Reflecting diffusions and hyperbolic Brownian motions in multidimensional spheres

Diffusion processes $(\underline{\bf X}_d(t))_{t\geq 0}$ moving inside spheres $S_R^d \subset\mathbb{R}^d$ and reflecting orthogonally on their surfaces $\partial S_R^d$ are considered. The stochastic differential equations governing the reflecting diffusions are presented and their kernels and distributions explicitly derived. Reflection is obtained by means of the inversion with respect to the sphere $S_R^d$. The particular cases of Ornstein-Uhlenbeck process and Brownian motion are examined in detail. The hyperbolic Brownian motion on the Poincar\`e half-space $\mathbb{H}_d$ is examined in the last part of the paper and its reflecting counterpart within hyperbolic spheres is studied. Finally a section is devoted to reflecting hyperbolic Brownian motion in the Poincar\`e disc $D$ within spheres concentric with $D$

Synergistic streptococcal phage λSA2 and B30 endolysins kill streptococci in cow milk and in a mouse model of mastitis

Bovine mastitis results in billion dollar losses annually in the United States alone. Streptococci are among the most relevant causative agents of this disease. Conventional antibiotic therapy is often unsuccessful and contributes to development of antibiotic resistance. Bacteriophage endolysins represent a new class of antimicrobials against these bacteria. In this work, we characterized the endolysins (lysins) of the streptococcal phages λSA2 and B30 and evaluated their potential as anti-mastitis agents. When tested in vitro against live streptococci, both enzymes exhibited near-optimum lytic activities at ionic strengths, pH, and Ca(2+) concentrations consistent with cow milk. When tested in combination in a checkerboard assay, the lysins were found to exhibit strong synergy. The λSA2 lysin displayed high activity in milk against Streptococcus dysgalactiae (reduction of CFU/ml by 3.5 log units at 100 μg/ml), Streptococcus agalactiae (2 log), and Streptococcus uberis (4 log), whereas the B30 lysin was less effective. In a mouse model of bovine mastitis, both enzymes significantly reduced intramammary concentrations of all three streptococcal species (except for B30 vs. S. dysgalactiae), and the effects on mammary gland wet weights and TNFα concentrations were consistent with these findings. Unexpectedly, the synergistic effect determined for the two enzymes in vitro was not observed in the mouse model. Overall, our results illustrate the potential of endolysins for treatment of Streptococcus-induced bovine mastitis