Elastic, electrostatic and electrokinetic forces influencing membrane curvature.

Many cellular and intracellular processes critically depend on membrane shape, but the shape generating mechanisms are still to be fully understood. In this study we evaluate how electrostatic/electrokinetic forces contribute to membrane curvature. Membrane bilayer had finite thickness and was either elastically anisotropic or anisotropic overall, but isotropic per sections (heads and tails). The physics of the situation was evaluated using a coupled system of elastic and electrostatic/electrokinetic (Poisson-Nernst-Planck) equations. The fixed charges present only on the upper membrane surface lead to the accumulation of counter-ions and depletion of co-ions that decay spatially very rapidly (Debye length<1nm), as does the potential and electric field. Spatially uneven electric field and the permittivity mismatch also induce charges at the membrane-solution interface, which are not fixed but influence the electrostatics nevertheless. Membrane bends due to - Coulomb force (caused by fixed membrane charges in the electric field) and the dielectric force (due to the non-uniform electric field and the permittivity mismatch between the membrane and the solution). Both act as membrane surface forces, and both depend supra-linearly on the fixed charge density. Regardless of sign of the fixed charges, the membrane bends toward the charged (upper) surface owing to the action of the Coulomb force, but this is opposed by the smaller dielectric force. The spontaneous membrane curvature becomes very pronounced at high fixed charge densities, leading to very small spontaneous radii (<50nm). In conclusion the electrostatic/electrokinetic forces contribute significantly to the membrane curvature.

Strain, stress and energy in lipid bilayer induced by electrostatic/electrokinetic forces.

Lipid bilayer was deformed by the electrostatic/electrokinetic forces induced by the fixed charges on the top monolayer-solution interface. The strains, stresses and energy were simulated using finite element method. The elastic moduli of the heads were four times greater than those of tails sections, but were individually isotropic. The physics of the situation was evaluated using a coupled system of linear elastic equations and electrostatic-electrokinetic (Poisson-Nernst-Planck) equations. The Coulomb force (due to fixed charges in the electric field), and the dielectric force (due to uneven electric field and the solution-membrane permittivity mismatch) bend the membrane, but unevenly. Whereas the bottom monolayer extends vertically (towards charged surface), the top monolayer compresses. In contrast the top monolayer extends horizontally, but the bottom monolayer compresses. The horizontal normal stress is higher in the heads than in the tails sections, but is similar in two monolayers, whereas the vertical normal stress is small. The horizontal normal stress is associated with horizontal normal strain, and vertical with both vertical and horizontal strain. Surprisingly, the shear stress (an indicator where the membrane will deform), is greater in the tails sections. Finally, the elastic energy (which is clearly greater in the heads sections) is dominated by its horizontal component and peaks in the middle of the membrane. The shear component dominates in the tails sections, and is minimal in the membrane center. Even spatially uniform external force thus leads to complex membrane deformation and generates complex profiles of stress and elastic energy.

Extrusion of transmitter, water and ions generates forces to close fusion pore.

During exocytosis the fusion pore opens rapidly, then dilates gradually, and may subsequently close completely, but what controls its dynamics is not well understood. In this study we focus our attention on forces acting on the pore wall, and which are generated solely by the passage of transmitter, ions and water through the open fusion pore. The transport through the charged cylindrical nano-size pore is simulated using a coupled system of Poisson-Nernst-Planck and Navier-Stokes equations and the forces that act radially on the wall of the fusion pore are then estimated. Four forces are considered: a) inertial force, b) pressure, c) viscotic force, and d) electrostatic force. The inertial and viscotic forces are small, but the electrostatic force and the pressure are typically significant. High vesicular pressure tends to open the fusion pore, but the pressure induced by the transport of charged particles (glutamate, ions), which is predominant when the pore wall charge density is high tends to close the pore. The electrostatic force, which also depends on the charge density on the pore wall, is weakly repulsive before the pore dilates, but becomes attractive and pronounced as the pore dilates. Given that the vesicular concentration of free transmitter can change rapidly due to the release, or owing to the dissociation from the gel matrix, we evaluated how much and how rapidly a change of the vesicular K(+)-glutamate(-) concentration affects the concentration of glutamate(-) and ions in the pore and how such changes alter the radial force on the wall of the fusion pore. A step-like rise of the vesicular K(+)-glutamate(-) concentration leads to a chain of events. Pore concentration (and efflux) of both K(+) and glutamate(-) rise reaching their new steady-state values in less than 100 ns. Interestingly within a similar time interval the pore concentration of Na(+) also rises, whereas that of Cl(-) diminishes, although their extra-cellular concentration does not change. Finally such changes affect also the water movement. Water efflux changes bi-phasically, first increasing before decreasing to a new, but lower steady-state value. Nevertheless, even under such conditions an overall approximate neutrality of the pore is maintained remarkably well, and the electrostatic, but also inertial, viscotic and pressure forces acting on the pore wall remain constant. In conclusion the extrusion of the vesicular content generates forces, primarily the force due to the electro-kinetically induced pressure and electrostatic force (both influenced by the pore radius and even more by the charge density on the pore wall), which tend to close the fusion pore.

