Stochastic model of central synapses: slow diffusion of transmitter interacting with spatially distributed receptors and transporters.

A detailed mathematical analysis of the diffusion process of neurotransmitter inside the synaptic cleft is presented and the spatio-temporal concentration profile is calculated. Using information about the experimentally observed time course of glutamate in the cleft the effective diffusion coefficient Dnet is estimated as Dnet approximately 20-50 nm(2) microseconds(-1), implying a strong reduction compared with free diffusion in aqueous solution. The tortuosity of the cleft and interactions with transporter molecules are assumed to affect the transmitter motion. We estimate the transporter density to be 5170 to 8900 micrometer(-2) in the synaptic cleft and its vicinity, using the experimentally observed time constant of glutamate. Furthermore a theoretical model of synaptic transmission is presented, taking the spatial distribution of post-synaptic (AMPA-) receptors into account. The transmitter diffusion and receptor dynamics are modeled by Monte Carlo simulations preserving the typically observed noisy character of post-synaptic responses. Distributions of amplitudes, rise and decay times are calculated and shown to agree well with experiments. Average open probabilities are computed from a novel kinetic model and are shown to agree with averages over many Monte Carlo runs. Our results suggest that post-synaptic currents are only weakly potentiated by clustering of post-synaptic receptors, but increase linearly with the total number of receptors. Distributions of amplitudes and rise times are used to discriminate between different morphologies, e.g. simple and perforated synapses. A skew in the miniature amplitude distribution can be caused by multiple release of pre-synaptic vesicles at perforated synapses.     

Modulation of glutamate mobility reveals the mechanism underlying slow-rising AMPAR EPSCs and the diffusion coefficient in the synaptic cleft

Fast- and slow-rising AMPA receptor-mediated EPSCs occur at central synapses. Fast-rising EPSCs are thought to be mediated by rapid local release of glutamate. However, two controversial mechanisms have been proposed to underlie slow-rising EPSCs: prolonged local release of transmitter via a fusion pore, and spillover of transmitter released rapidly from distant sites. We have investigated the mechanism underlying slow-rising EPSCs and the diffusion coefficient of glutamate in the synaptic cleft (Dglut) at cerebellar mossy fiber-granule cell synapses using a combination of diffusion modeling and patch-clamp recording. Simulations show that modulating Dglut has different effects on the peak amplitudes and time courses of EPSCs mediated by these two mechanisms. Slowing diffusion with the macromolecule dextran slowed slow-rising EPSCs and had little effect on their amplitude, indicating that glutamate spillover underlies these currents. Our results also suggest that under control conditions Dglut is approximately 3-fold lower than in free solution.     

Exocytotic catecholamine release is not associated with cation flux through channels in the vesicle membrane but Na+ influx through the fusion pore

Release of charged neurotransmitter molecules through a narrow fusion pore requires charge compensation by other ions. It has been proposed that this may occur by ion flow from the cytosol through channels in the vesicle membrane, which would generate a net outward current. This hypothesis was tested in chromaffin cells using cell-attached patch amperometry that simultaneously measured catecholamine release from single vesicles and ionic current across the patch membrane. No detectable current was associated with catecholamine release indicating that <2% of cations, if any, enter the vesicle through its membrane. Instead, we show that flux of catecholamines through the fusion pore, measured as an amperometric foot signal, decreases when the extracellular cation concentration is reduced. The results reveal that the rate of transmitter release through the fusion pore is coupled to net Na+ influx through the fusion pore, as predicted by electrodiffusion theory applied to fusion-pore permeation, and suggest a prefusion rather than postfusion role for vesicular cation channels.     

Temperature dependence of fusion kinetics and fusion pores in Ca2+-triggered exocytosis from PC12 cells

The temperature dependence of Ca(2+)-triggered exocytosis was studied using carbon fiber amperometry to record the release of norepinephrine from PC12 cells. Single-vesicle fusion events were examined at temperatures varying from 12 to 28 degrees C, and with release elicited by depolarization. Measurements were made of the initial and maximum frequencies of exocytotic events, of fusion pore lifetime, flux through the open fusion pore, kiss-and-run versus full-fusion probability, and parameters associated with the shapes of amperometric spikes. The fusion pore open-state flux, and all parameters associated with spike shape, including area, rise time, and decay time, had weak temperature dependences and activation energies in the range expected for bulk diffusion in an aqueous solution. Kiss-and-run events also varied with temperature, with lower temperatures increasing the relative probability of kiss-and-run events by approximately 50%. By contrast, kinetic parameters relating to the frequency of exocytotic events and fusion pore transitions depended much more strongly on temperature, suggesting that these processes entail structural rearrangements of proteins or lipids or both. The weak temperature dependence of spike shape suggests that after the fusion pore has started to expand, structural transitions of membrane components are no longer kinetically limiting. This indicates that the content of a vesicle is expelled completely after fusion pore expansion.     

