Known shape-invariant potentials for the constant-mass Schrödinger equation are taken as effective potentials in a position-dependent effective mass (PDEM) one. The corresponding shape-invariance condition turns out to be deformed. Its solvability imposes the form of both the deformed superpotential and the PDEM. A lot of new exactly solvable potentials associated with a PDEM background are generated in this way. A novel and important condition restricting the existence of bound states whenever the PDEM vanishes at an end point of the interval is identified. In some cases, the bound-state spectrum results from a smooth deformation of that of the conventional shape-invariant potential used in the construction. In others, one observes a generation or suppression of bound states, depending on the mass-parameter values. The corresponding wavefunctions are given in terms of some deformed classical orthogonal polynomials.

An ATP-dependent activity of NSF (N-ethylmaleimidesensitive factor) that rearranges soluble NSF attachment protein (SNAP) receptor (SNARE) protein complexes was proposed to be the driving force for membrane fusion. The Ca 2؉-activated fusion of secretory vesicles with the plasma membrane in permeable PC12 cells requires ATP; however, the ATP requirement is for a priming step that precedes the Ca 2؉ -triggered fusion reaction. While phosphoinositide phosphorylation is a key reaction required for priming, additional ATP-dependent reactions are also necessary. Here we report that the NSF-catalyzed rearrangement of SNARE protein complexes occurs during ATP-dependent priming. NSF with ␣-SNAP (soluble NSF attachment protein) were required for ATP-dependent priming but not Ca 2؉ -triggered fusion, indicating that NSF acts at an ATP-dependent prefusion step rather than at fusion itself. NSFcatalyzed activation of SNARE proteins may reorganize membranes to generate a vesicle-plasma membrane prefusion intermediate that is poised for conversion to full fusion by Ca 2؉ -dependent mechanisms.The regulated fusion of vesicles with the plasma membrane in neural and endocrine cells requires a core complex of proteins (synaptobrevin, syntaxin, and SNAP-25) that are specific substrates for clostridial neurotoxin proteases (1-4). This complex is proposed to function in vesicle targeting, docking or fusion. Identification of these neuronal synaptic proteins (termed SNAREs) 1 as receptors for SNAP proteins that mediate the membrane association of NSF, a protein required for constitutive membrane fusion (1), suggested that NSF may be required for Ca 2ϩ -regulated neurosecretion (5). Genetic studies in Drosophila have established an essential role for NSF in neural function (6). Stimulatory effects of ␣-SNAP on neurotransmitter secretion from chromaffin cells and squid neurons have been reported (7,8). However, the precise stage in the regulated secretory pathway at which NSF acts has not been directly established. In vitro biochemical studies demonstrated that a 20 S complex of SNAREs, NSF, and ␣/␤-SNAP was disassembled by the ATP-dependent activity of NSF, and it was suggested that NSF-catalyzed SNARE protein rearrangements drive membrane fusion (9). However, previous studies with permeable PC12 and adrenal cells had shown that MgATP was required for a priming step that precedes the final fusion steps triggered by Ca 2ϩ (10,11). In the present studies, the execution point of NSF and ␣-SNAP was established as the ATP-dependent priming step that precedes Ca 2ϩ -activated fusion. EXPERIMENTAL PROCEDURES Preparation of Permeable PC12 Cells and Secretion Assays-PC12 cells were labeled with [3 H]norepinephrine (NE; Amersham Corp.) and permeabilized with a ball homogenizer (10, 12). Two stage secretion assays were in KGlu buffer (20 mM HEPES, pH 7.2, 120 mM potassium glutamate, 20 mM potassium acetate, 2 mM EGTA) with 0.1% bovine serum albumin. Thirty-min priming incubations at 30°C contained 2 mM MgATP and 1.0 mg/ml rat brain cytosol, whic...