Forces and stresses acting on fusion pore membrane during secretion.

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.

Parametric spectral analysis of nonstationary fluctuations of excitatory synaptic currents.

We assessed on Monte-Carlo simulated excitatory post-synaptic currents the ability of autoregressive (AR)-model fitting to evaluate their fluctuations. AR-model fitting consists of a linear filter describing the process that generates the fluctuations when driven with a white noise. Its fluctuations provide a filtered version of the signal and have a spectral density depending on the properties of the linear filter. When the spectra of the non-stationary fluctuations of excitatory post-synaptic currents were estimated by fitting AR-models to the segments of current fluctuations, assumed to be stationary and independent, the parameter and spectral estimates were scattered. The scatter was much reduced if the time-variant AR-models were fitted using stochastic adaptive estimators (Kalman, recursive least squares and least mean squares). The ability of time-variant AR-models to accurately fit the current fluctuations was monitored by comparing the fluctuations with predicted fluctuations, and by evaluating the model-learning rate. The median frequency of current fluctuations, which could be rapidly tracked and estimated from the individual quantal events (either Monte-Carlo simulated or recorded from pyramidal neurons of rat hippocampus), rose during the rise phase, before declining to a lower steady-state level during the decay phase of quantal event, whereas the variance showed a broad peak. The closing rate of AMPA channels directly affects the steady-state median frequency, whereas the transient peak can be modulated by a variety of factors-number of molecules released, ability of glutamate molecules to re-enter the synaptic cleft, diffusion constant of glutamate in the cleft and opening rate of AMPA channels. In each case, the effect on the amplitude and decay time of mEPSCs and on the current fluctuations differs. Each factor thus leaves its own kinetic fingerprint arguing that the contribution of such factors can be inferred from the combined kinetic properties of individual mEPSCs.

Glutamate, water and ion transport through a charged nanosize pore.

The transport of transmitter, ions and water through a positively-charged nanopore was investigated through computer simulations. The physics of the problem is described by a coupled set of Poisson-Nernst-Planck and Navier-Stokes equations in a computational domain consisting a cylindrical pore, whose radius ranged from 1 to 8 nm and which was flanked by two compartments representing the vesicular interior and extra-cellular space. The concentration of co-ions is suppressed and of counter-ions enhanced, especially near the pore wall owing to electrostatic interactions. Glutamate (i.e. the transmitter considered) is negatively charged and is simulated as a counter-ion. The electro-kinetically induced pressure due to the movement of ions is negative and very pronounced near the pore wall where the concentration and flux of counter-ions is very high. The water velocity peaks in the pore center, diminishes to zero at the pore wall, but is constant along the pore axis. The mean velocity of the water/fluid is proportional to the vesicular pressure and pore cross-sectional area. Interestingly it is inversely related to the vesicular glutamate concentration. The factors determining the glutamate flux are complex. The diffusive flux generally predominates for narrow pore, and convective flux may dominate for wide pore if the vesicular pressure is high. Surprisingly at low vesicular pressure the mean total glutamate flux per unit cross-sectional pore area is higher for narrow pores. Higher flux is probably due to the rise of glutamate concentration in the nanopore, which is much more pronounced for narrow nanopores, due to the maintenance of approximate neutrality of charges in the pore and on the pore wall. In conclusion intra-vesicular pressure helps 'flushing-out' the transmitter, but the induced pressure 'drags-out' the water into the extra-cellular space.