Evaluation of characteristic parameters for the neurotransmitter release mechanisms at the neuromuscular junction

The process of neurotransmitter release at the neuromuscular junction needs to be represented appropriately in modeling of the synaptic chemical transmission as a reaction-diffusion system. The release mechanisms of the expanding pore and the acceleration are analyzed by the computer simulation with respect to the effects of the characteristic parameters in the mechanisms on spontaneous generation of the miniature endplate current (MEPC), leading to the following evaluation. In the expanding pore mechanism the expanding rate of the pore more than 10 nm ms(-1) and the diffusion coefficient of acetylcholine in the synaptic cleft (D(c)) of about 1.0 x 10(-6) cm2 s(-1) yield the maximum amplitude, the rise time and the decay time constant of the MEPC in agreement with the empirical data. In the active release mechanism the 10-fold acceleration of the natural diffusion and a similar value of D(c) are required to suit for the empirical MEPC.     

Transmitter concentration profiles in the synaptic cleft: an analytical model of release and diffusion.

A three-dimensional model for release and diffusion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a diffusion function describing the spread of transmitter in the cleft. Concentration profiles of transmitter at the postsynaptic side were calculated for different transmitter concentrations in a vesicle, release scenarios, and diffusion coefficients. From the concentration profiles the receptor occupancy could be determined using alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor kinetics. It turned out that saturation of receptors and sufficiently fast currents could only be obtained if the diffusion coefficient was one order of magnitude lower than generally assumed, and if the postsynaptic receptors formed clusters with a diameter of roughly 100 nm directly opposite the release sites. Under these circumstances the gradient of the transmitter concentration at the postsynaptic membrane outside the receptor clusters was steep, with minimal cross-talk among neighboring receptor clusters. These findings suggest that for each release site a corresponding receptor aggregate exists, subdividing an individual synapse into independent functional subunits without the need for specific lateral diffusion barriers.     

A voltage clamp study of the glutamate responsive neuromuscular junction in Drosophila melanogaster

The point and single electrode voltage clamp methods have been used to study the characteristics of junctional currents in Drosophila melanogaster larvae muscle fibers and the modulation of these currents by excitatory amino acids, short and long chain n-alkanols, and pentobarbital. The decay phase of junctional currents in Drosophila was found to be dominated by cooperativity in transmitter binding associated with reverberation, that is, repeated binding of transmitter with receptors as the transmitter molecules diffuse away from the active region. The current decay does not directly reflect the closure of ion channels and is qualitatively similar to the decay of miniature end-plate currents at the mouse neuromuscular junction after poisoning of acetylcholinesterase by paraoxon. In Drosophila an increase in membrane hyperpolarization both slows the time course of current decay and increases the degree of reverberation. The application of excitatory amino acids including glutamate, N-methyl-D-aspartate, quisqualate, and kainate causes a significant decrease in the amplitude of the junctional currents, a prolongation of the decay time course, and a reduction in reverberation of transmitter. The height of junctional currents is also diminished by the n-alkanols ethanol, pentanol, and octanol and by the barbiturate pentobarbital; ethanol also hastened the time course of decay of the currents.     

Kinetic characteristics of inhibitory postsynaptic currents in cultured chick embryo spinal cord neurons

Decay of inhibitory postsynaptic currents (IPSC) was analyzed in dissociated culture of chick embryo spinal cord. Differences in the kinetic characteristics of low-amplitude and giant IPSC were revealed. Decay of currents in the first group was single-exponential, while decay in the second group was double-exponential. The time constant of single-exponential current decay increased during membrane depolarization and decreased during rise in temperature of the solution. Decay of the double-exponential currents depended little on potential, while temperature changes acted only on its slow component. Strychnine in submaximum concentrations produced not only a decrease in amplitude of giant IPSC, but also a deceleration of decay due to the slow component. The regularity of these phenomena suggests that decay of giant IPSC, as distinguished from that of low-amplitude currents, is determined by removal of transmitter from the synaptic cleft.A. A. Bogomolets Institute of Physiology, Academy of Sciences of the USSR, Kiev. Translated from Neirofiziologiya, Vol. 23, No. 4, pp. 427–435, July–August, 1991.     

