Hubble's law and faster than light expansion speeds

Naively applying Hubble's law to a sufficiently distant object gives a receding velocity larger than the speed of light. By discussing a very similar situation in special relativity, we argue that Hubble's law is meaningful only for nearby objects with non-relativistic receding speeds. To support this claim, we note that in a curved spacetime manifold it is not possible to directly compare tangent vectors at different points, and thus there is no natural definition of relative velocity between two spatially separated objects in cosmology. We clarify the geometrical meaning of the Hubble's receding speed v by showing that in a Friedmann-Robertson-Walker spacetime if the four-velocity vector of a comoving object is parallel-transported along the straight line in flat comoving coordinates to the position of a second comoving object, then v/c actually becomes the rapidity of the local Lorentz transformation, which maps the fixed four-velocity vector to the transported one.Comment: 5 pages, 2 figures, to appear in Am. J. Phy

Isoform-selective susceptibility of DISC1/phosphodiesterase-4 complexes to dissociation by elevated intracellular cAMP levels

Disrupted-in-schizophrenia 1 (DISC1) is a genetic susceptibility factor for schizophrenia and related severe psychiatric conditions. DISC1 is a multifunctional scaffold protein that is able to interact with several proteins, including the independently identified schizophrenia risk factor phosphodiesterase-4B (PDE4B). Here we report that the 100 kDa full-length DISC1 isoform (fl-DISC1) can bind members of each of the four gene, cAMP-specific PDE4 family. Elevation of intracellular cAMP levels, so as to activate protein kinase A, caused the release of PDE4D3 and PDE4C2 isoforms from fl-DISC1 while not affecting binding of PDE4B1 and PDE4A5 isoforms. Using a peptide array strategy, we show that PDE4D3 binds fl-DISC1 through two regions found in common with PDE4B isoforms, the interaction of which is supplemented because of the presence of additional PDE4B-specific binding sites. We propose that the additional binding sites found in PDE4B1 underpin its resistance to release during cAMP elevation. We identify, for the first time, a functional distinction between the 100 kDa long DISC1 isoform and the short 71 kDa isoform. Thus, changes in the expression pattern of DISC1 and PDE4 isoforms offers a means to reprogram their interaction and to determine whether the PDE4 sequestered by DISC1 is released after cAMP elevation. The PDE4B-specific binding sites encompass point mutations in mouse Disc1 that confer phenotypes related to schizophrenia and depression and that affect binding to PDE4B. Thus, genetic variation in DISC1 and PDE4 that influence either isoform expression or docking site functioning may directly affect psychopathology

A mathematical investigation into the uptake kinetics of nanoparticles in vitro

Nanoparticles have the potential to increase the efficacy of anticancer drugs whilst reducing off-target side effects. However, there remain uncertainties regarding the cellular uptake kinetics of nanoparticles which could have implications for nanoparticle design and delivery. Polymersomes are nanoparticle candidates for cancer therapy which encapsulate chemotherapy drugs. Here we develop a mathematical model to simulate the uptake of polymersomes via endocytosis, a process by which polymersomes bind to the cell surface before becoming internalised by the cell where they then break down, releasing their contents which could include chemotherapy drugs. We focus on two in vitro configurations relevant to the testing and development of cancer therapies: a well-mixed culture model and a tumour spheroid setup. Our mathematical model of the well-mixed culture model comprises a set of coupled ordinary differential equations for the unbound and bound polymersomes and associated binding dynamics. Using a singular perturbation analysis we identify an optimal number of ligands on the polymersome surface which maximises internalised polymersomes and thus intracellular chemotherapy drug concentration. In our mathematical model of the spheroid, a multiphase system of partial differential equations is developed to describe the spatial and temporal distribution of bound and unbound polymersomes via advection and diffusion, alongside oxygen, tumour growth, cell proliferation and viability. Consistent with experimental observations, the model predicts the evolution of oxygen gradients leading to a necrotic core. We investigate the impact of two different internalisation functions on spheroid growth, a constant and a bond dependent function. It was found that the constant function yields faster uptake and therefore chemotherapy delivery. We also show how various parameters, such as spheroid permeability, lead to travelling wave or steady-state solutions

Development and characterisation of in vitro human oral mucosal equivalents derived from immortalised oral keratinocytes.

