Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation

Simulation Approach for Timing Analysis of Genetic Logic Circuits

Constructing genetic logic circuits is an application of synthetic biology in which parts of the DNA of a living cell are engineered to perform a dedicated Boolean function triggered by an appropriate concentration of certain proteins or by different genetic components. These logic circuits work in a manner similar to electronic logic circuits, but they are much more stochastic and hence much harder to characterize. In this article, we introduce an approach to analyze the threshold value and timing of genetic logic circuits. We show how this approach can be used to analyze the timing behavior of single and cascaded genetic logic circuits. We further analyze the timing sensitivity of circuits by varying the degradation rates and concentrations. Our approach can be used not only to characterize the timing behavior but also to analyze the timing constraints of cascaded genetic logic circuits, a capability that we believe will be important for design automation in synthetic biology

Conformational spread as a mechanism for cooperativity in the bacterial flagellar switch

The bacterial flagellar switch that controls the direction of flagellar rotation during chemotaxis has a highly cooperative response. This has previously been understood in terms of the classic two-state, concerted model of allosteric regulation. Here, we used high-resolution optical microscopy to observe switching of single motors and uncover the stochastic multistate nature of the switch. Our observations are in detailed quantitative agreement with a recent general model of allosteric cooperativity that exhibits conformational spread—the stochastic growth and shrinkage of domains of adjacent subunits sharing a particular conformational state. We expect that conformational spread will be important in explaining cooperativity in other large signaling complexes

Glucose-lactate metabolic cooperation in cancer: insights from a spatial mathematical model and implications for targeted therapy

A recent study has hypothesised a glucose–lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose–lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system—although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity—and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wild-type hypoxia and only weakly with wild-type symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, thus raising the new question of what relationship might exist between symbiosis and tumour malignancy

An ordinary differential equation model for full thickness wounds and the effects of diabetes

Wound healing is a complex process in which a sequence of interrelated phases contributes to a reduction in wound size. For diabetic patients, many of these processes are compromised, so that wound healing slows down. In this paper we present a simple ordinary differential equation model for wound healing in which attention focusses on the dominant processes that contribute to closure of a full thickness wound. Asymptotic analysis of the resulting model reveals that normal healing occurs in stages: the initial and rapid elastic recoil of the wound is followed by a longer proliferative phase during which growth in the dermis dominates healing. At longer times, fibroblasts exert contractile forces on the dermal tissue, the resulting tension stimulating further dermal tissue growth and enhancing wound closure. By fitting the model to experimental data we find that the major difference between normal and diabetic healing is a marked reduction in the rate of dermal tissue growth for diabetic patients. The model is used to estimate the breakdown of dermal healing into two processes: tissue growth and contraction, the proportions of which provide information about the quality of the healed wound. We show further that increasing dermal tissue growth in the diabetic wound produces closure times similar to those associated with normal healing and we discuss the clinical implications of this hypothesised treatment

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

Orchestration of Network Services Across Multiple Operators: The 5G Exchange Prototype

Future 5G networks will rely on the coordinated allocation of compute, storage, and networking resources in order to meet the functional requirements of 5G services as well as guaranteeing efficient usage of the network infrastructure. However, the 5G service provisioning paradigm will also require a unified infrastructure service market that integrates multiple operators and technologies. The 5G Exchange (5GEx) project, building heavily on the Software-Defined Network (SDN) and the Network Function Virtualization (NFV) functionalities, tries to overcome this market and technology fragmentation by designing, implementing, and testing a multi-domain orchestrator (MdO) prototype for fast and automated Network Service (NS) provisioning over multiple-technologies and spanning across multiple operators. This paper presents a first implementation of the 5GEx MdO prototype obtained by extending existing open source software tools at the disposal of the 5GEx partners. The main functions of the 5GEx MdO prototype are showcased by demonstrating how it is possible to create and deploy NSs in the context of a Slice as a Service (SlaaS) use-case, based on a multi-operator scenario. The 5GEx MdO prototype performance is experimentally evaluated running validation tests within the 5GEx sandbox. The overall time required for the NS deployment has been evaluated considering NSs deployed across two operators

Endoscopic Management of Perforation of Right Hepatic Duct Following Non-Surgical Abdominal Trauma

Isolated bile duct injuries after blunt abdominal trauma are rare. Surgery is the usual mode of treatment. We report a patient with a right hepatic duct injury following blunt abdominal trauma who was managed successfully by endoscopic papillotomy

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