The Convective Instability of the Boundary-Layer Flow over Families of Rotating Spheroids

The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis. We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity. For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case

A Computational Study of the Glycine-Rich Loop of Mitochondrial Processing Peptidase

<div><p>An all atomic, non-restrained molecular dynamics (MD) simulation in explicit water was used to study in detail the structural features of the highly conserved glycine-rich loop (GRL) of the α-subunit of the yeast mitochondrial processing peptidase (MPP) and its importance for the tertiary and quaternary conformation of MPP. Wild-type and GRL-deleted MPP structures were studied using non-restrained MD simulations, both in the presence and the absence of a substrate in the peptidase active site. Targeted MD simulations were employed to study the mechanism of substrate translocation from the GRL to the active site. We demonstrate that the natural conformational flexibility of the GRL is crucial for the substrate translocation process from outside the enzyme towards the MPP active site. We show that the α-helical conformation of the substrate is important not only during its initial interaction with MPP (i.e. substrate recognition), but also later, at least during the first third of the substrate translocation trajectory. Further, we show that the substrate remains in contact with the GRL during the whole first half of the translocation trajectory and that hydrophobic interactions play a major role. Finally, we conclude that the GRL acts as a precisely balanced structural element, holding the MPP subunits in a partially closed conformation regardless the presence or absence of a substrate in the active site.</p> </div

Scheme of substrate translocation from the GRL to the MPP active site.

<p>Panel A shows the overall structure of MPP. The van der Waals surface of α-MPP and β-MPP subunits and GRL is in yellow, orange and green, respectively. Panel B shows the conformation and position of the substrate during its recognition by the α-MPP GRL (<i>GRL-bound </i><i>structure</i>; red tube) and just prior to its subsequent proteolysis in MPP active site (<i>AS-bound </i><i>structure</i>; pink tube). The direction of substrate translocation between these two boundary positions is indicated by blue arrow. In the <i>GRL-bound </i><i>structure</i> residue F10 contributes to the hydrophobic interaction with GRL and residue R8 (i.e. the R-2 motif) is exposed to the β-MPP subunit. In the <i>AS-bound </i><i>structure</i> the substrate is bound in an extended conformation and its R8 residue interacts with the R-2-binding motif. The zinc-binding motif and R-2-binding motif are shown schematically as cyan and orange spheres which correspond to the zinc-ion and residues E160 and D164 residues of the β-MPP subunit. The distances between the substrate R8 residue and the R-2-binding motif in the <i>GRL-bound</i> and <i>AS-bound </i><i>structure</i> are shown as dashed black lines.</p

Scheme showing the positions of the R8 residue along the substrate translocation trajectory.

<p>The R8 residue is located in position -2 relative to the substrate cleavage site and thus represents the R-2 motif. The R-2-binding motif is shown schematically as an orange sphere representing the δ-carbon atom of the β-subunit E160 residue and the GRL is displayed as a green semi-transparent van der Waals surface whose backbone chain is displayed as a tube. In the <i>GRL-bound </i><i>structure</i> the substrate is bound to GRL and residue R8 (red sticks) is exposed to the β-MPP subunit. In the <i>AS-bound </i><i>structure</i> (purple sticks), on the other hand, the substrate is bound in the MPP active site and the R8 residue interacts with the R-2-binding motif. The positions of the R8 residues in <i>Structure 30-100</i> (yellow sticks) and <i>Structure 50-100</i> (blue stick) were obtained at the end of a 100-ns-long non-restrained MD simulation performed on the structures corresponding to the snapshots from a targeted MD simulation when the substrate reached the first third and the mid part of its translocation trajectory. The numbers in brackets mark the time steps along the substrate translocation trajectory. The distances between the R8 residue and the R-2-binding motif are shown as dashed black lines. Note that while <i>Structure 30-100</i> has the R8 residue oriented away from the GRL, in <i>Structure 50-100</i> it is oriented towards the R-2-binding motif and its distance from it is almost the same as in the <i>AS-bound </i><i>structure</i>.</p

Detail structures of GRLs of MPP and M16 peptidase from <i>Sphingomonas sp.</i>

<p>Panel A shows the GRL region of MPP while panel B shows the “embryonal” GRL of M16 peptidase. The α-subunit is shown in yellow, β-subunit in orange, and the GRL in green. The side chains of amino acids 285–300 of the MPP GRL and 290–296 of the M16 peptidase GRL are represented as sticks. Panel C shows a sequence alignment of both GRLs.</p

Time-based RMSD of backbone Cα atoms of WT MPP and ΔGRL MPP.

<p>Panel A shows the change in the RMSD of the WT MPP structure over the course of a 100 ns simulation with respect to the initial model. Runs both with (red) and without (blue) a active site-bound peptide substrate are shown. Panel B shows the same information, but for the ΔGRL MPP structure. The ΔGRL MPP structure was produced by deleting residues 285-300 from the α-MPP structure. Figure S2 displays the same information in 2D RMSD plots.</p

Residue-based RMSD of backbone Cα atoms of WT MPP and ΔGRL MPP.

