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.

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.

Switching between apparently redundant iron-uptake mechanisms benefits bacteria in changeable environments.

Bacteria often possess multiple siderophore-based iron uptake systems for scavenging this vital resource from their environment. However, some siderophores seem redundant, because they have limited iron-binding efficiency and are seldom expressed under iron limitation. Here, we investigate the conundrum of why selection does not eliminate this apparent redundancy. We focus on Pseudomonas aeruginosa, a bacterium that can produce two siderophores-the highly efficient but metabolically expensive pyoverdine, and the inefficient but metabolically cheap pyochelin. We found that the bacteria possess molecular mechanisms to phenotypically switch from mainly producing pyoverdine under severe iron limitation to mainly producing pyochelin when iron is only moderately limited. We further show that strains exclusively producing pyochelin grew significantly better than strains exclusively producing pyoverdine under moderate iron limitation, whereas the inverse was seen under severe iron limitation. This suggests that pyochelin is not redundant, but that switching between siderophore strategies might be beneficial to trade off efficiencies versus costs of siderophores. Indeed, simulations parameterized from our data confirmed that strains retaining the capacity to switch between siderophores significantly outcompeted strains defective for one or the other siderophore under fluctuating iron availabilities. Finally, we discuss how siderophore switching can be viewed as a form of collective decision-making, whereby a coordinated shift in behaviour at the group level emerges as a result of positive and negative feedback loops operating among individuals at the local scale.

Effect of Knotting on the Shape of Polymers

Momentary configurations of long polymers at thermal equilibrium usually deviate from spherical symmetry and can be better described, on average, by a prolate ellipsoid. The asphericity and nature of asphericity (or prolateness) that describe these momentary ellipsoidal shapes of a polymer are determined by specific expressions involving the three principal moments of inertia calculated for configurations of the polymer. Earlier theoretical studies and numerical simulations have established that as the length of the polymer increases, the average shape for the statistical ensemble of random configurations asymptotically approaches a characteristic universal shape that depends on the solvent quality. It has been established, however, that these universal shapes differ for linear, circular, and branched chains. We investigate here the effect of knotting on the shape of cyclic polymers modeled as random isosegmental polygons. We observe that random polygons forming different knot types reach asymptotic shapes that are distinct from the ensemble average shape. For the same chain length, more complex knots are, on average, more spherical than less complex knots.

Probability of achieving optimal molecular response to imatinib in chronic myeloid leukemia (CML) patients: Pharmacokinetic/Pharmacodynamic (PK/PD) relationships observed under field-conditions

Objectives: Imatinib has been increasingly proposed for therapeutic drug monitoring (TDM), as trough concentrations (Cmin) correlate with response rates in CML patients. This analysis aimed to evaluate the impact of imatinib exposure on optimal molecular response rates in a large European cohort of patients followed by centralized TDM.¦Methods: Sequential PK/PD analysis was performed in NONMEM 7 on 2230 plasma (PK) samples obtained along with molecular response (PD) data from 1299 CML patients. Model-based individual Bayesian estimates of exposure, parameterized as to initial dose adjusted and log-normalized Cmin (log-Cmin) or clearance (CL), were investigated as potential predictors of optimal molecular response, while accounting for time under treatment (stratified at 3 years), gender, CML phase, age, potentially interacting comedication, and TDM frequency. PK/PD analysis used mixed-effect logistic regression (iterative two-stage method) to account for intra-patient correlation.¦Results: In univariate analyses, CL, log-Cmin, time under treatment, TDM frequency, gender (all p<0.01) and CML phase (p=0.02) were significant predictors of the outcome. In multivariate analyses, all but log-Cmin remained significant (p<0.05). Our model estimates a 54.1% probability of optimal molecular response in a female patient with a median CL of 14.4 L/h, increasing by 4.7% with a 35% decrease in CL (percentile 10 of CL distribution), and decreasing by 6% with a 45% increased CL (percentile 90), respectively. Male patients were less likely than female to be in optimal response (odds ratio: 0.62, p<0.001), with an estimated probability of 42.3%.¦Conclusions: Beyond CML phase and time on treatment, expectedly correlated to the outcome, an effect of initial imatinib exposure on the probability of achieving optimal molecular response was confirmed in field-conditions by this multivariate analysis. Interestingly, male patients had a higher risk of suboptimal response, which might not exclusively derive from their 18.5% higher CL, but also from reported lower adherence to the treatment. A prospective longitudinal study would be desirable to confirm the clinical importance of identified covariates and to exclude biases possibly affecting this observational survey.

Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers

Recent technological advances in remote sensing have enabled investigation of the morphodynamics and hydrodynamics of large rivers. However, measuring topography and flow in these very large rivers is time consuming and thus often constrains the spatial resolution and reach-length scales that can be monitored. Similar constraints exist for computational fluid dynamics (CFD) studies of large rivers, requiring maximization of mesh-or grid-cell dimensions and implying a reduction in the representation of bedform-roughness elements that are of the order of a model grid cell or less, even if they are represented in available topographic data. These ``subgrid'' elements must be parameterized, and this paper applies and considers the impact of roughness-length treatments that include the effect of bed roughness due to ``unmeasured'' topography. CFD predictions were found to be sensitive to the roughness-length specification. Model optimization was based on acoustic Doppler current profiler measurements and estimates of the water surface slope for a variety of roughness lengths. This proved difficult as the metrics used to assess optimal model performance diverged due to the effects of large bedforms that are not well parameterized in roughness-length treatments. However, the general spatial flow patterns are effectively predicted by the model. Changes in roughness length were shown to have a major impact upon flow routing at the channel scale. The results also indicate an absence of secondary flow circulation cells in the reached studied, and suggest simpler two-dimensional models may have great utility in the investigation of flow within large rivers. Citation: Sandbach, S. D. et al. (2012), Application of a roughness-length representation to parameterize energy loss in 3-D numerical simulations of large rivers, Water Resour. Res., 48, W12501, doi: 10.1029/2011WR011284.

Total curvature and total torsion of knotted polymers

Previous work on radius of gyration and average crossing number has demonstrated that polymers with fixed topology show a different scaling behavior with respect to these characteristics than polymers with unrestricted topology. Using numerical simulations, we show here that the difference in the scaling behavior between polymers with restricted and unrestricted topology also applies to the total curvature and total torsion. For each knot type, the equilibrium length with respect to a given spatial characteristic is the number of edges at which the value of the characteristic is the same as the average for all polygons. This number appears to be correlated to physical properties of macromolecules, for example gel mobility as measured by the separation between distinct knot types. We also find that, on average, closed polymers require slightly more total curvature and slightly less total torsion than open polymers with the corresponding number of monomers.

Physiologically based pharmacokinetic modeling of arsenic in the mouse

A remarkable feature of the carcinogenicity of inorganic arsenic is that while human exposures to high concentrations of inorganic arsenic in drinking water are associated with increases in skin, lung, and bladder cancer, inorganic arsenic has not typically caused tumors in standard laboratory animal test protocols. Inorganic arsenic administered for periods of up to 2 yr to various strains of laboratory mice, including the Swiss CD-1, Swiss CR:NIH(S), C57Bl/6p53(+/-), and C57Bl/6p53(+/+), has not resulted in significant increases in tumor incidence. However, Ng et al. (1999) have reported a 40% tumor incidence in C57Bl/6J mice exposed to arsenic in their drinking water throughout their lifetime, with no tumors reported in controls. In order to investigate the potential role of tissue dosimetry in differential susceptibility to arsenic carcinogenicity, a physiologically based pharmacokinetic (PBPK) model for inorganic arsenic in the rat, hamster, monkey, and human (Mann et al., 1996a, 1996b) was extended to describe the kinetics in the mouse. The PBPK model was parameterized in the mouse using published data from acute exposures of B6C3F1 mice to arsenate, arsenite, monomethylarsonic acid (MMA), and dimethylarsinic acid (DMA) and validated using data from acute exposures of C57Black mice. Predictions of the acute model were then compared with data from chronic exposures. There was no evidence of changes in the apparent volume of distribution or in the tissue-plasma concentration ratios between acute and chronic exposure that might support the possibility of inducible arsenite efflux. The PBPK model was also used to project tissue dosimetry in the C57Bl/6J study, in comparison with tissue levels in studies having shorter duration but higher arsenic treatment concentrations. The model evaluation indicates that pharmacokinetic factors do not provide an explanation for the difference in outcomes across the various mouse bioassays. Other possible explanations may relate to strain-specific differences, or to the different durations of dosing in each of the mouse studies, given the evidence that inorganic arsenic is likely to be active in the later stages of the carcinogenic process. [Authors]

