Mathematics in Modern Immunology

Mathematical and statistical methods enable multi-disciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, de ne measurable observables and reconcile disparate results. We collect a representative sample of studies in cell biology that illustrate the benefits of modelling-experimental collaborations and that have proven valuable or even ground-breaking. We conclude that it is possible to nd excellent examples of synergy between mathematical modelling and experiment in Immunology, which have brought signi cant insight that would not be available without these collaborations, but that much remains to be discovered

A Feynman integral in Lifshitz-point and Lorentz-violating theories in R^D ⨁ R<i>^m</i>

We evaluate a 1-loop, 2-point, massless Feynman integral ID,m(p,q) relevant for perturbative field theoretic calculations in strongly anisotropic d=D+m dimensional spaces given by the direct sum RD ⨁ Rm . Our results are valid in the whole convergence region of the integral for generic (noninteger) codimensions D and m. We obtain series expansions of ID,m(p,q) in terms of powers of the variable X:=4p2/q4, where p=|p|, q=|q|, p Є RD, q Є Rm, and in terms of generalised hypergeometric functions 3F2(−X), when X&lt;1. These are subsequently analytically continued to the complementary region X≥1. The asymptotic expansion in inverse powers of X1/2 is derived. The correctness of the results is supported by agreement with previously known special cases and extensive numerical calculations

A comparison of benzodiazepine and related drug use in Nova Scotia and Australia

Objective: Benzodiazepines can be a problem if used for long periods, or in at-risk populations, such as the elderly. We compared the use of benzodiazepine and related prescription medicines in Nova Scotia and Australia

Adaptive Significance of the Formation of Multi-Species Fish Spawning Aggregations near Submerged Capes

BACKGROUND: Many fishes are known to spawn at distinct geomorphological features such as submerged capes or "promontories," and the widespread use of these sites for spawning must imply some evolutionary advantage. Spawning at these capes is thought to result in rapid offshore transport of eggs, thereby reducing predation levels and facilitating dispersal to areas of suitable habitat. METHODOLOGY/PRINCIPAL FINDINGS: To test this "off-reef transport" hypothesis, we use a hydrodynamic model and explore the effects of topography on currents at submerged capes where spawning occurs and at similar capes where spawning does not occur, along the Mesoamerican Barrier Reef. All capes modeled in this study produced eddy-shedding regimes, but specific eddy attributes differed between spawning and non-spawning sites. Eddies at spawning sites were significantly stronger than those at non-spawning sites, and upwelling and fronts were the products of the eddy formation process. Frontal zones, present particularly at the edges of eddies near the shelf, may serve to retain larvae and nutrients. Spawning site eddies were also more predictable in terms of diameter and longevity. Passive particles released at spawning and control sites were dispersed from the release site at similar rates, but particles from spawning sites were more highly aggregated in their distributions than those from control sites, and remained closer to shore at all times. CONCLUSIONS/SIGNIFICANCE: Our findings contradict previous hypotheses that cape spawning leads to high egg dispersion due to offshore transport, and that they are attractive for spawning due to high, variable currents. Rather, we show that current regimes at spawning sites are more predictable, concentrate the eggs, and keep larvae closer to shore. These attributes would confer evolutionary advantages by maintaining relatively similar recruitment patterns year after year

A Critical Dialogue: Communicating with Type 2 Diabetes Patients about Cardiovascular Risk

Patients with type 2 diabetes mellitus (DM) are at increased risk for cardiovascular disease (CVD), and many patients are inadequately treated for risk factors such as hyperglycemia, hyperlipidemia, hypertension, and smoking. Providing individualized risk information in a clear and engaging manner may serve to encourage both patients and their physicians to intensify risk-reducing behaviors and therapies. This review outlines simple and effective methods for making CVD risk infomation understandable to persons of all levels of literacy and mathematical ability. To allow the patient to understand what might happen and how, personal risk factors should be clearly communicated and the potential consequences of a CVD event should be presented in a graphic but factual manner. Risk calculation software can provide CVD risk estimates, and the resulting information can be made understandable by assigning risk severity (eg, “high”) by comparing clinical parameters with accepted treatment targets and by comparing the individual's risk with that of the “average” person. Patients must also be informed about how they might reduce their CVD risk and be supported in these efforts. Thoughtful risk communication using these techniques can improve access to health information for individuals of low literacy, especially when interactive computer technology is employed. Research is needed to find the best methods for communicating risk in daily clinical practice

Biological Function and Molecular Mapping of M Antigen in Yeast Phase of Histoplasma capsulatum

Histoplasmosis, due to the intracellular fungus Histoplasma capsulatum, can be diagnosed by demonstrating the presence of antibodies specific to the immunodominant M antigen. However, the role of this protein in the pathogenesis of histoplasmosis has not been elucidated. We sought to structurally and immunologically characterize the protein, determine yeast cell surface expression, and confirm catalase activity. A 3D-rendering of the M antigen by homology modeling revealed that the structures and domains closely resemble characterized fungal catalases. We generated monoclonal antibodies (mAbs) to the protein and determined that the M antigen is present on the yeast cell surface and in cell wall/cell membrane preparations. Similarly, we found that the majority of catalase activity was in extracts containing fungal surface antigens and that the M antigen is not significantly secreted by live yeast cells. The mAbs also identified unique epitopes on the M antigen. The localization of the M antigen to the cell surface of H. capsulatum yeast and the characterization of the protein's major epitopes have important implications since it demonstrates that although the protein may participate in protecting the fungus against oxidative stress it is also accessible to host immune cells and antibody

Correction to: Water Resources in Africa under Global Change: Monitoring Surface Waters from Space

International audienc