Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

REST/NRSF governs the expression of dense-core vesicle gliosecretion in astrocytes.

Astrocytes are the brain nonnerve cells that are competent for gliosecretion, i.e., for expression and regulated exocytosis of clear and dense-core vesicles (DCVs). We investigated whether expression of astrocyte DCVs is governed by RE-1-silencing transcription factor (REST)/neuron-restrictive silencer factor (NRSF), the transcription repressor that orchestrates nerve cell differentiation. Rat astrocyte cultures exhibited high levels of REST and expressed neither DCVs nor their markers (granins, peptides, and membrane proteins). Transfection of a dominant-negative construct of REST induced the appearance of DCVs filled with secretogranin 2 and neuropeptide Y (NPY) and distinct from other organelles. Total internal reflection fluorescence analysis revealed NPY-monomeric red fluorescent protein-labeled DCVs to undergo Ca(2+)-dependent exocytosis, which was largely prevented by botulinum toxin B. In the I-II layers of the human temporal brain cortex, all neurons and microglia exhibited the expected inappreciable and high levels of REST, respectively. In contrast, astrocyte REST was variable, going from inappreciable to high, and accompanied by a variable expression of DCVs. In conclusion, astrocyte DCV expression and gliosecretion are governed by REST. The variable in situ REST levels may contribute to the well-known structural/functional heterogeneity of astrocytes.

Total curvature and total torsion of knotted polymers

Previous work on radius of gyration and average crossing number has demonstrated that polymers with fixed topology show a different scaling behavior with respect to these characteristics than polymers with unrestricted topology. Using numerical simulations, we show here that the difference in the scaling behavior between polymers with restricted and unrestricted topology also applies to the total curvature and total torsion. For each knot type, the equilibrium length with respect to a given spatial characteristic is the number of edges at which the value of the characteristic is the same as the average for all polygons. This number appears to be correlated to physical properties of macromolecules, for example gel mobility as measured by the separation between distinct knot types. We also find that, on average, closed polymers require slightly more total curvature and slightly less total torsion than open polymers with the corresponding number of monomers.

Nuclear curvature energy in relativistic models

The difficulties arising in the calculation of the nuclear curvature energy are analyzed in detail, especially with reference to relativistic models. It is underlined that the implicit dependence on curvature of the quantal wave functions is directly accessible only in a semiclassical framework. It is shown that also in the relativistic models quantal and semiclassical calculations of the curvature energy are in good agreement.

Model for curvature-driven pearling instability in membranes

A phase-field model for dealing with dynamic instabilities in membranes is presented. We use it to study curvature-driven pearling instability in vesicles induced by the anchorage of amphiphilic polymers on the membrane. Within this model, we obtain the morphological changes reported in recent experiments. The formation of a homogeneous pearled structure is achieved by consequent pearling of an initial cylindrical tube from the tip. For high enough concentration of anchors, we show theoretically that the homogeneous pearled shape is energetically less favorable than an inhomogeneous one, with a large sphere connected to an array of smaller spheres.

The t-SNAREs syntaxin 1 and SNAP-25 are present on organelles that participate in synaptic vesicle recycling

Syntaxin 1 and synaptosome-associated protein of 25 kD (SNAP-25) are neuronal plasmalemma proteins that appear to be essential for exocytosis of synaptic vesicles (SVs). Both proteins form a complex with synaptobrevin, an intrinsic membrane protein of SVs. This binding is thought to be responsible for vesicle docking and apparently precedes membrane fusion. According to the current concept, syntaxin 1 and SNAP-25 are members of larger protein families, collectively designated as target-SNAP receptors (t-SNAREs), whose specific localization to subcellular membranes define where transport vesicles bind and fuse. Here we demonstrate that major pools of syntaxin 1 and SNAP-25 recycle with SVs. Both proteins cofractionate with SVs and clathrin-coated vesicles upon subcellular fractionation. Using recombinant proteins as standards for quantitation, we found that syntaxin 1 and SNAP-25 each comprise approximately 3% of the total protein in highly purified SVs. Thus, both proteins are significant components of SVs although less abundant than synaptobrevin (8.7% of the total protein). Immunoisolation of vesicles using synaptophysin and syntaxin specific antibodies revealed that most SVs contain syntaxin 1. The widespread distribution of both syntaxin 1 and SNAP-25 on SVs was further confirmed by immunogold electron microscopy. Botulinum neurotoxin C1, a toxin that blocks exocytosis by proteolyzing syntaxin 1, preferentially cleaves vesicular syntaxin 1. We conclude that t-SNAREs participate in SV recycling in what may be functionally distinct forms.

