release probability and also the fraction of that probability that can be attributed to single domain gating. This method was applied first to simplified, low and high CaV density model release sites and then to published data on the contrasting frog NMJ and the rodent calyx of Held native synapses. We report 3 main predictions: the SV-sensor is positioned very close to the point at which the SV fuses with the membrane; single domain-release gating predominates even at synapses where the SV abuts a large cluster of CaVs, and even relatively remote CaVs can contribute significantly to single domain-based gating.

The structure and function of 'active zone material' at synapses

The docking of synaptic vesicles on the presynaptic membrane and their priming for fusion with it to mediate synaptic transmission of nerve impulses typically occur at structurally specialized regions on the membrane called active zones. Stable components of active zones include aggregates of macromolecules, 'active zone material' (AZM), attached to the presynaptic membrane, and aggregates of Ca(2+)-channels in the membrane, through which Ca(2+) enters the cytosol to trigger impulse-evoked vesicle fusion with the presynaptic membrane by interacting with Ca(2+)-sensors on the vesicles. This laboratory has used electron tomography to study, at macromolecular spatial resolution, the structure and function of AZM at the simply arranged active zones of axon terminals at frog neuromuscular junctions. The results support the conclusion that AZM directs the docking and priming of synaptic vesicles and essential positioning of Ca(2+)-channels relative to the vesicles' Ca(2+)-sensors. Here we review the findings and comment on their applicability to understanding mechanisms of docking, priming and Ca(2+)-triggering at other synapses, where the arrangement of active zone components differs.

Variable priming of a docked synaptic vesicle

The priming of a docked synaptic vesicle determines the probability of its membrane (VM) fusing with the presynaptic membrane (PM) when a nerve impulse arrives. To gain insight into the nature of priming, we searched by electron tomography for structural relationships correlated with fusion probability at active zones of axon terminals at frog neuromuscular junctions. For terminals fixed at rest, the contact area between the VM of docked vesicles and PM varied >10-fold with a normal distribution. There was no merging of the membranes. For terminals fixed during repetitive evoked synaptic transmission, the normal distribution of contact areas was shifted to the left, due in part to a decreased number of large contact areas, and there was a subpopulation of large contact areas where the membranes were hemifused, an intermediate preceding complete fusion. Thus, fusion probability of a docked vesicle is related to the extent of its VM-PM contact area. For terminals fixed 1 h after activity, the distribution of contact areas recovered to that at rest, indicating the extent of a VM-PM contact area is dynamic and in equilibrium. The extent of VM-PM contact areas in resting terminals correlated with eccentricity in vesicle shape caused by force toward the PM and with shortness of active zone material macromolecules linking vesicles to PM components, some thought to include Ca(2+) channels. We propose that priming is a variable continuum of events imposing variable fusion probability on each vesicle and is regulated by force-generating shortening of active zone material macromolecules in dynamic equilibrium.

Quantitative analysis linking inner hair cell voltage changes and postsynaptic conductance change: a modelling study

This paper presents a computational model which estimates the postsynaptic conductance change of mammalian Type I afferent peripheral process when airborne acoustic waves impact on the tympanic membrane. A model of the human auditory periphery is used to estimate the inner hair cell potential change in response to airborne sound. A generic and tunable topology of the mammalian synaptic ribbon is generated and the voltage dependence of its substructures is used to calculate discrete and probabilistic neurotransmitter vesicle release. Results suggest an almost linear relationship between increasing sound level (in dB SPL) and the postsynaptic conductance for frequencies considered too high for neurons to phase lock with (i.e., a few kHz). Furthermore coordinated vesicle release is shown for up to 300–400 Hz and a mechanism of phase shifting the subharmonic content of a stimulating signal is suggested. Model outputs suggest that strong onset response and highly synchronised multivesicular release rely on compound fusion of ribbon tethered vesicles.

Microdomain calcium fluctuations as a colored noise process

Calcium ions play a key role in subcellular signaling as localized transients of the intracellular calcium concentration modify the activity of ion channels, enzymes and transcription factors, among others. The intracellular calcium concentration is inherently noisy, as diffusion, the transient binding to and dissociation from buffer molecules and stochastically gating calcium channels contribute to the fluctuations of the local copy number of Ca²⁺ ions. We study the properties of the fluctuating calcium concentration in sub-femtoliter volumes using an exact stochastic simulation algorithm and approximations to the exact stochastic solution. It is shown that the time course of the local calcium concentration represents a colored noise process whose autocorrelation time is a function of buffer kinetics and diffusion constants. Using the chemical Langevin description and the excess buffer approximation of the process, fast approximative algorithms and theoretical connections to the Ornstein-Uhlenbeck process are obtained. In a generic example, we show how calcium noise can couple to the dynamics of a single variable moving in a double-well potential, leading to a colored noise induced transition. Our work shows how a multitude of intracellular signaling pathways may be influenced by the inherent stochasticity of calcium signals, a key messenger in virtually any cell type, and how the calcium signal can be implemented efficiently in cellular signaling models.

