Mathematical models for vulnerable plaques

A plaque is an accumulation and swelling in the artery walls and typically consists of cells, cell debris, lipids, calcium deposits and fibrous connective tissue. A person is likely to have many plaques inside his/her body even if they are healthy. However plaques may become "vulnerable", "high-risk" or "thrombosis-prone" if the person engages in a high-fat diet and does not exercise regularly. In this study group, we proposed two mathematical models to describe plaque growth and rupture. The first model is a mechanical one that approximately treats the plaque as an inflating elastic balloon. In this model, the pressure inside the core increases and then decreases suggesting that plaque stabilization and prevention of rupture is possible. The second model is a biochemical one that focuses on the role of MMPs in degrading the fibrous plaque cap. The cap stress, MMP concentration, plaque volume and cap thickness are coupled together in a system of phenomenological equations. The equations always predict an eventual rupture since the volume, stresses and MMP concentrations generally grow without bound. The main weakness of the model is that many of the important parameters that control the behavior of the plaque are unknown. The two simple models suggested by this group could serve as a springboard for more realistic theoretical studies. But most importantly, we hope they will motivate more experimental work to quantify some of the important mechanical and biochemical properties of vulnerable plaques

A Covariant Approach To Ashtekar's Canonical Gravity

A Lorentz and general co-ordinate co-variant form of canonical gravity, using Ashtekar's variables, is investigated. A co-variant treatment due to Crnkovic and Witten is used, in which a point in phase space represents a solution of the equations of motion and a symplectic functional two form is constructed which is Lorentz and general co-ordinate invariant. The subtleties and difficulties due to the complex nature of Ashtekar's variables are addressed and resolved.Comment: 18 pages, Plain Te

The application of plastic compression to modulate fibrin hydrogel mechanical properties.

The inherent biocompatibility of fibrin hydrogels makes them an attractive material for use in a wide range of tissue engineering applications. Despite this, their relatively low stiffness and high compliance limits their potential for certain orthopaedic applications. Enhanced mechanical properties are desirable so as to withstand surgical handling and in vivo loading after implantation and additionally, can provide important cues to cells seeded within the hydrogel. Standard methods used to enhance the mechanical properties of biological scaffolds such as chemical or thermal crosslinking cannot be used with fibrin hydrogels as cell seeding and gel formation occurs simultaneously. The objective of this study was to investigate the use of plastic compression as a means to improve the mechanical properties of chondrocyte-seeded fibrin hydrogels and to determine the influence of such compression on cell viability within these constructs. It was found that the application of 80% strain to fibrin hydrogels for 30 min (which resulted in a permanent strain of 47.4%) produced a 2.1-fold increase in the subsequent compressive modulus. Additionally, chondrocyte viability was maintained in the plastically compressed gels with significant cellular proliferation and extracellular matrix accumulation observed over 28 days of culture. In conclusion, plastic compression can be used to modulate the density and mechanical properties of cell-seeded fibrin hydrogels and represents a useful tool for both in theatre and in vitro tissue engineering applications

Feedback control architecture and the bacterial chemotaxis network.

PMCID: PMC3088647This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Bacteria move towards favourable and away from toxic environments by changing their swimming pattern. This response is regulated by the chemotaxis signalling pathway, which has an important feature: it uses feedback to 'reset' (adapt) the bacterial sensing ability, which allows the bacteria to sense a range of background environmental changes. The role of this feedback has been studied extensively in the simple chemotaxis pathway of Escherichia coli. However it has been recently found that the majority of bacteria have multiple chemotaxis homologues of the E. coli proteins, resulting in more complex pathways. In this paper we investigate the configuration and role of feedback in Rhodobacter sphaeroides, a bacterium containing multiple homologues of the chemotaxis proteins found in E. coli. Multiple proteins could produce different possible feedback configurations, each having different chemotactic performance qualities and levels of robustness to variations and uncertainties in biological parameters and to intracellular noise. We develop four models corresponding to different feedback configurations. Using a series of carefully designed experiments we discriminate between these models and invalidate three of them. When these models are examined in terms of robustness to noise and parametric uncertainties, we find that the non-invalidated model is superior to the others. Moreover, it has a 'cascade control' feedback architecture which is used extensively in engineering to improve system performance, including robustness. Given that the majority of bacteria are known to have multiple chemotaxis pathways, in this paper we show that some feedback architectures allow them to have better performance than others. In particular, cascade control may be an important feature in achieving robust functionality in more complex signalling pathways and in improving their performance

