Fractional models for the migration of biological cells in complex spatial domains

Travelling wave phenomena are observed in many biological applications. Mathematical theory of standard reaction-diffusion problems shows that simple partial differential equations exhibit travelling wave solutions with constant wavespeed and such models are used to describe, for example, waves of chemical concentrations, electrical signals, cell migration, waves of epidemics and population dynamics. However, as in the study of cell motion in complex spatial geometries, experimental data are often not consistent with constant wavespeed. Non-local spatial models have successfully been used to model anomalous diffusion and spatial heterogeneity in different physical contexts. In this paper, we develop a fractional model based on the Fisher-Kolmogoroff equation and analyse it for its wavespeed properties, attempting to relate the numerical results obtained from our simulations to experimental data describing enteric neural crest-derived cells migrating along the intact gut of mouse embryos. The model proposed essentially combines fractional and standard diffusion in different regions of the spatial domain and qualitatively reproduces the behaviour of neural crest-derived cells observed in the caecum and the hindgut of mouse embryos during in vivo experiments.

Children exposure assessment to ultrafine particles and black carbon: The role of transport and cooking activities

An accurate evaluation of the airborne particle dose-response relationship requires detailed measurements of the actual particle concentration levels that people are exposed to, in every microenvironment in which they reside. The aim of this work was to perform an exposure assessment of children in relation to two different aerosol species: ultrafine particles (UFPs) and black carbon (BC). To this purpose, personal exposure measurements, in terms of UFP and BC concentrations, were performed on 103 children aged 8-11 years (10.1 ± 1.1 years) using hand-held particle counters and aethalometers. Simultaneously, a time-activity diary and a portable GPS were used to determine the children’s daily time-activity pattern and estimate their inhaled dose of UFPs and BC. The median concentration to which the study population was exposed was found to be comparable to the high levels typically detected in urban traffic microenvironments, in terms of both particle number (2.2×104 part. cm-3) and BC (3.8 μg m-3) concentrations. Daily inhaled doses were also found to be relatively high and were equal to 3.35×1011 part. day-1 and 3.92×101 μg day-1 for UFPs and BC, respectively. Cooking and using transportation were recognized as the main activities contributing to overall daily exposure, when normalized according to their corresponding time contribution for UFPs and BC, respectively. Therefore, UFPs and BC could represent tracers of children exposure to particulate pollution from indoor cooking activities and transportation microenvironments, respectively.

Confirmation that Xq27 and Xq28 are susceptibility loci for migraine in independent pedigrees and a case-control cohort

Investigations into migraine genetics have suggested that susceptibility loci exist on the X chromosome. These reports are supported by evidence that demonstrates male probands as having a higher proportion of affected first-degree relatives as well as the female preponderance of 3:1 that the disorder displays. We have previously implicated the Xq24-28 locus in migraine using two independent multigenerational Australian pedigrees that demonstrated excess allele sharing at the Xq24, Xq27 and Xq28 loci. Here, we expand this work to investigate a further six independent migraine pedigrees using 11 microsatellite markers spanning the Xq27–28 region. Furthermore, 11 candidate genes are investigated in an Australian case-control cohort consisting of 500 cases and 500 controls. Microsatellite analysis showed evidence of excess allele sharing to the Xq27 marker DXS8043 (LOD* 1.38 P = 0.005) in MF879 whilst a second independent pedigree showed excess allele sharing to DXS8061 at Xq28 (LOD* 1.5 P = 0.004). Furthermore, analysis of these key markers in a case control cohort showed significant association to migraine in females at the DXS8043 marker (T1 P = 0.009) and association with MO at DXS8061 (T1 P = 0.05). Further analysis of 11 key genes across these regions showed significant association of a three-marker risk haplotype in the NSDHL gene at Xq28 (P = 0.0082). The results of this study add further support to the presence of migraine susceptibility loci on chromosome Xq27 and Xq28 as well as point to potential candidate genes in the regions that warrant further investigation.

Evidence for allelic association of the dopamine β-hydroxylase gene (DBH) with susceptibility to typical migraine

Migraine is a debilitating neurological disorder characterized by recurrent attacks of severe headache. The disorder is highly prevalent, affecting approximately 12% of Caucasian populations. It is well known that migraine has a strong genetic component, although the type and number of genes involved is not yet clear. However, the calcium channel gene, CACNA1A, on chromosome 19 contains mutations responsible for familial hemiplegic migraine, a rare and severe subtype of migraine. There is also evidence to suggest that serotonin- and dopamine-related genes may be involved in the pathogenesis of migraine. This study employed a linkage and association approach to investigate neurotransmitter-related migraine candidate genes. Polymorphisms within the dopamine beta-hydroxylase (DBH) gene, serotonin transporter gene (SERT), and dopamine receptor gene (DRD2) were tested in 177 unrelated Caucasian migraineurs and 182 control individuals. In addition, an independent sample of 82 families affected with migraine was examined. Unrelated case-control association analysis of a DBH intragenic dinucleotide polymorphism indicated altered allelic distribution between migraine and control groups (L2=16.53, P=0.019). Furthermore, the transmission/disequilibrium test, which was implemented on the family data, also indicated distortion of allele transmission for the same DBH marker (L2=4.44, P=0.035). Together, these results provide evidence for allelic association of the DBH gene with typical migraine susceptibility (Fisher's combined P value=0.006) and indicate that further research into the role of the DBH gene in the etiology of migraine is warranted.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

Diffusion-sensitive magnetic resonance spectroscopy and imaging in biomedical sciences

We present a mini-review of the development and contemporary applications of diffusion-sensitive nuclear magnetic resonance (NMR) techniques in biomedical sciences. Molecular diffusion is a fundamental physical phenomenon present in all biological systems. Due to the connection between experimentally measured diffusion metrics and the microscopic environment sensed by the diffusing molecules, diffusion measurements can be used for characterisation of molecular size, molecular binding and association, and the morphology of biological tissues. The emergence of magnetic resonance was instrumental to the development of biomedical applications of diffusion. We discuss the fundamental physical principles of diffusion NMR spectroscopy and diffusion MR imaging. The emphasis is placed on conceptual understanding, historical evolution and practical applications rather than complex technical details. Mathematical description of diffusion is presented to the extent that it is required for the basic understanding of the concepts. We present a wide range of spectroscopic and imaging applications of diffusion magnetic resonance, including colloidal drug delivery vehicles; protein association; characterisation of cell morphology; neural fibre tractography; cardiac imaging; and the imaging of load-bearing connective tissues. This paper is intended as an accessible introduction into the exciting and growing field of diffusion magnetic resonance.