A new asymptotic analysis of the nth order reaction-diffusion problem: analytical and numerical studies

We present a new formulation of the steady state, isothermal, nonlinear reaction-diffusion problem involving nth order reaction kinetics for slab geometry. This results in tractable expressions for the effectiveness factor as a function of the Thiele modulus, the Thiele modulus as a function of the centerline concentration, and the concentration profiles in the slab. The expressions are valid asymptotically in the limit of large orders n. We compare these results with the exact numerical solutions obtained by transforming the nonlinear differential equation into an integral form, using Green's function methods, and solving by successive approximations. The formulation for a membrane is also given, and the nature of the asymmetrical solution discussed. The analysis is facilitated through the introduction of pseudo-reaction orders. A comparison of the asymptotic Thiele modulus obtained herein with a previously given expression shows the present theory to be an improvement.     

Multicellular computer simulation of morphogenesis: blastocoel roof thinning and matrix assembly in Xenopus laevis

In the blastocoel roof (BCR) of the Xenopus laevis embryo, epibolic movements are driven by the radial intercalation of deep cell layers and the coordinate spreading of the overlying superficial cell layer. Thinning of the lateral margins of the BCR by radial intercalation requires fibronectin (FN), which is produced and assembled into fibrils by the inner deep cell layer of the BCR. A cellular automata (CA) computer model was developed to analyze the spatial and temporal movements of BCR cells during epiboly. Simulation parameters were defined based on published data and independent results detailing initial tissue geometry, cell numbers, cell intercalation rates, and migration rates. Hypotheses regarding differential cell adhesion and FN assembly were also considered in setting system parameters. A 2-dimensional model simulation was developed that predicts BCR thinning time of 4.8 h, which closely approximates the time required for the completion of gastrulation in vivo. Additionally, the model predicts a temporal increase in FN matrix assembly that parallels fibrillogenesis in the embryo. The model is capable of independent predictions of cell rearrangements during epiboly, and here was used to predict successfully the lateral dispersion of a patch of cells implanted in the BCR, and increased assembly of FN matrix following inhibition of radial intercalation by N-cadherin over-expression.     

Concanavalin A and wheat germ agglutinin binding to sea urchin embryo basal laminae

Summary The basal laminae and inner extracellular matrices of Lytechinus pictus and Arbacia punctulata embryos were characterized on the basis of lectin binding. Developmental stage specific patterns of lectin binding were observed after microinjection of Con A-FITC and WGA-FITC. Lectin-specific patterns differed between control, sulfate free sea water (SFSW) and tunicamycin treated embryos. Con A injection resulted in the rounding-up of cells in the epithelium and was most pronounced in embryos cultured in the presence of tunicamycin. Basal laminae were isolated by Triton X-100 extraction of whole embryos. Proteins were separated by SDS-PAGE, electrophoretically transferred to nitrocellulose and incubated in biotinylated lectins. Lectin-binding glycoproteins were detected with avidin peroxidase. The electrophoretic pattern of Con A-binding proteins in early developmental stages of Arbacia was similar with several low molecular weight species appearing at gastrulation in control and SFSW embryos. WGA-binding in Arbacia and Lytechinus control embryos was limited to a 125,000 Mr glycoprotein (gp125). In addition to gp125, several high molecular weight WGA-binding glycoproteins were also detected in SFSW embryos. The evidence suggests that mesenchyme migration and gastrulation are correlated with changes in the molecular composition of the ECM.     

