A microscopic approach to nonlinear Reaction-Diffusion: the case of morphogen gradient formation

We develop a microscopic theory for reaction-difusion (R-D) processes based on a generalization of Einstein's master equation with a reactive term and we show how the mean field formulation leads to a generalized R-D equation with non-classical solutions. For the $n$-th order annihilation reaction $A+A+A+...+A\rightarrow 0$, we obtain a nonlinear reaction-diffusion equation for which we discuss scaling and non-scaling formulations. We find steady states with either solutions exhibiting long range power law behavior (for $n>\alpha$) showing the relative dominance of sub-diffusion over reaction effects in constrained systems, or conversely solutions (for $n<\alpha<n+1$) with finite support of the concentration distribution describing situations where diffusion is slow and extinction is fast. Theoretical results are compared with experimental data for morphogen gradient formation.Comment: Article, 10 pages, 5 figure

Natural Enemies of Cranberry Fruitworm, \u3ci\u3eAcrobasis Vaccinii\u3c/i\u3e, (Lepidoptera: Pyraudae) in Michigan Highbush Blueberries

A two-year study was conducted in Michigan highbush blueberries to determine the complex of parasitoids attacking cranberry fruitworm, Acrobasis vaccinii. Eight parasitoid species and one fungal pathogen were collected. Parasitism of collected hosts ranged from 6.6% to 28.1%. The more common larval parasitoid encountered was Campoletis patsuiketorum (Hymenoptera: Ichneumonidae). The more common parasitoid recovered from fruitworm hibernacula was Villa lateralis (Diptera: Bombyliidae). This study documented six unreported natural enemies of cranberry fruitworm, including C. patsuiketorum; V. lateralis; Diadegma compressum (Hymenoptera: Ichneumonidae); Compsilura concinnata (Diptera: Tachinidae); Memorilla pyste (Diptera: Tachinidae); an undescribed Microtypus species (Hymenoptera: Braconidae); and a fungal pathogen, Paecilomyces near farinosus. This is the first known host association for the undescribed Microtypus species, and increases the known parasitoid complex of cranberry fruitworm to 17 species

Facilitated diffusion. The case of carbon monoxide.

Abstract An application of a singular perturbation method to the case of carbon monoxide similar to that used previously for the case of oxygen (Murray, J. D., Proc. Roy. Soc. London B Biol. Sci., 178, 95 (1971)) shows that the absence of any observed facilitation of diffusion of this ligand by either hemoglobin or myoglobin in all of the experiments so far performed results from the very high affinity of both proteins for the gas. At every point in the solution both proteins were essentially at equilibrium with the gas but it was evidently impossible to reduce the pressure of carbon monoxide on the low pressure face of the solution sufficiently to remove a significant amount of the carbon monoxide from combination with the macromolecular carrier. The principle that a macromolecule can only function as a carrier under conditions in which its saturation with the ligand is incomplete in some region of the solution is quite general

Consuming transgenic goats' milk containing the antimicrobial protein lysozyme helps resolve diarrhea in young pigs.

Childhood diarrhea is a significant problem in many developing countries and E. coli is a main causative agent of diarrhea in young children. Lysozyme is an antimicrobial protein highly expressed in human milk, but not ruminant milk, and is thought to help protect breastfeeding children against diarrheal diseases. We hypothesized that consumption of milk from transgenic goats which produce human lysozyme (hLZ-milk) in their milk would accelerate recovery from bacterial-induced diarrhea. Young pigs were used as a model for children and infected with enterotoxigenic E. coli. Once clinical signs of diarrhea developed, pigs were fed hLZ-milk or non-transgenic control goat milk three times a day for two days. Clinical observations and complete blood counts (CBC) were performed. Animals were euthanized and samples collected to assess differences in histology, cytokine expression and bacterial translocation into the mesenteric lymph node. Pigs consuming hLZ-milk recovered from clinical signs of infection faster than pigs consuming control milk, with significantly improved fecal consistency (p = 0.0190) and activity level (p = 0.0350). The CBC analysis showed circulating monocytes (p = 0.0413), neutrophils (p = 0.0219), and lymphocytes (p = 0.0222) returned faster to pre-infection proportions in hLZ-milk fed pigs, while control-fed pigs had significantly higher hematocrit (p = 0.027), indicating continuing dehydration. In the ileum, pigs fed hLZ-milk had significantly lower expression of pro-inflammatory cytokine IL-8 (p = 0.0271), longer intestinal villi (p&lt;0.0001), deeper crypts (p = 0.0053), and a thinner lamina propria (p = 0.0004). These data demonstrate that consumption of hLZ-milk helped pigs recover from infection faster, making hLZ-milk an effective treatment of E. coli-induced diarrhea