<p>Panels A and B show the RMSD per residue of the WT MPP and ΔGRL MPP structures, respectively. The red lines show the RMSD of the structures in the presence of the active site-bound substrate and the blue lines represent the unbound structures at the end of a 100-ns-long MD simulation. The bars along the <i>x</i>-axes indicate the residues which belong to the α (yellow) and β-MPP (orange) subunits, while the green bar in panel A indicates the position of the GRL (residues 285-300) which was deleted in the ΔGRL MPP structure. Panels C and D show, respectively, the WT MPP and ΔGRL MPP structures colored to reflect their per-residue RMSDs and structurally aligned according to the parts with the lovest fluctuation of RMSD. Both structures are colored according to RMSD scale bar in the bottom right corner of panel D. The red circle marks the position of the GRL. Note that the ΔGRL MPP dimer appears to be more open than the WT structure and that the RMSDs of the areas farthest from the dimer interface are notably higher.</p

GRL-substrate interaction after half the substrate translocation.

<p>Panel A (Structure 50-0) shows a snapshot from the targeted MD simulation corresponding to the situation at time 0.84 ns of a 1.6-ns-long restraint period. Panel B (Structure 50-100) shows the GRL-substrate interaction after a 100-ns-long non-restrained MD simulation performed on <i>Structure 50-0</i>. The structural elements are represented as in Figure 2. Note that (i) the substrate has now shifted completely away from the GRL towards the MPP active site, (ii) the R8-E160 distance decreased from 8 to 4 Å and that (iii) the R8 residue has reoriented towards the R-2-binding motif.</p

GRL-substrate interaction after the substrate has completed the first third of its translocation.

<p>Panel A (Structure 30-0) shows a snapshot from the targeted MD simulation corresponding to the situation after 0.48 ns out of a 1.6-ns-long restraint period. Panel B (Structure 30-100) shows the GRL-substrate interaction after a 100-ns-long, non-restrained MD simulation performed on <i>Structure 30-0</i>. The GRL lies at the entrance to the active site cavity between the α-MPP and β-MPP subunits and is displayed as a semi-transparent van der Waals surface, colored according to residue hydrophobicity [34]. The backbone trace can be seen within this surface and is displayed as a tube. The backbone trace of the substrate is displayed as a magenta tube. Residues K296, M298, Y299 and Y303 of the GRL and residues F10 and R8 (i.e. the R-2 motif) of the substrate are shown as sticks. The α and β prefixes in residue names refer to the α- or β-MPP subunits, respectively. The numbers in brackets show the position of the given residue with respect to the substrate cleavage site. The orange sphere shows the positions of the δ-carbon of the E160 residue and thus represents schematically the R-2-binding motif. The distance between the ζ-carbon atom of the R8 residue and the R-2-binding motif (i.e. δ-carbon of the E160) and the distance between the δ-carbon of residue F10 and the hydrophobic patch of the GRL (represented by the ε-carbon of the α-subunit Y303 residue) are shown as dashed lines in blue (“R8-E160”) and orange (“F10-Y303”), respectively. Panel C shows these two distances over the course of the non-restrained MD simulation. Note that (i) the N-terminus of the substrate shifted while the substrate has curled into an α-helix. Moreover, note that during the whole non-restrained MD simulation (ii) the GRL-substrate interaction was stable (the R8-E160 and F10-Y303 distances were largely unchanged) and (iii) the substrate F10 residue interacted with the hydrophobic patch created by GRL residues M298 and Y303.</p

New Cholinesterase Inhibitory Constituents from <i>Lonicera quinquelocularis</i>

<div><p>A phytochemical investigation on the ethyl acetate soluble fraction of <i>Lonicera quinquelocularis</i> (whole plant) led to the first time isolation of one new phthalate; <i>bis(7-acetoxy-2-ethyl-5-methylheptyl) phthalate</i> (<b>3</b>) and two new benzoates; <i>neopentyl-4-ethoxy-3, 5-bis (3-methyl-2-butenyl benzoate</i> (<b>4</b>) <i>and neopentyl-4-hydroxy-3, 5-bis (3-methyl-2-butenyl benzoate</i> (<b>5</b>) along with two known compounds <i>bis (2-ethylhexyl phthalate</i> (<b>1</b>) and <i>dioctyl phthalate</i> (<b>2</b>). Their structures were established on the basis of spectroscopic analysis and by comparison with available data in the literature. All the compounds (<b>1–5</b>) were tested for their acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) inhibitory activities in dose dependent manner. The IC₅₀ (50% inhibitory effect) values of compounds <b>3</b> and <b>5</b> against AChE were 1.65 and 3.43 µM while the values obtained against BChE were 5.98 and 9.84 µM respectively. Compounds <b>2</b> and <b>4</b> showed weak inhibition profile.</p></div