Laplace's equation on convex polyhedra via the unified method.

We provide a new method to study the classical Dirichlet problem for Laplace's equation on a convex polyhedron. This new approach was motivated by Fokas' unified method for boundary value problems. The central object in this approach is the global relation: an integral equation which couples the known boundary data and the unknown boundary values. This integral equation depends holomorphically on two complex parameters, and the resulting analysis takes place on a Banach space of complex analytic functions closely related to the classical Paley-Wiener space. We write the global relation in the form of an operator equation and prove that the relevant operator is bounded below using some novel integral identities. We give a new integral representation to the solution to the underlying boundary value problem which serves as a concrete realization of the fundamental principle of Ehrenpreis.

The multiple actions of black widow spider toxins and their selective use in neurosecretion studies.

The black widow spider venom contains several large protein toxins--latrotoxins--that are selectively targeted against different classes of animals: vertebrates, insects, and crustaceans. These toxins are synthesised as large precursors that undergo proteolytic processing and activation in the lumen of the venom gland. The mature latrotoxins demonstrate strong functional structure conservation and contain multiple ankyrin repeats, which mediate toxin oligomerisation. The three-dimensional structure has been determined for alpha-latrotoxin (alphaLTX), a representative venom component toxic to vertebrates. This reconstruction explains the mechanism of alphaLTX pore formation by showing that it forms tetrameric complexes, harbouring a central channel, and that it is able to insert into lipid membranes. All latrotoxins cause massive release of neurotransmitters from nerve terminals of respective animals after binding to specific neuronal receptors. A G protein-coupled receptor latrophilin and a single-transmembrane receptor neurexin have been identified as major high-affinity receptors for alphaLTX. Latrotoxins act by several Ca(2+)-dependent and -independent mechanisms based on pore formation and activation of receptors. Mutant recombinant alphaLTX that does not form pores has been used to dissect the multiple actions of this toxin. As a result, important insights have been gained into the receptor signalling and the role of intracellular Ca(2+) stores in the effect of alphaLTX.

alpha-Latrotoxin, acting via two Ca2+-dependent pathways, triggers exocytosis of two pools of synaptic vesicles.

alpha-Latrotoxin stimulates three types of [(3)H]gamma-aminobutyric acid and [(14)C]glutamate release from synaptosomes. The Ca(2+)-independent component (i) is insensitive to SNAP-25 cleavage or depletion of vesicle contents by bafilomycin A1 and represents transmitter efflux mediated by alpha-latrotoxin pores. Two other components of release are Ca(2+)-dependent and vesicular but rely on distinct mechanisms. The fast receptor-mediated pathway (ii) involves intracellular Ca(2+) stores and acts upon sucrose-sensitive readily releasable vesicles; this mechanism is insensitive to inhibition of phosphatidylinositol 4-kinase (PI 4-kinase). The delayed pore-dependent exocytotic component (iii) is stimulated by Ca(2+) entering through alpha-latrotoxin pores; it requires PI 4-kinase and occurs mainly from depot vesicles. Lanthanum perturbs alpha-latrotoxin pores and blocks the two pore-mediated components (i, iii) but not the receptor-mediated release (ii). alpha-Latrotoxin mutant (LTX(N4C)) cannot form pores and stimulates only the Ca(2+)-dependent receptor-mediated amino acid exocytosis (ii) (detectable biochemically and electrophysiologically). These findings explain experimental data obtained by different laboratories and implicate the toxin receptors in the regulation of the readily releasable pool of synaptic vesicles. Our results also suggest that, similar to noradrenergic vesicles, amino acid-containing vesicles at some point in their cycle require PI 4-kinase.

Tetramerisation of alpha-latrotoxin by divalent cations is responsible for toxin-induced non-vesicular release and contributes to the Ca(2+)-dependent vesicular exocytosis from synaptosomes.