SDF 1-alpha (CXCL12) triggers glutamate exocytosis from astrocytes on a millisecond time scale: Imaging analysis at the single-vesicle level with TIRF microscopy

Chemokines are small chemotactic molecules widely expressed throughout the central nervous system. A number of papers, during the past few years, have suggested that they have physiological functions in addition to their roles in neuroinflammatory diseases. In this context, the best evidence concerns the CXC-chemokine stromal cell-derived factor (SDF-1alpha or CXCL12) and its receptor CXCR4, whose signalling cascade is also implicated in the glutamate release process from astrocytes. Recently, astrocytic synaptic like microvesicles (SLMVs) that express vesicular glutamate transporters (VGLUTs) and are able to release glutamate by Ca(2+)-dependent regulated exocytosis, have been described both in tissue and in cultured astrocytes. Here, in order to elucidate whether SDF-1alpha/CXCR4 system can participate to the brain fast communication systems, we investigated whether the activation of CXCR4 receptor triggers glutamate exocytosis in astrocytes. By using total internal reflection (TIRF) microscopy and the membrane-fluorescent styryl dye FM4-64, we adapted an imaging methodology recently developed to measure exocytosis and recycling in synaptic terminals, and monitored the CXCR4-mediated exocytosis of SLMVs in astrocytes. We analyzed the co-localization of VGLUT with the FM dye at single-vesicle level, and observed the kinetics of the FM dye release during single fusion events. We found that the activation of CXCR4 receptors triggered a burst of exocytosis on a millisecond time scale that involved the release of Ca(2+) from internal stores. These results support the idea that astrocytes can respond to external stimuli and communicate with the neighboring cells via fast release of glutamate.

Application of the center manifold theory to the study of slewing flexible Non-ideal structures with nonlinear curvature: a case study

In this paper is Analyzed the local dynamical behavior of a slewing flexible structure considering nonlinear curvature. The dynamics of the original (nonlinear) governing equations of motion are reduced to the center manifold in the neighborhood of an equilibrium solution with the purpose of locally study the stability of the system. In this critical point, a Hopf bifurcation occurs. In this region, one can find values for the control parameter (structural damping coefficient) where the system is unstable and values where the system stability is assured (periodic motion). This local analysis of the system reduced to the center manifold assures the stable / unstable behavior of the original system around a known solution.

Synaptic vesicle pool size, release probability and synaptic depression are sensitive to Ca2+ buffering capacity in the developing rat calyx of Held

The calyx of Held, a specialized synaptic terminal in the medial nucleus of the trapezoid body, undergoes a series of changes during postnatal development that prepares this synapse for reliable high frequency firing. These changes reduce short-term synaptic depression during tetanic stimulation and thereby prevent action potential failures during a stimulus train. We measured presynaptic membrane capacitance changes in calyces from young postnatal day 5-7 (p5-7) or older (p10-12) rat pups to examine the effect of calcium buffer capacity on vesicle pool size and the efficiency of exocytosis. Vesicle pool size was sensitive to the choice and concentration of exogenous Ca2+ buffer, and this sensitivity was much stronger in younger animals. Pool size and exocytosis efficiency in p5-7 calyces were depressed by 0.2 mM EGTA to a greater extent than with 0.05 mM BAPTA, even though BAPTA is a 100-fold faster Ca2+ buffer. However, this was not the case for p10-12 calyces. With 5 mM EGTA, exocytosis efficiency was reduced to a much larger extent in young calyces compared to older calyces. Depression of exocytosis using pairs of 10-ms depolarizations was reduced by 0.2 mM EGTA compared to 0.05 mM BAPTA to a similar extent in both age groups. These results indicate a developmentally regulated heterogeneity in the sensitivity of different vesicle pools to Ca2+ buffer capacity. We propose that, during development, a population of vesicles that are tightly coupled to Ca2+ channels expands at the expense of vesicles more distant from Ca2+ channels.

