Fluxes theory in experiments with random distributed channels on vesicles

When channels are randomly distributed in a population of vesicles, disregarding the number of channels per vesicle, these channels follow a Poisson distribution. This has been verified in many cases, determining the average of channels per vesicle. However, to determine kinetic parameters in population studies, a mathematical expression for the mean flux of solute through channels per vesicle is necessary. Hence, here, this mean flux is calculated, assuming Poisson distributed channels in a population of vesicle. Moreover, this result has been generalized to any number of different kinds of channels (i.e., channels with different permeabilities). These results, useful for in vitro experiments with mixed both channels and vesicles, can be supplemented with those from other techniques, in order to understanding how the nature of the lipid membrane affects kinetic parameters of channel.     

An estimate of the number of Ca2+-dependent K+ channels in the human red cell

An original approach has been designed to count Ca2+-dependent K+ channels in the human red cell using a preparation of inside-out vesicles. The relative frequency of vesicles having no K+ channels is estimated from the fraction of 42K+ (or 86Rb+) which is not released from loaded vesicles on maximal stimulation with Ca2+. The mean number of channels per vesicle is then calculated from this figure assuming a Poisson distribution for the K+ channels. From this value and the mean vesicular radius, computed from the volume/surface ratio, the mean number of channels per cell can be estimated. A value of 142 +/- 27 (mean +/- S.E.) was obtained, which is well above that estimated by comparison of unitary conductance and tracer equilibration rate measurements (about 10 channels/cell, Grygorczyk, R. Schwarz, W. and Passow, H. (1984) Biophys. J. 45, 693-698), but compares favourably with the channel density inferred from comparison with the number of Na+ pumps in a similar preparation of inside-out vesicles (100-200/cell, Lew, V.L., Muallem, S. and Seymour, C.A. (1982) Nature 296, 742-744). The procedure described here can be considered for general application as an alternative to other known procedures.     

Building a bilayer model of the neuromuscular synapse

Progress over the past 10 years has made it possible to construct a simple model of neurotransmitter release. Currently, some models use artificially formed vesicles to represent synaptic vesicles and a planar lipid bilayer as a presynaptic membrane. Fusion of vesicles with the bilayer is via channel proteins in the vesicle membrane and an osmotic gradient. In this paper, a framework is presented for the successful construction of a more complete model of synaptic transmission. This model includes real synaptic vesicles that fuse with a planar bilayer. The bilayer contains acetylcholine receptor (AChR) channels which function as autoreceptors in the membrane. Vesicle fusion is initiated following a Ca²⁺ flux through voltage-gated Ca²⁺ channels. Key steps in the plan are validated by mathematical modeling. Specifically, the probability that a reconstituted AChR channel opens following the release of ACh from a fusing vesicle, is calculated as a function of time, quantal content, and number of reconstituted AChRs. Experimentally obtainable parameters for construction of a working synapse are given. The inevitable construction of a full working model will mean that the minimal structures necessary for synaptic transmission are identified. This will open the door in determining regulatory and modulatory factors of transmitter release.     

Analysis of the all or nothing behaviour of Ca-dependent K channels in one-step inside-out vesicles from human red cell membranes

The all or nothing behaviour of Ca2+-dependent K+ channels has been analyzed in one-step inside-out vesicles. There is a threshold for Ca2+ below which the K+ channels remain silent, and which ranges between the 10(-6) and 10(-8) M for different vesicles under the experimental conditions tested, in the absence of Mg2+. The increase of Ca2+ concentration within this range recruits a larger fraction of the vesicles to the active (permeable to 86Rb+) state. The apparent rate of 86Rb+ transport through each individual channel was found to increase, however, with Ca2+ concentration. This finding is not an artefact due to size heterogeneity of the vesicle population, and it is consistent with the variations of the mean open time of the channels with Ca2+ concentration reported previously in patch-clamp experiments. The electron donor system ascorbate + phenazine-methosulphate increases the rate of 86Rb+ transport through the channels whereas oxidized cytochrome c has the opposite effect.     

