Recent advances on the global regularity for irrotational water waves.

We review recent progress on the long-time regularity of solutions of the Cauchy problem for the water waves equations, in two and three dimensions. We begin by introducing the free boundary Euler equations and discussing the local existence of solutions using the paradifferential approach. We then describe in a unified framework, using the Eulerian formulation, global existence results for three- and two-dimensional gravity waves, and our joint result (with Deng and Pausader) on global regularity for the gravity-capillary model in three dimensions. We conclude this review with a short discussion about the formation of singularities and give a few additional references to other interesting topics in the theory.This article is part of the theme issue 'Nonlinear water waves'.

Interactions between Borrelia burgdorferi and eukaryote cells: comparative ultrastructural aspects.

In the present study, mammalian VERO cells, human polymorphonuclear leukocytes (PMN) and mouse peritoneal macrophages (MPM) were coincubated with B31 Borrelia burgdorferi strain (Bb) and examined by transmission electron microscopy. The results indicate that the spirochete adheres to the mammalian cells mainly by the apical pole and less frequently by the lateral wall. In VERO cells and MPM cell penetration is accomplished especially by cytoplasmic membrane destruction, the spirochete appearing free in the cytoplasm, but also by phagocytosis. In this latter case the pathogen is seen in phagosome. In PMN the internalization takes place exclusively by phagocytosis, the spirochete undergoing destruction in phagosomes. Sometimes an alteration of the phagosomal membrane is observable, probably produced by the pathogen as a mechanism to avoid fusion with the lysosome. Other aspects indicate the contribution of the parasitized cell cytoskeleton to the spreading of Borrelia to adjacent cells. MPM does not represent a very efficient barrier against Bb, as can be seen from the cellular behaviour of the spirochetes in this study, PMN seems to a more efficient barrier, by its unique capacity to destroy the microorganism after phagocytosis.

Presence of IgE class antibodies with cardiolipinic and treponemal specificity in syphilis. Quantitative evaluation by IgE prist radio-immuno-assay.

60 serum samples (reactive in VDRL, ELISA-Reiter, FTA-Abs tests) from 25-45 years old male patients with untreated latent syphilis (EL) (30 cases) and persistent positive treated syphilis (ET+) (30 cases) were tested for IgE by IgE-PRIST. On 30 sera from 25-45 years old male healthy persons, normal mean value for serum IgE was established: 159.63 +/- 124.09 U/ml. Cardiolipin and group treponemal IgE fractions were indirectly calculated by the difference between the specific activity induced by sera as such and that induced by sera absorbed with cardiolipin and group treponemal sorbents. In EL, total IgE level was 197 +/- 107 U/ml; cardiolipin IgE -24.9 +/- 8.3 U/ml and group treponemal IgE 35.8 +/- 6.6 U/ml. In ET, total IgE value was 152.6 +/- 122.5 U/ml, cardiolipin IgE -11 +/- 10.5 and group treponemal IgE -26.6 +/- 14.2 U/ml. Summing up the two specificities, the total specific IgE represent about 1/3 from total IgE in EL and 1/5 in ET+. Taking into account the short half-life (2-3 days) of IgE presence of a significant proportion of specific IgE in those two stages proves, by their continuous synthesis paralleling antigenic stimulation, the presence in various tissular zones of viable treponemas as sources of antigens.

Quantitative profile of cardiolipin and group treponemal IgD antibodies in syphilis estimated by single radial immunodiffusion technique (SRID).

150 serum samples (reactive in VDRL, Reiter-ELISA, FTA-Abs tests), from male patients 25-45 years old, in various stages of syphilis whether treated or untreated, were tested for IgD by SRID. On 154 sera from healthy males 25-45 years old, the reference normal values for IgD levels were established, as: 0-131.2 IU/ml with a mean of 29.92 +/- 29.61 IU/ml. Cardiolipin and group treponemal fraction values for IgD class were obtained by assessing the difference between the immunodiffusion diameter values produced by sera before and after complete absorption with VDRL antigen or delipidated T. reiteri suspension. The individual, mean +/- SD values (expressed in IU/ml) and the percentage of cardiolipin and treponemal IgD of the total IgD class were calculated for each stage. The mean value of the total IgD class, excepting secondary syphilis (sigma 2) 52.53 +/- 26.66 IU/ml), did not overstep the normal levels but all minimal individual values from syphilitic patients (7.09-14.89 IU/ml) surpassed significantly the normal minimal values which were less than or equal to 3.54 IU/ml. The total lack of cardiolipin (IgD and the presence of group treponemal IgD in all sera of the syphilis stages studied were manifest. The group treponemal IgD mean values ranged between 7-9 IU/ml, with a maximum of 19.32 +/- 10.58 IU/ml in sigma 2 followed by latent syphilis (sigma lat) with a mean value of 9.37 +/- 4.9 IU/ml. A significant percentage of treponemal IgD vs total IgD was recorded: primary syphilis (sigma 1) 32.01%, primary-secondary syphilis (sigma 1-2) 28.76%, sigma 2 36.77%, sigma lat and treated persistent seroreactive syphilis (sigma t+) 29.61%. The high proportion of treponemal IgD in latent and treated persistent reactive syphilis suggests a steady activation of B lymphocytes by treponemal antigens and presumably is an expression of an active infectious process. The absence of cardiolipin IgD and the presence of only the treponemal IgD, in all sera from all stages, might confer to their detection an extremely specific diagnostic value in syphilis.