The effect of lysobisphosphatidic acid (LBPA) on α-tocopherol transfer protein (α-TTP) binding to lipid membranes

The a-tocopherol transfer protein (a-TTP) is responsible for the retention of the atocopherol form of vitamin E in living organisms. The detailed ligand transfer mechanism by a-TTP is still yet to be fully elucidated. To date, studies show that a-TTP transfers a-tocopherol from late endosomes in liver cells to the plasma membrane where it is repackaged into very low density lipoprotein (VLDL) and released into the circulation. Late endosomes have been shown to contain a lipid known as lysobisphosphatidic acid (LBP A) that is unique to this cellular compartment. LBPA plays a role in intracellular trafficking and controlling membrane curvature. Taking these observations into account plus the fact that certain proteins are recruited to membranes based on membrane curvature, the specific aim of this project was to examine the effect of LBP A on a-TTP binding to lipid membranes. To achieve this objective, dual polarization interferometry (DPI) and a vesicle binding assay were employed. Whilst DPI allows protein binding affinity to be measured on a flat lipid surface, the vesicle binding assay determines protein binding affinity to lipid vesicles mimicking curved membranes. DPI analysis revealed that the amount of a-TTP bound to lipid membranes is higher when LBPA is present. Using the vesicle binding assay, a similar result was seen where a greater amount of protein is bound to large unilamellar vesicles (LUV s) containing LBP A. However, the effect of LBP A was attenuated when small unilamellar vesicles (SUVs) were replaced with LUVs. The outcome of this project suggests that aTTP binding to membranes is influenced by membrane curvature, which in turn is induced by the presence of LBP A.

Mechanism of tocopherol transfer by human α-tocopherol transfer protein (α-hTTP)

Vitamin E is a well known fat soluble chain breaking antioxidant. It is a general tenn used to describe a family of eight stereoisomers of tocopherols. Selective retention of a-tocopherol in the human circulation system is regulated by the a -Tocopherol Transfer Protein (a-TIP). Using a fluorescently labelled a-tocopherol (NBD-a-Toc) synthesized in our laboratory, a fluorescence resonance energy transfer (FRET) assay was developed to monitor the kinetics of ligand transfer by a-hTTP in lipid vesicles. Preliminary results implied that NBD-a-Toe simply diffused from 6-His-a-hTTP to acceptor membranes since the kinetics of transfer were not responsive to a variety of conditions tested. After a series of trouble shooting experiments, we identified a minor contaminant, E coli. outer membrane porin F (OmpF) that co-purified with 6-His-a-hTTP from the metal affinity column as the source of the problem. In order to completely avoid OmpF contamination, a GST -a-hTTP fusion protein was purified from a glutathione agarose column followed by an on-column thrombin digestion to remove the GST tag. We then demonstrated that a-hTTP utilizes a collisional mechanism to deliver its ligand. Furthennore, a higher rate of a-tocopherol transfer to small unilamellar vesicles (SUV s) versus large unilamellar vesicles (LUV s) indicated that transfer is sensitive to membrane curvature. These findings suggest that ahTTP mediated a-Toc transfer is dominated by the hydrophobic nature of a-hTTP and the packing density of phospholipid head groups within acceptor membranes. Based on the calculated free energy change (dG) when a protein is transferred from water to the lipid bilayer, a model was generated to predict the orientation of a-hTTP when it interacts with lipid membranes. Guided by this model, several hydrophobic residues expected to penetrate deeply into the bilayer hydrophobic core, were mutated to either aspartate or alanine. Utilizing dual polarization interferometry and size exclusion vesicle binding assays, we identified the key residues for membrane binding to be F 165, F 169 and 1202. In addition, the rates of ligand transfer of the u-TTP mutants were directly correlated to their membrane binding capabilities, indicating that membrane binding was likely the rate limiting step in u-TTP mediated transfer of u-Toc. The propensity of u-TTP for highly curved membrane provides a connection to its colocalization with u-Toc in late endosomes.