An excess-calcium-binding-site model predicts neurotransmitter release at the neuromuscular junction

Despite decades of intense experimental studies, we still lack a detailed understanding of synaptic function. Fortunately, using computational approaches, we can obtain important new insights into the inner workings of these important neural systems. Here, we report the development of a spatially realistic computational model of an entire frog active zone in which we constrained model parameters with experimental data, and then used Monte Carlo simulation methods to predict the Ca(2+)-binding stoichiometry and dynamics that underlie neurotransmitter release. Our model reveals that 20-40 independent Ca(2+)-binding sites on synaptic vesicles, only a fraction of which need to bind Ca(2+) to trigger fusion, are sufficient to predict physiological release. Our excess-Ca(2+)-binding-site model has many functional advantages, agrees with recent data on synaptotagmin copy number, and is the first (to our knowledge) to link detailed physiological observations with the molecular machinery of Ca(2+)-triggered exocytosis. In addition, our model provides detailed microscopic insight into the underlying Ca(2+) dynamics during synapse activation.

Presynaptic calcium influx controls neurotransmitter release in part by regulating the effective size of the readily releasable pool

The steep calcium dependence of synaptic strength that has been observed at many synapses is thought to reflect a calcium dependence of the probability of vesicular exocytosis (p), with the cooperativity of three to six corresponding to the multiple calcium ion binding sites on the calcium sensor responsible for exocytosis. Here we test the hypothesis that the calcium dependence of the effective size of the readily releasable pool (RRP) also contributes to the calcium dependence of release at the calyx of Held synapse in mice. Using two established methods of quantifying neurotransmitter release evoked by action potentials (effective RRP), we find that when calcium influx is changed by altering the external calcium concentration, the calcium cooperativity of p is insufficient to account for the full calcium dependence of EPSC size; the calcium dependence of the RRP size also contributes. Reducing calcium influx by blocking R-type voltage-gated calcium channels (VGCCs) with Ni(2+), or by blocking P/Q-type VGCCs with ω-agatoxin IVA also changes EPSC amplitude by reducing both p and the effective RRP size. This suggests that the effective RRP size is dependent on calcium influx through VGCCs. Furthermore, activation of GABAB receptors, which reduces presynaptic calcium through VGCCs without other significant effects on release, also reduces the effective RRP size in addition to reducing p. These findings indicate that calcium influx regulates the RRP size along with p, which contributes to the calcium dependence of synaptic strength, and it influences the manner in which presynaptic modulation of presynaptic calcium channels affects neurotransmitter release.

Sharp Ca²⁺ nanodomains beneath the ribbon promote highly synchronous multivesicular release at hair cell synapses

Hair cell ribbon synapses exhibit several distinguishing features. Structurally, a dense body, or ribbon, is anchored to the presynaptic membrane and tethers synaptic vesicles; functionally, neurotransmitter release is dominated by large EPSC events produced by seemingly synchronous multivesicular release. However, the specific role of the synaptic ribbon in promoting this form of release remains elusive. Using complete ultrastructural reconstructions and capacitance measurements of bullfrog amphibian papilla hair cells dialyzed with high concentrations of a slow Ca²⁺ buffer (10 mM EGTA), we found that the number of synaptic vesicles at the base of the ribbon correlated closely to those vesicles that released most rapidly and efficiently, while the rest of the ribbon-tethered vesicles correlated to a second, slower pool of vesicles. Combined with the persistence of multivesicular release in extreme Ca²⁺ buffering conditions (10 mM BAPTA), our data argue against the Ca²⁺-dependent compound fusion of ribbon-tethered vesicles at hair cell synapses. Moreover, during hair cell depolarization, our results suggest that elevated Ca²⁺ levels enhance vesicle pool replenishment rates. Finally, using Ca²⁺ diffusion simulations, we propose that the ribbon and its vesicles define a small cytoplasmic volume where Ca²⁺ buffer is saturated, despite 10 mM BAPTA conditions. This local buffer saturation permits fast and large Ca²⁺ rises near release sites beneath the synaptic ribbon that can trigger multiquantal EPSCs. We conclude that, by restricting the available presynaptic volume, the ribbon may be creating conditions for the synchronous release of a small cohort of docked vesicles.

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.

