Tension Propagation Research Articles

Localized soft elasticity in liquid crystal elastomers.

Synthetic approaches to prepare designer materials that localize deformation, by combining rigidity and compliance in a single material, have been widely sought. Bottom-up approaches, such as the self-organization of liquid crystals, offer potential advantages over top–down patterning methods such as photolithographic control of crosslink density, relating to the ease of preparation and fidelity of resolution. Here, we report on the directed self-assembly of materials with spatial and hierarchical variation in mechanical anisotropy. The highly nonlinear mechanical properties of the liquid crystalline elastomers examined here enables strain to be locally reduced >15-fold without introducing compositional variation or other heterogeneities. Each domain (⩾0.01 mm2) exhibits anisotropic nonlinear response to load based on the alignment of the molecular orientation with the loading axis. Accordingly, we design monoliths that localize deformation in uniaxial and biaxial tension, shear, bending and crack propagation, and subsequently demonstrate substrates for globally deformable yet locally stiff electronics.

Chaperone-assisted translocation of flexible polymers in three dimensions.

Polymer translocation through a nanometer-scale pore assisted by chaperones binding to the polymer is a process encountered in vivo for proteins. Studying the relevant models by computer simulations is computationally demanding. Accordingly, previous studies are either for stiff polymers in three dimensions or flexible polymers in two dimensions. Here, we study chaperone-assisted translocation of flexible polymers in three dimensions using Langevin dynamics. We show that differences in binding mechanisms, more specifically, whether a chaperone can bind to a single site or multiple sites on the polymer, lead to substantial differences in translocation dynamics in three dimensions. We show that the single-binding mode leads to dynamics that is very much like that in the constant-force driven translocation and accordingly mainly determined by tension propagation on the cis side. We obtain β≈1.26 for the exponent for the scaling of the translocation time with polymer length. This fairly low value can be explained by the additional friction due to binding particles. The multiple-site binding leads to translocation the dynamics of which is mainly determined by the trans side. For this process we obtain β≈1.36. This value can be explained by our derivation of β=4/3 for constant-bias translocation, where translocated polymer segments form a globule on the trans side. Our results pave the way for understanding and utilizing chaperone-assisted translocation where variations in microscopic details lead to rich variations in the emerging dynamics.

Tendon-Driven Continuum Robot for Endoscopic Surgery: Preclinical Development and Validation of a Tension Propagation Model.

In this paper, we present a tendon-driven continuum robot for endoscopic surgery. The robot has two sections for articulation actuated by tendon wires. By actuating the two sections independently, the robot can generate a variety of tip positions while maintaining the tip direction. This feature offers more flexibility in positioning the tip for large viewing angles of up to 180 degrees than does a conventional endoscope. To accurately estimate the tip position at large viewing angles, we employed kinematic mapping with a tension propagation model including friction between the tendon wires and the robot body. In a simulation study using this kinematic-mapping, the two-section robot at a target scale (outer diameter 1.7 mm and length 60 mm) produced a variety of tip positions within 50-mm ranges at the 180°-angle view. In the experimental validation, a 10:1 scale prototype performed three salient postures with different tip positions at the 180°-angle view. The proposed forward kinematic mapping (FKM) predicted the tip position within a tip-to-tip error of 6 mm over the 208-mm articulating length. The tip-to-tip error by FKM was significantly less than the one by conventional piecewise-constant-curvature approximation (PCCA) (FKM: 5.9 ± 2.9 mm vs. PCCA: 23.7 ± 3.6 mm, n=15, P < 0.01).

Theory of polymer translocation through a flickering nanopore under an alternating driving force.

We develop a theory for polymer translocation driven by a time-dependent force through an oscillating nanopore. To this end, we extend the iso-flux tension propagation theory [Sarabadani et al., J. Chem. Phys. 141, 214907 (2014)] for such a setup. We assume that the external driving force in the pore has a component oscillating in time, and the flickering pore is similarly described by an oscillating term in the pore friction. In addition to numerically solving the model, we derive analytical approximations that are in good agreement with the numerical simulations. Our results show that by controlling either the force or pore oscillations, the translocation process can be either sped up or slowed down depending on the frequency of the oscillations and the characteristic time scale of the process. We also show that while in the low and high frequency limits, the translocation time τ follows the established scaling relation with respect to chain length N0, in the intermediate frequency regime small periodic, fluctuations can have drastic effects on the dynamical scaling. The results can be easily generalized for non-periodic oscillations and elucidate the role of time dependent forces and pore oscillations in driven polymer translocation.