A Test of New Aggregate Damand Curvature Properties.

In This Paper We Present and Implement an Econometric Test of Both Negative Semi-Definiteness of the Matrix of Compensated Price Effects and of the Negative Quasi-Definiteness of the Matrix of Uncompensated Price Effects. This Test Allows Us to Evaluate Two Alternative Characterizations of Aggregate Demand Systems: the First, That They Behave Like Individual Demand Fuctions, and the Second, That They Respect the Properties Implied by the Assumptions Proposed by Hidebrand (1983) Or Grandmont (1984).

Nuclear curvature energy in relativistic models

The difficulties arising in the calculation of the nuclear curvature energy are analyzed in detail, especially with reference to relativistic models. It is underlined that the implicit dependence on curvature of the quantal wave functions is directly accessible only in a semiclassical framework. It is shown that also in the relativistic models quantal and semiclassical calculations of the curvature energy are in good agreement.

Role of Rab5 in synaptic vesicle recycling

During synaptic transmission, NT-filled synaptic vesicles are released by Ca2+-triggered exocytosis at the active zone. Following exocytosis, SV membrane is immediately re-internalized and synaptic vesicles (SVs) are regenerated by a local recycling mechanism within the presynaptic terminal. It is debated whether an endosomal compartment is involved in this recycling process. In contrast, it is well known from cultured mammalian cells, that endocytic vesicles fuse to the early sorting endosome. The early endosome is a major sorting station of the cell where cargo is send into the degradative pathway to late endosome and lysosome or towards recycling. Each trafficking step is mediated by a certain protein of the Rab family. Rab proteins are small GTPases belonging to the Ras superfamily. They accumulate at their target compartments and have thereby been used as markers for the different endocytic organelles in cultured mammalian cells. Rab5 controls trafficking from the PM to the early endosome and has thereby been used as marker for this compartment. A second marker is based on the specific binding of the FYVE zinc finger protein domain to the lipid PI(3)P that is specifically generated at the early endosomal membrane. This study used the Drosophila NMJ as a model system to investigate the SV recycling process. In particular, three questions were addressed: First, is an endosomal compartment present at the synapse? Second, do SVs recycle through an endosome? Third, is Rab5 involved in SV recycling? We used GFP fusions of Rab5 and 2xFYVE to visualize endosomal compartments at the presynaptic terminal of Drosophila third instar larval NMJs. Furthermore, the endosomes are located within the pool of recycling SVs, labeled with the styryl-dye FM5-95. Using the temperature-sensitive mutation in Dynamin, shibirets, we showed that SV recycling involves trafficking through an intermediate endosomal compartment. In cultured mammalian cells, interfering with Rab5 function by expressing the dominant negative version, Rab5SN causes the fragmentation of the endosome and the accumulation of endocytic vesicles. In contrast, when Rab5 is overexpressed enlarged endosomal compartments were observed. In Drosophila, the endosomal compartment was disrupted when loss of function and dominant negative mutants of Rab5 were expressed. In addition, at the ultrastructural we observed an accumulation of endocytic vesicles in Rab5S43N expressing terminals and enlarged endosomes when Rab5 was overexpressed. Furthermore, interfering with Rab5 function using the dominant negative Rab5S43N caused a decrease in the SV recycling kinetics as shown by FM1-43 experiments. In contrast, overexpression of Rab5 or GFP-Rab5 caused an increase in the FM1-43 internalization rate. Finally, standard electrophysiological techniques were used to measure synaptic function. We found that the Rab5-mediated endosomal SV recycling pathway generates vesicles with a higher fusion efficacy during Ca2+-triggered release, compared to SVs recycled when Rab5 function was impaired. We therefore suggest a model in which the endosome serves as organelle to control the SV fusion efficacy and thereby the synaptic strength. Since changes in the synaptic strength are occuring during learning and memory processes, controlling endosomal SV recycling might be a new molecular mechanism involved in learning and memory.