A novel procedure of alpha-latrotoxin (alpha LTX) purification has been developed. Pure alpha LTX has been demonstrated to exist as a very stable homodimer. Such dimers further assemble into tetramers, and Ca(2+), Mg(2+) or higher toxin concentrations facilitate this process. However, when the venom is treated with EDTA, purified alpha LTX loses the ability to tetramerise spontaneously; the addition of Mg(2+) or Ca(2+) restores this ability. This suggests that alphaLTX has some intrinsically bound divalent cation(s) that normally support its tetramerisation. Single-particle cryoelectron microscopy and statistical image analysis have shown that: 1) the toxin has a non-compact, branching structure; 2) the alpha LTX dimers are asymmetric; and 3) the tetramers are symmetric and have a 25 A-diameter channel in the centre. Both alpha LTX oligomers bind to the same receptors in synaptosomes and rat brain sections. To study the effects of the dimers and tetramers on norepinephrine release from rat cerebrocortical synaptosomes, we used the EDTA-treated and untreated toxin preparations. The number of tetramers present in a preparation correlates with alpha LTX pore formation, suggesting that the tetramers are the pore-forming species of alpha LTX. The toxin actions mediated by the pore include: 1) Ca(2+) entry from the extracellular milieu; and 2) passive efflux of neurotransmitters via the pore that occurs independently of Ca(2+). The Ca(2+)-dependent alpha LTX-stimulated secretion conforms to all criteria of vesicular exocytosis but also depends upon intact intracellular Ca(2+) stores and functional phospholipase C (PLC). The Ca(2+)-dependent effect of the toxin is stronger when dimeric alpha LTX is used, indicating that higher receptor occupancy leads to its stronger activation, which contributes to stimulation of neuroexocytosis. In contrast, the Ca(2+)-independent release measured biochemically represents leakage of neurotransmitters through the toxin pore. These results are discussed in relation to the previously published observations.

A late phase of exocytosis from synaptosomes induced by elevated [Ca2+]i is not blocked by Clostridial neurotoxins.

Treatment of rat cerebrocortical synaptosomes with botulinum toxin types E and C1 or tetanus toxin removed the majority of intact SNAP-25, syntaxin 1A/1B, and synaptobrevin and diminished Ca(2+)-dependent K+ depolarization-induced noradrenaline secretion. With botulinum toxin type E, <10% of intact SNAP-25 remained and K(+)-evoked release of glutamate and GABA was inhibited. The large component of noradrenaline release evoked within 120 s by inclusion of the Ca2+ ionophore A23187 with the K+ stimulus was also attenuated by these toxins; additionally, botulinium neurotoxin type E blocked the first 60 s of ionophore-induced GABA and glutamate exocytosis. However, exposure to A23187 for longer periods induced a phase of secretion nonsusceptible to any of these toxins (>120 s for noradrenaline; >60 s for glutamate or GABA). Most of this late phase of release represented exocytosis because of its Ca2+ dependency, ATP requirement, and sensitivity to a phosphatidylinositol 4-kinase inhibitor. Based on these collective findings, we suggest that the ionophore-induced elevation of [Ca2+]i culminates in the disassembly of complexes containing nonproteolyzed SNAP receptors protected from the toxins that can then contribute to neuroexocytosis.

Structure of alpha-latrotoxin oligomers reveals that divalent cation-dependent tetramers form membrane pores.

We report here the first three-dimensional structure of alpha-latrotoxin, a black widow spider neurotoxin, which forms membrane pores and stimulates secretion in the presence of divalent cations. We discovered that alpha-latrotoxin exists in two oligomeric forms: it is dimeric in EDTA but forms tetramers in the presence of Ca2+ or Mg2+. The dimer and tetramer structures were determined independently at 18 A and 14 A resolution, respectively, using cryo-electron microscopy and angular reconstitution. The alpha-latrotoxin monomer consists of three domains. The N- and C-terminal domains have been identified using antibodies and atomic fitting. The C4-symmetric tetramers represent the active form of alpha-latrotoxin; they have an axial channel and can insert into lipid bilayers with their hydrophobic base, providing the first model of alpha-latrotoxin pore formation.

