Scaling behavior and equilibrium lengths of knotted polymers

We use numerical simulations to investigate how the chain length and topology of freely fluctuating knotted polymer rings affect their various spatial characteristics such as the radius of the smallest sphere enclosing momentary configurations of simulated polymer chains. We describe how the average value of a characteristic changes with the chain size and how this change depends on the topology of the modeled polymers. Although the scaling profiles of a spatial characteristic for distinct knot types do not intersect (at least, in the range of our data), the profiles for nontrivial knots intersect the corresponding profile obtained for phantom polymers, i.e., those that are free to explore all available topological states. For each knot type, this point of intersection defines its equilibrium length with respect to the spatial characteristic. At this chain length, a polymer forming a given knot type will not tend to increase or decrease. on average, the value of the spatial characteristic when the polymer is released from its topological constraint. We show interrelations between equilibrium lengths defined with respect to spatial characteristics of different character and observe that they are related to the lengths of ideal geometric configurations of the corresponding knot types.

The average crossing number of equilateral random polygons.

In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form . A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type can be described by a function of the form where a, b and c are constants depending on and n0 is the minimal number of segments required to form . The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the ACN profile of all closed walks. These points of intersection define the equilibrium length of , i.e., the chain length at which a statistical ensemble of configurations with given knot type -upon cutting, equilibration and reclosure to a new knot type -does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration Rg.

Response to comment on "the geometric structure of the brain fiber pathways".

In response to Catani et al., we show that corticospinal pathways adhere via sharp turns to two local grid orientations; that our studies have three times the diffusion resolution of those compared; and that the noted technical concerns, including crossing angles, do not challenge the evidence of mathematically specific geometric structure. Thus, the geometric thesis gives the best account of the available evidence.

The bioavailability of bromazepam, omeprazole and paracetamol given by nasogastric feeding tube.

AIMS: To characterize and compare the pharmacokinetic profiles of bromazepam, omeprazole and paracetamol when administered by the oral and nasogastric routes to the same healthy cohort of volunteers. METHODS: In a prospective, monocentric, randomized crossover study, eight healthy volunteers received the three drugs by the oral (OR) and nasogastric routes (NT). Sequential plasma samples were analyzed by high-performance liquid chromatography-UV, pharmacokinetic parameters (Cmax, AUC(0-infinity), t(1/2), k(e), tmax) were compared statistically, and Cmax, AUC(0-infinity) and t(max) were analyzed for bioequivalence. RESULTS: A statistically significant difference was seen in the AUC(0-infinity) of bromazepam, with nasogastric administration decreasing availability by about 25%: AUC(OR) = 2501 ng mL(-1) h; AUC(NT) = 1855 ng mL(-1) h (p < 0.05); ratio (geometric mean) = 0.74 [90% confidence interval (CI) 0.64-0.87]. However, this does not appear to be clinically relevant given the usual dosage range and the drug's half-life (approx. 30 h). A large interindividual variability in omeprazole parameters prevented any statistical conclusion from being drawn in terms of both modes of administration despite their similar average profile: AUC(OR) = 579 ng mL(-1) h; AUC(NT) = 587 ng mL(-1) h (p > 0.05); ratio (geometric mean) = 1.01 (90% CI 0.64-1.61). An extended study with a larger number of subjects may possibly provide clearer answers. The narrow 90% confidence limits of paracetamol indicate bioequivalence: AUC(OR) = 37 microg mL(-1) h; AUC(NT) = 41 microg mL(-1) h(p > 0.05); ratio (geometric mean) = 1.12 (90% CI 0.98-1.28). CONCLUSION: The results of this study show that the nasogastric route of administration does not appear to cause marked, clinically unsuitable alterations in the bioavailability of the tested drugs.

The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

Impact of Anti-T-Cell Therapy in the Immunogenicity of Seasonal Influenza Vaccine in Kidney Transplant Recipients.