Monte Carlo simulation of release of vesicular content in neuroendocrine cells.

The release of transmitter from the vesicle, its diffusion through the fusion pore, and the cleft and its interaction with the carbon electrode were simulated using the Monte Carlo method. According to the simulation the transmitter release is largely determined by geometric factors--the ratio of the fusion pore cross-sectional and vesicular areas, if the diffusion constant is as in the aqueous solution--but the speed of transmitter dissociation from the gel matrix plays an important role during the rise phase of release. Transmitter is not depleted near the entrance to the fusion pore and there is no cleft-to-vesicle feedback, but the depletion becomes evident if the diffusion constant is reduced, especially if the pore is wide. In general, the time course of amperometric currents closely resembles the time course of the simulated transmitter concentration in the cleft and the time course of release. Surprisingly, even a tenfold change of the electrode efficiency has only a marginal effect on the amplitude or the time course of amperometric currents. Greater electrode efficiency however lowers the cleft concentration, but only if the cleft is narrow. As the cleft widens the current amplitudes diminish and rise times lengthen, but the decay times are less affected. Moreover, the amplitude dependence of the rise and decay times becomes steeper as the cleft widens and/or as the release kinetics slows. Finally, lower diffusion constant of transmitter in the narrow cleft does not further prolong the amperometric currents, whose slow time course reflects slow release kinetics.

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.

Rapid change of quantal size in PC-12 cells detected by neural networks.

The basic building block of synaptic transmission-the number of molecules released per vesicle (quantal size (QS)) often changes with stimulation, but there is no agreement about what factors regulate it. To throw more light on this problem spontaneous quantal release was recorded amperometrically in PC-12 cells. Amperometric current spikes, representing single vesicle release, were detected by thresholding and were separated from spurious events on the basis of their amplitude and time course using a pattern recognition system based on the principal component neural network methods. The frequency of current spikes, their amplitude, quantal size, rise time and decay time were typically non-stationary, even in the absence of stimulation. Their running values changed much more than those of memoryless stationary random data with the same probability density distribution. Irrespective of how much the quantal size, rise and decay times varied, their amplitude dependence remained constant, or changed with a very different time course. In conclusion, the quantal size is highly labile in PC-12 cells. The lability does not appear to result from the changes of fusion pore dynamics or the mechanism of release of vesicular content, but because of the preferential release of large vesicles.

Simulation and parameter estimation of dynamics of synaptic depression.

Synaptic release was simulated using a Simulink sequential storage model with three vesicular pools. Modeling was modular and easily extendable to the systems with greater number of vesicular pools, parallel input, or time-varying parameters. Given an input (short or long tetanic trains, patterned or random stimulation) and the storage model, the vesicular release, the replenishment of various vesicular pools, and the vesicular content of all pools could be simulated for the time-invariant and time-varying storage systems. From the input stimuli and either a noiseless or a noisy output, the parameters of such storage systems could also be estimated using the optimization technique that minimizes in the least square sense the error between the observed release and the predicted release. All parameters of the storage model could be evaluated with sufficiently long input-output data pairs. Not surprisingly, the parameters characterizing the processes near the release locus, such as the fractional release and the size of the immediately available pool and its coupling to the small store, as well as the state variables associated with the immediately available pool, such as its vesicular content and replenishment, could be determined with fewer stimuli. The possibility of estimating parameters with random inputs extends the applicability of the method to in vivo synapses with the physiological inputs. The parameter estimation was also possible under the time-variant, but slowly changing, conditions as well as for open systems that are part of larger vesicular storage systems but whose parameters can either not be reliably determined or are of no interest. The quality of parameter estimation was monitored continuously by comparing the observed and predicted output and/or estimated parameters with the true values. Finally, the method was tested experimentally using the rat phrenic-diaphragm neuromuscular junction.

Wavelet analysis of nonstationary fluctuations of Monte Carlo-simulated excitatory postsynaptic currents.