Dynamic Scaling Theory of the Forced Translocation of a Semi-flexible Polymer Through a Nanopore

We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P , its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. At the blob size P/a^2 , where a is the size of a monomer, the statistics becomes that of an ideal chain. As the blob size further decreases to below the persistence length P, the statistics is that of a rigid rod. We argue that semi-flexible polymer in translocation should include the three regions: a self-avoiding region, an ideal chain region and a rigid rod region, under uneven tension propagation, instead of a uniform scaling picture as in the case of a completely flexible polymer. In various regimes under the effect of weak, intermediate and strong driving forces we derive equations from which we can calculate the translocation time of the polymer. The translocation exponent is given by \alpha=1+\mu, where \mu is an effective exponent for the end-to-end distance of the semi-flexible polymer, having a value between 1/2 and 3/5, depending on the total contour length of the polymer. Our results are of relevance for forced translocation of biological polymers such as DNA through a nanopore.

Driven anomalous diffusion: An example from polymer stretching

The way tension propagates along a chain is a key to govern many anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.

Iso-flux tension propagation theory of driven polymer translocation: the role of initial configurations.

We investigate the dynamics of pore-driven polymer translocation by theoretical analysis and molecular dynamics (MD) simulations. Using the tension propagation theory within the constant flux approximation we derive an explicit equation of motion for the tension front. From this we derive a scaling relation for the average translocation time τ, which captures the asymptotic result τ∝N0(1+ν), where N0 is the chain length and ν is the Flory exponent. In addition, we derive the leading correction-to-scaling term to τ and show that all terms of order N0(2ν) exactly cancel out, leaving only a finite-chain length correction term due to the effective pore friction, which is linearly proportional to N0. We use the model to numerically include fluctuations in the initial configuration of the polymer chain in addition to thermal noise. We show that when the cis side fluctuations are properly accounted for, the model not only reproduces previously known results but also considerably improves the estimates of the monomer waiting time distribution and the time evolution of the translocation coordinate s(t), showing excellent agreement with MD simulations.

Chain-like structures' motion - metamodeling of the translocation time in some specific situations

This article discusses an application of an algorithm for modeling the chain-like structures' motion. The basic and the most important assumption of the adopted approach is sequentialization of the moves. In the presented version of the algorithm there is a possi- bility of modeling the tension propagation mechanism. The main purpose of the paper is to investigate the impact of different algorithm parameters on final movement characteristics. Based on the Monte Carlo experiments metamodels describing the relationship between the translocation time and selected algorithm parameters are proposed and discussed.

Influence of pore friction on the universal aspects of driven polymer translocation

We derive a scaling ansatz for the mean first passage time (MFPT) τ of a driven polymer chain through a nanopore as a function of the chain length N, the external bias f, and the effective pore-polymer friction η, and demonstrate that the pore-polymer interaction, which we introduce as a correction term to asymptotic scaling, is responsible for the dominant finite-size effect. This ansatz provides a simple procedure to extract the asymptotic τ in the large-N limit from a finite chain length data (obtained either from experiment or simulation) by eliminating the correction-to-scaling term. We validate the ansatz applying it on a large set of data for τ obtained using Brownian dynamics (BD) and Brownian dynamics tension propagation (BDTP) simulation results (Ikonen T. et al., Phys. Rev. E, 85 (2012) 051803; J. Chem. Phys., 137 (2013) 085101) for a variety of combination for N, f, and η. As an important practical application we demonstrate how the rescaling procedure can be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we extend the BDTP theory to incorporate Zimm dynamics and find that the asymptotic results for τ (or the translocation exponent) remains unaltered with the inclusion of the hydrodynamics interactions (HI), although the convergence is slower than what we observe for Rouse dynamics. Using the rescaling ansatz we find that these new findings are in good agreement with the existing experimental results as well as with lattice Boltzmann results for driven polymer translocation (PT) for small N.

