Bending Dynamics Research Articles

Control of Ionic Polymer-Metal Composites for Active Catheter Systems via Linear Parameter-Varying Approach

The ionic polymer metal composite (IPMC) is one type of electro-active material with the characteristics of low electric driving potential, large deformation, and aquatic manipulation. It is highly attractive to biomedical applications as an actuator or a sensor. The main purpose of this study is to explore closed-loop control schemes to an IPMC actuator for active catheter systems. In this article, by measuring frequency responses of a 20 mm × 5 mm × 200 μm IPMC, an empirical model is developed and used for closed-loop control. From previous work, two resonant peaks ranged at 3—4 Hz and 18—20 Hz are found in the Bode diagram for the frequency responses of IPMC. Based on this fact, a 4th order transfer function was modeled to describe the system. A parameter-dependent transfer function was then created to describe the bending dynamics of IPMC in response to different driving voltages. As IPMC actuators are nonlinear and slow time-varying systems, the controller was designed using linear parameter varying (LPV) approach. Compared with the conventional closed-loop PID control, the maximum overshoot and steady-state error was decreased to 2% and 1.32%, respectively. The rise time was about 0.186 s, which is within the limit for many biomedical applications.

Statistics of Time-Limited Ensembles of Bent DNA Conformations

The paper considers statistical properties of ensembles of chain conformations obtained by short-time Brownian dynamics (BD) of a coarse-grained DNA model in order to find out if the conditions necessary for accurate evaluation of the polymer elasticity are attainable in atom-level molecular dynamics (MD) simulations. To measure the bending persistence length (PL) with a 10% error using data accumulated in a single trajectory of a double helix of 15 base pairs, dynamics should be continued for a few microseconds. However, these estimates should be scaled down by about 2 orders of magnitude because the bending dynamics of short double helices in MD features much smaller relaxation times. As a result, good qualitative agreement with the worm-like chain (WLC) theory is reached in MD after tens of nanoseconds. The presently accessible durations of MD trajectories provide reasonably accurate evaluation of DNA elasticity and allow modeling of its mesoscopic properties. The surprisingly fast bending dynamics of short double helices in MD suggests that the microscopic mechanisms of DNA flexibility differ from a simple harmonic model.

Nonequilibrium Microtubule Fluctuations in a Model Cytoskeleton

Biological activity gives rise to nonequilibrium fluctuations in the cytoplasm of cells; however, there are few methods to directly measure these fluctuations. Using a reconstituted actin cytoskeleton, we show that the bending dynamics of embedded microtubules can be used to probe local stress fluctuations. We add myosin motors that drive the network out of equilibrium, resulting in an increased amplitude and modified time dependence of microtubule bending fluctuations. We show that this behavior results from steplike forces on the order of 10 pN driven by collective motor dynamics.

Multi-Scale Distributed Port-Hamiltonian Representation of Ionic Polymer-Metal Composite

This paper shows that one of soft actuators, Ionic Polymer-Metal Composite (IPMC) can be modeled in terms of distributed port-Hamiltonian systems with multi-scale. The physical structure of IPMC consists of three parts. The first part is an electric double layer at the interface between the polymer and the metal electrodes. The frequency response of the polymer-metal interface shows a fractal degree of gain slope. Then we adopt a black-box circuit model to this part and give considerations for distributed impedance parameters. The second part is an electrostress diffusion coupling model with bending and relaxation dynamics. This part is represented by an electro-osmosis, which is a water transport by an electric field, and a streaming potential, which is an electric field created by a water transport. We discuss the relationship of stress and bending moment induced by swelling. The third part is a mechanical system modeled as a flexible beam with large deformations. The representation has the capability extracting the control structure based on passivity from distributed parameter systems possessing a complex behavior.