Tracking spectral changes of rapidly varying signals is a demanding task. In this study, we explore on Monte Carlo-simulated glutamate-activated AMPA patch and synaptic currents whether a wavelet analysis offers such a possibility. Unlike Fourier methods that determine only the frequency content of a signal, the wavelet analysis determines both the frequency and the time. This is owing to the nature of the basis functions, which are infinite for Fourier transforms (sines and cosines are infinite), but are finite for wavelet analysis (wavelets are localized waves). In agreement with previous reports, the frequency of the stationary patch current fluctuations is higher for larger currents, whereas the mean-variance plots are parabolic. The spectra of the current fluctuations and mean-variance plots are close to the theoretically predicted values. The median frequency of the synaptic and nonstationary patch currents is, however, time dependent, though at the peak of synaptic currents, the median frequency is insensitive to the number of glutamate molecules released. Such time dependence demonstrates that the "composite spectra" of the current fluctuations gathered over the whole duration of synaptic currents cannot be used to assess the mean open time or effective mean open time of AMPA channels. The current (patch or synaptic) versus median frequency plots show hysteresis. The median frequency is thus not a simple reflection of the overall receptor saturation levels and is greater during the rise phase for the same saturation level. The hysteresis is due to the higher occupancy of the doubly bound state during the rise phase and not due to the spatial spread of the saturation disk, which remains remarkably constant. Albeit time dependent, the variance of the synaptic and nonstationary patch currents can be accurately determined. Nevertheless the evaluation of the number of AMPA channels and their single current from the mean-variance plots of patch or synaptic currents is not highly accurate owing to the varying number of the activatable AMPA channels caused by desensitization. The spatial nonuniformity of open, bound, and desensitized AMPA channels, and the time dependence and spatial nonuniformity of the glutamate concentration in the synaptic cleft, further reduce the accuracy of estimates of the number of AMPA channels from synaptic currents. In conclusion, wavelet analysis of nonstationary fluctuations of patch and synaptic currents expands our ability to determine accurately the variance and frequency of current fluctuations, demonstrates the limits of applicability of techniques currently used to evaluate the single channel current and number of AMPA channels, and offers new insights into the mechanisms involved in the generation of unitary quantal events at excitatory central synapses.

Change of quantal size and parameters of release with stimulation in bovine chromaffin cells.

Changes in quantal size and in the parameters of release were examined in chromaffin cells using amperometric recordings during and following various stimuli that induce secretion. As a general rule, a greater quantal content was associated with a greater quantal size. Following a short depolarizing pulse (0.5-2 s; 100 mV from a holding potential of -80 mV), the mean value of quantal size increased by 54% over several seconds before gradually (over tens of seconds) returning toward the control value, whilst its variability rose by 62%. The changes observed following 30-s applications of high extracellular K+ (50 mM) were more modest. A rapid application of short depolarizing pulses (2 s every 10-20 s; 100 mV from a holding potential of -80 mV) also led, at least initially, to greater quantal content and quantal size. Mean quantal size rose initially by 68%, but decreased subsequently to 31% below pre-stimulation levels. In whole-clamped cells, the frequency of quantal release can rise abruptly, probably owing to a mechanical disturbance that makes the membrane leaky to Ca2+. In such cases, a marked rise in quantal content (>ten-fold) was paralleled by an almost as dramatic (up to ten-fold) rise in quantal size and an important, although less pronounced and slower, rise in its variability (up to four-fold). The return toward control values of mean quantal size occurred over several minutes, whilst its variability decayed more slowly. The release parameters were evaluated directly from the number of events to avoid a large and time-dependent contribution of the amplitude variability of spontaneous amperometric current spikes (minis). In general, the greater probability of release contributed more than the greater size of the immediately available store to the increase in quantal output. In conclusion, quantal size was found to be highly labile. Its change can alter strongly the facilitation and depression of evoked quantal output and probably occurs due to a preferential release of large vesicles that are more efficient barriers to Ca2+ diffusion when Ca2+ rises rapidly following a synchronous opening of several Ca2+ channels. When intracellular Ca2+ levels rise slowly to threshold levels for secretion, as during an asynchronous and generally spontaneous release, vesicles are less effective diffusion barriers and quantal size changes less.

Monte Carlo evaluation of quantal analysis in the light of Ca2+ dynamics and the geometry of secretion.