Norepinephrine exocytosis stimulated by alpha-latrotoxin requires both external and stored Ca2+ and is mediated by latrophilin, G proteins and phospholipase C.

alpha-latrotoxin (LTX) stimulates massive release of neurotransmitters by binding to a heptahelical transmembrane protein, latrophilin. Our experiments demonstrate that latrophilin is a G-protein-coupled receptor that specifically associates with heterotrimeric G proteins. The latrophilin-G protein complex is very stable in the presence of GDP but dissociates when incubated with GTP, suggesting a functional interaction. As revealed by immunostaining, latrophilin interacts with G alpha q/11 and G alpha o but not with G alpha s, G alpha i or G alpha z, indicating that this receptor may couple to several G proteins but it is not promiscuous. The mechanisms underlying LTX-evoked norepinephrine secretion from rat brain nerve terminals were also studied. In the presence of extracellular Ca2+, LTX triggers vesicular exocytosis because botulinum neurotoxins E, Cl or tetanus toxin inhibit the Ca(2+)-dependent component of the toxin-evoked release. Based on (i) the known involvement of G alpha q in the regulation of inositol-1,4,5-triphosphate generation and (ii) the requirement for Ca2+ in LTX action, we tested the effect of inhibitors of Ca2+ mobilization on the toxin-evoked norepinephrine release. It was found that aminosteroid U73122, which inhibits the coupling of G proteins to phospholipase C, blocks the Ca(2+)-dependent toxin's action. Thapsigargin, which depletes intracellular Ca2+ stores, also potently decreases the effect of LTX in the presence of extracellular Ca2+. On the other hand, clostridial neurotoxins or drugs interfering with Ca2+ metabolism do not inhibit the Ca2(+)-independent component of LTX-stimulated release. In the absence of Ca2+, the toxin induces in the presynaptic membrane non-selective pores permeable to small fluorescent dyes; these pores may allow efflux of neurotransmitters from the cytoplasm. Our results suggest that LTX stimulates norepinephrine exocytosis only in the presence of external Ca2+ provided intracellular Ca2+ stores are unperturbed and that latrophilin, G proteins and phospholipase C may mediate the mobilization of stored Ca2+, which then triggers secretion.

Vesicle exocytosis stimulated by alpha-latrotoxin is mediated by latrophilin and requires both external and stored Ca2+.

alpha-Latrotoxin (LTX) stimulates massive neurotransmitter release by two mechanisms: Ca2+-dependent and -independent. Our studies on norepinephrine secretion from nerve terminals now reveal the different molecular basis of these two actions. The Ca2+-dependent LTX-evoked vesicle exocytosis (abolished by botulinum neurotoxins) is 10-fold more sensitive to external Ca2+ than secretion triggered by depolarization or A23187; it does not, however, depend on the cation entry into terminals but requires intracellular Ca2+ and is blocked by drugs depleting Ca2+ stores and by inhibitors of phospholipase C (PLC). These data, together with binding studies, prove that latrophilin, which is linked to G proteins and inositol polyphosphate production, is the major functional LTX receptor. The Ca2+-independent LTX-stimulated release is not inhibited by botulinum neurotoxins or drugs interfering with Ca2+ metabolism and occurs via pores in the presynaptic membrane, large enough to allow efflux of neurotransmitters and other small molecules from the cytoplasm. Our results unite previously contradictory data about the toxin's effects and suggest that LTX-stimulated exocytosis depends upon the co-operative action of external and intracellular Ca2+ involving G proteins and PLC, whereas the Ca2+-independent release is largely non-vesicular.

Microtubules and microfilaments participate in the inhibition of synaptosomal noradrenaline release by tetanus toxin.

