A Markov Chain Approach to Randomly Grown Graphs

A Markov chain approach to the study of randomly grown graphs is proposed and applied to some popular models that have found use in biology and elsewhere. For most randomly grown graphs used in biology, it is not known whether the graph or properties of the graph converge (in some sense) as the number of vertices becomes large. Particularly, we study the behaviour of the degree sequence, that is, the number of vertices with degree 0,1,…, in large graphs, and apply our results to the partial duplication model. We further illustrate the results by application to real data

Exact Analysis of Intrinsic Qualitative Features of Phosphorelays using Mathematical Models

Phosphorelays are a class of signaling mechanisms used by cells to respond to changes in their environment. Phosphorelays (of which two-component systems constitute a special case) are particularly abundant in prokaryotes and have been shown to be involved in many fundamental processes such as stress response, osmotic regulation, virulence, and chemotaxis. We develop a general model of phosphorelays extending existing models of phosphorelays and two-component systems. We analyze the model analytically under the assumption of mass-action kinetics and prove that a phosphorelay has a unique stable steady-state. Furthermore, we derive explicit functions relating stimulus to the response in any layer of a phosphorelay and show that a limited degree of ultrasensitivity (the ability to respond to changes in stimulus in a switch-like manner) in the bottom layer of a phosphorelay is an intrinsic feature which does not depend on any reaction rates or substrate amounts. On the other hand, we show how adjusting reaction rates and substrate amounts may lead to higher degrees of ultrasensitivity in intermediate layers. The explicit formulas also enable us to prove how the response changes with alterations in stimulus, kinetic parameters, and substrate amounts. Aside from providing biological insight, the formulas may also be used to avoid time-consuming simulations in numerical analyses and simulations

<i>Staphylococcus aureus</i> Bacteremia from Diffuse Muscular Infection Following Acupuncture Visualized by F-FDG PET/CT and MRI

We describe the clinical course of a 60-year old male admitted with Staphylococcus aureus bacteremia and back-pain. The patient was suspected of having spondylitis and treated as such with antibiotics; however, both fluorine-18 fluoro-2-deoxy-d-glucose (18F-FDG) positron-emission tomography and magnetic resonance imaging (MRI) with iv contrast showed significant inflammation of muscles and subcutaneous soft tissue in relation to the patients back and left shoulder, but no signs of the working diagnosis of spondylitis. The unusual location of the infection was not explained until a few days prior to being discharged when the patient reported visits to a local physiotherapist where he would have acupuncture performed for non-specific back pain. His last acupunctural procedure had been performed 6 days prior to admission. This case is, to our knowledge, the first to show muscular inflammation on both 18-F-FDG PET/CT and MRI following acupuncture due to S. aureus. This case highlights the need for clinicians to search for alternative explanations when imaging does not support the diagnosis