Simulation strategies for calcium microdomains and calcium-regulated calcium channels

In this article, we present an overview of simulation strategies in the context of subcellular domains where calcium-dependent signaling plays an important role. The presentation follows the spatial and temporal scales involved and represented by each algorithm. As an exemplary cell type, we will mainly cite work done on striated muscle cells, i.e. skeletal and cardiac muscle. For these cells, a wealth of ultrastructural, biophysical and electrophysiological data is at hand. Moreover, these cells also express ubiquitous signaling pathways as they are found in many other cell types and thus, the generalization of the methods and results presented here is straightforward.The models considered comprise the basic calcium signaling machinery as found in most excitable cell types including Ca(2+) ions, diffusible and stationary buffer systems, and calcium regulated calcium release channels. Simulation strategies can be differentiated in stochastic and deterministic algorithms. Historically, deterministic approaches based on the macroscopic reaction rate equations were the first models considered. As experimental methods elucidated highly localized Ca(2+) signaling events occurring in femtoliter volumes, stochastic methods were increasingly considered. However, detailed simulations of single molecule trajectories are rarely performed as the computational cost implied is too large. On the mesoscopic level, Gillespie's algorithm is extensively used in the systems biology community and with increasing frequency also in models of microdomain calcium signaling. To increase computational speed, fast approximations were derived from Gillespie's exact algorithm, most notably the chemical Langevin equation and the τ-leap algorithm. Finally, in order to integrate deterministic and stochastic effects in multiscale simulations, hybrid algorithms are increasingly used. These include stochastic models of ion channels combined with deterministic descriptions of the calcium buffering and diffusion system on the one hand, and algorithms that switch between deterministic and stochastic simulation steps in a context-dependent manner on the other. The basic assumptions of the listed methods as well as implementation schemes are given in the text. We conclude with a perspective on possible future developments of the field.

From the stochasticity of molecular processes to the variability of synaptic transmission

The variability of the postsynaptic response following a single action potential arises from two sources: the neurotransmitter release is probabilistic, and the postsynaptic response to neurotransmitter release has variable timing and amplitude. At individual synapses, the number of molecules of a given type that are involved in these processes is small enough that the stochastic (random) properties of molecular events cannot be neglected. How the stochasticity of molecular processes contributes to the variability of synaptic transmission, its sensitivity and its robustness to molecular fluctuations has important implications for our understanding of the mechanistic basis of synaptic transmission and of synaptic plasticity.

An ion-insensitive cAMP biosensor for long term quantitative ratiometric fluorescence resonance energy transfer (FRET) measurements under variable physiological conditions

Ratiometric measurements with FRET-based biosensors in living cells using a single fluorescence excitation wavelength are often affected by a significant ion sensitivity and the aggregation behavior of the FRET pair. This is an important problem for quantitative approaches. Here we report on the influence of physiological ion concentration changes on quantitative ratiometric measurements by comparing different FRET pairs for a cAMP-detecting biosensor. We exchanged the enhanced CFP/enhanced YFP FRET pair of an established Epac1-based biosensor by the fluorophores mCerulean/mCitrine. In the case of enhanced CFP/enhanced YFP, we showed that changes in proton, and (to a lesser extent) chloride ion concentrations result in incorrect ratiometric FRET signals, which may exceed the dynamic range of the biosensor. Calcium ions have no direct, but an indirect pH-driven effect by mobilizing protons. These ion dependences were greatly eliminated when mCerulean/mCitrine fluorophores were used. For such advanced FRET pairs the biosensor is less sensitive to changes in ion concentration and allows consistent cAMP concentration measurements under different physiological conditions, as occur in metabolically active cells. In addition, we verified that the described FRET pair exchange increased the dynamic range of the FRET efficiency response. The time window for stable experimental conditions was also prolonged by a faster biosensor expression rate in transfected cells and a greatly reduced tendency to aggregate, which reduces cytotoxicity. These properties were verified in functional tests in single cells co-expressing the biosensor and the 5-HT(1A) receptor.

Neuronal plasticity and thalamocortical sleep and waking oscillations

Throughout life, thalamocortical (TC) network alternates between activated states (wake or rapid eye movement sleep) and slow oscillatory state dominating slow-wave sleep. The patterns of neuronal firing are different during these distinct states. I propose that due to relatively regular firing, the activated states preset some steady state synaptic plasticity and that the silent periods of slow-wave sleep contribute to a release from this steady state synaptic plasticity. In this respect, I discuss how states of vigilance affect short-, mid-, and long-term synaptic plasticity, intrinsic neuronal plasticity, as well as homeostatic plasticity. Finally, I suggest that slow oscillation is intrinsic property of cortical network and brain homeostatic mechanisms are tuned to use all forms of plasticity to bring cortical network to the state of slow oscillation. However, prolonged and profound shift from this homeostatic balance could lead to development of paroxysmal hyperexcitability and seizures as in the case of brain trauma.

