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

Experimentally monitored calcium dynamics at synaptic active zones during neurotransmitter release in neuron-muscle cell cultures

Ca2+-dependent K+ (BK) channels at varicosities in Xenopus nerve-muscle cell cultures were used to quantify experimentally the instantaneous active zone [Ca2+]AZ resulting from different rates and durations of Ca2+ entry in the absence of extrinsic buffers and correlate this with neurotransmitter release. Ca2+ tail currents produce mean peak [Ca2+]AZ ~ 30 μM; with continued influx, [Ca2+]AZ reaches ~45-60 μM at different rates depending on Ca2+ driving force and duration of influx. Both IBK and release are dependent on Ca2+ microdomains composed of both N- and L-type Ca channels. Domains collapse with a time constant of ~0.6 ms. We have constructed an active zone (AZ) model that approximately fits this data, and depends on incorporation of the high-capacity, low-affinity fixed buffer represented by phospholipid charges in the plasma membrane. Our observations suggest that in this preparation, (1) some BK channels, but few if any of the Ca2+ sensors that trigger release, are located within Ca2+ nanodomains while a large fraction of both are located far enough from Ca channels to be blockable by EGTA, (2) the IBK is more sensitive than the excitatory postsynaptic current (EPSC) to [Ca2+]AZ (K1/2-26 μM vs. ~36 μM [Ca2+]AZ); (3) with increasing [Ca2+]AZ, the IBK grows with a Hill coefficient of 2.5, the EPSC with a coefficient of 3.9; (4) release is dependent on the highest [Ca2+] achieved, independent of the time to reach it; (5) the varicosity synapses differ from mature frog nmjs in significant ways; and (6) BK channels are useful reporters of local [Ca2+]AZ.

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.

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.

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.

Doc2 is a Ca2+ sensor required for asynchronous neurotransmitter release

Synaptic transmission involves a fast synchronous phase and a slower asynchronous phase of neurotransmitter release that are regulated by distinct Ca(2+) sensors. Though the Ca(2+) sensor for rapid exocytosis, synaptotagmin I, has been studied in depth, the sensor for asynchronous release remains unknown. In a screen for neuronal Ca(2+) sensors that respond to changes in [Ca(2+)] with markedly slower kinetics than synaptotagmin I, we observed that Doc2--another Ca(2+), SNARE, and lipid-binding protein--operates on timescales consistent with asynchronous release. Moreover, up- and downregulation of Doc2 expression levels in hippocampal neurons increased or decreased, respectively, the slow phase of synaptic transmission. Synchronous release, when triggered by single action potentials, was unaffected by manipulation of Doc2 but was enhanced during repetitive stimulation in Doc2 knockdown neurons, potentially due to greater vesicle availability. In summary, we propose that Doc2 is a Ca(2+) sensor that is kinetically tuned to regulate asynchronous neurotransmitter release.

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.

N-type Ca2+ channels carry the largest current: implications for nanodomains and transmitter release

Presynaptic terminals favor intermediate-conductance Ca(V)2.2 (N type) over high-conductance Ca(V)1 (L type) channels for single-channel, Ca(2+) nanodomain-triggered synaptic vesicle fusion. However, the standard Ca(V)1>Ca(V)2>Ca(V)3 conductance hierarchy is based on recordings using nonphysiological divalent ion concentrations. We found that, with physiological Ca(2+) gradients, the hierarchy was Ca(V)2.2>Ca(V)1>Ca(V)3. Mathematical modeling predicts that the Ca(V)2.2 Ca(2+) nanodomain, which is ∼25% more extensive than that generated by Ca(V)1, can activate a calcium-fusion sensor located on the proximal face of the synaptic vesicle.

Control of neurotransmitter release: From Ca2+ to voltage dependent G-protein coupled receptors

This review discusses two theories that try to explain mechanisms of control of neurotransmitter release in fast synapses: the Ca(2+) hypothesis and the Ca(2+) voltage hypothesis. The review summarizes experimental results that are incompatible with predictions from the Ca(2+) hypothesis and concludes that Ca(2+) is involved in the control of the amount of release but not in the control of the time course of evoked release, i.e., initiation and termination of evoked release. Results summarizing direct effects of changes in membrane potential on the release machinery are then presented. These changes in membrane potential affect the affinity (for the transmitter) of presynaptic autoinhibitory G-protein coupled receptors (GPCRs). The voltage dependence of these GPCRs and their pivotal role in determining the time course of evoked release is discussed.

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.

Frequency-coded chemical sensors

We have developed a new method to intelligently sample analytes and introduce the analytes to sensors. The method automatically adjusts sampling duration according to the sensors' response to the analytes and converts the amplitude of the sensor output to a frequency output, giving us another opportunity to reduce noise in the signal. It also addresses some of the common sensor issues such as response time, saturation, chemical dynamic range, and sensor protection, saving precious detection time, protecting sensors, and enabling sensitive sensors built for low-concentration detection to be used for high-concentration detection as well. We have put together a system using a tuning fork chemical sensor as a sample sensor to demonstrate the feasibility and benefits of the new sensing technique.

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.

Systematic search for the rate constants that control the exocytotic process from chromaffin cells by a Genetic Algorithm

We have recently created a kinetic model that reproduces the dynamics of exocytosis with high accuracy. The reconstruction necessitated a search, in a multi-dimensional parameter space, for 37 parameters that described the system, with no assurance that the parameters, which reconstructed the observations, are a unique set. In the present study, a Genetic Algorithm (GA) was used for a thorough search in the unknown parameter space, using a strategy of gradual increase of the complexity of the analyzed input data. Upon systematic incorporation of one to four measurable parameters, used as input signals for the analysis, the constraint set on the GA search imposed the convergence of the free parameters into a single narrow range. The mean values for each adjustable parameter represent a minimum for the fitness function in the multi-dimensional parameter space. The GA search demonstrates that the parameters that control the kinetics of exocytosis are the rate constants of the steps downstream to synaptotagmin binding, and that the equilibrium constant of the binding of calcium to Munc13 controls the calcium-dependent priming process. Thus, the systematic use of the GA creates a link between specific reactions in the process of exocytosis and experimental phenotypes.