Using the Monte Carlo technique, Ca2+ dynamics were simulated in the absence and presence of vesicles to gain better insight into what governs quantal release. A vesicle, represented as a flat, infinitely thin surface, was positioned parallel to the plasma membrane at a chosen distance from the locus of Ca2+ entry. Because vesicles act as important diffusion barriers after the synchronous opening of Ca2+ channels (as occurs during evoked release), [Ca2+] close to the plasma membrane reaches higher levels than it would in the absence of vesicles. The rise in [Ca2+] is greater under larger vesicles close to the plasma membrane, which thus have a higher probability of release. The power-law relationship between the [Ca2+] and the probability of release, and the cubic relationship between the vesicular diameter and its volume can make this relationship very steep. In contrast, when release occurs owing to fluctuations of [Ca2+]--as a result of Ca2+ release from an internal store or asynchronous opening of Ca2+ channels (during spontaneous release)--the effect of vesicles as diffusion barriers is less pronounced and vesicles of different sizes should have a similar probability of release. Since the preferential release of large vesicles depends on how the Ca2+ needed for secretion is raised (synchronously versus asynchronously), the quantal size of evoked and spontaneous release should differ. The main factors influencing the preferential release of large vesicles are the distance between vesicles and the plasma membrane, the concentration of Ca2+ buffers, and single-channel Ca2+ flux. Vesicles also have a pronounced effect on Ca2+ binding to buffers and on the spatio-temporal distribution of bound buffers. The greater the vesicular size and the closer their position to the plasma membrane, the more fixed buffers will be bound near the plasma membrane because of limited diffusion of Ca2+. Since bound fixed buffers act as "memory elements", such a change in their spatial distribution will further enhance the probability of release of large vesicles during stimulation.

Monte carlo simulation of vesicular release, spatiotemporal distribution of glutamate in synaptic cleft and generation of postsynaptic currents.

The release of vesicular glutamate, spatiotemporal changes in glutamate concentration in the synaptic cleft and the subsequent generation of fast excitatory postsynaptic currents at a hippocampal synapse were modeled using the Monte Carlo method. It is assumed that glutamate is released from a spherical vesicle through a cylindrical fusion pore into the synaptic cleft and that S-alpha-amino-3-hydroxy -5-methyl-4-isoxazolepropionic acid (AMPA) receptors are uniformly distributed postsynaptically. The time course of change in vesicular concentration can be described by a single exponential, but a slow tail is also observed though only following the release of most of the glutamate. The time constant of decay increases with vesicular size and a lower diffusion constant, and is independent of the initial concentration, becoming markedly shorter for wider fusion pores. The cleft concentration at the fusion pore mouth is not negligible compared to vesicular concentration, especially for wider fusion pores. Lateral equilibration of glutamate is rapid, and within approximately 50 micros all AMPA receptors on average see the same concentration of glutamate. Nevertheless the single-channel current and the number of channels estimated from mean-variance plots are unreliable and different when estimated from rise- and decay-current segments. Greater saturation of AMPA receptor channels provides higher but not more accurate estimates. Two factors contribute to the variability of postsynaptic currents and render the mean-variance nonstationary analysis unreliable, even when all receptors see on average the same glutamate concentration. Firstly, the variability of the instantaneous cleft concentration of glutamate, unlike the mean concentration, first rapidly decreases before slowly increasing; the variability is greater for fewer molecules in the cleft and is spatially nonuniform. Secondly, the efficacy with which glutamate produces a response changes with time. Understanding the factors that determine the time course of vesicular content release as well as the spatiotemporal changes of glutamate concentration in the cleft is crucial for understanding the mechanism that generates postsynaptic currents.

Effect of cyclothiazide on spontaneous miniature excitatory postsynaptic currents in rat hippocampal pyramidal cells.