Transmembrane flux and receptor desensitization measured with membrane vesicles. Homogeneity of vesicles investigated by computer simulation.

The use of membrane vesicles to make quantitative studies of transmembrane transport and exchange processes involves an assumption of homogeneity of the membrane vesicles. In studies of 86Rb+ exchange mediated by acetylcholine receptor from the electric organ of Electrophorus electricus and of 36Cl- exchange mediated by GABA receptor from rat brain, measurements of ion exchange and receptor desensitization precisely followed first order kinetics in support of this assumption. In other measurements a biphasic decay of receptor activity was seen. To elucidate the molecular properties of receptors from such measurements it is important to appreciate what the requirements of vesicle monodispersity are for meaningful results and what the effect of vesicle heterogeneity would be. The experiments were simulated with single vesicle populations with variable defined size distributions as well as with mixtures of different populations of vesicles. The properties of the receptors and their density in the membrane could be varied. Different receptors could be present on the same or different membrane vesicles. The simulated measurements were not very sensitive to size dispersity. A very broad size distribution of a single vesicle population was necessary to give rise to detectable deviations from first order kinetics or errors in the determined kinetic constants. Errors could become significant with mixtures of different vesicle populations, where the dispersity in initial ion exchange rate constant, proportional to the receptor concentration per internal volume, became large. In this case the apparent rate of receptor desensitization would diverge in opposite directions from the input value when measured by two different methods, suggesting an experimental test for such kinetic heterogeneity. A biphasic decrease of receptor activity could not be attributed to vesicle heterogeneity and must be due to desensitization processes with different rates. Significant errors would not arise from the size dispersity apparent in subpopulations of vesicles seen by imaging techniques in membrane preparations.     

A single tryptic fragment of colicin E1 can form an ion channel: stoichiometry confirms kinetics.

The molecularity of the ion channel formed by peptide fragments of colicin has taken on particular significance since the length of the active peptide has been shown to be less than 90 amino acids and the lumen size at least 8 A. Cell survival experiments show that killing by colicin obeys single-hit statistics, and ion leakage rates from phospholipid vesicles are first order in colicin concentration. However, interpretation in molecular terms is generally complicated by the requirement of large numbers of colicin molecules per cell or vesicle. We have measured the discharge of potential across membranes of small phospholipid vesicles by following the changes in binding of potential sensitive spin labeled phosphonium ions as a function of the number of colicin fragments added. Because of the sensitivity of the method, it was possible to reliably investigate the effect of colicin in a range where there was no more than 0.2 colicins per vesicle. The quantitative results of these experiments yield a direct molecular stoichiometry and demonstrate that one C-terminal fragment of the colicin molecule per one vesicle is sufficient to induce a rapid ion flux in these vesicles. In addition, the experiments confirm earlier findings that the colicin fragments do not migrate from one vesicle to another at pH 4.5. Similar results are obtained with large unilamellar vesicles.     

Morphological studies of stimulated adrenergic axon varicosities in the mouse vas deferens

The postganglionic axons of sympathetic neurons innervating the mouse vas deferens were stimulated transmurally in vitro by passing square pulses between two platinum electrodes. The ultrastructural appearance of the adrenergic nerve terminals was compared to samples fixed immediately after 30 min of stimulation and in samples allowed to recover for 2 h before fixation. The contralateral vasa deferentia served as controls, and these were incubated in Krebs solution for the same period as stimulated muscles. For each of four experiments, the mean number of large and small dense-core vesicles per square micrometer was calculated, as were the mean area and perimeter of the axon varicosities in each group. It was found that the number of small vesicles per square micrometer decreased by 60% during the stimulation period, but returned almost to control levels 2 h later. Large vesicles did not change in number during the stimulation or recovery periods. The proportion of vesicles containing cores was also determined for each group and found to decline just after stimulation in the small vesicle population, but to remain constant in the large vesicle population. The core depletion was partly reversed after 2 h. The vesicle recovery process was studied by use of the extracellular tracer horseradish peroxidase (HRP). When HRP was present in the extracellular space during stimulation, large numbers of vesicles contained the marker after recovery from stimulation. Thus, it is proposed that adrenergic axon varicosities recycle vesicle membrane through the plasma membrane in a manner similar to that already described for cholinergic nerve terminals.     