A cell-semiconductor synapse: transistor recording of vesicle release in chromaffin cells

The release of dense-core vesicles in bovine chromaffin cells is a model for the presynaptic process in neurons. It is usually studied by microamperometry of catecholamines with carbon fibers. Here we introduce transistor recording as a tool to study vesicle release. When we stimulate a chromaffin cell placed on a field-effect transistor, the gate voltage exhibits peaks that correlate with a simultaneously performed amperometric recording. We attribute the transistor signal to a release of protons from the extruded matrix of vesicles that lowers the extracellular pH and changes the electrical surface potential of the gate oxide. The rise time of the transistor signals is similar to that of amperometric responses, whereas their duration is distinctly longer. In a model computation, the rise time is identified with the extrusion of vesicle matrix into the narrow extracellular space between cell and gate oxide, and the decay time is attributed to pH equilibration through slow diffusion in the extruded matrix. Because the transistor recording relies on protons, it can be applied to acidic vesicles with electrochemically inactive hormones or transmitters.     

Quantal transmission at purinergic junctions: stochastic interaction between ATP and its receptors.

The time course of most quantal currents recorded with a small diameter electrode placed over visualized varicosities of sympathetic nerve terminals that secrete ATP was determined: these had a time to reach 90% of peak of 1.3-1.8 ms and a time constant of decay of 12-18 ms; they were unaffected by blocking ectoenzymes or the uptake of adenosine. Monte Carlo methods were used to analyze the stochastic interaction between ATP, released in a packet from a varicosity, and the underlying patch of purinoceptors, to reconstitute the time course of the quantal current. This leads to certain restrictions on the possible number of ATP molecules in a quantum (about 1000) and the density of purinoceptors at the junctions (about 1000 microns-1), given the known geometry of the junction and the kinetics of ATP action. The observed quantal current has a relatively small variability (coefficient of variation < 0.1), and this stochastic property is reproduced for a given quantum of ATP. Potentiation effects (of about 12%) occur if two quanta are released from the same varicosity because the receptor patch is not saturated even by the release of two quanta. The simulations show that quantal currents have a characteristically distinct shape for varicosities with different junctional cleft widths (50-200 nm). Finally, incorporation of an ectoenzyme with the known kinetics of ATPase into the junctional cleft allows for a quantal current of the observed time course, provided the number of ATP molecules in a quantum is increased over the number in the absence of the ATPase.     

Release of small transmitters through kiss-and-run fusion pores in rat pancreatic beta cells

Exocytosis of secretory vesicles begins with a fusion pore connecting the vesicle lumen to the extracellular space. This pore may then expand or it may close to recapture the vesicle intact. The contribution of the latter, termed kiss-and-run, to exocytosis of pancreatic beta cell large dense-core vesicles (LDCVs) is controversial. Examination of single vesicle fusion pores demonstrated that rat beta cell LDCVs can undergo exocytosis by rapid pore expansion, by the formation of stable pores, or via small transient kiss-and-run fusion pores. Elevation of cAMP shifted LDCV fusion pore openings to the transient mode. Under this condition, the small fusion pores were sufficient for release of ATP, stored within LDCVs together with insulin. Individual ATP release events occurred coincident with amperometric "stand alone feet" representing kiss-and-run. Therefore, the LDCV kiss-and-run fusion pores allow small transmitter release but likely retain the larger insulin peptide. This may represent a mechanism for selective intraislet signaling.     

Mechanisms generating the time course of dual component excitatory synaptic currents recorded in hippocampal slices

We studied with the whole-cell recording techniques, the mechanisms underlying the time course of the slow N-methyl-D-aspartate (NMDA), and fast non-NMDA receptor-mediated excitatory postsynaptic currents (EPSCs) in hippocampal slices. The rising phase of the NMDA receptor-mediated component of the EPSC as well as the decaying phase of the NMDA and non-NMDA component were highly temperature-sensitive, suggesting that neither of these processes is determined by free diffusion of transmitter. Moreover, glutamate uptake blockers enhanced the responses to exogenously applied glutamate, but had no effect on the decay of either the NMDA or non-NMDA components of the EPSCs. On the other hand, open channel blockers known to modify NMDA channel kinetics reduced the EPSC decay time. Thus, the present results support a model in which the rise time and decay of the NMDA component are determined primarily by slow channel kinetics and the decay of the non-NMDA component is due either to channel kinetics or to desensitization.     

