Stripe to spot transition in a plant root hair initiation model

A generalised Schnakenberg reaction-diffusion system with source and loss terms and a spatially dependent coefficient of the nonlinear term is studied both numerically and analytically in two spatial dimensions. The system has been proposed as a model of hair initiation in the epidermal cells of plant roots. Specifically the model captures the kinetics of a small G-protein ROP, which can occur in active and inactive forms, and whose activation is believed to be mediated by a gradient of the plant hormone auxin. Here the model is made more realistic with the inclusion of a transverse co-ordinate. Localised stripe-like solutions of active ROP occur for high enough total auxin concentration and lie on a complex bifurcation diagram of single and multi-pulse solutions. Transverse stability computations, confirmed by numerical simulation show that, apart from a boundary stripe, these 1D solutions typically undergo a transverse instability into spots. The spots so formed typically drift and undergo secondary instabilities such as spot replication. A novel 2D numerical continuation analysis is performed that shows the various stable hybrid spot-like states can coexist. The parameter values studied lead to a natural singularly perturbed, so-called semi-strong interaction regime. This scaling enables an analytical explanation of the initial instability, by describing the dispersion relation of a certain non-local eigenvalue problem. The analytical results are found to agree favourably with the numerics. Possible biological implications of the results are discussed.Comment: 28 pages, 44 figure

Spot dynamics in a reaction-diffusion model of plant root hair initiation

We study pattern formation in a 2-D reaction-diffusion (RD) sub-cellular model characterizing the effect of a spatial gradient of a plant hormone distribution on a family of G-proteins associated with root-hair (RH) initiation in the plant cell Arabidopsis thaliana. The activation of these G-proteins, known as the Rho of Plants (ROPs), by the plant hormone auxin, is known to promote certain protuberances on root hair cells, which are crucial for both anchorage and the uptake of nutrients from the soil. Our mathematical model for the activation of ROPs by the auxin gradient is an extension of the model of Payne and Grierson [PLoS ONE, 12(4), (2009)], and consists of a twocomponent Schnakenberg-type RD system with spatially heterogeneous coefficients on a 2-D domain. The nonlinear kinetics in this RD system model the nonlinear interactions between the active and inactive forms of ROPs. By using a singular perturbation analysis to study 2-D localized spatial patterns of active ROPs, it is shown that the spatial variations in the nonlinear reaction kinetics, due to the auxin gradient, lead to a slow spatial alignment of the localized regions of active ROPs along the longitudinal midline of the plant cell. Numerical bifurcation analysis, together with time-dependent numerical simulations of the RD system are used to illustrate both 2-D localized patterns in the model, and the spatial alignment of localized structures

Epigenetics in Glaucoma

Primary open angle glaucoma (POAG) is defined as a “genetically complex trait”, where modifying factors act on a genetic predisposing background. For the majority of glaucomatous conditions, DNA variants are not sufficient to explain pathogenesis. Some genes are clearly underlying the more “Mendelian” forms, while a growing number of related polymorphisms in other genes have been identified in recent years. Environmental, dietary, or biological factors are known to influence the development of the condition, but interactions between these factors and the genetic background are poorly understood. Several studies conducted in recent years have led to evidence that epigenetics, that is, changes in the pattern of gene expression without any changes in the DNA sequence, appear to be the missing link. Different epigenetic mechanisms have been proven to lead to glaucomatous changes in the eye, principally DNA methylation, post-translational histone modification, and RNA-associated gene regulation by non-coding RNAs. The aim of this work is to define the principal epigenetic actors in glaucoma pathogenesis. The identification of such mechanisms could potentially lead to new perspectives on therapeutic strategies

Numerical bifurcation study of superconducting patterns on a square

This paper considers the extreme type-II Ginzburg-Landau equations that model vortex patterns in superconductors. The nonlinear PDEs are solved using Newton's method, and properties of the Jacobian operator are highlighted. Specifically, it is illustrated how the operator can be regularized using an appropriate phase condition. For a two-dimensional square sample, the numerical results are based on a finite-difference discretization with link variables that preserves the gauge invariance. For two exemplary sample sizes, a thorough bifurcation analysis is performed using the strength of the applied magnetic field as a bifurcation parameter and focusing on the symmetries of this system. The analysis gives new insight in the transitions between stable and unstable states, as well as the connections between stable solution branches.Comment: 31 page