Flux theory for Poisson distributed pores with Gaussian permeability

The mean of the solute flux through membrane pores depends on the random distribution and permeability of the pores. Mathematical models including such randomness factors make it possible to obtain statistical parameters for pore characterization. Here, assuming that pores follow a Poisson distribution in the lipid phase and that their permeabilities follow a Gaussian distribution, a mathematical model for solute dynamics is obtained by applying a general result from a previous work regarding any number of different kinds of randomly distributed pores.

The new proposed theory is studied using experimental parameters obtained elsewhere, and a method for finding the mean single pore flux rate from liposome flux assays is suggested. This method is useful for pores without requiring studies by patch-clamp in single cells or single-channel recordings. However, it does not apply in the case of ion-selective channels, in which a more complex flux law combining the concentration and electrical gradient is required.     

Analysis of gated flux from or into sealed membrane fragments

Physico-chemical factors that determine tracer substance flux from or into sealed vesicular structures are examined. Flux amplitudes are dependent on the average volume of a vesicle, while flux rates depend on the average number of transmembrane channels per vesicle. Gating processes leading to channel opening and/or closing affect both amplitudes and rates. Averaging over inhomogeneities in vesicle size and channel density leads to an explicit expression for time-dependent tracer content. Means for experimentally determining all variable factors in this expression are discussed.     

Optical characterization of liposomes by right angle light scattering and turbidity measurement

Liposomes have frequently been used as models of biomembranes or vehicles for drug delivery. However, the systematic characterization of lipid vesicles by right angle light scattering and turbidity has not been carried out despite the usefulness of such studies for size estimation. In this study, liposomes of various sizes were prepared by sonication and extrusion. The mean cumulant radii of the vesicles were determined by dynamic light scattering. The lamellarities were estimated based on fluorescence quenching of N-(7-nitrobenz-2-oxa-1,3-diazol-4-yl)dipalmitoyl-L-alpha-phosph ati dylethanolamine by sodium dithionite. Right angle light scattering intensity and optical density at 436 nm per unit lipid concentration were measured as a function of vesicle radius. With a vesicle radius < or =100 nm, the optical parameters could be well explained by the Rayleigh-Gans-Debye theory in which the liposomes were modeled as homogeneous spheres with mean refractive indices determined by the volume fractions of lipids in vesicles.     

EFFECT OF ELECTRICAL STIMULATION ON THE YIELD AND COMPOSITION OF SYNAPTIC VESICLES FROM THE CHOLINERGIC SYNAPSES OF THE ELECTRIC ORGAN OF TORPEDO: A COMBINED BIOCHEMICAL, ELECTROPHYSIOLOGICAL AND MORPHOLOGICAL STUDY

Abstract— The effect of stimulating the electric organ of Torpedo marmorata , anaesthetized with 0.01% Tricaine methane sulphonate, by means of electrical stimulation (5/s) administered via an electrode placed on the electric lobe has been studied electrophysiologically, biochemically and morphologically. The response of the organ declined to about 50 per cent of its initial value after about 500 stimuli, by a further 10 per cent after another 500 stimuli and then to about 12 per cent of the initial value after a further 1000 stimuli. Thereafter the response fell off progressively. However, even when the response was less than 1 per cent of its initial value, the organ had considerable powers of recuperation during a 30-s rest period, to 30–50 per cent of its initial value.
The fall in response was accompanied by a reduction in vesicle size and number, an increase in the area of the presynaptic membrane and a fall in the protein, total nucleotide, ATP and acetylcholine content of the vesicle fraction isolated from the stimulated tissue. However, whereas vesicle numbers and the protein and total nucleotide content of the vesicle fraction fell by only about 50 per cent, vesicular ATP and acetylcholine levels were reduced to about 10 per cent. An analysis of the covariance of vesicular ATP and acetylcholine showed an initial loss of an acetylcholine-rich (relative to ATP) population of vesicles. The early loss of vesicular protein and nucleotide and vesicle numbers as well as the morphological changes seen would be consistent with a loss of vesicles due to fusion with the external membrane. The preferential loss of acetylcholine and ATP from the vesicle fraction indicates that the vesicles surviving the stimulation procedure have been utilized in a number of cycles causing the progressive fall in vesicle volume, and acetylcholine and ATP content.     