The effects of geometrical parameters on synaptic transmission: a Monte Carlo simulation study

Monte Carlo simulations of transmitter diffusion and its interactions with postsynaptic receptors have been used to study properties of quantal responses at central synapses. Fast synaptic responses characteristic of those recorded at glycinergic junctions on the teleost Mauthner cell (time to peak approximately 0.3-0.4 ms and decay time constant approximately 3-6 ms) served as the initial reference, and smaller contacts with fewer postsynaptic receptors were also modeled. Consistent with experimental findings, diffusion, simulated using a random walk algorithm and assuming a diffusion coefficient of 0.5-1.0 x 10(-5) cm2 s(-1), was sufficiently fast to account for transmitter removal from the synaptic cleft. Transmitter-receptor interactions were modeled as a two-step binding process, with the double-bound state having opened and closed conformations. Addition of a third binding step only slightly decreased response amplitude but significantly slowed both its rising and decay phases. The model allowed us to assess the sources of response variability and the likelihood of postsynaptic saturation as functions of multiple kinetic and spatial parameters. The method of nonstationary fluctuation analysis, typically used to estimate the number of functional channels at a synapse and single channel current, proved unreliable, presumably because the receptors in the postsynaptic matrix are not uniformly exposed to the same profile of transmitter concentration. Thus, the time course of the probability of channel opening most likely varies among receptors. Finally, possible substrates for phenomena of synaptic plasticity, such as long-term potentiation, were explored, including the diameter of the contact zone, defined by the region of pre- and postsynaptic apposition, the number and distribution of the receptors, and the degree of vesicle filling. Surprisingly, response amplitude is quite sensitive to the size of the receptor-free annulus surrounding the receptor cluster, such that expansion of the contact zone could produce an appreciable increase in quantal size, normally attributed to either the presence of more receptors or the release of more transmitter molecules.     

Variability of excitatory currents due to single-channel noise, receptor number and morphological heterogeneity

Patch clamp recordings of excitatory postsynaptic currents (EPSCs) in central neurons reveal large fluctuations in amplitudes and decay times of AMPA-receptor-mediated EPSCs. By using Monte Carlo simulations of synaptic transmission in brainstem interneurons, we tested several hypothesis that could account for the observed variability. The coefficient of variation (CV) of 0.5 for miniature amplitudes cannot be explained by fluctuations in vesicle content or receptor distribution, but is traced to variations in receptor number, which is estimated as 77+/-39 receptors per bouton. As the variability of rise times reflects fluctuations in size of the post-synaptic density and heterogeneity of the receptor distribution, the relatively small CV=0.37 of experimentally determined values points to a homogeneous arrangement of receptors. Within our model the large variability of decay times (CV=0.49) can only be explained by fluctuations in the transmitter time course (mean residence times of 0.4+/-0.13 ms), presumably resulting from heterogeneities in synaptic morphology. Hence, our simulations indicate that different noise sources control the variability of amplitudes, rise and decay times. In particular, the distribution of decay times yields information about the synaptic transmission process, which cannot be obtained from other observables.     

Fusion pore modulation as a presynaptic mechanism contributing to expression of long-term potentiation

Working on the idea that postsynaptic and presynaptic mechanisms of long-term potentiation (LTP) expression are not inherently mutually exclusive, we have looked for the existence and functionality of presynaptic mechanisms for augmenting transmitter release in hippocampal slices. Specifically, we asked if changes in glutamate release might contribute to the conversion of 'silent synapses' that show N-methyl-D-aspartate (NMDA) responses but no detectable alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) responses, to ones that exhibit both. Here, we review experiments where NMDA receptor responses provided a bioassay of cleft glutamate concentration, using opposition between peak [glu](cleft )and a rapidly reversible antagonist, L-AP5. We discuss findings of a dramatic increase in peak [glu](cleft) upon expression of pairing-induced LTP (Choi). We present simulations with a quantitative model of glutamatergic synaptic transmission that includes modulation of the presynaptic fusion pore, realistic cleft geometry and a distributed array of postsynaptic receptors and glutamate transporters. The modelling supports the idea that changes in the dynamics of glutamate release can contribute to synaptic unsilencing. We review direct evidence from Renger et al., in accord with the modelling, that trading off the strength and duration of the glutamate transient can markedly alter AMPA receptor responses with little effect on NMDA receptor responses. An array of additional findings relevant to fusion pore modulation and its proposed contribution to LTP expression are considered.     