Tissue engineered oral mucosal equivalents (OME) are being increasingly used to measure toxicity, drug delivery, and to model oral diseases. Current OME are mainly comprised of normal oral keratinocytes (NOK) cultured on top of a normal oral fibroblasts (NOF)-containing matrix. However, the commercial supply of NOK is limited, restricting widespread use of these mucosal models. In addition, NOK suffer from poor longevity and donor-to-donor variability. Therefore, we constructed, characterised and tested the functionality of oral mucosal equivalents based on commercial TERT2-immortalised oral keratinocytes (FNB6) in order to produce a more readily available alternative to NOK-based OME. FNB6 OME cultured at an air-to-liquid interface for 14 days exhibited expression of differentiation markers cytokeratin 13 in the suprabasal layers and cytokeratin 14 in basal layer of the epithelium. Proliferating cells were restricted to the basal epithelium and there was immuno-positive expression of E-cadherin confirming the presence of established cell-to-cell contacts. The histology and expression of these structural markers paralleled those observed in the normal oral mucosa and NOK-based models. Upon stimulation with TNFα & IL-1, FNB6 OME displayed a similar global gene expression profile to NOK-based OME with increased expression of many common pro-inflammatory molecules such as chemokines (CXCL8), cytokines (IL-6) and adhesion molecules (ICAM-1) when analysed by gene array and qPCR. Similarly, pathway analysis showed that both FNB6 and NOK models initiated similar intracellular signalling upon stimulation. Gene expression in FNB6 OME was more consistent than NOK-based OME that suffered from donor variation in response to stimuli. Mucosal equivalents based on immortalised FNB6 cells are accessible, reproducible and will provide an alternative animal experimental system for studying mucosal drug delivery systems, host-pathogen interactions and drug-induced toxicity

Implementing telephone triage in general practice: a process evaluation of a cluster randomised controlled trial

Background: Telephone triage represents one strategy to manage demand for face-to-face GP appointments in primary care. However, limited evidence exists of the challenges GP practices face in implementing telephone triage. We conducted a qualitative process evaluation alongside a UK-based cluster randomised trial (ESTEEM) which compared the impact of GP-led and nurse-led telephone triage with usual care on primary care workload, cost, patient experience, and safety for patients requesting a same-day GP consultation. The aim of the process study was to provide insights into the observed effects of the ESTEEM trial from the perspectives of staff and patients, and to specify the circumstances under which triage is likely to be successfully implemented. Here we report perspectives of staff. Methods: The intervention comprised implementation of either GP-led or nurse-led telephone triage for a period of 2-3 months. A qualitative evaluation was conducted using staff interviews recruited from eight general practices (4 GP triage, 4 Nurse triage) in the UK, implementing triage as part of the ESTEEM trial. Qualitative interviews were undertaken with 44 staff members in GP triage and nurse triage practices (16 GPs, 8 nurses, 7 practice managers, 13 administrative staff). Results: Staff reported diverse experiences and perceptions regarding the implementation of telephone triage, its effects on workload, and on the benefits of triage. Such diversity were explained by the different ways triage was organised, the staffing models used to support triage, how the introduction of triage was communicated across practice staff, and by how staff roles were reconfigured as a result of implementing triage. Conclusion: The findings from the process evaluation offer insight into the range of ways GP practices participating in ESTEEM implemented telephone triage, and the circumstances under which telephone triage can be successfully implemented beyond the context of a clinical trial. Staff experiences and perceptions of telephone triage are shaped by the way practices communicate with staff, prepare for and sustain the changes required to implement triage effectively, as well as by existing practice culture, and staff and patient behaviour arising in response to the changes made. Trial registration: Current Controlled Trials ISRCTN20687662. Registered 28 May 2009

Challenging Social Cognition Models of Adherence:Cycles of Discourse, Historical Bodies, and Interactional Order

Attempts to model individual beliefs as a means of predicting how people follow clinical advice have dominated adherence research, but with limited success. In this article, we challenge assumptions underlying this individualistic philosophy and propose an alternative formulation of context and its relationship with individual actions related to illness. Borrowing from Scollon and Scollon’s three elements of social action – “historical body,” “interaction order,” and “discourses in place” – we construct an alternative set of research methods and demonstrate their application with an example of a person talking about asthma management. We argue that talk- or illness-related behavior, both viewed as forms of social action, manifest themselves as an intersection of cycles of discourse, shifting as individuals move through these cycles across time and space. We finish by discussing how these dynamics of social action can be studied and how clinicians might use this understanding when negotiating treatment with patients