Combined surface acoustic wave and surface plasmon resonance measurement of collagen and fibrinogen layers

We use an instrument combining optical (surface plasmon resonance) and acoustic (Love mode acoustic wave device) real-time measurements on a same surface for the identification of water content in collagen and fibrinogen protein layers. After calibration of the surface acoustic wave device sensitivity by copper electrodeposition, the bound mass and its physical properties -- density and optical index -- are extracted from the complementary measurement techniques and lead to thickness and water ratio values compatible with the observed signal shifts. Such results are especially usefully for protein layers with a high water content as shown here for collagen on an hydrophobic surface. We obtain the following results: collagen layers include 70+/-20 % water and are 16+/-3 to 19+/-3 nm thick for bulk concentrations ranging from 30 to 300 ug/ml. Fibrinogen layers include 50+/-10 % water for layer thicknesses in the 6+/-1.5 to 13+/-2 nm range when the bulk concentration is in the 46 to 460 ug/ml range.Comment: 50 pages, 8 figures, 1 tabl

Front propagation directed by a line of fast diffusion: large diffusion and large time asymptotics

The system under study is a reaction-diffusion equation in a horizontal strip, coupled to a diffusion equation on its upper boundary via an exchange condition of the Robin type. This class of models was introduced by H. Berestycki, L. Rossi and the second author in order to model biological invasions directed by lines of fast diffusion. They proved, in particular, that the speed of invasion was enhanced by a fast diffusion on the line, the spreading velocity being asymptotically proportional to the square root of the fast diffusion coefficient. These results could be reduced, in the logistic case, to explicit algebraic computations. The goal of this paper is to prove that the same phenomenon holds, with a different type of nonlinearity, which precludes explicit computations. We discover a new transition phenomenon, that we explain in detail