Unique Physical Signature of DNA Curvature and Its Implications for Structure and Dynamics

A particularly sensitive birefringence technique is used to analyze a curved DNA fragment with 118 bp and a standard DNA with 119 bp. At salt concentrations from 0.5 to 10 mM, both fragments show the usual negative stationary birefringence and monotonic transients - differences are relatively small. At 100 mM salt the curved DNA shows a positive stationary birefringence and non-monotonic transients with processes having amplitudes of opposite sign, whereas signals of the standard DNA remain as usual. Transients induced by reversal of the field vector indicate the existence of a permanent dipole for the curved DNA. 2-MHz-ac pulses induce a negative stationary birefringence in both DNAs. These results are consistent with calculations on models for curved DNA predicting a quasi-permanent dipole and a positive dichroism/birefringence. The quasi-permanent dipole results from the loss of symmetry in the charge distribution of the curved polyelectrolyte. The appearance of the unique signature of curvature at high salt is mainly due to a strong decrease of the polarizability by about 2 orders of magnitude. The special mode of orientation resulting from the quasi-permanent dipole is expected to contribute to the gel migration anomaly. The time constants of birefringence decay for the curved fragment are shorter than those of the 119 bp fragment by a factor of approximately 1.10 at 0.6 mM salt, whereas this factor is approximately 1.20 at 100 mM Na+. If both fragments were normal DNA with 3.4 A rise per base pair, the factor would be approximately 1.02. At high salt and high electric field strengths the factor increases up to 1.37. The implications for the bending dynamics and the potential to distinguish static from dynamic persistence by field reversal experiments are discussed. The dependence of the curvature on the salt concentration indicated by the time constants is consistent with a clear decrease of the electrophoretic anomaly at decreasing salt concentration.

Synapsis of loxP Sites by Cre Recombinase

Cre recombinase catalyzes site-specific recombination between 34-bp loxP sites in a variety of topological and cellular contexts. An obligatory step in the recombination reaction is the association, or synapsis, of Cre-bound loxP sites to form a tetrameric protein assembly that is competent for strand exchange. Using analytical ultracentrifugation and electrophoresis approaches, we have studied the energetics of Cre-mediated synapsis of loxP sites. We found that synapsis occurs with a high affinity (Kd = 10 nM) and is pH-dependent but does not require divalent cations. Surprisingly, the catalytically inactive Cre K201A mutant is fully competent for synapsis of loxP sites, yet the inactive Y324F and R173K mutants are defective for synapsis. These findings have allowed us to determine the first crystal structures of a pre-cleavage Cre-loxP synaptic complex in a configuration representing the starting point in the recombination pathway. When combined with a quantitative analysis of synapsis using loxP mutants, the structures explain how the central 8 bp of the loxP site are able to dictate the order of strand exchange in the Cre system.

Bending Dynamics of Fluctuating Biopolymers Probed by Automated High-Resolution Filament Tracking

Microscope images of fluctuating biopolymers contain a wealth of information about their underlying mechanics and dynamics. However, successful extraction of this information requires precise localization of filament position and shape from thousands of noisy images. Here, we present careful measurements of the bending dynamics of filamentous (F-)actin and microtubules at thermal equilibrium with high spatial and temporal resolution using a new, simple but robust, automated image analysis algorithm with subpixel accuracy. We find that slender actin filaments have a persistence length of ∼17 μm, and display a q −4-dependent relaxation spectrum, as expected from viscous drag. Microtubules have a persistence length of several millimeters; interestingly, there is a small correlation between total microtubule length and rigidity, with shorter filaments appearing softer. However, we show that this correlation can arise, in principle, from intrinsic measurement noise that must be carefully considered. The dynamic behavior of the bending of microtubules also appears more complex than that of F-actin, reflecting their higher-order structure. These results emphasize both the power and limitations of light microscopy techniques for studying the mechanics and dynamics of biopolymers.