Monte Carlo simulation of buffered diffusion into and out of a model synapse

Buffered diffusion occurs when ligands enter or leave a restricted space, such as a chemical synapse, containing a high density of binding sites. This study used Monte Carlo simulations to determine the time and spatial dependences of buffered diffusion without a priori assumptions about kinetics. The synapse was modeled as a box with receptors on one inner face. The exterior was clamped to some ligand concentration and ligands diffused through two sides. Onset and recovery simulations were carried out and the effects of receptor density, ligand properties and synapse geometry were investigated. This study determined equilibration times for binding and the spatial gradient of unliganded receptors. Onset was characterized by a high spatial gradient; equilibration was limited by the time needed for sufficient ligands to enter the synapse. Recovery showed a low spatial gradient with receptor equilibration limited by ligand rebinding. Decreasing ligand association rate or increasing ligand diffusion coefficient reduced the role of buffered diffusion and decreased the spatial gradient. Simulations with irreversible ligands showed larger, persistent spatial gradients. These simulations identify characteristics that can be used to test whether a synaptic process is governed by buffered diffusion. They also indicate that fundamental differences in synapse function may occur with irreversible ligands.

Sensitivity of intracellular calcium-binding sites for exo- and endocytosis of synaptic vesicles to Sr, Ba, and Mg ions

Experiments on frog cutaneous-thoracic muscle preparations using electrophysiological (intra- and extracellular recording of postsynaptic signals) and optical (confocal microscopy with the fluorescent endocytic stain FM 1-43) methods were performed to study neurotransmitter secretion and the processes of exo- and endocytosis of synaptic vesicles in motor nerve endings on substitution of extracellular Ca ions with other alkaline earth metals (Sr, Ba, or Mg). Massive asynchronous exocytosis was induced by high-potassium solution, while synchronous exocytosis was induced by prolonged high-frequency stimulation of the motor nerve. The calcium-binding site for asynchronous exocytosis was found to be sensitive to Sr, Ba, and Mg ions, while the site for synchronous exocytosis was only sensitive to Sr ions. During stimulation of both asynchronous and synchronous exocytosis, the calcium-binding site for endocytosis was sensitive to Sr and Ba ions and had the lowest affinity for Sr ions. These experiments led to the conclusion that different intracellular calcium-binding sites exist for the exocytosis and endocytosis of synaptic vesicles and that they have different sensitivities for alkaline earth metals.

The organization of the secretory machinery in chromaffin cells as a major factor in modeling exocytosis

The organization of cytoplasm in excitable cells was a largely ignored factor when mathematical models were developed to understand intracellular calcium and secretory behavior. Here we employed a combination of fluorescent evanescent and transmitted light microscopy to explore the F-actin cytoskeletal organization in the vicinity of secretory sites in cultured bovine chromaffin cells. This technique and confocal fluorescent microscopy show chromaffin granules associated with the borders of cortical cytoskeletal cages forming an intricate tridimensional network. Furthermore, the overexpression of SNAP-25 in these cells also reveals the association of secretory machinery clusters with the borders of these cytoskeletal cages. The importance of these F-actin cage borders is stressed when granules appear to interact and remain associated during exocytosis visualized in acridin orange loaded vesicles. These results will prompt us to propose a model of cytoskeletal cages, where the secretory machinery is associated with its borders. Both the calcium level and the secretory response are enhanced in this geometrical arrangement when compared with a random distribution of the secretory machinery that is not restricted to the borders of the cage.

Cooperative regulation of neurotransmitter release by Rab3a and synapsin II

To understand how the presynaptic proteins synapsin and Rab3a may interact in the regulation of the synaptic vesicle cycle and the release process, we derived a double knockout (DKO) mouse lacking both synapsin II and Rab3a. We found that Rab3a deletion rescued epileptic-like seizures typical for synapsin II gene deleted animals (Syn II(-)). Furthermore, action potential evoked release was drastically reduced in DKO synapses, although spontaneous release remained normal. At low Ca2+ conditions, quantal content was equally reduced in Rab3a(-) and DKO synapses, but as Ca2+ concentration increased, the increase in quantal content was more prominent in Rab3a(-). Electron microscopy analysis revealed that DKO synapses have a combined phenotype, with docked vesicles being reduced similar to Rab3a(-), and intraterminal vesicles being depleted similar to Syn II(-). Consistently, both Syn II(-) and DKO terminals had increased synaptic depression and incomplete recovery. Taken together, our results suggest that synapsin II and Rab3a have separate roles in maintaining the total store of synaptic vesicles and cooperate in promoting the latest steps of neuronal secretion.