Tetanus toxin (TeTX) has been demonstrated to inhibit transmitter release by two mechanisms: Zn(2+)-dependent proteolytic cleavage of synaptobrevin and activation of a neuronal transglutaminase. Herein, attenuation of TeTX-induced blockade of noradrenaline release from synaptosomes was achieved by prior disassembly of microfilaments with cytochalasin D or breakdown of microtubules by colchicine or nocodazole. These drugs and monodansylcadaverine, a transglutaminase inhibitor, displayed some additivity in antagonizing the inhibitory effect of the toxin on synaptosomal transmitter release; as none of them reduced synaptobrevin cleavage, all appear to work independently of the toxin's proteolytic action. Prior stabilization of microtubules with taxol prevented the antagonism seen with colchicine, highlighting that this cytoskeletal component is the locus of the effect of colchicine. Replacement of Ca2+ with Ba2+ caused disappearance of the fraction of evoked secretion whose inhibition by TeTX is reliant on polymerized actin but did not alter the blockade by toxin that is dependent on microtubules. Two temporally distinguished phases of release were reduced by TeTX, and colchicine lessened its effects on both. Blockade of the fast phase (< or = 10 s) of secretion by TeTX was unaffected by cytochalasin D, but it clearly antagonized the toxin-induced inhibition of the slow (10-s to > or = 5-min) component; it is notable that such antagonism was accentuated during a second bout of evoked release. These findings are consistent with sustained release requiring dissociation of synaptic vesicles from the microfilaments, a step that seems to be perturbed by TeTX.

Tetanus toxin inhibits neuroexocytosis even when its Zn(2+)-dependent protease activity is removed.

Tetanus toxin (TeTX) is a dichain protein that blocks neuroexocytosis, an action attributed previously to Zn(2+)-dependent proteolysis of synaptobrevin (Sbr) by its light chain (LC). Herein, its cleavage of Sbr in rat cerebrocortical synaptosomes was shown to be minimized by captopril, an inhibitor of certain metalloendoproteases, whereas this agent only marginally antagonized the inhibition of noradrenaline release, implicating a second action of the toxin. This hypothesis was proven by preparing three mutants (H233A, E234A, H237A) of the LC lacking the ability to cleave Sbr and reconstituting them with native heavy chain. The resultant dichains were found to block synaptosomal transmitter release, albeit with lower potency than that made from wild type LC; as expected, captopril attenuated only the inhibition caused by the protease-active wild type toxin. Moreover, these protease-inactive toxins or their LCs blocked evoked quantal release of transmitter when micro-injected inside Aplysia neurons. TeTX was known to stimulate in vitro a Ca(2+)-dependent transglutaminase (TGase) (Facchiano, F., and Luini, A. (1992) J. Biol. Chem. 267, 13267-13271), an affect found here to be reduced by an inhibitor of this enzyme, monodansylcadaverine. Accordingly, treatment of synaptosomes with the latter antagonized the inhibition of noradrenaline release by TeTX while not affecting Sbr cleavage. This drug also attenuated the inhibitory action of all the mutants. Hence, it is concluded that TeTX inhibits neurotransmitter release by proteolysis of Sbr and a protease-independent activation of a neuronal TGase.

Botulinum A like type B and tetanus toxins fulfils criteria for being a zinc-dependent protease.

Although botulinum neurotoxin (BoNT) types A and B and tetanus toxin (TeTx) are specific inhibitors of transmitter release whose light chains contain a zinc-binding motif characteristic of metalloendoproteases, only the latter two proteolyse synaptobrevin. Chelation of zinc or its readdition at high concentration hindered blockade of neuromuscular transmission by BoNT/A and B, indicating that type A also acts via a zinc-dependent mechanism. Such treatments prevented proteolysis of synaptobrevin II in rat brain synaptic vesicles by BoNT/B and TeTx but only the activity of the latter was antagonised appreciably by ASQFETS, a peptide spanning their cleavage site. The toxin's neuroparalytic activities were attenuated by phosphoramidon or captopril, inhibitors of certain zinc requiring proteases. However, these agents were ineffective in reducing the toxins' degradation of synaptobrevin except that a high concentration of captopril partially blocked the activity of TeTx but not BoNT/B, as also found for these drugs when tested on synaptosomal noradrenaline release. These various criteria establish that a zinc-dependent protease activity underlies the neurotoxicity of BoNT/A, a finding confirmed at motor nerve endings for type B and TeTx. Moreover, the low potencies of captopril and phosphoramidon in counteracting the toxins' effects necessitate the design of improved inhibitors for possible use in the clinical treatment of tetanus or botulism.

Microtubule-dissociating drugs and A23187 reveal differences in the inhibition of synaptosomal transmitter release by botulinum neurotoxins types A and B.