Long-wavelength dispersion of transverse acoustic phonons in untwinnedYBa2Cu3O7−δsingle crystals

High-resolution ($\Delta E$=1.3 meV) inelastic X-ray scattering (IXS) in optimally doped untwinned YBa$_2$Cu$_3$O$_{7-\delta}$ single crystals show that the dispersion of transverse acoustic phonons in the a-direction remains linear with no softening due to bending modes in the long wavelength limit, down to q=0.02. The sound velocity is found to be 2700 +/- 70 m s$^{-1}$, in excellent agreement with ultrasound measurements, and unchanged upon cooling from room temperature to 98 K. These results rule out a strong coupling between bending dynamics of the CuO$_2$ planes and charge carriers in cuprates.

Use of plasmon coupling to reveal the dynamics of DNA bending and cleavage by single EcoRV restriction enzymes

Pairs of Au nanoparticles have recently been proposed as "plasmon rulers" based on the dependence of their light scattering on the interparticle distance. Preliminary work has suggested that plasmon rulers can be used to measure and monitor dynamic distance changes over the 1- to 100-nm length scale in biology. Here, we substantiate that plasmon rulers can be used to measure dynamical biophysical processes by applying the ruler to a system that has been investigated extensively by using ensemble kinetic measurements: the cleavage of DNA by the restriction enzyme EcoRV. Temporal resolutions of up to 240 Hz were obtained, and the end-to-end extension of up to 1,000 individual dsDNA enzyme substrates could be simultaneously monitored for hours. The kinetic parameters extracted from our single-molecule cleavage trajectories agree well with values obtained in bulk through other methods and confirm well known features of the cleavage process, such as DNA bending before cleavage. Previously unreported dynamical information is revealed as well, for instance, the degree of softening of the DNA just before cleavage. The unlimited lifetime, high temporal resolution, and high signal/noise ratio make the plasmon ruler a unique tool for studying macromolecular assemblies and conformational changes at the single-molecule level.

The nature of “unusual” electro-optical transients observed for DNA

Unusual electro-optical transients have been observed for many different polymers and colloidal systems. These effects provoked serious confusion, because a simple-minded interpretation can be completely misleading. The case of double helical DNA is of particular interest, because DNA has been studied in more detail than other systems and because of its biological function. DNA is subject to bending, which implies a loss of symmetry. Due to its high charge density, non-symmetric conformations must have a non-symmetric distribution of charges leading to a torque of considerable magnitude in the presence of external electric fields. The dipole moment describing this torque must be calculated in a coordinate system with its origin at the center of diffusion. The resulting dipole values are in the range of thousands of Debye units. Because the new dipole type is analogous to but not identical with permanent dipoles, the notation “quasi-permanent” dipole is suggested. Application of this concept, using commonly accepted parameters for DNA and established procedures for calculation of electro-optical transients, leads to “unusual” transients. Thus, these transients must be expected from well-known parameters of DNA double helices. The influence of the quasi-permanent dipole moment may be amplified considerably by hydrodynamic coupling. This effect has been demonstrated for the case of smoothly bent rods. Both model calculations and experiments illustrate the danger of getting data that may be completely misleading. For example, depending on pulse amplitudes and/or pulse lengths, electro-optical decays may be accelerated artificially due to superposition of decay components with opposite amplitudes. Experiments show that unusual transients and apparent acceleration effects disappear, when high frequency sine pulses are used for the electro-optical analysis of DNA. Electro-optical effects depend upon the internal dynamics of the object under investigation. In general, the dynamics of DNA bending was assumed to be fast compared to rotational diffusion. Because stacking rearrangements in single stranded nucleic acids are relatively slow and recently the dynamics of the B–A transition was observed in the time range >1 μs, it is likely that there are also relatively slow rearrangements between bending conformers. Bending transitions are expected to be relatively fast, when there are no activation barriers in the bending pathway, and may be slow, when activation barriers must be passed between bending conformers.