Neurotransmitter and peptide hormone secretion require fusion between secretory vesicles and the plasma membrane, an exocytotic process activated by cytoplasmic Ca 2ϩ elevation. Understanding regulated secretion requires identification of molecular components that mediate docking and fusion reactions and delineation of rate-limiting steps that are Ca 2ϩ -regulated (1). The synaptic vesicle protein synaptobrevin and the presynaptic membrane proteins syntaxin and SNAP-25 1 are required components of the exocytotic apparatus as indicated by the inhibitory action of BoNTs and Tetx, which involves the specific endoproteolytic cleavage of these protein substrates (2, 3). The three toxin substrates were independently identified as receptors for SNAPs, proteins required for the membrane binding of NSF, a late acting component in constitutive membrane fusion reactions (4). A characterized ternary complex containing synaptobrevin, syntaxin, and SNAP-25 was suggested to represent a docking complex that mediates the targeting, docking, or fusion of secretory vesicles (5, 6). Identification of an ATP-dependent catalytic activity of NSF/SNAP that promotes the disassembly of ternary complexes in vitro led to the suggestion that a similar reaction in vivo was responsible for late steps in membrane fusion (7). Ca 2ϩ -triggered secretion in permeable neuroendocrine cells requires ATP; however, the requirement for ATP precedes that for Ca 2ϩ (8, 9). ATP hydrolysis is required for prefusion events that prime the exocytotic apparatus, whereas Ca 2ϩ -activated fusion proceeds in the absence of ATP (8 -11).2 In priming, ATP serves as a substrate for polyphosphoinositide synthesis (10, 11) and as a substrate for the SNAP-dependent ATPase activity of NSF that catalyzes rearrangement of docking protein complexes.2 These studies experimentally identify a late step in the exocytotic pathway beyond LDCV docking and ATP utilization that is proximal to Ca 2ϩ -dependent fusion reactions. To characterize events that lead to or are directly involved in membrane fusion, it is important to identify molecular components that act at this late Ca were permeabilized by passage through a ball homogenizer (12). Secretion assays were conducted either as single stage or as two-stage assays (9,14). For the former, permeable cells were incubated for 15 min at 30°C in KGlu-BSA buffer supplemented with CaCl 2 (to achieve 10 M Ca 2ϩ f ), 0.002 M MgATP, and 0.5 mg/ml rat brain cytosol. Two-stage assays were conducted as separate priming incubations (30 min at 30°C in KGlu-BSA buffer supplemented with 0.002 M MgATP plus 1 mg/ml rat brain cytosol) followed by triggering incubations (1-3 min at 30°C in KGlu-BSA buffer supplemented with 10 M Ca 2ϩ plus 0.5 mg/ml rat brain cytosol) with extensive washing between incubations. [ 3 H]NE release was determined by centrifugation of permeable cells at 800 ϫ g for 30 min and scintillation counting of 3 H in supernatants and in cell pellets to express NE release as percent of the total 3 H. The SNAP-25 antibody used to inhi...

Using a novel approach to measure exocytosis in vitro from semi-intact synaptosomes, we establish that the Ca2+-dependent release of glutamate requires cytosolic factors for mobilization from the reserve pool. The cytosolic activity for glutamate release was not satisfied by CAPS, a soluble component required for norepinephrine (NE) release. Moreover, the CAPS-independent glutamate release from synaptic vesicles (SVs) was 200-fold less sensitive to Ca2+ than that required for dense core vesicles (DCVs). The differential regulation of exocytosis by CAPS, Ca2+, and potential novel cytosolic factor(s) suggests that the docking and fusion machinery controlling DCVs has diverged from that regulating glutamate-containing SVs.

The important anticancer drug paclitaxel binds to the -subunit of the R -tubulin dimer in the microtubule in a stoichiometric ratio, promoting microtubule polymerization and stability. The conformation of microtubule-bound drug has been the subject of intense study, and various suggestions have been proposed. In previous work we presented experimental and theoretical evidence that paclitaxel adopts a T-shaped conformation when it is bound to tubulin. In this study we report additional experimental data and calculations that delineate the allowable parameters for effective paclitaxel-tubulin interactions.