The inhibitory effects of botulinum neurotoxins types A and B on Ca2(+)-dependent evoked release of [3H]noradrenaline from rat cerebrocortical synaptosomes were compared and their molecular basis investigated. A23187, a Ca2+ ionophore, proved more efficacious in reversing the blockade produced by type A than that by B, whereas the actions of neither were changed by increasing intraterminal cyclic GMP levels using 8-bromo-cyclic GMP of nitroprusside. Disruption of the actin-based cytoskeleton with cytochalasin D did not alter the inhibition seen subsequently with either toxin. However, prior disassembly of microtubules with colchicine, nocodazole, or griseofulvin reduced the potency of type B toxin, but not that of type A toxin; stabilization of the microtubules with taxol counteracted this effect of colchicine. Because colchicine treatment of synaptosomes did not interfere with the measurable binding of type B toxin or its apparent uptake, it appears to act intracellularly. Collectively, these data suggest that botulinum neurotoxins types A and B inactivate transmitter release by interaction at different sites in the process. Based on the consistent results observed with four different drugs known to affect selectively microtubules, their involvement in the action of the type B neurotoxin is proposed.

Clues to the multi-phasic inhibitory action of botulinum neurotoxins on release of transmitters.

1. With the aim of gaining insight into the mechanism of Ca2(+)-dependent secretion, inhibition of transmitter release by botulinum neurotoxins or their fragments was studied at mammalian motor nerve terminals, cerebrocortical synaptosomes and PC-12 cells. 2. Relative to BoNT type A, the feeble neuromuscular paralytic activity of its two chains and the lack of activity observed with a proteolytic fragment, H2L (lacking H1, the C-terminal half of the heavy chain) highlight a requirement of the intact, disulphide-linked dichain protein for efficient targetting (binding/uptake) to peripheral cholinergic nerve endings. 3. In PC-12 cells, the renatured light chain alone proved equally potent as the whole toxin in reducing Ca2(+)-evoked noradrenaline release, when digitonin-permeabilization was used to overcome the uptake barrier. Treatment of BoNT A with 10 mM dithiothreitol, under non-denaturing conditions, was not very effective in reducing its inter-chain disulphide bond(s) and had little influence on the level of inhibition seen. 4. Altering the intra-synaptosomal concentrations of cyclic nucleotides (c-AMP, c-GMP) or protein kinase C activity failed to affect the reduction of Ca2(+)-dependent K(+)-stimulated noradrenaline release caused by BoNT A or B. On the other hand, raising the cytosolic Ca2+ concentration with the ionophore A23187 reversed the inhibitory effect of BoNT A to a greater extent than that of type B, revealing differences in their actions. 5. Whereas BoNT-induced decrease of Ca2(+)-dependent K(+)-evoked release of noradrenaline was unaffected by destruction of the actin-based cytoskeleton in synaptosomes with cytochalasin D, disassembly of microtubules with colchicine, nocodazole or griseofulvin antagonised the intracellular action of type B but not A. It is speculated that BoNT B blocks transmitter release by interfering with the proposed detachment of synaptic vesicles from microtubules. Establishing the precise involvement of tubulin in the toxin's action may provide a valuable clue to the mechanism of neurotransmitter release or its control.

ADP-ribosylation of cerebrocortical synaptosomal proteins by cholera, pertussis and botulinum toxins.