Influence of experimental removal of large woody debris on spatial patterns of three‐dimensional flow in a meander bend

AbstractThis study reports the results of a large woody debris (LWD) removal experiment in a meander bend along a low‐energy stream in the Midwestern United States. The LWD obstacle was located in the center of the channel at the bend exit and consisted of a mature tree with an intact soil‐covered root wad and a large accumulation of logs, branches and pieces of lumber on top of and adjacent to the main tree. The results indicate that the LWD obstruction influenced 3D flow structure in this bend at all flow stages. The main effect of LWD is to dramatically decelerate flow throughout the majority of the bend, while locally accelerating flow where it passes through the narrow chute at the downstream end of the LWD obstruction. Results from the LWD removal experiment indicate that patterns of three‐dimensional flow structure in meander bends are sensitive to complete removal of LWD. After the removal of LWD from the bend, both downstream and secondary velocities increased and, though still weak, secondary flow intensified. Large, relatively stable, obstructions that span a significant portion of the channel may act as natural dams, effectively ponding water upstream of the LWD, thereby producing substantial convective deceleration of the flow. This research is the first to document three‐dimensional flow structure before and after a controlled removal of LWD from a meander bend. Studies of the type reported here represent a first step toward determining the ensemble of process interactions between LWD and bend dynamics. Copyright © 2006 John Wiley & Sons, Ltd.

Influence of hydroxyl-water interaction on structural transformations during Cs + exchange in microporous H-CST

Crystalline silicotitanate (CST) molecular sieve is being tested as an ion exchanger for targeted removal of Cs from high level radioactive nuclear waste solutions. CST is resistant to high radiation fields and highly alkaline/acidic solutions which make it an ideal sequestration candidate. The mechanisms and dynamics of the crystallographic structural changes involved are the fundamental properties of selectivity in this material, and have not been studied previously. This study investigates the molecular processes of ion exchange in real time using neutron and X-ray diffraction as well molecular dynamics (MD) simulations. These techniques in unison have provided the most complete description of the Cs exchange process in hydrogen form of CST (H-CST). In the H-CST structure, the elliptical channels cannot accommodate Cs due to unacceptable short Cs–O bond distances. From time-resolved X-ray diffraction studies, the elliptical channels in H-CST transform to circular geometry after 8 wt.% Cs exchange. Although structural transformations were observed and the symmetry changed from space group P42/mbc to P42/mcm, the mechanisms were still unknown. Identifying all atom types and positions in the CST structure will ultimately explain the mechanisms of selectivity for Cs in H-CST. Time-resolved and static neutron diffraction studies added the proton positions on the water molecules and hydroxyl units to the model derived from X-ray scattering. The results show that as Cs diffuses through the structure, water molecules must change orientations and positions to hydrate Cs and maintain the hydrogen bond network. The new configuration of the proton on the water sites are closer to the framework and force close proton–proton repulsion with the framework hydroxyl. This repulsion bends the hydroxyl and drives the transformation of the CST structure. Hydroxyl bending and water dynamics have been confirmed using MD simulations. The short timescales of MD simulations is ideal to study these fast molecular motions and emphasizes the important role hydrogen has in CST toward Cs selectivity.

Dynamics of Electron Transport by Elastic Bending of Short DNA Duplexes. Experimental Study and Quantitative Modeling of the Cyclic Voltammetric Behavior of 3‘-Ferrocenyl DNA End-Grafted on Gold

The dynamics of electron transport within a molecular monolayer of 3'-ferrocenylated-(dT)(20) strands, 5'-thiol end-grafted onto gold electrode surfaces via a short C2-alkyl linker, is analyzed using cyclic voltammetry as the excitation/measurement technique. It is shown that the single-stranded DNA layer behaves as a diffusionless system, due to the high flexibility of the ss-DNA chain. Upon hybridization by the fully complementary (dA)(20) target, the DNA-modified gold electrode displays a highly unusual voltammetric behavior, the faradaic signal even ultimately switching off at a high enough potential scan rate. This remarkable extinction phenomenon is qualitatively and quantitatively justified by the model of elastic bending diffusion developed in the present work which describes the motion of the DNA-borne ferrocene moiety as resulting from the elastic bending of the duplex DNA toward and away from the electrode surface. Its use allows us to demonstrate that the dynamics of electron transport within the hybridized DNA layer is solely controlled by the intrinsic bending elasticity of ds-DNA. Fast scan rate cyclic voltammetry of end-grafted, redox-labeled DNA layers is shown to be an extremely efficient method to probe the bending dynamics of short-DNA fragments in the submillisecond time range. The persistence length of the end-anchored ds-DNA, a parameter quantifying the flexibility of the nanometer-long duplex, can then be straightforwardly and accurately determined from the voltammetry data.

