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.

Direct simulation of interface dynamics: linking capillary pressure, interfacial area and surface energy

We perform direct numerical simulations of drainage by solving Navier- Stokes equations in the pore space and employing the Volume Of Fluid (VOF) method to track the evolution of the fluid-fluid interface. After demonstrating that the method is able to deal with large viscosity contrasts and to model the transition from stable flow to viscous fingering, we focus on the definition of macroscopic capillary pressure. When the fluids are at rest, the difference between inlet and outlet pressures and the difference between the intrinsic phase average pressure coincide with the capillary pressure. However, when the fluids are in motion these quantities are dominated by viscous forces. In this case, only a definition based on the variation of the interfacial energy provides an accurate measure of the macroscopic capillary pressure and allows separating the viscous from the capillary pressure components.

Tightening of DNA knots by supercoiling facilitates their unknotting by type II DNA topoisomerases.

Using numerical simulations, we compare properties of knotted DNA molecules that are either torsionally relaxed or supercoiled. We observe that DNA supercoiling tightens knotted portions of DNA molecules and accentuates the difference in curvature between knotted and unknotted regions. The increased curvature of knotted regions is expected to make them preferential substrates of type IIA topoisomerases because various earlier experiments have concluded that type IIA DNA topoisomerases preferentially interact with highly curved DNA regions. The supercoiling-induced tightening of DNA knots observed here shows that torsional tension in DNA may serve to expose DNA knots to the unknotting action of type IIA topoisomerases, and thus explains how these topoisomerases could maintain a low knotting equilibrium in vivo, even for long DNA molecules.

Altérations anatomopathologiques liées au traitement par cerclage des globes oculaires atteints de décollement de rétine [Histological changes related to scleral buckling for treatment of retinal detachment].

Treatment of retinal detachment frequently uses biocompatible materials to obtain scleral buckling. These materials are not devoid of consequences on surrounding tissues. In 3 eyes enucleated for failure of surgical treatment using scleral buckling materials, the changes prompted by episcleral implants could be observed. The sclera underwent both an inversion of its curvature and a reduction of its thickness under the material, as well as an encapsulation of the material was observed. While a silicone sponge was used in part to encircle one of these eyes, its capsular inner surface was regular and smooth. In contrast, hydrogel implants used in the three eyes showed a peripheral fragmentation prompting in two of them a typical foreign body giant cell granulomatous reaction. Changes in scleral curvature and scleral thinning were observed reflecting the consequences of the buckling procedure. The capsule formation occurred as it does for any nonabsorbable matérial implanted in tissues. Degradation and fragmentation of the hydrogel material suscitated a granuloma in response to fragments. These hydrogel specific changes should be recognized on microscopic examination of slides of either capsule or eyes previously in contact with this implanted material. They attested of the instability of hydrogel after implantation.

Tight open knots.

The tightest open conformations of a few prime knots (3(1), 4(1), 5(1), 5(2), and 6(3)) found with the use of the SONO algorithm are presented and discussed. The conformations are obtained from the tightest closed conformations of the knots by cutting and opening them at different locations. The length of the rope engaged in each of the open conformations is calculated. The curvature and torsion profiles of the unique tightest conformations of the 3(1) and 4(1) open knots are presented and discussed. In particular, symmetry properties of the knots reflected within their curvature and torsion profiles are analysed. Connections with the physics of polymers are discussed.

Multilevel oblique corpectomy for cervical spondylotic myelopathy preserves segmental motion.

PURPOSE: To document the neurological outcome, spinal alignment and segmental range of movement after oblique cervical corpectomy (OCC) for cervical compressive myelopathy. METHODS: This retrospective study included 109 patients--93 with cervical spondylotic myelopathy and 16 with ossified posterior longitudinal ligament in whom spinal curvature and range of segmental movements were assessed on neutral and dynamic cervical radiographs. Neurological function was measured by Nurick's grade and modified Japanese Orthopedic Association (JOA) scores. Eighty-eight patients (81%) underwent either a single- or two-level corpectomy; the remaining (19%) undergoing three- or four-level corpectomies. The average duration of follow-up was 30.52 months. RESULTS: The Nurick's grade and the JOA scores showed statistically significant improvements after surgery (p < 0.001). The mean postoperative segmental angle in the neutral position straightened by 4.7 ± 6.5°. The residual segmental range of movement for a single-level corpectomy was 16.7° (59.7% of the preoperative value), for two-level corpectomy it was 20.0° (67.2%) and for three-level corpectomies it was 22.9° (74.3%). 63% of patients with lordotic spines continued to have lordosis postoperatively while only one became kyphotic without clinical worsening. Four patients with preoperative kyphotic spines showed no change in spine curvature. None developed spinal instability. CONCLUSIONS: The OCC preserves segmental motion in the short-term, however, the tendency towards straightening of the spine, albeit without clinical worsening, warrants serial follow-up imaging to determine whether this motion preservation is long lasting.

