A two-fluid model for tissue growth within\ud a dynamic flow environment

We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89).\ud \ud The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population

Environment of compact extragalactic radio sources

We have studied the interrelation of young AGN with their hosts. The objects of study are the young and powerful GPS and CSS radio sources. Due to their small size, GPS and CSS sources are excellent probes of this relation. Furhthermore, their young age allows us to compare them to the larger, old radio sources and establish a time-line evolution of this relation. Combining imaging and spectroscopy at UV, optical and radio wavelengths we find evidence of strong interaction between the host and the radio source. The presence and expansion of the radio source clearly affects the properties and evolution of the host. Furthermore, the radio source and host significantly affect each other's evolution. We describe our results and how these interactions take place.Comment: 6 pages. To appear in "Highlights of Spanisg astrophysics IV. Proceedings of the VII scientific meeting of the Spanish Astronomical Society". Editors: F. Figueras, J.M. Girart, M.Hernanz, C. Jordi. Springe

Optical spectroscopy of faint gigahertz peaked spectrum sources

We present spectroscopic observations of a sample of faint Gigahertz Peaked Spectrum (GPS) radio sources drawn from the Westerbork Northern Sky Survey (WENSS). Redshifts have been determined for 19 (40%) of the objects. The optical spectra of the GPS sources identified with low redshift galaxies show deep stellar absorption features. This confirms previous suggestions that their optical light is not significantly contaminated by AGN-related emission, but is dominated by a population of old (>9 Gyr) and metal-rich (>0.2 [Fe/H]) stars, justifying the use of these (probably) young radio sources as probes of galaxy evolution. The optical spectra of GPS sources identified with quasars are indistinguishable from those of flat spectrum quasars, and clearly different from the spectra of Compact Steep Spectrum (CSS) quasars. The redshift distribution of the GPS quasars in our radio-faint sample is comparable to that of the bright samples presented in the literature, peaking at z ~ 2-3. It is unlikely that a significant population of low redshift GPS quasars is missed due to selection effects in our sample. We therefore claim that there is a genuine difference between the redshift distributions of GPS galaxies and quasars, which, because it is present in both the radio-faint and bright samples, can not be due to a redshift-luminosity degeneracy. It is therefore unlikely that the GPS quasars and galaxies are unified by orientation, unless the quasar opening angle is a strong function of redshift. We suggest that the GPS quasars and galaxies are unrelated populations and just happen to have identical observed radio-spectral properties, and hypothesise that GPS quasars are a sub-class of flat spectrum quasars.Comment: LaTeX, 13 pages. Accepted by MNRAS. For related papers see http://www.ast.cam.ac.uk/~snelle

Multiscale analysis of pattern formation via intercellular signalling

Lateral inhibition, a juxtacrine signalling mechanism by which a cell adopting a particular fate inhibits neighbouring cells from doing likewise, has been shown to be a robust mechanism for the formation of fine-grained spatial patterns (in which adjacent cells in developing tissues diverge to achieve contrasting states of differentiation), provided that there is sufficiently strong feedback. The fine-grained nature of these patterns poses problems for analysis via traditional continuum methods since these require that significant variation takes place only over lengthscales much larger than an individual cell and such systems have therefore been investigated primarily using discrete methods. Here, however, we apply a multiscale method to derive systematically a continuum model from the discrete Delta-Notch signalling model of Collier \emph{et al.} (Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling, \emph{J. Theor. Biol.}, 183, 1996, 429--446) under particular assumptions on the parameters, which we use to analyse the generation of fine-grained patterns. We show that, on the macroscale, the contact-dependent juxtacrine signalling interaction manifests itself as linear diffusion, motivating the use of reaction-diffusion-based models for such cell-signalling systems. We also analyse the travelling-wave behaviour of our system, obtaining good quantitative agreement with the discrete system

The isolation of spatial patterning modes in a mathematical model of juxtacrine cell signalling

Juxtacrine signalling mechanisms are known to be crucial in tissue and organ development, leading to spatial patterns in gene expression. We investigate the patterning behaviour of a discrete model of juxtacrine cell signalling due to Owen \& Sherratt (\emph{Math. Biosci.}, 1998, {\bf 153}(2):125--150) in which ligand molecules, unoccupied receptors and bound ligand-receptor complexes are modelled. Feedback between the ligand and receptor production and the level of bound receptors is incorporated. By isolating two parameters associated with the feedback strength and employing numerical simulation, linear stability and bifurcation analysis, the pattern-forming behaviour of the model is analysed under regimes corresponding to lateral inhibition and induction. Linear analysis of this model fails to capture the patterning behaviour exhibited in numerical simulations. Via bifurcation analysis we show that, since the majority of periodic patterns fold subcritically from the homogeneous steady state, a wide variety of stable patterns exists at a given parameter set, providing an explanation for this failure. The dominant pattern is isolated via numerical simulation. Additionally, by sampling patterns of non-integer wavelength on a discrete mesh, we highlight a disparity between the continuous and discrete representations of signalling mechanisms: in the continuous case, patterns of arbitrary wavelength are possible, while sampling such patterns on a discrete mesh leads to longer wavelength harmonics being selected where the wavelength is rational; in the irrational case, the resulting aperiodic patterns exhibit `local periodicity', being constructed from distorted stable shorter-wavelength patterns. This feature is consistent with experimentally observed patterns, which typically display approximate short-range periodicity with defects