Ion transport across the frog olfactory mucosa: the action of cyclic nucleotides on the basal and odorant-stimulated states

The action of cyclic nucleotides on the short-circuit current across the isolated bullfrog olfactory mucosa was studied both in the absence and presence of odorants. 8-Bromo-cAMP applied to the ciliated side of the mucosa caused a concentration-dependent, reversible increase in the basal short-circuit current, but not when it was applied to the submucosal side. The current had a sigmoidal concentration dependence described by the Hill equation. The magnitude of the odorant-evoked current was enhanced after bathing the ciliated side with cAMP analogs or modulators of intracellular cAMP. GTP gamma S added to the ciliated side increased the odorant-evoked current, while GDP beta S caused a decrease. Current transients induced by stimulating the ciliated side with either pulses of odorant or 8-bromo-cAMP were partially suppressed by amiloride, but only when amiloride and stimulant were presented simultaneously. Pulses of 8-bromo-cAMP and odorant presented simultaneously resulted in currents that added nonlinearly. In the absence of odorant, 8-bromo-cGMP caused a concentration-dependent decrease in net inward current that was reversed by 8-bromo-cAMP. Odorant-evoked currents were also reduced by 8-bromo-cGMP, and these could not be reversed by 8-bromo-cAMP. The results indicate that one type of olfactory transduction process involves the activation by cAMP of an inward current through an amiloride-sensitive apical ion channel and that this mechanism is mediated by a stimulatory G-protein.     

Corn fiber oil lowers plasma cholesterol levels and increases cholesterol excretion greater than corn oil and similar to diets containing soy sterols and soy stanols in hamsters

The aims of this study were to compare the cholesterol-lowering properties of corn fiber oil (CFO) to corn oil (CO), whether the addition of soy stanols or soy sterols to CO at similar levels in CFO would increase CO's cholesterol-lowering properties, and the mechanism(s) of action of these dietary ingredients. Fifty male Golden Syrian hamsters were divided into 5 groups of 10 hamsters each, based on similar plasma total cholesterol (TC) levels. The first group of hamsters was fed a chow-based hypercholesterolemic diet containing either 5% coconut oil + 0.24% cholesterol (coconut oil), 5% CO, 5% CFO, 5% CO + 0.6% soy sterols (sterol), or 5% CO + 0.6% soy stanols (stanol) in place of the coconut oil for 4 weeks. The stanol diet significantly inhibited the elevation of plasma TC compared to all other dietary treatments. Also, the CFO and sterol diets significantly inhibited the elevation of plasma TC compared to the CO and coconut oil diets. The CFO, sterol, and stanol diets significantly inhibited the elevation of plasma non-high density lipoprotein cholesterol compared to the CO and coconut oil diets. The stanol diet significantly inhibited the elevation of plasma high density lipoprotein cholesterol (HDL-C) compared to all other dietary treatments. The sterol diet significantly inhibited the elevation of plasma HDL-C compared to the CO and coconut oil diets, whereas the CFO diet significantly inhibited the elevation of plasma HDL-C compared to the coconut oil diet only. No differences were observed between the CFO and CO for plasma HDL-C. There were no differences observed between groups for plasma triglycerides. The CO and CFO diets had significantly less hepatic TC compared to the coconut oil, sterol, and stanol diets. The CO and CFO diets had significantly less hepatic free cholesterol compared to the sterol and stanol diets but not compared to the coconut oil diet; whereas the coconut oil and sterol diets had significantly less hepatic free cholesterol compared to the stanol diet. The CFO, sterol, and stanol diets excreted significantly more fecal cholesterol compared to the coconut oil and CO diets. In summary, CFO reduces plasma and hepatic cholesterol concentrations and increases fecal cholesterol excretion greater than CO through some other mechanism(s) in addition to increase dietary sterols and stanols-possibly oryzanols.     