Dynamics of Supercoiled and Linear pBluescript II SK(+) Phagemids Probed with a Long-lifetime Metal-ligand Complex

We extended the measurable time scale of DNA dynamics to microsecond using [Ru(phen)(2)(dppz)](2+)(phen = 1,10-phenanthroline, dppz=dipyrido[3,2-a:2',3'-c]phenazine)(RuPD) , which displays a mean lifetime near 500 ns. To evaluate the usefulness of this luminophore (RuPD) for probing nucleic acid dynamics, its intensity and anisotropy decays when intercalated into supercoiled and linear pBluescript (pBS) II SK(+) phagemids were examined using frequency-domain fluorometry with a blue light-emitting diode (LED) as the modulated light source. The mean lifetime for the supercoiled phagemids (<tau> = 489.7 ns) was somewhat shorter than that for the linear phagemids (<tau> = 506.4 ns), suggesting a more efficient shielding from water by the linear phagemids. The anisotropy decay data also showed somewhat shorter slow rotational correlation times for supercoiled phagemids (997.2 ns) than for the linear phagemids (1175.6 ns). The slow and fast rotational correlation times appear to be consistent with the bending and torsional motions of the phagemids, respectively. These results indicate that RuPD can have applications in studies of both bending and torsional dynamics of nucleic acids.

Electrostress Diffusion Coupling Model for Polyelectrolyte Gels

To describe the deformation dynamics of polyelectrolyte gel, we formulate the electrostress diffusion coupling model. The model describes the interplay of the deformation of gel, permeation of water, and the transport of ions. The model gives a microscopic expression for the Onsager coefficient and allows us to discuss the effect of ionic radius. The model is then applied to the bending dynamics of a thin strip of ionic gels under stepwise application of electric field. The model qualitatively explains the relaxation behavior of an ionic gel (Nafion 117) for various kinds of ions including large counterions such as TEA+ (tetraethylammonium).

Identification of linear parameter-varying state-space models with application to helicopter rotor dynamics

A considerable amount of work has been dedicated in the past to the problem of the system identification of helicopter flight dynamics, while much less activity has been oriented to the goal of developing suitable identification procedures for rotor dynamics, mainly because of the difficulties associated with the task. This paper shows that subspace and optimization based identification techniques can be used to determine discrete-time linear parameter-varying models that have the potential to provide accurate descriptions for the (intrinsically time-varying) dynamics of a rotor blade. The identification techniques are presented and applied to simulated data generated by a physical model that describes the out-of-plane bending dynamics of a helicopter rotor blade.

A Galerkin formulation for shear deformable plate bending dynamics

AbstractA Galerkin boundary element formulation for shear deformable plate bending dynamics is developed. The formulation makes use of the static fundamental solutions for the weighted residual integral equations. The domain integrals carrying the inertia terms and generic static loads are considered as body forces and approximated with boundary values using the dual reciprocity method. The load is modelled as a series of impact loads of time varying intensity and moving in space in a predetermined path. The formulation was implemented and tested solving a benchmark problem. The results are compared with finite element solutions. Copyright © 2004 John Wiley &amp; Sons, Ltd.

Identification of biomechanical factors involved in stem shape variability between apricot tree varieties.

