Pressure moderation and effective pressure in Navier-Stokes flows

We study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.PostprintPeer reviewe

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

Novel associations for hypothyroidism include known autoimmune risk loci

Hypothyroidism is the most common thyroid disorder, affecting about 5% of the general population. Here we present the first large genome-wide association study of hypothyroidism, in 2,564 cases and 24,448 controls from the customer base of 23andMe, Inc., a personal genetics company. We identify four genome-wide significant associations, two of which are well known to be involved with a large spectrum of autoimmune diseases: rs6679677 near _PTPN22_ and rs3184504 in _SH2B3_ (p-values 3.5e-13 and 3.0e-11, respectively). We also report associations with rs4915077 near _VAV3_ (p-value 8.3e-11), another gene involved in immune function, and rs965513 near _FOXE1_ (p-value 3.1e-14). Of these, the association with _PTPN22_ confirms a recent small candidate gene study, and _FOXE1_ was previously known to be associated with thyroid-stimulating hormone (TSH) levels. Although _SH2B3_ has been previously linked with a number of autoimmune diseases, this is the first report of its association with thyroid disease. The _VAV3_ association is novel. These results suggest heterogeneity in the genetic etiology of hypothyroidism, implicating genes involved in both autoimmune disorders and thyroid function. Using a genetic risk profile score based on the top association from each of the four genome-wide significant regions in our study, the relative risk between the highest and lowest deciles of genetic risk is 2.1

Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration

In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult life1, and are an important model for organ regeneration. Hair stem cells located in the follicle bulge2 are regulated by the surrounding microenvironment, or niche3. The activation of such stem cells is cyclic, involving periodic -catenin activity4, 5, 6, 7. In the adult mouse, regeneration occurs in waves in a follicle population, implying coordination among adjacent follicles and the extrafollicular environment. Here we show that unexpected periodic expression of bone morphogenetic protein 2 (Bmp2) and Bmp4 in the dermis regulates this process. This BMP cycle is out of phase with the WNT/-catenin cycle, thus dividing the conventional telogen into new functional phases: one refractory and the other competent for hair regeneration, characterized by high and low BMP signalling, respectively. Overexpression of noggin, a BMP antagonist, in mouse skin resulted in a markedly shortened refractory phase and faster propagation of the regenerative wave. Transplantation of skin from this mutant onto a wild-type host showed that follicles in donor and host can affect their cycling behaviours mutually, with the outcome depending on the equilibrium of BMP activity in the dermis. Administration of BMP4 protein caused the competent region to become refractory. These results show that BMPs may be the long-sought 'chalone' inhibitors of hair growth postulated by classical experiments. Taken together, results presented in this study provide an example of hierarchical regulation of local organ stem cell homeostasis by the inter-organ macroenvironment. The expression of Bmp2 in subcutaneous adipocytes indicates physiological integration between these two thermo-regulatory organs. Our findings have practical importance for studies using mouse skin as a model for carcinogenesis, intra-cutaneous drug delivery and stem cell engineering studies, because they highlight the acute need to differentiate supportive versus inhibitory regions in the host skin

Hair organ regeneration via the bioengineered hair follicular unit transplantation

Organ regenerative therapy aims to reproduce fully functional organs to replace organs that have been lost or damaged as a result of disease, injury, or aging. For the fully functional regeneration of ectodermal organs, a concept has been proposed in which a bioengineered organ is developed by reproducing the embryonic processes of organogenesis. Here, we show that a bioengineered hair follicle germ, which was reconstituted with embryonic skin-derived epithelial and mesenchymal cells and ectopically transplanted, was able to develop histologically correct hair follicles. The bioengineered hair follicles properly connected to the host skin epithelium by intracutaneous transplantation and reproduced the stem cell niche and hair cycles. The bioengineered hair follicles also autonomously connected with nerves and the arrector pili muscle at the permanent region and exhibited piloerection ability. Our findings indicate that the bioengineered hair follicles could restore physiological hair functions and could be applicable to surgical treatments for alopecia

Defending the genome from the enemy within:mechanisms of retrotransposon suppression in the mouse germline

The viability of any species requires that the genome is kept stable as it is transmitted from generation to generation by the germ cells. One of the challenges to transgenerational genome stability is the potential mutagenic activity of transposable genetic elements, particularly retrotransposons. There are many different types of retrotransposon in mammalian genomes, and these target different points in germline development to amplify and integrate into new genomic locations. Germ cells, and their pluripotent developmental precursors, have evolved a variety of genome defence mechanisms that suppress retrotransposon activity and maintain genome stability across the generations. Here, we review recent advances in understanding how retrotransposon activity is suppressed in the mammalian germline, how genes involved in germline genome defence mechanisms are regulated, and the consequences of mutating these genome defence genes for the developing germline

Integrating transposable elements in the 3D genome

Chromosome organisation is increasingly recognised as an essential component of genome regulation, cell fate and cell health. Within the realm of transposable elements (TEs) however, the spatial information of how genomes are folded is still only rarely integrated in experimental studies or accounted for in modelling. Whilst polymer physics is recognised as an important tool to understand the mechanisms of genome folding, in this commentary we discuss its potential applicability to aspects of TE biology. Based on recent works on the relationship between genome organisation and TE integration, we argue that existing polymer models may be extended to create a predictive framework for the study of TE integration patterns. We suggest that these models may offer orthogonal and generic insights into the integration profiles (or "topography") of TEs across organisms. In addition, we provide simple polymer physics arguments and preliminary molecular dynamics simulations of TEs inserting into heterogeneously flexible polymers. By considering this simple model, we show how polymer folding and local flexibility may generically affect TE integration patterns. The preliminary discussion reported in this commentary is aimed to lay the foundations for a large-scale analysis of TE integration dynamics and topography as a function of the three-dimensional host genome