Wormlike Chain Research Articles

Role of F, Cl, Br and I in the wormlike micelles formation when combining C14TAB with 4-halogenbenzoates

The combination of cationic surfactants with some aromatic anions can result in the formation of long aggregates, named as wormlike micelles. Like polymers, they can be used as viscosity controllers. The stabilization of the aromatic anions inserted into the micelles and their position at the surface is central to change the curvature of the aggregates and its consequent growth. Therefore, the affinity between these two components defines the potential to wormlike micelle formation and the understand of the molecular aspects that driven the process is central. In this sense, in this work it was investigated the effect of the presence of F, Cl Br or I at the position 4 of the aromatic ring of halogenbenzoates on the incorporation of the anions into the micelles of C14TAB. By using the isothermal titration calorimetry, the spontaneity of the process was determined by measuring the magnitude of the energy released and the critical concentration for wormlike micelle formation. Wormlike micelles are only formed for Cl, Br and I, and the formation is more pronounced for halogen atom more voluminous. It can be expected that the fitting into the water structure of the anion with a more voluminous halogen is more difficult. Therefore, the hydrophobic effect is an important driven force to the partitioning of the aromatic anion from water to the micellar pseudo-phase. The processes of formation, growth and shortening of the wormlike micelle chains were determined by measuring the hydrodynamic radius of the aggregates and correlated with the enthalpimetric curves. In high concentration regime, the micelles are entangled and the characteristics of the supramolecular gel-like formed were investigated by using linear and non-linear rheology.

Conformation of Pullulan in Aqueous Solution Studied by Small-Angle X-Ray Scattering.

Small-angle X-ray scattering functions were measured for six pullulan samples with molecular weights ranging from 2.3 × 104 to 7.4 × 105 in 0.05 M aqueous NaCl at 25 °C and fitted by the perturbed wormlike chain model, comprising touched-bead sub-bodies, to obtain wormlike chain parameters. The parameter values determined were consistent with those determined from previously reported dilute solution properties of aqueous pullulan. Because radii of gyration of not only pullulan polymers, but also pullulan oligomers were consistently explained by the touched-bead wormlike chain model perturbed by the excluded volume effect, the pullulan chain takes a local conformation considerably different from the amylose chain, although both polysaccharides are flexible polymers with an approximately same characteristic ratio.

Nematic ordering of worm-like polymers near an interface.

The phase behavior of semi-flexible polymers is integral to various contexts, from materials science to biophysics, many of which utilize or require specific confinement geometries as well as the orientational behavior of the polymers. Inspired by collagen assembly, we study the orientational ordering of semi-flexible polymers, modeled as Maier-Saupe worm-like chains, using self-consistent field theory. We first examine the bulk behavior of these polymers, locating the isotropic-nematic transition and delineating the limit of stability of the isotropic and nematic phases. This effort explains how nematic ordering emerges from the isotropic phase and offers insight into how different (e.g., mono-domain vs multi-domain) nematic phases form. We then clarify the influence of planar confinement on the nematic ordering of the polymers. We find that while the presence of a single confining wall does not shift the location of nematic transition, it aligns the polymers in parallel to the wall; above the onset of nematic transition, this preference tends to propagate into the bulk phase. Introducing a second, perpendicular, wall leads to a nematic phase that is parallel to both walls, allowing the ordering direction to be uniquely set by the geometry of the experimental setup. The advantage of wall-confinement is that it can be used to propagate mono-domain nematic phases into the bulk phase.

Multiscale Network Modeling of Fibrin Fibers and Fibrin Clots with Protofibril Binding Mechanics.

The multiscale mechanical behavior of individual fibrin fibers and fibrin clots was modeled by coupling atomistic simulation data and microscopic experimental data. We propose a new protofibril element composed of a nonlinear spring network, and constructed this based on molecular simulations and atomic force microscopy results to simulate the force extension behavior of fibrin fibers. This new network model also accounts for the complex interaction of protofibrils with one another, the effects of the presence of a solvent, Coulombic attraction, and other binding forces. The network model was formulated to simulate the force–extension mechanical behavior of single fibrin fibers from atomic force microscopy experiments, and shows good agreement. The validated fibrin fiber network model was then combined with a modified version of the Arruda–Boyce eight-chain model to estimate the force extension behavior of the fibrin clot at the continuum level, which shows very good correlation. The results show that our network model is able to predict the behavior of fibrin fibers as well as fibrin clots at small strains, large strains, and close to the break strain. We used the network model to explain why the mechanical response of fibrin clots and fibrin fibers deviates from worm-like chain behavior, and instead behaves like a nonlinear spring.

Hydrodynamics of polymers in an active bath.

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

On the mechanical response of the actomyosin cortex during cell indentations.