Postfusional control of quantal current shape

Whether glutamate is released rapidly, in an all-or-none manner, or more slowly, in a regulated manner, is a matter of debate. We analyzed the time course of excitatory postsynaptic currents (EPSCs) at glutamatergic neuromuscular junctions of Drosophila and found that the decay phase of EPSCs was protracted to a variable extent. The protraction was more pronounced in evoked and spontaneous quantal EPSCs than in action potential-evoked multiquantal EPSCs; reduced in quantal EPSCs from endophilin null mutants, which maintain release via kiss-and-run; and dependent on synaptotagmin isoform, calcium, and protein phosphorylation. Our data indicate that glutamate is released from individual synaptic vesicles for milliseconds through a fusion pore. Quantal glutamate discharge time course depends on presynaptic calcium inflow and the molecular composition of the release machinery.     

Effect of sodium nitroprusside on the mediator release and functional properties of the postsynaptic membrane at the neuromuscular junction]

The effect of nitric oxide donor sodium nitroprusside on the end-plate currents was studied under two-electrode voltage-clamp condition at frog neuro-muscular junction. Sodium nitroprusside (10(-4) M) reduced to the half the amplitude of end-plate currents while did not change miniature end-plate currents indicating the presynaptic nature of end-plate depression. In keeping with such suggestion sodium nitroprusside essentially (to 33%) suppressed the frequency of miniature end-plate currents but did not affect the decay time constant and voltage-dependence of miniature end-plate decay. In contrast to another presynaptic inhibitors sodium nitroprusside rather reduced than increased the presynaptic facilitation and did not change postsynaptic potentials. Thus, nitric oxide is the powerful inhibitor of both evoked and spontaneous transmitter release and did not change postsynaptic potential.     

Facilitation, augmentation, and potentiation of synaptic transmission at the superior cervical ganglion of the rabbit

The effect of repetitive stimulation on synaptic transmission was studied in the isolated superior cervical ganglion of the rabbit under conditions of reduced quantal content. Excitatory postsynaptic potentials (EPSP) were recorded with the sucrose gap technique to obtain estimates of transmitter release. Four components of increased transmitter release, with time constants of decay similar to those observed at the frog neuromuscular junction at 20 degrees C, were found in the ganglion at 34 degrees C: a first component of facilitation, which decayed with a time constant of 59 +/- 14 ms (mean +/- SD); a second component of facilitation, which decayed with a time constant of 388 +/- 97 ms; augmentation, which decayed with a time constant of 7.2 +/- 1 s; and potentiation, which decayed with a time constant of 88 +/- 25 s. The addition of 0.1-0.2 mM Ba2+ to the Locke solution increased the magnitude but not the time constant of decay of augmentation. Ba2+ had little effect on potentiation. The addition of 0.2-0.8 mM Sr2+ to the Locke solution appeared to increase the magnitude of the second component of facilitation. Sr2+ had little effect on augmentation or potentiation. These selective effects of Ba2+ and Sr2+ on the components of increased transmitter release in the rabbit ganglion are similar to the effects of these ions at the frog neuromuscular junction. Although the effects of Ba2+ and Sr2+ are similar in the two preparations, the magnitudes of augmentation and the second component of facilitation after a single impulse were about 6-10 times greater in the rabbit ganglion than at the frog neuromuscular junction. These results suggest that the underlying mechanisms in the nerve terminal that give rise to the components of increased transmitter release in the rabbit ganglion and frog neuromuscular junction are similar but not identical.     

Aging differentially affects multiple aspects of vesicle fusion kinetics

How fusion pore formation during exocytosis affects the subsequent release of vesicle contents remains incompletely understood. It is unclear if the amount released per vesicle is dependent upon the nature of the developing fusion pore and whether full fusion and transient kiss and run exocytosis are regulated by similar mechanisms. We hypothesise that if consistent relationships exist between these aspects of exocytosis then they will remain constant across any age. Using amperometry in mouse chromaffin cells we measured catecholamine efflux during single exocytotic events at P0, 1 month and 6 months. At all ages we observed full fusion (amperometric spike only), full fusion preceded by fusion pore flickering (pre-spike foot (PSF) signal followed by a spike) and pure "kiss and run" exocytosis (represented by stand alone foot (SAF) signals). We observe age-associated increases in the size of all 3 modes of fusion but these increases occur at different ages. The release probability of PSF signals or full spikes alone doesn't alter across any age in comparison with an age-dependent increase in the incidence of "kiss and run" type events. However, the most striking changes we observe are age-associated changes in the relationship between vesicle size and the membrane bending energy required for exocytosis. Our data illustrates that vesicle size does not regulate release probability, as has been suggested, that membrane elasticity or flexural rigidity change with age and that the mechanisms controlling full fusion may differ from those controlling "kiss and run" fusion.