Spontaneous miniature excitatory postsynaptic currents (mEPSCs) were recorded from the CA1 region of slices using the whole-cell patch-clamp technique. Cyclothiazide (0.1 mM), a complete blocker of desensitization of (S)-alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) channels, was applied to determine the changes in amplitude and kinetics of mEPSCs occurring with complete suppression of desensitization. The amplitude of mEPSC (A) was not affected significantly by cyclothiazide, but both the rise (taur) and the decay time (taud) were consistently increased (from 2.3 to 6.5 ms and from 9.9 to 22.2 ms respectively). The amplitude dependence of both taud and taur became much greater, but there was no upward shift of the best-fitting lines. The slopes of the control best-fitting lines were (+/-SD; ms/pA; n=5) 0.39+/-0.05 for taud:A and 0.12+/-0.07 for taur:A, but, in the presence of cyclothiazide, the corresponding slopes were much steeper (2.1+/-0.60 and 0.68+/-0. 21; holding potential was -50 mV and temperature 32 degreesC). These changes, which were slow to develop, suggest that cyclothiazide blocks AMPA receptor channel desensitization, whilst having no effect on the closing rate of AMPA channels. Judging by the extent of change, the speed of diffusion of glutamate in the synaptic cleft is probably similar to that in water. In conclusion, this study provides evidence that: (1) under control conditions, desensitization of AMPA channels plays a major role in shaping the time course of synaptic currents in CA1; and (2) cyclothiazide prolongs their time course solely by abolishing desensitization.

Comparison of vesicular volume and quantal size in bovine chromaffin cells.

Electrochemical measurements of vesicular content released were compared with the morphometric measurements of vesicular size in bovine chromaffin cells. Cross-sectional vesicular diameters were determined from electron micrographs. Two methods were used to determine the frequency histograms of "true" vesicular diameters (i.e. diameters of the vesicles in the equatorial plane): (i) "peeling off" method [Coupland R. E. (1968), Nature 217, 384-388], and (ii) summation of individual probabilities of "true" vesicular diameters. Quantal size was estimated from the area under the spontaneous current spike detected electrochemically. The frequency histograms of "true" vesicular diameters are found to be skewed (thus not well described by a Gaussian function) irrespective of the method used to calculate them, as are the frequency histograms of the cube roots of the quantal sizes. Furthermore, we also find that the frequency histograms of electrochemical measurements (the cube roots of quantal sizes) have lower skews and coefficients of variation than those of morphometric measurements ("true" vesicular diameters), with discrepancy being especially pronounced for noradrenaline-secreting cells. Such a difference in both coefficients of variation and skews suggests that the intravesicular catecholamine concentration is not uniform, but that it is lower for vesicles of larger size. In conclusion a variety of factors--vesicular volume, vesicular surface area to volume ratio, binding capacity of chromogranin and/or ATP, likely determines the amount of catecholamine stored in the vesicle.

Monte Carlo simulation of spontaneous miniature excitatory postsynaptic currents in rat hippocampal synapse in the presence and absence of desensitization.

Using the Monte Carlo method, spontaneous fast excitatory postsynaptic currents (mEPSCs) at a hippocampal synapse were simulated by releasing 150-20,000 glutamate molecules from a point source centred 15 nm above a rectangular grid of 14 x 14 alpha-amino-3-hydroxy-methyl-isoxazole (AMPA) receptors and assuming the channel kinetics to be as reported by Jonas et al. [J Physiol (Lond) 472:615; 1993]. The relationship between the amplitudes of mEPSCs and their time constants of decay is positive, but not pronounced in physiological conditions (except when the number of molecules released is very high). It increases as desensitization is reduced and becomes highly pronounced when it is eliminated. mEPSCs are prolonged with repeated opening of AMPA channels due to enhancement of two concentration-dependent processes: (1) binding of glutamate molecules by AMPA receptors, and (2) occupancy of both activatable bound states. In contrast, the time constant of decay of the patch currents evoked by a short glutamate pulse is independent of glutamate concentration and current amplitude in control conditions, and only moderately concentration dependent in the absence of desensitization. The fast application protocol thus fails to reproduce synaptic currents reliably when there is repeated binding of glutamate molecules to AMPA receptors. During an mEPSC, the occupancy of desensitized states increases rapidly and it strongly depends on the number of glutamate molecules released. Desensitization reaches its maximum after an mEPSC decays to very low levels, and recovers very slowly (from tens to hundreds of milliseconds), and in a concentration-dependent manner. In conclusion, under physiological conditions the desensitization of AMPA receptors plays a major role in shaping the time course of mEPSCs by minimizing the repeated opening of AMPA channels.

Changes of spontaneous miniature excitatory postsynaptic currents in rat hippocampal pyramidal cells induced by aniracetam.