BACKGROUND: The influence of anti-T-cell therapy in the immunogenicity of the influenza vaccine in kidney transplant recipients remains unclear. METHODS: During the 2010 to 2011 influenza season, we evaluated the immune response to the inactivated trivalent influenza vaccine in kidney transplant recipients having received Thymoglobulin or basiliximab as induction therapy. A hemagglutination inhibition assay was used to assess the immunogenicity of the vaccine. The primary outcome was geometric mean titers of hemagglutination inhibition after influenza vaccination. RESULTS: Sixty patients (Thymoglobulin n=22 and basiliximab n=38) were included. Patients in the Thymoglobulin group were older (P=0.16), showed higher creatinine levels (P=0.16) and had more frequently received a previous transplant (P=0.02). There were no significant differences in geometric mean titers for any of the three viral strains between groups (P=0.69 for H1N1, P=0.56 for H3N2, and P=0.7 for B strain). Seroconversion to at least one viral strain was seen in 15 (68%) of 22 patients in the Thymoglobulin group and 28 (73%) of 38 in the basiliximab group (P=0.77). In patients vaccinated during the first year after receiving anti-T-cell therapy (n=25), there was a trend toward lower vaccine responses in the Thymoglobulin group. Patients who received Thymoglobulin showed lower CD4 cell counts and lower levels of IgM, at an average of 16.2 months after transplantation. A multivariate analysis showed that only the absence of mycophenolate was associated with a better vaccine response (odds ratio=9.47; 95% confidence interval, 1.03-86.9; P=0.047). CONCLUSION: No significant differences were seen in immunogenicity of the influenza vaccine in kidney transplant recipients having received either Thymoglobulin or basiliximab.

Comparative testing of a miniature diffusion size classifier to assess airborne ultrafine particles under field conditions

Miniature diffusion size classifiers (miniDiSC) are novel handheld devices to measure ultrafine particles (UFP). UFP have been linked to the development of cardiovascular and pulmonary diseases; thus, detection and quantification of these particles are important for evaluating their potential health hazards. As part of the UFP exposure assessments of highwaymaintenance workers in western Switzerland, we compared a miniDiSC with a portable condensation particle counter (P-TRAK). In addition, we performed stationary measurements with a miniDiSC and a scanning mobility particle sizer (SMPS) at a site immediately adjacent to a highway. Measurements with miniDiSC and P-TRAK correlated well (correlation of r = 0.84) but average particle numbers of the miniDiSC were 30%âeuro"60% higher. This difference was significantly increased for mean particle diameters below 40 nm. The correlation between theminiDiSC and the SMPSduring stationary measurements was very high (r = 0.98) although particle numbers from the miniDiSC were 30% lower. Differences between the three devices were attributed to the different cutoff diameters for detection. Correction for this size dependent effect led to very similar results across all counters.We did not observe any significant influence of other particle characteristics. Our results suggest that the miniDiSC provides accurate particle number concentrations and geometric mean diameters at traffic-influenced sites, making it a useful tool for personal exposure assessment in such settings.

Geometric control of the cell cycle.

How do cells sense their own size and shape? And how does this information regulate progression of the cell cycle? Our group, in parallel to that of Paul Nurse, have recently demonstrated that fission yeast cells use a novel geometry-sensing mechanism to couple cell length perception with entry into mitosis. These rod-shaped cells measure their own length by using a medially-placed sensor, Cdr2, that reads a protein gradient emanating from cell tips, Pom1, to control entry into mitosis. Budding yeast cells use a similar molecular sensor to delay entry into mitosis in response to defects in bud morphogenesis. Metazoan cells also modulate cell proliferation in response to their own shape by sensing tension. Here I discuss the recent results obtained for the fission yeast system and compare them to the strategies used by these other organisms to perceive their own morphology.

Geometric morphometric analyses provide evidence for the adaptive character of the Tanganyikan cichlid fish radiations.