Localization of breakage points in knotted strings

It is a common macroscopic observation that knotted ropes or fishing lines under tension easily break at the knot. However, a more precise localization of the breakage point in knotted macroscopic strings is a difficult task. In the present work, the tightening of knots was numerically simulated, a comparison of strength of different knots was experimentally performed and a high velocity camera was used to precisely localize the site where knotted macroscopic strings break. In the case of knotted spaghetti, the breakage occurs at the position with high curvature at the entry to the knot. This localization results from joint contributions of loading, bending and friction forces into the complex process of knot breakage. The present simulations and experiments are in agreement with recent molecular dynamics simulations of a knotted polymer chain and with experiments performed on actin and DNA filaments. The strength of the knotted string is greatly reduced (down to 50%) by the presence of a knot, therefore reducing the resistance to tension of all materials containing chains of any sort. The present work with macroscopic strings revels some important aspects, which are not accessible by experiments with microscopic chains.

A pea plasma membrane protein exhibiting blue light-induced phosphorylation retains photosensitivity following triton solubilization.

Phosphorylation of a polypeptide of approximately 120 kD in pea (Pisum sativum L.) plasma membranes in response to blue light has been shown to be involved in phototropic curvature, but the relationship of this protein to the kinase and photoreceptor acting upon it is uncertain. Using two-phase aqueous partitioning to isolate right-side-out plasma membrane vesicles, we have obtained evidence suggesting that the photoreceptor, kinase, and substrate are localized to the plasma membrane fraction. Latent phosphorylation accessible through Triton X-100 or freeze/thaw treatments of purified plasma membrane vesicles indicates that at least the kinase moiety is present on the internal face of the plasma membrane. Effects of solubilization of vesicles on fluence-response characteristics and on phosphorylation levels provide evidence that the receptor, kinase, and protein substrate are present together in individual mixed detergent micelles, either as a stable complex or as domains of a single polypeptide. In vivo blue-light irradiation results in a small but significant decrease in mobility of the 120-kD phosphorylated protein on sodium dodecylsulfate gel electrophoresis. This mobility shift is evident on Coomassie-stained gels and on western blots probed with polyclonal antibodies raised against the 120-kD protein. Among the plasma membrane proteins bound to the reactive nucleotide analog fluorosulfonylbenzoyladenine (FSBA), a distinct protein band at 120 kD can be detected on blots probed with anti-FSBA antibodies. This band exhibits an in vivo light-dependent mobility shift identical to that observed for the protein band and antibodies specific for the 120-kD protein, implying that the 120-kD protein has an integral nucleotide binding site and consistent with the possibility that the substrate protein is also a kinase.

Determination of DNA persistence length by cryo-electron microscopy. Separation of the static and dynamic contributions to the apparent persistence length of DNA.

Axial deflection of DNA molecules in solution results from thermal motion and intrinsic curvature related to the DNA sequence. In order to measure directly the contribution of thermal motion we constructed intrinsically straight DNA molecules and measured their persistence length by cryo-electron microscopy. The persistence length of such intrinsically straight DNA molecules suspended in thin layers of cryo-vitrified solutions is about 80 nm. In order to test our experimental approach, we measured the apparent persistence length of DNA molecules with natural "random" sequences. The result of about 45 nm is consistent with the generally accepted value of the apparent persistence length of natural DNA sequences. By comparing the apparent persistence length to intrinsically straight DNA with that of natural DNA, it is possible to determine both the dynamic and the static contributions to the apparent persistence length.

Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method.

We present a method for segmenting white matter tracts from high angular resolution diffusion MR. images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.

Light-induced phosphorylation of a membrane protein plays an early role in signal transduction for phototropism in Arabidopsis thaliana.

Blue light is known to cause rapid phosphorylation of a membrane protein in etiolated seedlings of several plant species, a protein that, at least in etiolated pea seedlings and maize coleoptiles, has been shown to be associated with the plasma membrane. The light-driven phosphorylation has been proposed on the basis of correlative evidence to be an early step in the signal transduction chain for phototropism. In the Arabidopsis thaliana mutant JK224, the sensitivity to blue light for induction of first positive phototropism is known to be 20- to 30-fold lower than in wild type, whereas second positive curvature appears to be normal. While light-induced phosphorylation can be demonstrated in crude membrane preparations from shoots of the mutant, the level of phosphorylation is dramatically lower than in wild type, as is the sensitivity to blue light. Another A. thaliana mutant, JK218, that completely lacks any phototropic responses to up to 2 h of irradiation, shows a normal level of light-induced phosphorylation at saturation. Since its gravitropic sensitivity is normal, it is presumably blocked in some step between photoreception and the confluence of the signal transduction pathways for phototropism and gravitropism. We conclude from mutant JK224 that light-induced phosphorylation plays an early role in the signal transduction chain for phototropism in higher plants.