Ca2+ current versus Ca2+ channel cooperativity of exocytosis

Recently there has been significant interest and progress in the study of spatiotemporal dynamics of Ca(2+) that triggers exocytosis at a fast chemical synapse, which requires understanding the contribution of individual calcium channels to the release of a single vesicle. Experimental protocols provide insight into this question by probing the sensitivity of exocytosis to Ca(2+) influx. While varying extracellular or intracellular Ca(2+) concentration assesses the intrinsic biochemical Ca(2+) cooperativity of neurotransmitter release, varying the number of open Ca(2+) channels using pharmacological channel block or the tail current titration probes the cooperativity between individual Ca(2+) channels in triggering exocytosis. Despite the wide use of these Ca(2+) sensitivity measurements, their interpretation often relies on heuristic arguments. Here we provide a detailed analysis of the Ca(2+) sensitivity measures probed by these experimental protocols, present simple expressions for special cases, and demonstrate the distinction between the Ca(2+) current cooperativity, defined by the relationship between exocytosis rate and the whole-terminal Ca(2+) current magnitude, and the underlying Ca(2+) channel cooperativity, defined as the average number of channels involved in the release of a single vesicle. We find simple algebraic expressions that show that the two are different but linearly related. Further, we use three-dimensional computational modeling of buffered Ca(2+) diffusion to analyze these distinct Ca(2+) cooperativity measures, and demonstrate the role of endogenous Ca(2+) buffers on such measures. We show that buffers can either increase or decrease the Ca(2+) current cooperativity of exocytosis, depending on their concentration and the single-channel Ca(2+) current.

Synaptic ribbon enables temporal precision of hair cell afferent synapse by increasing the number of readily releasable vesicles: a modeling study

Synaptic ribbons are classically associated with mediating indefatigable neurotransmitter release by sensory neurons that encode persistent stimuli. Yet when hair cells lack anchored ribbons, the temporal precision of vesicle fusion and auditory nerve discharges are degraded. A rarified statistical model predicted increasing precision of first-exocytosis latency with the number of readily releasable vesicles. We developed an experimentally constrained biophysical model to test the hypothesis that ribbons enable temporally precise exocytosis by increasing the readily releasable pool size. Simulations of calcium influx, buffered calcium diffusion, and synaptic vesicle exocytosis were stochastic (Monte Carlo) and yielded spatiotemporal distributions of vesicle fusion consistent with experimental measurements of exocytosis magnitude and first-spike latency of nerve fibers. No single vesicle could drive the auditory nerve with requisite precision, indicating a requirement for multiple readily releasable vesicles. However, plasmalemma-docked vesicles alone did not account for the nerve's precision--the synaptic ribbon was required to retain a pool of readily releasable vesicles sufficiently large to statistically ensure first-exocytosis latency was both short and reproducible. The model predicted that at least 16 readily releasable vesicles were necessary to match the nerve's precision and provided insight into interspecies differences in synaptic anatomy and physiology. We confirmed that ribbon-associated vesicles were required in disparate calcium buffer conditions, irrespective of the number of vesicles required to trigger an action potential. We conclude that one of the simplest functions ascribable to the ribbon--the ability to hold docked vesicles at an active zone--accounts for the synapse's temporal precision.

Modeling study of the effects of membrane surface charge on calcium microdomains and neurotransmitter release

Synchronous neurotransmitter release is mediated by the opening of voltage-gated Ca(2+) channels and the build-up of submembrane Ca(2+) microdomains. Previous models of Ca(2+) microdomains have neglected possible electrostatic interactions between Ca(2+) ions and negative surface charges on the inner leaflet of the plasma membrane. To address the effects of these interactions, we built a computational model of ion electrodiffusion described by the Nernst-Planck and Poisson equations. We found that inclusion of a negative surface charge significantly alters the spatial characteristics of Ca(2+) microdomains. Specifically, close to the membrane, Ca(2+) ions accumulate, as expected from the strong electrostatic attraction exerted on positively charged Ca(2+) ions. Farther away from the membrane, increasing the surface charge density results in a reduction of the Ca(2+) concentration because of the preferential spread of Ca(2+) ions along lateral directions. The model also predicts that the negative surface charge will decrease the spatial gradient of the Ca(2+) microdomain in the lateral direction, resulting in increased overlap of microdomains originating from different Ca(2+) channels. Finally, we found that surface charge increases the probability of vesicle release if the Ca(2+) sensor is located within the electrical double layer, whereas this probability is decreased if the Ca(2+) sensor lies at greater distances from the membrane. Our data suggest that membrane surface charges exert a significant influence on the profile of Ca(2+) microdomains, and should be taken into account in models of neurotransmitter release.