Definition of indicators of appropriateness in the management of neovascular age-related macular degeneration: An expert opinion

Wet age-related macular degeneration is a chronic condition culminating, in most cases, in blindness. The introduction of anti-angiogenic agents in 2006 has represented a major breakthrough in the treatment of the disease, but timely and effective treatment with regular follow-up and monitoring is mandatory to stabilize and preserve visual acuity. In clinical practice, however, appropriate therapy provision is frequently challenged by economic and organizational issues that result in suboptimal visual outcomes and increased incidence of legal blindness. International Guidelines have defined a diagnostic and therapeutic pathway to ensure the best practice in wet age-related macular degeneration management, but reference parameters to evaluate and compare the performance of Retina Centers are lacking. To address the appropriateness of wet age-related macular degeneration management in Italy, a multidisciplinary panel of ten experts gathered in three meetings. They defined three sets of indicators and relative benchmark values that each Center should comply with to ensure patients optimal care already from the first access: (a) clinical intervention indicators, to determine the possible Center\u2019s deviation from the diagnostic and therapeutic pathway; (b) outcome indicator, to evaluate the socioeconomic impact of the healthcare systems\u2019 performance; (c) management indicators, to test the size of the gap between the Center\u2019s supply and demand. Once the indicators have been analyzed, healthcare systems can plan actions to improve appropriateness and monitor their effects. However, to put this in practice, a concerted effort by all parts involved in healthcare provision is required, together with adequate systems to analyze clinical and administrative documentation

Efficacy of Three Different Prophylactic Treatments for Postoperative Nausea and Vomiting after Vitrectomy: A Randomized Clinical Trial

Postoperative nausea and vomiting (PONV) after vitreoretinal surgery may potentially be associated with severe complications, such as suprachoroidal hemorrhage. The purpose of the present multicenter clinical trial (NCT02386059) was to assess the efficacy of three different prophylactic treatments for PONV after vitrectomy under local anesthesia. Patients undergoing primary vitrectomy were randomized to the control arm or to one of the treatment arms (4 mg ondansetron, 4 mg dexamethasone, combination of the two drugs). The primary outcome measure was the proportion of complete response (no nausea, no vomiting, no retching, and no use of antiemetic rescue medication) during 24 h after vitrectomy. Secondary outcomes included the severity standardized score of PONV, postoperative pain standardized score, and rate of ocular and non-ocular adverse events. Baseline demographics of the 1287 patients were comparable between the four arms. The combined therapy group showed a statistically significant lower incidence of PONV compared to the placebo and monotherapy (p < 0.001). PONV severity was also reduced in the combination group compared to the others (p < 0.001). Postoperative pain scores and adverse events were comparable among the four groups. Combined therapy with dexamethasone and ondansetron was the most effective treatment for reducing the incidence and severity of PONV in patients undergoing vitrectomy under local anesthesia

Characterization of the pathophysiological role of CD47 in uveal melanoma

Uveal melanoma (UM) represents the most frequent primary intraocular tumor, however, limited therapeutic options are still available. We have previously shown that cluster of differentiation 47 (CD47) is significantly upregulated in UM cells following inflammatory stimuli and that it represents a predictor of disease progression. Here, we aimed to better characterize the pathophysiological role of CD47 in UM. We show that CD47 is not modulated at different cancer stages, although patients with the lowest expression of CD47 show significant better progression-free survival, after correcting for the presence of BAP1, GNAQ, and GNA11 mutations. By stratifying patients based on the expression of CD47 in the tumor, we observed that patients with high levels of CD47 have a significant increase in immune score as compared to patients with low levels of CD47. In particular, deconvolution analysis of infiltrating immune cell populations revealed that a significantly higher number of CD4+ and CD8+ T cells can be found in patients with high CD47 levels, with the most enriched populations being the Th2, Treg, and CD8+ Tcm cells. We also show that a large number of transcripts are significantly modulated between the groups of patients with high and low levels of CD47, with a significant enrichment of interferon IFN-alpha regulated genes. The results from this study may propel the development of anti-CD47 therapies for UM patients