Roles of ADAM13-regulated Wnt activity in early Xenopus eye development

Pericellular proteolysis by ADAM family metalloproteinases has been widely implicated in cell signaling and development. We recently found that Xenopus ADAM13, an ADAM metalloproteinase, is required for activation of canonical Wnt signaling during cranial neural crest (CNC) induction by regulating a novel crosstalk between Wnt and ephrin B (EfnB) signaling pathways (Wei et al., 2010b). In the present study we show that the metalloproteinase activity of ADAM13 also plays important roles in eye development in Xenopus tropicalis. Knockdown of ADAM13 results in reduced expression of eye field markers pax6 and rx1, as well as that of the pan-neural marker sox2. Activation of canonical Wnt signaling or inhibition of forward EfnB signaling rescues the eye defects caused by loss of ADAM13, suggesting that ADAM13 functions through regulation of the EfnB-Wnt pathway interaction. Downstream of Wnt, the head inducer Cerberus was identified as an effector that mediates ADAM13 function in early eye field formation. Furthermore, ectopic expression of the Wnt target gene snail2 restores cerberus expression and rescues the eye defects caused by ADAM13 knockdown. Together these data suggest an important role of ADAM13-regulated Wnt activity in eye development in Xenopus.     

The K+-H+ exchanger, nigericin, modulates taste cell pH and chorda tympani taste nerve responses to acidic stimuli

The relationship between acidic pH, taste cell pH(i), and chorda tympani (CT) nerve responses was investigated before and after incorporating the K(+)-H(+) exchanger, nigericin, in the apical membrane of taste cells. CT responses were recorded in anesthetized rats in vivo, and changes in pH(i) were monitored in polarized fungiform taste cells in vitro. Under control conditions, stimulating the tongue with 0.15 M potassium phosphate (KP) or 0.15 M sodium phosphate (NaP) buffers of pHs between 8.0 and 4.6, KP or NaP buffers did not elicit a CT response. Post-nigericin (500 × 10(-6) M), KP buffers, but not NaP buffers, induced CT responses at pHs ≤ 6.6. The effect of nigericin was reversed by the topical lingual application of carbonyl cyanide 3-chloro-phenylhydrazone, a protonophore. Post-nigericin (150 × 10(-6) M), KP buffers induced a greater decrease in taste cell pH(i) relative to NaP buffers and to NaP and KP buffers under control conditions. A decrease in pH(i) to about 6.9 induced by KP buffers was sufficient to elicit a CT response. The results suggest that facilitating apical H(+) entry via nigericin decreases taste cell pH(i) and demonstrates directly a strong correlation between pH(i) and the magnitude of the CT response.     

Novel platforms for vascular carriers with controlled geometry

The first-generation platforms for vascular drug delivery adopted spherical morphologies. These carriers relied primarily on the size dependence of the enhanced permeability and retention effect to passively target vasculature, resulting in inefficient delivery due to significant variation in endothelial permeability. Enhanced delivery typically requires active targeting via receptor-mediated endocytosis by surface conjugation of targeting ligands. However, vascular carriers (VCs) still face numerous challenges en route to reaching their targets before delivery. The control of carrier shape offers opportunities to overcome in vivo barriers and enhance vascular drug delivery. Geometric features influence the ability of carrier particles to navigate physiological flow patterns, evade biological clearance mechanisms, sustain circulation, adhere to the vascular surface, and finally transport across or internalize into the endothelium. Although previous formulation strategies limited the fabrication of nonspherical carriers, numerous recent advances in both top-down and bottom-up fabrication techniques have enabled shape modulation as a key design element. As part of a series on vascular drug delivery, this review focuses on recent developments in novel vascular platforms with controlled geometry that enhance or modulate delivery functions. Starting with an overview of controlled geometry platforms, we review their shape-dependent functional characteristics for each stage of their vascular journey in vivo. We sequentially explore carrier geometries that evade reticuloendothelial system uptake, display enhanced circulation persistence and margination dynamics in flow, encourage adhesion to the vascular surface or extravasation through endothelium, and impact extravascular transport and cell internalization. The eventual biodistribution of VCs results from the culmination of their successive navigation of all these barriers and is profoundly influenced by their morphology. To enhance delivery efficacy, carrier designs synergistically combining controlled geometry with standard drug delivery strategies such as targeting moieties, surface decorations, and bulk material properties are discussed. Finally, we speculate on possibilities for innovation, harnessing shape as a design parameter for the next generation of vascular drug delivery platforms.