A Bipolar Clamp Mechanism for Activation of Jak-Family Protein Tyrosine Kinases

Most cell surface receptors for growth factors and cytokines dimerize in order to mediate signal transduction. For many such receptors, the Janus kinase (Jak) family of non-receptor protein tyrosine kinases are recruited in pairs and juxtaposed by dimerized receptor complexes in order to activate one another by trans-phosphorylation. An alternative mechanism for Jak trans-phosphorylation has been proposed in which the phosphorylated kinase interacts with the Src homology 2 (SH2) domain of SH2-B, a unique adaptor protein with the capacity to homo-dimerize. Building on a rule-based kinetic modeling approach that considers the concerted nature and combinatorial complexity of modular protein domain interactions, we examine these mechanisms in detail, focusing on the growth hormone (GH) receptor/Jak2/SH2-Bβ system. The modeling results suggest that, whereas Jak2-(SH2-Bβ)2-Jak2 heterotetramers are scarcely expected to affect Jak2 phosphorylation, SH2-Bβ and dimerized receptors synergistically promote Jak2 trans-activation in the context of intracellular signaling. Analysis of the results revealed a unique mechanism whereby SH2-B and receptor dimers constitute a bipolar ‘clamp’ that stabilizes the active configuration of two Jak2 molecules in the same macro-complex

The fidelity of dynamic signaling by noisy biomolecular networks

This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.We acknowledge support from a Medical Research Council and Engineering and Physical Sciences Council funded Fellowship in Biomedical Informatics (CGB) and a Scottish Universities Life Sciences Alliance chair in Systems Biology (PSS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Calibration of X-ray imaging devices for accurate intensity measurement

National Security Technologies (NSTec) has developed calibration procedures for X-ray imaging systems. The X-ray sources that are used for calibration are both diode type and diode/fluorescer combinations. Calibrating the X-ray detectors is key to accurate calibration of the X-ray sources. Both energy dispersive detectors and photodiodes measuring total flux were used. We have developed calibration techniques for the detectors using radioactive sources that are traceable to the National Institute of Standards and Technology (NIST). The German synchrotron at Physikalische Technische Bundestalt (PTB) is used to calibrate silicon photodiodes over the energy range from 50 eV to 60 keV. The measurements on X-ray cameras made using the NSTec X-ray sources have included quantum efficiency averaged over all pixels, camera counts per photon per pixel, and response variation across the sensor. The instrumentation required to accomplish the calibrations is described. X-ray energies ranged from 720 eV to 22.7 keV. The X-ray sources produce narrow energy bands, allowing us to determine the properties as a function of X-ray energy. The calibrations were done for several types of imaging devices. There were back illuminated and front illuminated CCD (charge coupled device) sensors, and a CID (charge injection device) type camera. The CCD and CID camera types differ significantly in some of their properties that affect the accuracy of X-ray intensity measurements. All cameras discussed here are silicon based. The measurements of quantum efficiency variation with X-ray energy are compared to models for the sensor structure. Cameras that are not back-thinned are compared to those that are

Second Order Perturbations in the Randall-Sundrum Infinite Brane-World Model

We discuss the non-linear gravitational interactions in the Randall-Sundrum single brane model. If we naively write down the 4-dimensional effective action integrating over the fifth dimension with the aid of the decomposition with respect to eigen modes of 4-dimensional d'Alembertian, the Kaluza-Klein mode coupling seems to be ill-defined. We carefully analyze second order perturbations of the gravitational field induced on the 3-brane under the assumption of the static and axial-symmetric 5-dimensional metric. It is shown that there remains no pathological feature in the Kaluza-Klein mode coupling after the summation over all different mass modes. Furthermore, the leading Kaluza-Klein corrections are shown to be sufficiently suppressed in comparison with the leading order term which is obtained by the zero mode truncation. We confirm that the 4-dimensional Einstein gravity is approximately recovered on the 3-brane up to second order perturbations.Comment: 15 pages, 2 figures, comment and reference added, typos correcte

Communitarian perspectives on social enterprise

Concepts of social enterprise have been debated repeatedly, and continue to cause confusion. In this paper, a meta-theoretical framework is developed through discussion of individualist and communitarian philosophy. Philosophers from both traditions build social theories that emphasise either consensus (a unitarist outlook) or diversity (a pluralist outlook). The various discourses in corporate governance reflect these assumptions and create four distinct approaches that impact on the relationship between capital and labour. In rejecting the traditional discourse of private enterprise, social enterprises have adopted other approaches to tackle social exclusion, each derived from different underlying beliefs about the purpose of enterprise and the nature of governance. The theoretical framework offers a way to understand the diversity found within the sector, including the newly constituted Community Interest Company (CIC).</p