Extended emission around GPS radio sources

Extended radio emission detected around a sample of GHz Peaked Spectrum (GPS) radio sources is discussed. Evidence for extended emission which is related to the GPS source is found in 6 objects out of 33. Three objects are associated with quasars with core-jet pc-scale morphology, and three are identified with galaxies with symmetric (CSO) radio morphology. We conclude that the core-jet GPS quasars are likely to be beamed objects with a continuous supply of energy from the core to the kpc scale. It is also possible that low surface brightness extended radio emission is present in other GPS quasars but the emission is below our detection limit due to the high redshifts of the objects. On the other hand, the CSO/galaxies with extended large scale emission may be rejuvenated sources where the extended emission is the relic of previous activity. In general, the presence of large scale emission associated with GPS galaxies is uncommon, suggesting that in the context of the recurrent activity model, the time scale between subsequent bursts is in general longer than the radiative lifetime of the radio emission from the earlier activity.Comment: 18 paged, 18 figures, accepted for publication on A&

Atomic hydrogen in the one-sided "compact double" radio galaxy 2050+364

European VLBI Network spectral imaging of the "compact double" radio source 2050+364 in the UHF band at 1049 MHz has resolved the HI absorbing region, and has shown a faint continuum component to the North (N), in addition to the well-known East-West double (E, W). Re-examination of VLBI continuum images at multiple frequencies suggests that 2050+364 may well be a one-sided core-jet source, which appears as a double over a limited frequency range. One of the dominant features, W, would then be the innermost visible portion of the jet, and could be at or adjacent to the canonical radio core. The other, E, is probably related to shocks at a sudden bend of the jet, towards extended steep-spectrum region N. A remarkably deep and narrow HI absorption line component extends over the entire projected extent of 2050+364. It coincides in velocity with the [OIII] optical doublet lines to within 10 km/s. This HI absorption could arise in the atomic cores of NLR clouds, and the motion in the NLR is then remarkably coherent both along the line-of-sight and across a projected distance of > 300 pc on the plane of the sky. Broader, shallower HI absorption at lower velocities covers only the plausible core area W. This absorption could be due to gas which is either being entrained by the inner jet or is flowing out from the accretion region; it could be related to the BLR.Comment: 10 pages, 7 figures. Accepted in A&

The interplay between tissue growth and scaffold degradation in engineered tissue constructs

In vitro tissue engineering is emerging as a potential tool to meet the high demand for replacement tissue, caused by the increased incidence of tissue degeneration and damage. A key challenge in this field is ensuring that the mechanical properties of the engineered tissue are appropriate for the in vivo environment. Achieving this goal will require detailed understanding of the interplay between cell proliferation, extracellular matrix (ECM) deposition and scaffold degradation.\ud \ud In this paper, we use a mathematical model (based upon a multiphase continuum framework) to investigate the interplay between tissue growth and scaffold degradation during tissue construct evolution in vitro. Our model accommodates a cell population and culture medium, modelled as viscous fluids, together with a porous scaffold and ECM deposited by the cells, represented as rigid porous materials. We focus on tissue growth within a perfusion bioreactor system, and investigate how the predicted tissue composition is altered under the influence of (i) differential interactions between cells and the supporting scaffold and their associated ECM, (ii) scaffold degradation, and (iii) mechanotransduction-regulated cell proliferation and ECM deposition.\ud \ud Numerical simulation of the model equations reveals that scaffold heterogeneity typical of that obtained from μCT scans of tissue engineering scaffolds can lead to significant variation in the flow-induced mechanical stimuli experienced by cells seeded in the scaffold. This leads to strong heterogeneity in the deposition of ECM. Furthermore, preferential adherence of cells to the ECM in favour of the artificial scaffold appears to have no significant influence on the eventual construct composition; adherence of cells to these supporting structures does, however, lead to cell and ECM distributions which mimic and exaggerate the heterogeneity of the underlying scaffold. Such phenomena have important ramifications for the mechanical integrity of engineered tissue constructs and their suitability for implantation in vivo