Kinetics of the micelle-to-vesicle transition: aqueous lecithin-bile salt mixtures

Important routes to lipid vesicles (liposomes) are detergent removal techniques, such as dialysis or dilution. Although they are widely applied, there has been only limited understanding about the structural evolution during the formation of vesicles and the parameters that determine their properties. We use time-resolved static and dynamic light scattering to study vesicle formation in aqueous lecithin-bile salt mixtures. The kinetic rates and vesicle sizes are found to strongly depend on total amphiphile concentration and, even more pronounced, on ionic strength. The observed trends contradict equilibrium calculations, but are in agreement with a kinetic model that we present. This model identifies the key kinetic steps during vesicle formation: rapid formation of disk-like intermediate micelles, growth of these metastable micelles, and their closure to form vesicles once line tension dominates bending energy. A comparison of the rates of growth and closure provides a kinetic criterion for the critical size at which disks close and thus for the vesicle size. The model suggests that liposomes are nonequilibrium, kinetically trapped structures of very long lifetime. Their properties are hence controlled by kinetics rather than thermodynamics.     

The effects of different methods of fixation on central nervous system synaptic pinocytotic vesicles

Summary Synaptic pinocytotic vesicles (invaginating from the surface membrane) and coated vesicles inside rat mossy fiber endings were counted after the use of different kinds of fixatives. Significantly greater numbers of pinocytotic vesicles and coated pinocytotic vesicles per unit length of membrane were found when osmium was used as the first fixative. A high positive correlation was found between these values and the number of coated vesicles per unit area of mossy fiber ending profiles. These results emphasize the need for caution when considering the theory that in vivo synaptic vesicle recycling involves a coated vesicle invagination of the surface membrane followed by internalisation and loss of coat of the vesicle.The authors are indebted to Mrs. M.L. Brito and M.M. Pacheco and Mr. L.B. Nunes for technical assistance. This work has been supported by I.A.C. (Lisbon)     

One transporter per vesicle: determination of the basis of the insulin effect on glucose transport

The basis for insulin stimulation of glucose transport in rat adipocytes has been investigated by determining the relative number of functional glucose transporters in the plasma and microsomal membranes from basal and insulin-treated cells. Each fraction was solubilized with cholate and then reconstituted into vesicles of about 500 A in diameter through removal of the cholate by dialysis. This procedure distributed the glucose transporters into the vesicles at a density of either one or none per vesicle. Consequently the fraction of the intravesicular volume that rapidly equilibrated with D-glucose provided an estimate of the relative number of functional transporters. By means of this one-transporter-per-vesicle method, it was found that insulin increased the number of transporters in the plasma membrane by a factor of 2.4 and decreased the number in the microsomes to 68% of the original value. These results provide independent evidence for the hypothesis that insulin causes the translocation of functional transporters from an intracellular location to the plasma membrane.     