Spontaneous miniature excitatory postsynaptic currents (mEPSCs) in rat hippocampal pyramidal neurones in slices (CA1 region) were recorded at 35-37 degrees C using the whole-cell patch-clamp technique before and after addition of aniracetam (1 mM) to determine how a partial blockade of desensitization alters the relationship between the amplitude (A) and kinetics of mEPSCs, and to evaluate the factors that determine their variability. The rise time (taur) and the time constant of decay of mEPSCs (taud) are essentially amplitude independent in control conditions, but become clearly amplitude dependent in the presence of aniracetam. The slopes of the best fitting lines to taud:A and taur:A data pairs were (+/- SD; ms/pA; n = 5): (1) (control) 0.07 +/- 0.02 and 0.008 +/- 0.003; (2) (aniracetam) 0.40 +/- 0.19 and 0.22 +/- 0.22. The amplitude-dependent prolongation of taud is explained by the concentration dependence of two related processes, the buffering of glutamate molecules by AMPA receptor channels, and the occupancy of the double-bound activatable states. A slower deactivation makes an amplitude-independent contribution. Desensitization reduces the amplitude dependence of taud by minimizing repeated openings of alpha-amino-3-hydroxy-methyl-isoxazole (AMPA) receptor channels. A greater amplitude dependence of taur probably involves both pre- and postsynaptic factors. The variability of A and taud values did not change significantly, but the factors underlying the variability of taud values were much affected. The greater amplitude dependence and the greater scatter about the best fitting lines to taud:A data pairs are approximately balanced by the greater mean values. The greater scatter of taud about the best fitting lines probably occurs because the saturation of AMPA receptors is not the same at different synapses with different numbers of AMPA receptors.

Comparison of parzen density and frequency histogram as estimators of probability density functions.

In neurobiology, and in other fields, the frequency histogram is a traditional tool for determining the probability density function (pdf) of random processes, although other methods have been shown to be more efficient as their estimators. In this study, the frequency histogram is compared with the Parzen density estimator, a method that consists of convolving each measurement with a weighting function of choice (Gaussian, rectangular, etc) and using their sum as an estimate of the pdf of the random process. The difference in their performance in evaluating two types of pdfs that occur commonly in quantal analysis (monomodal and multimodal with equidistant peaks) is demonstrated numerically by using the integrated square error criterion and assuming a knowledge of the "true" pdf. The error of the Parzen density estimates decreases faster as a function of the number of observations than that of the frequency histogram, indicating that they are asymptotically more efficient. A variety of "reasonable" weighting functions can provide similarly efficient Parzen density estimates, but their efficiency greatly depends on their width. The optimal widths determined using the integrated square error criterion, the harmonic analysis (applicable only to multimodal pdfs with equidistant peaks), and the "test graphs" (the graphs of the second derivatives of the Parzen density estimates that do not assume a knowledge of the "true" pdf, but depend on the distinction between the "essential features" of the pdf and the "random fluctuations") were compared and found to be similar.

Temperature dependence of release of vesicular content in bovine chromaffin cells.

Recent studies suggest that the time course of secretion of the vesicular content in bovine chromaffin cells is much slower than in the peripheral or the central nervous system, but the reasons for this marked difference are not known. In this study we try to assess the importance of factors that may influence the time course of release of the vesicular content of bovine chromaffin cells, namely: (1) diffusion of catecholamines in the extracellular solution, (2) dissociation of catecholamines from the matrix of chromogranin A, and (3) the kinetics of opening and closing of the fusion pore. The temperature dependence of the time course and the amplitude of the spontaneous current spikes were examined using the carbon filament recording technique in amperometric mode. The change in amplitude was not statistically significant, but both the rise and the decay times were shortened (from 29 +/- 12 to 16 +/- 5 ms, and from 87 +/- 26 to 57 +/- 11 ms respectively) as temperature was raised by 20 degrees C [from 15 to 35 degrees C; n = 6; the changes were statistically significant at the level of P = 0.05; their respective temperature coefficients (Q10) were 1.4 and 1.3]. The areas underneath the spontaneous current spikes, however, were not altered significantly. Neither the relationship between the rise and the decay times nor the frequency of occurrence of the spontaneous current spikes changed consistently as the temperature was raised. However, the frequency histograms could, in all cases, be well described by a monoexponential function. It is concluded that the release of catecholamine content from the individual vesicles in bovine chromaffin cells is probably mostly determined by the dissociation of catecholamines from the matrix of chromogranin A.