Translocation dynamics of a semiflexible chain under a bias: Comparison with tension propagation theory

We study translocation dynamics of a semi-flexible polymer through a nanoscopic pore in two dimensions (2D) using Langevin dynamics simulation in presence of an external force inside the pore. We observe that for a given chain length N the mean first passage time (MFPT)〈τ〉 increases for a stiffer chain. By repeating the calculation for various chain lengths N and bending rigidity parameter κb we calculate the translocation exponent α (〈τ〉 ∼ Nα). For chain lengths N and bending rigidity κb considered in this paper we find that the translocation exponent satisfies the inequality α < 1 + ν, where is the equilibrium Flory exponent for a given chain stiffness, as previously observed in various simulation studies for fully flexible chains. We observe that the peak position of the residence time W(s) as a function of the monomer index s shifts at a lower s-value with increasing chain stiffness κb. We also monitor segmental gyration 〈Rg(s)〉 both at the cis and trans side during the translocation process and find that for κb ≠ 0 the late time cis conformations are nearly identical to the early time trans conformations, and this overlap continues to increase for stiffer chains. Finally, we try to rationalize dependence of various quantities on chain stiffness κb using Sakaue’s tension propagation (TP) theory [Phys. Rev. E 76, 021803 (2007)] and Brownian Dynamics Tension Propagation (BDTP) theory due to Ikonen et al. [Phys. Rev. E 85 051803 (2012); J. Chem. Phys. 137 085101 (2012)] originally developed for a fully flexible chain to a semi-flexible chain.

Driven translocation of a semi-flexible chain through a nanopore: A Brownian dynamics simulation study in two dimensions

We study translocation dynamics of a semi-flexible polymer chain through a nanoscopic pore in two dimensions using Langevin dynamics simulation in presence of an external bias F inside the pore. For chain length N and stiffness parameter κb considered in this paper, we observe that the mean first passage time <τ> increases as <τ(κb)>~<τ(κb=0)>lp(aN) , where κb and lp are the stiffness parameter and persistence length, respectively, and aN is a constant that has a weak N dependence. We monitor the time dependence of the last monomer xN(t) at the cis compartment and calculate the tension propagation time (TP) ttp directly from simulation data for <xN(t)> ~ t as alluded in recent nonequlibrium TP theory [T. Sakaue, Phys. Rev. E 76, 021803 (2007)] and its modifications to Brownian dynamics tension propagation theory [T. Ikonen, A. Bhattacharya, T. Ala-Nissila, and W. Sung, Phys. Rev. E 85, 051803 (2012); and J. Chem. Phys. 137, 085101 (2012)] originally developed to study translocation of a fully flexible chain. We also measure ttp from peak position of the waiting time distribution W(s) of the translocation coordinate s (i.e., the monomer inside the pore), and explicitly demonstrate the underlying TP picture along the chain backbone of a translocating chain to be valid for semi-flexible chains as well. From the simulation data, we determine the dependence of ttp on chain persistence length lp and show that the ratio ttp∕<τ> is independent of the bias F.

Translocation dynamics of a semi-flexible chain under a bias: comparison with tension propagation theory

Translocation dynamics of a semi-flexible chain under a bias: comparison with tension propagation theory

Repair of large area pores in supported double bilayers

We describe an experimental system where we can generate, and subsequently close, multiple large membrane ruptures in supported double bilayers. We show in this study for the first time that large membrane pores (∼10–150 μm in size) in flat phospholipid vesicles can be reduced in size or completely closed by a pore edge tension driven area reduction mechanism. We can dynamically control the membrane tension of a flat giant unilamellar vesicle and its interplay with the surface adhesion to a solid support. Adhesion to the support surface causes increased membrane tension, which eventually relaxes by the formation of several pores in the membrane. We show that the tension propagation time τmax is exceptionally long in this system, which allows for simultaneous opening of multiple pores. The pores can be stabilized by Ca2+-mediated pinning sites in the interior of the flat giant unilamellar vesicle. After pore formation followed by pinning, we depleted Ca2+ ions resulting in removal of pinning and relaxation of membrane tension. This allows the pore to close, driven by the pore edge tension.

Influence of non-universal effects on dynamical scaling in driven polymer translocation

We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the cis side subchain. We present theoretical and numerical evidence that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.