Ca(2+) channels and transmitter release at the active zone

Ca(2+)-dependent transmitter release is the most important signaling mechanism for fast information transfer between neurons. Transmitter release takes places at highly specialized active zones with sub-micrometer dimension, which contain the molecular machinery for vesicle docking and -fusion, as well as a high density of voltage-gated Ca(2+) channels. In the absence of direct evidence for the ultrastructural localization of Ca(2+) channels at CNS synapses, important insights into Ca(2+) channel-vesicle coupling has come from functional experiments relating presynaptic Ca(2+) current and transmitter release, at large and accessible synapses like the calyx of Held. First, high slope values in log-log plots of transmitter release versus presynaptic Ca(2+) current indicate that multiple Ca(2+) channels are involved in release control of a single vesicle. Second, release kinetics in response to step-like depolarizations revealed fast- and slowly releasable sub-pools of vesicles, FRP and SRP, which, according to the "positional" model, are distinguished by a differential proximity to Ca(2+) channels. Considering recent evidence for a rapid conversion of SRP- to FRP vesicles, however, we highlight that multivesicular release events and clearance of vesicle membrane from the active zone must be taken into account when interpreting kinetic release data. We conclude that the careful kinetic analysis of transmitter release at presynaptically accessible and molecularly targeted synapses has the potential to yield important insights into the molecular physiology of transmitter release.     

Ion channels from synaptic vesicle membrane fragments reconstituted into lipid bilayers.

Cholinergic synaptic vesicles were isolated from the electric organ of Torpedo californica. Vesicle membrane proteins were reconstituted into planar lipid bilayers by the nystatin/ergosterol fusion technique. After fusion, a variety of ion channels were observed. Here we identify four channels and describe two of them in detail. The two channels share a conductance of 13 pS. The first is anion selective and strongly voltage dependent, with a 50% open probability at membrane potentials of -15 mV. The second channel is slightly cation selective and voltage independent. It has a high open probability and a subconductance state. A third channel has a conductance of 4-7 pS, similar to the subconductance state of the second channel. This channel is fairly nonselective and has gating kinetics different from those of the cation channel. Finally, an approximately 10-pS, slightly cation selective channel was also observed. The data indicate that there are one or two copies of each of the above channels in every synaptic vesicle, for a total of six channels per vesicle. These observations confirm the existence of ion channels in synaptic vesicle membranes. It is hypothesized that these channels are involved in vesicle recycling and filling.     

One-vesicle hypothesis for neurotransmitter release: A possible molecular mechanism

Neurotransmitter-containing vesicles are clustered in release sites. Although a given site can contain tens of vesicles, there is evidence that under a wide range of conditions, following an action potential, rarely is more than one vesicle released from each site. Such findings led to the one vesicle hypothesis, for which this paper suggests a molecular mechanism. The release of a vesicle from a site provides a transient high concentration of transmitter in that site. It is proposed here that the local high transmitter concentration interrupts further vesicle releases from the same release site. The suggested mechanism for this ‘release interruption’ is based on a theory of release control by the authors wherein inhibitory transmitter autoreceptors play a central role. (That transmitter binding to these autoreceptors can inhibit release on a fast time scale has recently been shown experimentally.) A detailed kinetic scheme is presented for the proposed mechanism. Stochastic simulations of this scheme demonstrate how the mechanism accounts for the one vesicle hypothesis. In agreement with recent experiments, the simulations also show that changes in conditions that affect the release process can cause frequent release of more than one vesicle per site.     

Glucagon receptors on isolated hepatocytes and hepatocyte membrane vesicles. Discrete populations with ligand- and environment-dependent affinities

Analysis of glucagon and deshistidine glucagon binding to isolated canine hepatocytes and to hepatocyte membrane vesicles (formed by budding of hepatocytes in hypotonic medium) reveals two separate populations of hormone binding sites. Mathematical modeling further shows that the high affinity population represents 1% of the total in all four cases. Although calculated dissociation constants for hormone binding range from 0.2 to 400 nM, whether considering glucagon or deshistidine glucagon binding, or binding to the high affinity or low affinity receptor populations, receptor affinity increases 2- to 100-fold in the environment of the membrane vesicle; concomitant with this alteration in receptor affinity, receptor selectivity for the structure of the native hormone decreases 1.5- to 40-fold in hepatocyte-derived vesicles. Consideration of receptor affinity in relation to receptor number suggests that hepatocyte glucagon binding is distributed about equally between high and low affinity receptor populations at typical portal hormone levels. Nevertheless, consideration of receptor binding in relation to biological activity suggests that the activity of glucagon in inhibiting carbohydrate flux into glycogen is attributable to occupancy of the high affinity receptor population.