Debris flow susceptibility mapping at a regional scale along the National Road N7, Argentina

A first assessment of debris flow susceptibility at a large scale was performed along the National Road N7, Argentina. Numerous catchments are prone to debris flows and likely to endanger the road-users. A 1:50,000 susceptibility map was created. The use of a DEM (grid 30 m) associated to three complementary criteria (slope, contributing area, curvature) allowed the identification of potential source areas. The debris flow spreading was estimated using a process- and GISbased model (Flow-R) based on basic probabilistic and energy calculations. The best-fit values for the coefficient of friction and the mass-to-drag ratio of the PCM model were found to be ? = 0.02 and M/D = 180 and the resulting propagation on one of the calibration site was validated using the Coulomb friction model. The results are realistic and will be useful to determine which areas need to be prioritized for detailed studies.

Large fluctuations in the disassembly rate of microtubules revealed by atomic force microscopy.

Atomic force microscopy (AFM) in situ has been used to observe the cold disassembly dynamics of microtubules at a previously unrealised spatial resolution. Microtubules either electrostatically or covalently bound to aminosilane surfaces disassembled at room temperature under buffer solutions with no free tubulin present. This process was followed by taking sequential tapping-mode AFM images and measuring the change in the microtubule end position as a function of time, with an spatial accuracy down to +/-20nm and a temporal accuracy of +/-1s. As well as giving average disassembly rates on the order of 1-10 tubulin monomers per second, large fluctuations in the disassembly rate were revealed, indicating that the process is far from smooth and linear under these experimental conditions. The surface bound rates measured here are comparable to the rates for GMPCPP-tubulin microtubules free in solution, suggesting that inhibition of tubulin curvature through steric hindrance controls the average, relatively low disassembly rate. The large fluctuations in this rate are thought to be due to multiple pathways in the kinetics of disassembly with differing rate constants and/or stalling due to defects in the microtubule lattice. Microtubules that were covalently bound to the surface left behind the protofilaments covalently cross-linked to the aminosilane via glutaraldehyde during the disassembly process. Further work is needed to quantitatively assess the effects of surface binding on protofibril disassembly rates, reveal any differences in disassembly rates between the plus and minus ends and to enable assembly as well as disassembly to be imaged in the microscope fluid cell in real-time.

A new technique to measure micromotion distribution around a cementless femoral stem.

The interfacial micromotion is closely associated to the long-term success of cementless hip prostheses. Various techniques have been proposed to measure them, but only a few number of points over the stem surface can be measured simultaneously. In this paper, we propose a new technique based on micro-Computer Tomography (μCT) to measure locally the relative interfacial micromotions between the metallic stem and the surrounding femoral bone. Tantalum beads were stuck at the stem surface and spread at the endosteal surface. Relative micromotions between the stem and the endosteal bone surfaces were measured at different loading amplitudes. The estimated error was 10μm and the maximal micromotion was 60μm, in the loading direction, at 1400N. This pilot study provided a local measurement of the micromotions in the 3 direction and at 8 locations on the stem surface simultaneously. This technique could be easily extended to higher loads and a much larger number of points, covering the entire stem surface and providing a quasi-continuous distribution of the 3D interfacial micromotions around the stem. The new measurement method would be very useful to compare the induced micromotions of different stem designs and to optimize the primary stability of cementless total hip arthroplasty.

Reshaping the remodelled left ventricle: a new concept.

OBJECTIVE: Based on the law of Laplace, transventricular tension members were designed to diminish wall stress by changing the left ventricle (LV) globular shape to a bilobular one, thus reducing the ventricular wall radius of curvature. This concept was tested in a model of congestive heart failure. METHODS: Seven calves were used for the study (74.3+/-4.2 kg). Treatment efficacy was assessed with sonomicrometric wall motion analysis coupled with intraventricular pressure measurement. Preload increase was applied stepwise with tension members in released and tightened position. RESULTS: Tightening of the tension members improved systolic function for CVP>10 mmHg (dP/dt: 828+/-122 vs. 895+/-112 mmHg/s, P=0.019, for baseline and 20% stress level reduction respectively; wall thickening: 11.6+/-1.5 vs. 13.3+/-1.7%, P<0.001) and diastolic function (LV end-diastolic pressure: 15.9+/-4.8 vs. 13.6+/-2.7 mmHg, P<0.001, for CVP>10 mmHg; peak rate of wall thinning: -12.2+/-2.2 vs. -14+/-2.3 cm(2)/s, P<0.001 and logistic time constant of isovolumic relaxation: 48.4 +/-10.9 vs. 39.8+/-9.6ms, P<0.001, for CVP>5 mmHg). CONCLUSIONS: This less aggressive LV reduction method significantly improves contractility and relaxation parameters in this model of congestive heart failure.