Geometry and physics of knots

KNOTS are usually categorized in terms of topological properties that are invariant under changes in a knot's spatial configuration(1-4). Here we approach knot identification from a different angle, by considering the properties of particular geometrical forms which we define as 'ideal'. For a knot with a given topology and assembled from a tube of uniform diameter, the ideal form is the geometrical configuration having the highest ratio of volume to surface area. Practically, this is equivalent to determining the shortest piece of tube that can be closed to form the knot. Because the notion of an ideal form is independent of absolute spatial scale, the length-to-diameter ratio of a tube providing an ideal representation is constant, irrespective of the tube's actual dimensions. We report the results of computer simulations which show that these ideal representations of knots have surprisingly simple geometrical properties. In particular, there is a simple linear relationship between the length-to-diameter ratio and the crossing number-the number of intersections in a two-dimensional projection of the knot averaged over all directions. We have also found that the average shape of knotted polymeric chains in thermal equilibrium is closely related to the ideal representation of the corresponding knot type. Our observations provide a link between ideal geometrical objects and the behaviour of seemingly disordered systems, and allow the prediction of properties of knotted polymers such as their electrophoretic mobility(5).

Absolute requirement for the pre-T cell receptor alpha chain during NK1.1+ TCRalphabeta cell development.

Most natural killer T (NKT) cells express a highly skewed alphabeta TCR repertoire, consisting of an invariant V alpha14-J alpha281 chain paired preferentially with a polyclonal Vbeta8.2 chain. This repertoire is positively selected by the monomorphic CD1d molecule expressed on cells of hematopoietic origin. The origin of NKT cells and their lineage relationship to conventional T cells is controversial. We show here that the development of NKT cells is absolutely dependent on expression of the pre-TCRalpha chain, in marked contrast to conventional T cells which arise in significant numbers even in the absence of a functional pre-TCR. Distinct developmental requirements for pre-TCR expression in the NKT and T cell lineages may reflect differences in the ability of the TCRalphabeta to substitute functionally for the pre-TCR in immature precursor cells.

Advantages of digital holographic microscopy for real-time full field absolute phase imaging

Different interferometric techniques were developed last decade to obtain full field, quantitative, and absolute phase imaging, such as phase-shifting, Fourier phase microscopy, Hilbert phase microscopy or digital holographic microscopy (DHM). Although, these techniques are very similar, DHM combines several advantages. In contrast, to phase shifting, DHM is indeed capable of single-shot hologram recording allowing a real-time absolute phase imaging. On the other hand, unlike to Fourier phase or Hilbert phase microscopy, DHM does not require to record in focus images of the specimen on the digital detector (CCD or CMOS camera), because a numerical focalization adjustment can be performed by a numerical wavefront propagation. Consequently, the depth of view of high NA microscope objectives is numerically extended. For example, two different biological cells, floating at different depths in a liquid, can be focalized numerically from the same digital hologram. Moreover, the numerical propagation associated to digital optics and automatic fitting procedures, permits vibrations insensitive full- field phase imaging and the complete compensation for a priori any image distortion or/and phase aberrations introduced for example by imperfections of holders or perfusion chamber. Examples of real-time full-field phase images of biological cells have been demonstrated. ©2008 COPYRIGHT SPIE

Absolute height-specific thresholds to identify elevated blood pressure in children.

OBJECTIVE: : Identification of children with elevated blood pressure (BP) is difficult because of the multiple sex, age, and height-specific thresholds to define elevated BP. We propose a simple set of absolute height-specific BP thresholds and evaluate their performance to identify children with elevated BP in two different populations. METHODS: : Using the 95th sex, age, and relative-height BP US thresholds to define elevated BP in children (standard criteria), we derived a set of (non sex- and non age-specific) absolute height-specific BP thresholds for 11 height categories by 10 cm increments. Using data from large school-based surveys conducted in Switzerland (N = 5207; 2621 boys, 2586 girls; age range: 10.1-14.9 years) and in the Seychelles (N = 25 759; 13 048 boys, 12 711 girls; age range: 4.4-18.8 years), we evaluated the performance of these height-specific thresholds to identify children with elevated BP. We also derived sex-specific absolute height-specific BP thresholds and compared their performance. RESULTS: : In the Swiss and the Seychelles surveys, the prevalence of elevated BP (standard criteria) was 11.4 and 9.1%, respectively. The height-specific thresholds to identify elevated BP had a sensitivity of 80 and 84%, a specificity of 99 and 99%, a positive predictive value of 92 and 91%, and a negative predictive value of 97 and 98%, respectively. Performance of sex-specific absolute height-specific BP thresholds was similar. CONCLUSION: : A simple table of height-specific BP thresholds allowed identifying children with elevated BP with high sensitivity and excellent specificity.

Unilateral cricothyroid contraction and glottic configuration.

It is frequently stated that unilateral cricothyroid muscle (CT) paralysis can be diagnosed by physical examination, noting rotation of the glottis, and shortening and vertical displacement of the ipsilateral vocal fold. These signs, however, are inconsistently observed, and there is considerable controversy regarding the direction of glottic rotation. To determine the effects of CT contraction on three-dimensional glottic configuration, we performed computerized tomography on cadaver larynges before and after simulated CT contraction. Radiopaque makers were used to compute distances. Unilateral CT contraction equally increased the length of both membranous vocal folds, and rotated the posterior glottis less than 1 mm. CT contraction neither adducted the vocal processes, nor significantly their altered vertical level. These results suggest that unilateral CT paralysis cannot be diagnosed on the basis of any clinically apparent change in glottal configuration.

Immunosuppressive effects of streptozotocin-induced diabetes result in absolute lymphopenia and a relative increase of T regulatory cells.

OBJECTIVE Streptozotocin (STZ) is the most widely used diabetogenic agent in animal models of islet transplantation. However, the immunomodifying effects of STZ and the ensuing hyperglycemia on lymphocyte subsets, particularly on T regulatory cells (Tregs), remain poorly understood. RESEARCH DESIGN AND METHODS This study evaluated how STZ-induced diabetes affects adaptive immunity and the consequences thereof on allograft rejection in murine models of islet and skin transplantation. The respective toxicity of STZ and hyperglycemia on lymphocyte subsets was tested in vitro. The effect of hyperglycemia was assessed independently of STZ in vivo by the removal of transplanted syngeneic islets, using an insulin pump, and with rat insulin promoter diphtheria toxin receptor transgenic mice. RESULTS Early lymphopenia in both blood and spleen was demonstrated after STZ administration. Direct toxicity of STZ on lymphocytes, particularly on CD8(+) cells and B cells, was shown in vitro. Hyperglycemia also correlated with blood and spleen lymphopenia in vivo but was not lymphotoxic in vitro. Independently of hyperglycemia, STZ led to a relative increase of Tregs in vivo, with the latter retaining their suppressive capacity in vitro. The higher frequency of Tregs was associated with Treg proliferation in the blood, but not in the spleen, and higher blood levels of transforming growth factor-β. Finally, STZ administration delayed islet and skin allograft rejection compared with naive mice. CONCLUSIONS These data highlight the direct and indirect immunosuppressive effects of STZ and acute hyperglycemia, respectively. Thus, these results have important implications for the future development of tolerance-based protocols and their translation from the laboratory to the clinic.