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

Optical Activity From Extra Dimension

Optical activity, like Faraday effect, is a rotation of the plane of polarization of propagating light in a medium and can be attributed to different sources with distinct signatures. In this note we discuss the effect of optical activity {\it{in vacuum}} due to Kaluza-Klein scalar field $\phi$, in the presence of an external electro-magnetic field. The astrophysical implication of this effect is indicated. We also point out the possibility of observing the same in laboratory conditions.Comment: Four Page

Weak Interactions in Binary Mixtures of Chlorobenzene & Bromobenzene with o-, m- & p-Xylenes

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Evidence-based decision support for pediatric rheumatology reduces diagnostic errors.

BACKGROUND: The number of trained specialists world-wide is insufficient to serve all children with pediatric rheumatologic disorders, even in the countries with robust medical resources. We evaluated the potential of diagnostic decision support software (DDSS) to alleviate this shortage by assessing the ability of such software to improve the diagnostic accuracy of non-specialists. METHODS: Using vignettes of actual clinical cases, clinician testers generated a differential diagnosis before and after using diagnostic decision support software. The evaluation used the SimulConsult® DDSS tool, based on Bayesian pattern matching with temporal onset of each finding in each disease. The tool covered 5405 diseases (averaging 22 findings per disease). Rheumatology content in the database was developed using both primary references and textbooks. The frequency, timing, age of onset and age of disappearance of findings, as well as their incidence, treatability, and heritability were taken into account in order to guide diagnostic decision making. These capabilities allowed key information such as pertinent negatives and evolution over time to be used in the computations. Efficacy was measured by comparing whether the correct condition was included in the differential diagnosis generated by clinicians before using the software ( unaided ), versus after use of the DDSS ( aided ). RESULTS: The 26 clinicians demonstrated a significant reduction in diagnostic errors following introduction of the software, from 28% errors while unaided to 15% using decision support (p \u3c 0.0001). Improvement was greatest for emergency medicine physicians (p = 0.013) and clinicians in practice for less than 10 years (p = 0.012). This error reduction occurred despite the fact that testers employed an open book approach to generate their initial lists of potential diagnoses, spending an average of 8.6 min using printed and electronic sources of medical information before using the diagnostic software. CONCLUSIONS: These findings suggest that decision support can reduce diagnostic errors and improve use of relevant information by generalists. Such assistance could potentially help relieve the shortage of experts in pediatric rheumatology and similarly underserved specialties by improving generalists\u27 ability to evaluate and diagnose patients presenting with musculoskeletal complaints. TRIAL REGISTRATION: ClinicalTrials.gov ID: NCT02205086

Cell proliferation within small intestinal crypts is the principal driving force for cell migration on villi

The functional integrity of the intestinal epithelial barrier relies on tight coordination of cell proliferation and migration, with failure to regulate these processes resulting in disease. It is not known whether cell proliferation is sufficient to drive epithelial cell migration during homoeostatic turnover of the epithelium. Nor is it known precisely how villus cell migration is affected when proliferation is perturbed. Some reports suggest that proliferation and migration may not be related while other studies support a direct relationship. We used established cell-tracking methods based on thymine analog cell labeling and developed tailored mathematical models to quantify cell proliferation and migration under normal conditions and when proliferation is reduced and when it is temporarily halted. We found that epithelial cell migration velocities along the villi are coupled to cell proliferation rates within the crypts in all conditions. Furthermore, halting and resuming proliferation results in the synchronized response of cell migration on the villi. We conclude that cell proliferation within the crypt is the primary force that drives cell migration along the villus. This methodology can be applied to interrogate intestinal epithelial dynamics and characterize situations in which processes involved in cell turnover become uncoupled, including pharmacological treatments and disease models

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

A theoretical framework for transitioning from patient-level to population-scale epidemiological dynamics:influenza A as a case study

Multi-scale epidemic forecasting models have been used to inform population-scale predictions with within-host models and/or infection data collected in longitudinal cohort studies. However, most multi-scale models are complex and require significant modelling expertise to run. We formulate an alternative multi-scale modelling framework using a compartmental model with multiple infected stages. In the large-compartment limit, our easy-to-use framework generates identical results compared to previous more complicated approaches. We apply our framework to the case study of influenza A in humans. By using a viral dynamics model to generate synthetic patient-level data, we explore the effects of limited and inaccurate patient data on the accuracy of population-scale forecasts. If infection data are collected daily, we find that a cohort of at least 40 patients is required for a mean population-scale forecasting error below 10%. Forecasting errors may be reduced by including more patients in future cohort studies or by increasing the frequency of observations for each patient. Our work, therefore, provides not only an accessible epidemiological modelling framework but also an insight into the data required for accurate forecasting using multi-scale models

Extragalactic Radio Continuum Surveys and the Transformation of Radio Astronomy

Next-generation radio surveys are about to transform radio astronomy by discovering and studying tens of millions of previously unknown radio sources. These surveys will provide new insights to understand the evolution of galaxies, measuring the evolution of the cosmic star formation rate, and rivalling traditional techniques in the measurement of fundamental cosmological parameters. By observing a new volume of observational parameter space, they are also likely to discover unexpected new phenomena. This review traces the evolution of extragalactic radio continuum surveys from the earliest days of radio astronomy to the present, and identifies the challenges that must be overcome to achieve this transformational change.Comment: To be published in Nature Astronomy 18 Sept 201

Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling

In many developing tissues, adjacent cells diverge in character so as to create a fine-grained pattern of cells in contrasting states of differentiation. It has been proposed that such patterns can be generated through lateral inhibition—a type cells–cell interaction whereby a cell that adopts a particular fate inhibits its immediate neighbours from doing likewise. Lateral inhibition is well documented in flies, worms and vertebrates. In all of these organisms, the transmembrane proteins Notch and Delta (or their homologues) have been identified as mediators of the interaction—Notch as receptor, Delta as its ligand on adjacent cells. However, it is not clear under precisely what conditions the Delta-Notch mechanism of lateral inhibition can generate the observed types of pattern, or indeed whether this mechanism is capable of generating such patterns by itself. Here we construct and analyse a simple and general mathematical model of such contact-mediated lateral inhibition. In accordance with experimental data, the model postulates that receipt of inhibition (i.e. activation of Notch) diminishes the ability to deliver inhibition (i.e. to produce active Delta). This gives rise to a feedback loop that can amplify differences between adjacent cells. We investigate the pattern-forming potential and temporal behavior of this model both analytically and through numerical simulation. Inhomogeneities are self-amplifying and develop without need of any other machinery, provided the feedback is sufficiently strong. For a wide range of initial and boundary conditions, the model generates fine-grained patterns similar to those observed in living systems