Stem shape in angiosperms depends on several growth traits such as elongation direction, amount and position of axillary loads, stem dimensions, wood elasticity, radial growth dynamics and active re-orientation due to tension wood. This paper analyses the relationship between these biomechanical factors and stem shape variability. Three apricot tree varieties with contrasting stem shape were studied. Growth and bending dynamics, mechanical properties and amount of tension wood were measured on 40 1-year-old stems of each variety during one growth season. Formulae derived from simple biomechanical models are proposed to quantify the relationship between biomechanical factors and re-orientation of the stems. The effect of biomechanical factors is quantified combining their mechanical sensitivity and their actual variability. Re-orientations happened in three main periods, involving distinct biomechanical phenomena: (a) passive bending due to the increase of shoot and fruit load at the start of the season; (b) passive uprighting at the fall of fruits; (c) active uprighting due tension wood production at the end of the season. Differences between varieties mainly happened during periods (a) and (b). The main factors causing differences between varieties are the length/diameter and the load/cross-sectional area ratios during period (a). Wood elasticity does not play an important role because of its low inter-variety variability. Differences during period (b) are related to the dynamics of radial growth: varieties with early radial growth bend weakly upward because the new wood layers tend to set them in a bent position. The action of tension wood during period (c) is low when compared with passive phenomena involved in periods (a) and (b).

Contribution of Opening and Bending Dynamics to Specific Recognition of DNA Damage

Guanine-uracil (G·U) wobble base-pairs are a detrimental lesion in DNA. Previous investigations have shown that such wobble base-pairs are more prone to base-opening than the normal G·C base-pairs. To investigate the sequence-dependence of base-pair opening we have performed 5 ns molecular dynamics simulations on G·U wobble base-pairs in two different sequence contexts, TGT/AUA and CGC/GUG. Furthermore, we have investigated the effect of replacing the guanine base in each sequence with a fluorescent guanine analogue, 6-methylisoxanthopterin (6MI). Our results indicate that each sequence opens spontaneously towards the major groove in the course of the simulations. The TGT/AUA sequence has a greater proportion of structures in the open state than the CGC/GUG sequence. Incorporation of 6MI yields wobble base-pairs that open more readily than their guanine counterparts. In order of increasing open population, the sequences are ordered as CGC<TGT<CMC<TMT, where M represents 6MI. Both members of the base-pair open towards the major groove in a symmetrically coupled motion. Opening results in breakage of the H3(U)–O6(G/6MI) hydrogen bond, and distortion of the H1(G/6MI)–O2(U) hydrogen bond. Structural consequences of the opening include the formation of the H21(G/6MI)–O2(U) hydrogen bond and a change in local solvation in the grooves and particularly near N3–H3 of uracil. Additionally, DNA flexibility is reduced in the open state for bending towards the major groove generating two nearly discrete states: closed unbent and open bent. The observed differences in the local structural and dynamical properties of the G·U base-pair may play an important role in the activity of DNA repair enzymes that initiate base excision by distorting the DNA and flipping the target base from inside the DNA helix.

8-Oxoguanine enhances bending of DNA that favors binding to glycosylases.

Molecular dynamics (MD) simulations were carried out on the DNA oligonucleotide GGGAACAACTAG:CTAGTTGTTCCC in its native form and with guanine in the central G(19):C(6) base pair replaced by 8-oxoguanine (8oxoG). A box of explicit water molecules was used for solvation, and Na(+) counterions were added to neutralize the system. The direction and magnitude of global bending were assessed by a technique used previously to analyze simulations of DNA containing a thymine dimer. The presence of 8oxoG did not greatly affect the magnitude of DNA bending; however, bending into the major groove was significantly more probable when 8oxoG replaced G(19). Crystal structures of glycosylases bound to damaged-DNA substrates consistently show a sharp bend into the major groove at the damage site. We conclude that changes in bending dynamics that assist the formation of this kink are a part of the mechanism by which glycosylases of the base excision repair pathway recognize the presence of 8oxoG in DNA.