Linear random knots and their scaling behavior

We present here a nonbiased probabilistic method that allows us to consistently analyze knottedness of linear random walks with up to several hundred noncorrelated steps. The method consists of analyzing the spectrum of knots formed by multiple closures of the same open walk through random points on a sphere enclosing the walk. Knottedness of individual "frozen" configurations of linear chains is therefore defined by a characteristic spectrum of realizable knots. We show that in the great majority of cases this method clearly defines the dominant knot type of a walk, i.e., the strongest component of the spectrum. In such cases, direct end-to-end closure creates a knot that usually coincides with the knot type that dominates the random closure spectrum. Interestingly, in a very small proportion of linear random walks, the knot type is not clearly defined. Such walks can be considered as residing in a border zone of the configuration space of two or more knot types. We also characterize the scaling behavior of linear random knots.

Cumulative Shapes of Knotted Polymers

We investigate the influence of knotting and chirality on the shape of knotted polygons forming trefoil knots compared to unknotted polygons by aligning independent configurations along their principal inertial axes. While for six edge polygons forming trefoil knots the chiral knotted structure is revealed in the isodensity profiles, the distinct chiral signature of the trefoil is significantly diminished with 24 edges. We observe that as the number of edges in the polygons increases, the cumulative shapes of trefoil knots progressively approach the cumulative shapes for unknotted polygons.

Effect of knotting on polymer shapes and their enveloping ellipsoids.

We simulate freely jointed chains to investigate how knotting affects the overall shapes of freely fluctuating circular polymeric chains. To characterize the shapes of knotted polygons, we construct enveloping ellipsoids that minimize volume while containing the entire polygon. The lengths of the three principal axes of the enveloping ellipsoids are used to define universal size and shape descriptors analogous to the squared radius of gyration and the inertial asphericity and prolateness. We observe that polymeric chains forming more complex knots are more spherical and also more prolate than chains forming less complex knots with the same number of edges. We compare the shape measures, determined by the enveloping ellipsoids, with those based on constructing inertial ellipsoids and explain the differences between these two measures of polymer shape.

Probabilistic electrical resistivity tomography of a CO2 sequestration analog

Electrical resistivity tomography (ERT) is a well-established method for geophysical characterization and has shown potential for monitoring geologic CO2 sequestration, due to its sensitivity to electrical resistivity contrasts generated by liquid/gas saturation variability. In contrast to deterministic inversion approaches, probabilistic inversion provides the full posterior probability density function of the saturation field and accounts for the uncertainties inherent in the petrophysical parameters relating the resistivity to saturation. In this study, the data are from benchtop ERT experiments conducted during gas injection into a quasi-2D brine-saturated sand chamber with a packing that mimics a simple anticlinal geological reservoir. The saturation fields are estimated by Markov chain Monte Carlo inversion of the measured data and compared to independent saturation measurements from light transmission through the chamber. Different model parameterizations are evaluated in terms of the recovered saturation and petrophysical parameter values. The saturation field is parameterized (1) in Cartesian coordinates, (2) by means of its discrete cosine transform coefficients, and (3) by fixed saturation values in structural elements whose shape and location is assumed known or represented by an arbitrary Gaussian Bell structure. Results show that the estimated saturation fields are in overall agreement with saturations measured by light transmission, but differ strongly in terms of parameter estimates, parameter uncertainties and computational intensity. Discretization in the frequency domain (as in the discrete cosine transform parameterization) provides more accurate models at a lower computational cost compared to spatially discretized (Cartesian) models. A priori knowledge about the expected geologic structures allows for non-discretized model descriptions with markedly reduced degrees of freedom. Constraining the solutions to the known injected gas volume improved estimates of saturation and parameter values of the petrophysical relationship. (C) 2014 Elsevier B.V. All rights reserved.