Modeling of quantal neurotransmitter release kinetics in the presence of fixed and mobile calcium buffers

The local calcium concentration in the active zone of secretion determines the number and kinetics of neurotransmitter quanta released after the arrival of a nerve action potential in chemical synapses. The small size of mammalian neuromuscular junctions does not allow direct measurement of the correlation between calcium influx, the state of endogenous calcium buffers determining the local concentration of calcium and the time course of quanta exocytosis. In this work, we used computer modeling of quanta release kinetics with various levels of calcium influx and in the presence of endogenous calcium buffers with varying mobilities. The results of this modeling revealed the desynchronization of quanta release under low calcium influx in the presence of an endogenous fixed calcium buffer, with a diffusion coefficient much smaller than that of free Ca(2+), and synchronization occurred upon adding a mobile buffer. This corresponds to changes in secretion time course parameters found experimentally (Samigullin et al., Physiol Res 54:129-132, 2005; Bukharaeva et al., J Neurochem 100:939-949, 2007).

Determining Ca2+-sensor binding time and its variability in evoked neurotransmitter release

The speed and reliability of neuronal reactions are important factors for proper functioning of the nervous system. To understand how organisms use protein molecules to carry out very fast biological actions, we quantified single-molecule reaction time and its variability in synaptic transmission. From the synaptic delay of crayfish neuromuscular synapses the time for a few Ca(2+) ions to bind with their sensors in evoked neurotransmitter release was estimated. In standard crayfish saline at room temperature, the average Ca(2+) binding time was 0.12 ms for the first evoked quanta. At elevated extracellular Ca(2+) concentrations this binding time reached a limit due to saturation of Ca(2+) influx. Analysis of the synaptic delay variance at various Ca(2+) concentrations revealed that the variability of the Ca(2+)-sensor binding time is the major source of the temporal variability of synaptic transmission, and that the Ca(2+)-independent molecular reactions after Ca(2+) influx were less stochastic. The results provide insights into how organisms maximize reaction speed and reliability.

Ca2+ from one or two channels controls fusion of a single vesicle at the frog neuromuscular junction

Neurotransmitter release is triggered by the cooperative action of approximately five Ca2+ ions entering the presynaptic terminal through Ca2+ channels. Depending on the organization of the active zone (AZ), influx through one or many channels may be needed to cause fusion of a vesicle. Using a combination of experiments and modeling, we examined the number of channels that contribute Ca2+ for fusion of a single vesicle in a frog neuromuscular AZ. We compared Ca2+ influx to neurotransmitter release by measuring presynaptic action potential-evoked (AP-evoked) Ca2+ transients simultaneously with postsynaptic potentials. Ca2+ influx was manipulated by changing extracellular [Ca2+] (Ca(ext)) to alter the flux per channel or by reducing the number of open Ca2+ channels with omega-conotoxin GVIA (omega-CTX). When Ca(ext) was reduced, the exponent of the power relationship relating release to Ca2+ influx was 4.16 +/- 0.62 (SD; n = 4), consistent with a biochemical cooperativity of approximately 5. In contrast, reducing influx with omega-CTX yielded a power relationship of 1.7 +/- 0.44 (n = 5) for Ca(ext) of 1.8 mM and 2.12 +/- 0.44 for Ca(ext) of 0.45 mM (n = 5). Using geometrically realistic Monte Carlo simulations, we tracked Ca2+ ions as they entered through each channel and diffused in the terminal. Experimental and modeling data were consistent with two to six channel openings per AZ per AP; the Ca2+ that causes fusion of a single vesicle originates from one or two channels. Channel cooperativity depends mainly on the physical relationship between channels and vesicles and is insensitive to changes in the non-geometrical parameters of our model.