Certain microbial toxins ADP-ribosylate G proteins that may be related to those postulated to participate in secretion, whilst botulinum neurotoxins, produced by Clostridium botulinum, block Ca2(+)-dependent neurotransmitter release. Thus, botulinum, pertussis and cholera toxins were examined for ADP-ribosyl transferase activity using isolated nerve terminals. Although type D botulinum, cholera and pertussis toxins exhibited such enzymic activity, this was not detectable with types A or B botulinum neurotoxins or their individual chains, in any synaptosomal fraction. Botulinum type D and pertussis toxins ADP-ribosylated proteins with mol. wt approximately 24,000 and 42,000 respectively, whereas cholera toxin modified several proteins including a 51,000/47,000 mol. wt doublet. Pre-incubation of synaptosomes with type A, B or D toxins did not inhibit type D-induced labelling in the corresponding lysate. Similar pre-incubations with cholera or pertussis toxins reduced ADP-ribosylation of their substrates. Hence, under conditions in which these botulinum toxins were shown to block Ca2(+)-dependent transmitter release no ADP-ribosylated substrate was produced in the intact nerve terminals. Moreover, direct correlation was not found between the concentration dependencies of type D toxin for protein modification and inhibition of [3H]noradrenaline release from synaptosomes. These collective findings implicate C3, a non-neurotoxic contaminant of type D, in the enzymic action. The substrate for type D toxin was found in the cytosolic fraction and to a lesser extent in synaptic membranes, the reverse of the situation for pertussis toxin. A combination of the membranes and cytosol was required for maximal labelling of the 51,000/47,000 doublet by cholera toxin. Purified synaptic vesicles contained proteins labelled by type D and pertussis toxins but lacked major cholera toxin substrates. Future research will determine the possible involvement of these toxin-susceptible vesicular proteins in transmitter release.

Characterization of the inhibitory action of botulinum neurotoxin type A on the release of several transmitters from rat cerebrocortical synaptosomes.

Under optimised conditions for intoxication, botulinum neurotoxin type A was shown to inhibit approximately 90% of Ca2+-dependent K+-evoked release of [3H]acetylcholine, [3H]noradrenaline, and [3H]dopamine from rat cerebrocortical synaptosomes; cholinergic terminals were most susceptible. In each case, the dose-response curve for the neurotoxin was extended, with about 50% of evoked release being inhibited at approximately 10 nM whereas 200 nM was required for the maximal blockade. This may suggest some heterogeneity in the release process. The action of the toxin was time and temperature dependent and appeared to involve binding and sequestration steps prior to blockade of release. The neurotoxin failed to exert any effect on synaptosomal integrity or on Ca2+-independent release of the transmitters tested; it produced only minimal changes in neurotransmitter uptake although small secondary effects were detected with cholinergic terminals. Blockade by the neurotoxin of Ca2+-dependent resting release of transmitter was apparent; Sr2+, Ba2+, or high concentrations of Ca2+ restored the resting release of 3H-catecholamine but not [3H]acetylcholine. Interestingly, none of the latter conditions or 4-aminopyridine could reverse the toxin-induced blockade of evoked release. This lack of specificity in its action on synaptosomes, and other published findings, lead to the conclusion that toxin-sensitive component(s) exist in all nerve terminals that are concerned with transmitter release.

A sensitive and useful radioimmunoassay for neurotoxin and its haemagglutinin complex from Clostridium botulinum.

A sensitive radioimmunoassay for the detection of botulinum toxin, produced by Clostridium botulinum, was developed. This employs homogeneous botulinum neurotoxin type A and its 125I-labelled derivative of high specific radioactivity, rather than its complex with haemagglutinin as used hitherto. The sensitivity of the assay is 1 ng of neurotoxin per ml, which is equivalent to 80 LD50 units (half-lethal doses) in mice. Neurotoxin and its complex with haemagglutinin were measurable with equal sensitivity when using antibodies against botulinum neurotoxin type A. Specificity of the assay was demonstrated by the lack of response to type B and E botulinum toxins and to heat-inactivated botulinum toxin or extracts of Clostridium sporogenes strain BL46, which contains many surface antigenic determinants common to Clostridium botulinum. Using appropriate conditions, neurotoxin added to fish extract could be quantified accurately, proportionality being observed between the amounts of standard toxin added. In addition, the amounts of toxin species produced by culturing Clostridium botulinum in canned fish was measurable; the values obtained were comparable to those observed by the mouse bioassay. Moreover, the fish samples gave a dose-response curve in the competition radioimmunoassay which was paralleled by the response of botulinum neurotoxin standards. This assay offers the most sensitive, reliable immunological method available for the quantitation of molecular forms of botulinum toxin. As the technique can be used with unpurified fish extracts, it should be widely applicable to different types of samples contaminated with botulinum toxin; furthermore, the clinical diagnosis of human botulism could be substantiated with this method.