Biological pattern formation on two-dimensional domains: A nonlinear bifurcation analysis

A tissue interaction model for skin organ pattern formation is presented. Possible spatially patterned solutions on rectangular domains are investigated. Linear stability analysis suggests that the model can exhibit pattern formation. A weakly nonlinear two-dimensional perturbation analysis is then carried out. This demonstrates that when bifurcation occurs via a simple eigenvalue, patterns such as rolls, squares, and rhombi can be supported by the model equations. Our nonlinear analysis shows that more complex patterns are also possible if bifurcation occurs via a double eigenvalue. Surprisingly, hexagonal patterns could not develop from a primary bifurcation

Heterogeneity in Kv2 Channel Expression Shapes Action Potential Characteristics and Firing Patterns in CA1 versus CA2 Hippocampal Pyramidal Neurons.

The CA1 region of the hippocampus plays a critical role in spatial and contextual memory, and has well-established circuitry, function and plasticity. In contrast, the properties of the flanking CA2 pyramidal neurons (PNs), important for social memory, and lacking CA1-like plasticity, remain relatively understudied. In particular, little is known regarding the expression of voltage-gated K+ (Kv) channels and the contribution of these channels to the distinct properties of intrinsic excitability, action potential (AP) waveform, firing patterns and neurotransmission between CA1 and CA2 PNs. In the present study, we used multiplex fluorescence immunolabeling of mouse brain sections, and whole-cell recordings in acute mouse brain slices, to define the role of heterogeneous expression of Kv2 family Kv channels in CA1 versus CA2 pyramidal cell excitability. Our results show that the somatodendritic delayed rectifier Kv channel subunits Kv2.1, Kv2.2, and their auxiliary subunit AMIGO-1 have region-specific differences in expression in PNs, with the highest expression levels in CA1, a sharp decrease at the CA1-CA2 boundary, and significantly reduced levels in CA2 neurons. PNs in CA1 exhibit a robust contribution of Guangxitoxin-1E-sensitive Kv2-based delayed rectifier current to AP shape and after-hyperpolarization potential (AHP) relative to that seen in CA2 PNs. Our results indicate that robust Kv2 channel expression confers a distinct pattern of intrinsic excitability to CA1 PNs, potentially contributing to their different roles in hippocampal network function

On the role of buoyant flexure in glacier calving

Interactions between glaciers and the ocean are key for understanding the dynamics of the cryosphere in the climate system. Here we investigate the role of hydrostatic forces in glacier calving. We develop a mathematical model to account for the elastic deformation of glaciers in response to three effects: (i) marine and lake-terminating glaciers tend to enter water with a nonzero slope, resulting in upward flexure around the grounding line; (ii) horizontal pressure imbalances at the terminus are known to cause hydrostatic in-plane stresses and downward acting torque; (iii) submerged ice protrusions at the glacier front may induce additional buoyancy forces that can cause calving. Our model provides theoretical estimates of the importance of each effect and suggests geometric and material conditions under which a given glacier will calve from hydrostatic flexure. We find good agreement with observations. This work sheds light on the intricate processes involved in glacier calving and can be hoped to improve our ability to model and predict future changes in the ice-climate system