The cichlids of East Africa are renowned as one of the most spectacular examples of adaptive radiation. They provide a unique opportunity to investigate the relationships between ecology, morphological diversity, and phylogeny in producing such remarkable diversity. Nevertheless, the parameters of the adaptive radiations of these fish have not been satisfactorily quantified yet. Lake Tanganyika possesses all of the major lineages of East African cichlid fish, so by using geometric morphometrics and comparative analyses of ecology and morphology, in an explicitly phylogenetic context, we quantify the role of ecology in driving adaptive speciation. We used geometric morphometric methods to describe the body shape of over 1000 specimens of East African cichlid fish, with a focus on the Lake Tanganyika species assemblage, which is composed of more than 200 endemic species. The main differences in shape concern the length of the whole body and the relative sizes of the head and caudal peduncle. We investigated the influence of phylogeny on similarity of shape using both distance-based and variance partitioning methods, finding that phylogenetic inertia exerts little influence on overall body shape. Therefore, we quantified the relative effect of major ecological traits on shape using phylogenetic generalized least squares and disparity analyses. These analyses conclude that body shape is most strongly predicted by feeding preferences (i.e., trophic niches) and the water depths at which species occur. Furthermore, the morphological disparity within tribes indicates that even though the morphological diversification associated with explosive speciation has happened in only a few tribes of the Tanganyikan assemblage, the potential to evolve diverse morphologies exists in all tribes. Quantitative data support the existence of extensive parallelism in several independent adaptive radiations in Lake Tanganyika. Notably, Tanganyikan mouthbrooders belonging to the C-lineage and the substrate spawning Lamprologini have evolved a multitude of different shapes from elongated and Lamprologus-like hypothetical ancestors. Together, these data demonstrate strong support for the adaptive character of East African cichlid radiations.

Linear relations between writhe and minimal crossing number in Conway families of ideal knots and links

We showed earlier how to predict the writhe of any rational knot or link in its ideal geometric configuration, or equivalently the average of the 3D writhe over statistical ensembles of random configurations of a given knot or link (Cerf and Stasiak 2000 Proc. Natl Acad. Sci. USA 97 3795). There is no general relation between the minimal crossing number of a knot and the writhe of its ideal geometric configuration. However, within individual families of knots linear relations between minimal crossing number and writhe were observed (Katritch et al 1996 Nature 384 142). Here we present a method that allows us to express the writhe as a linear function of the minimal crossing number within Conway families of knots and links in their ideal configuration. The slope of the lines and the shift between any two lines with the same

A tutorial review of electrical neuroimaging from group-average to single-trial event-related potentials.

This tutorial review details some of the recent advances in signal analyses applied to event-related potential (ERP) data. These "electrical neuroimaging" analyses provide reference-independent measurements of response strength and response topography that circumvent statistical and interpretational caveats of canonical ERP analysis methods while also taking advantage of the greater information provided by high-density electrode montages. Electrical neuroimaging can be applied across scales ranging from group-averaged ERPs to single-subject and single-trial datasets. We illustrate these methods with a tutorial dataset and place particular emphasis on their suitability for studies of clinical and/or developmental populations.

Exhaled breath condensate as a matrix for combustion-based nanoparticle exposure and health effect evaluation

Health assessment and medical surveillance of workers exposed to combustion nanoparticles are challenging. The aim was to evaluate the feasibility of using exhaled breath condensate (EBC) from healthy volunteers for (1) assessing the lung deposited dose of combustion nanoparticles and (2) determining the resulting oxidative stress by measuring hydrogen peroxide (H2O2) and malondialdehyde (MDA). Methods: Fifteen healthy nonsmoker volunteers were exposed to three different levels of sidestream cigarette smoke under controlled conditions. EBC was repeatedly collected before, during, and 1 and 2 hr after exposure. Exposure variables were measured by direct reading instruments and by active sampling. The different EBC samples were analyzed for particle number concentration (light-scattering-based method) and for selected compounds considered oxidative stress markers. Results: Subjects were exposed to an average airborne concentration up to 4.3×10(5) particles/cm(3) (average geometric size ∼60-80 nm). Up to 10×10(8) particles/mL could be measured in the collected EBC with a broad size distribution (50(th) percentile ∼160 nm), but these biological concentrations were not related to the exposure level of cigarette smoke particles. Although H2O2 and MDA concentrations in EBC increased during exposure, only H2O2 showed a transient normalization 1 hr after exposure and increased afterward. In contrast, MDA levels stayed elevated during the 2 hr post exposure. Conclusions: The use of diffusion light scattering for particle counting proved to be sufficiently sensitive to detect objects in EBC, but lacked the specificity for carbonaceous tobacco smoke particles. Our results suggest two phases of oxidation markers in EBC: first, the initial deposition of particles and gases in the lung lining liquid, and later the start of oxidative stress with associated cell membrane damage. Future studies should extend the follow-up time and should remove gases or particles from the air to allow differentiation between the different sources of H2O2 and MDA.