Calcium microdomains in regulated exocytosis

Katz and co-workers showed that Ca(2+) triggers exocytosis. The existence of sub-micrometer domains of greater than 100 microM [Ca(2+)](i) was postulated on theoretical grounds. Using a modified, low-affinity aequorin, Llinas et al. were the first to demonstrate the existence of Ca(2+) 'microdomains' in squid presynaptic terminals. Over the past several years, it has become clear that individual Ca(2+) nano- and microdomains forming around the mouth of voltage-gated Ca(2+) channels ascertain the tight coupling of fast synaptic vesicle release to membrane depolarization by action potentials. Recent work has established different geometric arrangements of vesicles and Ca(2+) channels at different central synapses and pointed out the role of Ca(2+) syntillas - localized, store operated Ca(2+) signals - in facilitation and spontaneous release. The coupling between Ca(2+) increase and evoked exocytosis is more sluggish in peripheral terminals and neuroendocrine cells, where channels are less clustered and Ca(2+) comes from different sources, including Ca(2+) influx via the plasma membrane and the mobilization of Ca(2+) from intracellular stores. Finally, also non- (electrically) excitable cells display highly localized Ca(2+) signaling domains. We discuss in particular the organization of structural microdomains of Bergmann glia, specialized astrocytes of the cerebellum that have only recently been considered as secretory cells. Glial microdomains are the spatial substrate for functionally segregated Ca(2+) signals upon metabotropic activation. Our review emphasizes the large diversity of different geometric arrangements of vesicles and Ca(2+) sources, leading to a wide spectrum of Ca(2+) signals triggering release.

Vesicular roundness and compound release in PC-12 cells

The principal goals of this study were to establish a quantitative morphological analysis of spatial and regional properties of dense core vesicles, and to use this analysis to assess whether homotypic fusion is prominent in chronically treated PC-12 cells at elevated release levels. Simple computerized image processing of electron-micrographs provided the binary images of vesicular dense cores, whilst the artificial intelligence methods were needed to determine the vesicular membranes. As in the past, the presence of large, highly irregular vesicles, provided the morphological evidence of fused vesicles, but the irregularity of vesicular shape was assessed quantitatively-from its roundness. Free space of each vesicle was determined from the distance to its nearest-neighbor, or from the size of its Voronoi polygon. Within a Voronoi polygon, each point is closer to that vesicle than to any other vesicle. Large vesicles were not less round and did not have larger free space, as expected if they result from fusion of several smaller vesicles. In conclusion, we present a novel and rigorous morphological analysis of spatial and regional properties of dense core vesicles. The results demonstrate that the homotypic fusion is not prominent in PC-12 cells, before or following a chronic treatment that enhances release.

Spike-mediated and graded inhibitory synaptic transmission between leech interneurons: evidence for shared release sites

Inhibitory synaptic transmission between leech heart interneurons consist of two components: graded, gated by Ca2+ entering by low-threshold [low-voltage-activated (LVA)] Ca channels and spike-mediated, gated by Ca2+ entering by high-threshold [high-voltage-activated (HVA)] Ca channels. Changes in presynaptic background Ca2+ produced by Ca2+ influx through LVA channels modulate spike-mediated transmission, suggesting LVA channels have access to release sites controlled by HVA channels. Here we explore whether spike-mediated and graded transmission can use the same release sites and thus how Ca2+ influx by HVA and LVA Ca channels might interact to evoke neurotransmitter release. We recorded pre- and postsynaptic currents from voltage-clamped heart interneurons bathed in 0 mM Na+/5 mM Ca2+ saline. Using different stimulating paradigms and inorganic Ca channel blockers, we show that strong graded synaptic transmission can occlude high-threshold/spike-mediated synaptic transmission when evoked simultaneously. Suppression of LVA Ca currents diminishes graded release and concomitantly increases the ability of Ca2+ entering by HVA channels to release transmitter. Uncaging of Ca chelator corroborates that graded release occludes spike-mediated transmission. Our results indicate that both graded and spike-mediated synaptic transmission depend on the same readily releasable pool of synaptic vesicles. Thus Ca2+, entering cells through different Ca channels (LVA and HVA), acts to gate release of the same synaptic vesicles. The data argue for a closer location of HVA Ca channels to release sites than LVA Ca channels. The results are summarized in a conceptual model of a heart interneuron release site.

Location and function of vesicle clusters, active zones and Ca2+ channels in the lamprey presynaptic terminal

Synaptic transmission requires spatial and temporal coordination of a specific sequence of events. The trigger for synaptic vesicle exocytosis is Ca(2)(+) entry into presynaptic terminals, leading to neurotransmitter release at highly specialized sites known as active zones. Ca(2)(+) channel proximity to exocytotic proteins and vesicle clusters at active zones have been inferred from biochemical, histological and ultrastructural data, but direct evidence about functional relationships between these elements in central synapses is absent. We have utilized the lamprey giant reticulospinal synapse to characterize functional colocalization of known synaptic markers in the presynaptic terminal, as well as their reliability during repeated activation. Recycling vesicle clusters, surrounding actin filaments, and physiologically relevant Ca(2)(+) influx all show identical morphological distribution. Ca(2)(+) influx is mediated by clusters of Ca(2)(+) channels that colocalize with the vesicle clusters, defined by imaged sites of vesicle recycling and actin localization. Synaptic transmission is inhibited by block of actin depolymerization, but Ca(2)(+) signalling is unaffected. Functional Ca(2)(+) channels are localized to presynaptic clusters, and Ca(2)(+) transients at these sites account for neurotransmitter release based on their spatial and temporal profiles. Ca(2)(+) transients evoked by single axonal action potentials are mediated solely by voltage-operated Ca(2)(+) channel activation, and slower Ca(2)(+) rises observed throughout the axon result from Ca(2)(+) diffusion from the synaptic regions. We conclude that at lamprey giant reticulospinal synapses, Ca(2)(+) channels and release sites colocalize, creating a close spatial relationship between active zones and Ca(2)(+) entry sites, which is necessary for site-specific, Ca(2)(+)-dependent secretion.

