PTHR1 polymorphisms influence BMD variation through effects on the growing skeleton

We investigated whether polymorphisms in PTHR1 are associated with bone mineral density (BMD), to determine whether the association of this gene with BMD was due to effects on attainment of peak bone mass or effects on subsequent bone loss. The PTHR1 gene, including its 14 exons, their exon-intron boundaries, and 1,500 bp of its promoter region, was screened for polymorphisms by denaturing high-performance liquid chromatography (dHPLC) and sequencing in 36 osteoporotic cases. Eleven single-nucleotide polymorphisms (SNPs), one tetranucleotide repeat, and one tetranucleotide deletion were identified. A cohort of 634 families, including 1,236 men (39%) and 1,926 women (61%) ascertained with probands with low BMD (Z< -2.0) and the Children in Focus subset of the Avon Longitudinal Study of Parents and Children (ALSPAC) cohort (785 unrelated individuals, mean age 118 months), were genotyped for the five most informative SNPs (minor allele frequency >5%) and the tetranucleotide repeat. In our osteoporosis families, association was noted between lumbar spine BMD and alleles of a known functional tetranucleotide repeat (U4) in the PTHR1 promoter region (P = 0.042) and between two and three marker haplotypes of PTHR1 polymorphisms with lumbar spine, femoral neck, and total hip BMD (P = 0.021-0.047). This association was restricted to the youngest tertile of the population (age 16-39 years, P = 0.013-0.048). A similar association was found for the ALSPAC cohort: two marker haplotypes of SNPs A48609T and C52813T were associated with height (P = 0.006) and total body less head BMD (P = 0.02), corrected for age and gender, confirming the family findings. These findings suggest a role for PTHR1 variation in determining peak BMD.

The creative fulcrum : Where, how and why the creative workforce is growing

Contrary to the view that the creative workforce is shrinking, a decade of detailed research by the ARC Centre of Excellence for Creative Industries and Innovation (CCI) shows that the number of workers in creative occupations is growing strongly, and that these workers are spread right across the whole economy. Furthermore, these occupations can be thought of as a ‘creative fulcrum’ for innovations that leverage competitiveness in all sectors, and create positive job spirals that stimulate opportunities for many other occupation categories.

A growing good faith in contracts

The Supreme Court of Canada's ruling in Bhasin v Hrynew represents a significant step forward in harmonising the multiple strands of debate surrounding the existence of a good faith provision in common law contracting. Although a general principle of good faith (derived from Roman Law) is recognized by most civil law systems and a growing number of common law countries have embraced statutory provisions towards this end, Bhasin v Hrynew is argued to be a critical advance in catalysing uniform acceptance of good faith as a fundamental principle essential to support an increasingly integrated global commercial environment.

Exact solutions of coupled multispecies linear reaction–diffusion equations on a uniformly growing domain

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.

Exact solutions of linear reaction-diffusion on a uniformly growing domain: criteria for successful colonization

Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction—diffusion process on 0growing domain. Comparing our exact solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).