Propagation of tension along a polymer chain

We study the propagation of tension caused by an external force along a long polymeric molecule in two different settings, namely along a free polymer in three-dimensional (3D) space being pulled from one end, and along a prestretched circular polymer, confined in a narrow circular tube. We show that in both cases, the tension propagation is governed by a diffusion equation, and in particular, the tension front propagates as t(1/2) along the contour of the chain. The results are confirmed numerically, and by molecular dynamics simulations in the case of the 3D polymer. We also compare our results with the previously suggested ones for the translocation setting, and discuss why tension propagation is slower in that case.

Dragging a polymer in a viscous fluid: Steady state and transient

We study the conformation and dynamics of a single polymer chain that is pulled by a constant force applied at its one end with the other end free. Such a situation is relevant to the growing technology of manipulating individual macromolecules, which offers a paradigm research for probing far-from-equilibrium responses of long flexible biological polymers. We first analyze the Rouse model for the Gaussian chains for which the exact analytical results can be obtained. More realistic features such as the finite extensibility, the excluded volume, and the hydrodynamic interactions are taken into account with the help of the scaling argument, which leads to various nontrivial predictions such as the force-dependent friction constants. We elucidate (i) generalized dynamical equations of state describing extension and friction laws in steady-state and (ii) the tension propagation laws in the transient process. We point out that the time evolutions of the dynamic friction in the transient process crucially depend on the experimental protocol, i.e., either constant force or constant velocity ensemble. These predictions could be verified in experiments using giant DNAs and chromosomes.

Process time distribution of driven polymer transport

We discuss the temporal distribution of dynamic processes in driven polymer transport inherent to flexible chains due to stochastic tension propagation. The stochasticity originates from the disordered initial configuration of an equilibrium polymer coil, which results in random paths for tension propagation. We consider the process time for when translocation occurs across a fixed pore and when stretching occurs by pulling the chain end. A scaling argument for the mean and standard deviation of the process time is provided using the two-phase picture for stochastic propagation. The two cases are found to differ remarkably. The process time distribution of the translocation exhibits substantial spreading even in the long-chain limit, unlike that found for the dynamics of polymer stretching. In addition, the process time distribution in the driven translocation is shown to have a characteristic asymmetric shape.

Unifying model of driven polymer translocation

We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by solving the model for chain lengths up to 10^{10} monomers, we show that the chain lengths probed by experiments and simulations are typically orders of magnitude below the asymptotic limit. This explains both the considerable scatter in the observed scaling of translocation time with respect to chain length, and some of the shortcomings of present theories. Our study shows that for a quantitative theory of polymer translocation, explicit consideration of finite chain length effects is required.

Tension dynamics in semiflexible polymers. II. Scaling solutions and applications

In part I [O. Hallatschek, preceding paper, Phys. Rev. E 75, 031905 (2007)] of this contribution, a systematic coarse-grained description of the dynamics of a weakly bending semiflexible polymer was developed. Here, we discuss analytical solutions of the established deterministic partial integro-differential equation for the spatiotemporal relaxation of the backbone tension. For prototypal experimental situations, such as the sudden application or release of a strong external pulling force, it is demonstrated that the tensile dynamics reflects the self-affine conformational fluctuation spectrum in a variety of intermediate asymptotic power laws. Detailed and explicit analytical predictions for the tension propagation and relaxation and corresponding results for common observables, such as the end-to-end distance, are obtained.

Internal strain regulates the nucleotide binding site of the kinesin leading head.

In the presence of ATP, kinesin proceeds along the protofilament of microtubule by alternated binding of two motor domains on the tubulin binding sites. Because the processivity of kinesin is much higher than other motor proteins, it has been speculated that there exists a mechanism for allosteric regulation between the two monomers. Recent experiments suggest that ATP binding to the leading head (L) domain in kinesin is regulated by the rearward strain built on the neck-linker. We test this hypothesis by explicitly modeling a Calpha-based kinesin structure whose motor domains are bound on the tubulin binding sites. The equilibrium structures of kinesin on the microtubule show disordered and ordered neck-linker configurations for the L and trailing head, respectively. The comparison of the structures between the two heads shows that several native contacts present at the nucleotide binding site in the L are less intact than those in the binding site of the rear head. The network of native contacts obtained from this comparison provides the internal tension propagation pathway, which leads to the disruption of the nucleotide binding site in the L. Also, using an argument based on polymer theory, we estimate the internal tension built on the neck-linker to be f approximately 12-15 pN. Both of these conclusions support the experimental hypothesis.