Role of high-voltage-activated calcium channels in glucose-regulated beta-cell calcium homeostasis and insulin release

High-voltage-activated (HVA) calcium channels are known to be the primary source of calcium for glucose-stimulated insulin secretion. However, few studies have investigated how these channels can be regulated by chronically elevated levels of glucose. In the present study, we determined the level of expression of the four major HVA calcium channels (N-type, P/Q-type, L(C)-type, and L(D)-type) in rat pancreatic beta-cells. Using quantitative real-time PCR (QRT-PCR), we found the expression of all four HVA genes in rat insulinoma cells (INS-1) and in primary isolated rat islet cells. We then determined the role of each channel in insulin secretion by using channel-selective antagonists. Insulin secretion analysis revealed that N- and L-type channels are both involved in immediate glucose-induced insulin secretion. However, L-type was preferentially coupled to secretion at later time points. P/Q-type channels were not found to play a role in insulin secretion at any stage. It was also found that long-term exposure to elevated glucose increases basal calcium in these cells. Interestingly, chronically elevated glucose decreased the mRNA expression of the channels involved with insulin secretion and diminished the level of stimulated calcium influx in these cells. Using whole cell patch clamp, we found that N- and L-type channel currents increase gradually subsequent to lower intracellular calcium perfusion, suggesting that these channels may be regulated by glucose-induced changes in calcium.

Brevity of the Ca2+ Microdomain and Active Zone Geometry Prevent Ca2+-Sensor Saturation for Neurotransmitter Release

The brief time course of the calcium (Ca2+) channel opening combined with the molecular-level colocalization of Ca2+ channels and synaptic vesicles in presynaptic terminals predict sub-millisecond calcium concentration ([Ca2+]) transients of ≥100 μM in the immediate vicinity of the vesicle. This [Ca2+] is much higher than some of the recent estimates for the equilibrium dissociation constant of the Ca2+ sensor(s) that control neurotransmitter release, suggesting release should be close to saturation, yet it is well known that release is highly sensitive to changes in Ca2+ influx. We show that due to the brevity of the Ca2+ influx the binding kinetics of the Ca2+ sensor rather than its equilibrium affinity determine receptor occupancy. For physiologically relevant Ca2+ currents and forward Ca2+ binding rates, the effective affinity of the Ca2+ sensor can be several-fold lower than the equilibrium affinity. Using simple models, we show redundant copies of the binding sites increase effective affinity of the Ca2+ sensor for release. Our results predict that different levels of expression of Ca2+ binding sites could account for apparent differences in Ca2+ sensor affinities between synapses. Using Monte Carlo simulations of Ca2+ dynamics with nanometer resolution, we demonstrate that these kinetic constraints combined with vesicles acting as diffusion barriers can prevent saturation of the Ca2+-sensor(s) for neurotransmitter release. We further show the random positioning of the Ca2+-sensor molecules around the vesicle can result in the emergence of two distinct populations of the vesicles with low and high release probability. These considerations allow experimental evidence for the Ca2+ channel-vesicle colocalization to be reconciled with a high equilibrium affinity for the Ca2+ sensor of the release machinery.

A unified model of presynaptic release site gating by calcium channel domains

Calcium ions enter through discrete ion channels at presynaptic nerve terminals before binding to and activating transmitter release sites. Opposing models hold that release sites are gated either by calcium domains of single, closely associated channels or by extensive, overlapping domains from many remote channels. At the chick calyx synapse we find a linear relation between transmitter release and the number of open calcium channels, favouring single domain activation. This finding is consistent with results from the squid giant synapse but contrasts with steep power dependences reported in rodent synapses, suggestive of activation by extensive overlapping domains. These different reports were reconciled by plotting 'per cent domain overlap' against the external calcium concentration used for each species. This relationship predicts the involvement of local channels in the activation of release sites in all species. Further, it suggests that each release site is activated by calcium ions from its immediately associated channels and not by ions that enter through channels associated with a neighbouring release site.