A mechanical model is presented to analyze the mechanics and dynamics of the cell cortex during indentation. We investigate the impact of active contraction on the cross-linked actin network for different probe sizes and indentation rates. The essential molecular mechanisms of filament stretching, cross-linking and motor activity, are represented by an active and viscous mechanical continuum. The filaments behave as worm-like chains linked either by passive rigid linkers or by myosin motors. In the first example, the effects of probe size and loading rate are evaluated using the model for an idealized rounded cell shape in which properties are based on the results of parallel-plate rheometry available in the literature. Extreme cases of probe size and indentation rate are taken into account. Afterward, AFM experiments were done by engaging smooth muscle cells with both sharp and spherical probes. By inverse analysis with finite element software, our simulations mimicking the experimental conditions show the model is capable of fitting the AFM data. The results provide spatiotemporal dependence on the size and rate of the mechanical stimuli. The model captures the general features of the cell response. It characterizes the actomyosin cortex as an active solid at short timescales and as a fluid at longer timescales by showing (1) higher levels of contraction in the zones of high curvature; (2) larger indentation forces as the probe size increases; and (3) increase in the apparent modulus with the indentation depth but no dependence on the rate of the mechanical stimuli. The methodology presented in this work can be used to address and predict microstructural dependence on the force generation of living cells, which can contribute to understanding the broad spectrum of results in cell experiments.

Near-Critical Phase Behavior in Polyelectrolyte Solutions: Effect of Charge Fluctuations.

The critical behaviors in polyelectrolyte (PE) solutions are studied by a renormalized Gaussian fluctuation theory. PEs are fully charged linear wormlike chains. The electrostatic interactions are considered in a continuum solvent while ignoring other interactions. The effects of temperature on the criticality are explored in a salt-free polyanion solution, and the effects of salt are explored in a symmetric mixed solution of polycation and polyanion. An unphysical phase coexistence (UPPC), in which a metastable dense phase coexists with an unstable dilute phase, always exists in the phase diagram. In the near-critical region, the UPPC could interfere with the real phase coexistence. The classical critical point is replaced by a "critical line", giving a flat top for the phase diagram. These behaviors are due to the effect of charge fluctuation in the near-critical region. Our results explain why the mean field approach overestimates the critical salt density by about 10% to experimental data in the study of coacervation between oppositely charged PEs.

Analysis of Homotypic Interactions of Lactococcus lactis Pili Using Single-Cell Force Spectroscopy.

Cell surface proteins of Gram-positive bacteria play crucial roles in their adhesion to abiotic and biotic surfaces. Pili are long and flexible proteinaceous filaments known to enhance bacterial initial adhesion. They promote surface colonization and are thus considered as essential factors in biofilm cohesion. Our hypothesis is that pili mediate interactions between cells and may thereby directly affect biofilm formation. In this study, we use single-cell force spectroscopy (SCFS) to quantify the force of the homotypic pili interactions between individual bacterial cells, using different Lactococcus lactis strains producing pili or not as model bacteria. Moreover the force-distance curves were analyzed to determine the physical and nanomechanical properties of L. lactis pili. The results for pili-devoided strains showed a weak adhesion between cells (adhesion forces and work in the range of 100 pN and 7 × 10-18 J, respectively). On the contrary, the piliated strains showed high adhesion levels with adhesion forces and adhesion work over 200 pN and 50 × 10-18 J, respectively. The force-extension curves showed multiple adhesion events, typical of the unfolding of macromolecules. These unfolding force peaks were fitted using the physical worm-like chain model to get fundamental knowledge on the pili nanomechanical properties. In addition, SCFS applied to a L. lactis isolate expressing both pili and mucus-binding protein at its surface and two derivative mutants revealed the capacity of pili to interact with other surface proteins including mucus-binding proteins. This study demonstrates that pili are involved in L. lactis homotypic interactions and thus can influence biofilm structuring.

Understanding the paradoxical mechanical response of in-phase A-tracts at different force regimes.

A-tracts are A:T rich DNA sequences that exhibit unique structural and mechanical properties associated with several functions in vivo. The crystallographic structure of A-tracts has been well characterized. However, the mechanical properties of these sequences is controversial and their response to force remains unexplored. Here, we rationalize the mechanical properties of in-phase A-tracts present in the Caenorhabditis elegans genome over a wide range of external forces, using single-molecule experiments and theoretical polymer models. Atomic Force Microscopy imaging shows that A-tracts induce long-range (∼200 nm) bending, which originates from an intrinsically bent structure rather than from larger bending flexibility. These data are well described with a theoretical model based on the worm-like chain model that includes intrinsic bending. Magnetic tweezers experiments show that the mechanical response of A-tracts and arbitrary DNA sequences have a similar dependence with monovalent salt supporting that the observed A-tract bend is intrinsic to the sequence. Optical tweezers experiments reveal a high stretch modulus of the A-tract sequences in the enthalpic regime. Our work rationalizes the complex multiscale flexibility of A-tracts, providing a physical basis for the versatile character of these sequences inside the cell.

Determinants of cyclization-decyclization kinetics of short DNA with sticky ends.

Cyclization of DNA with sticky ends is commonly used to measure DNA bendability as a function of length and sequence, but how its kinetics depend on the rotational positioning of the sticky ends around the helical axis is less clear. Here, we measured cyclization (looping) and decyclization (unlooping) rates (kloop and kunloop) of DNA with sticky ends over three helical periods (100-130 bp) using single-molecule fluorescence resonance energy transfer (FRET). kloop showed a nontrivial undulation as a function of DNA length whereas kunloop showed a clear oscillation with a period close to the helical turn of DNA (∼10.5 bp). The oscillation of kunloop was almost completely suppressed in the presence of gaps around the sticky ends. We explain these findings by modeling double-helical DNA as a twisted wormlike chain with a finite width, intrinsic curvature, and stacking interaction between the end base pairs. We also discuss technical issues for converting the FRET-based cyclization/decyclization rates to an equilibrium quantity known as the J factor that is widely used to characterize DNA bending mechanics.

Distribution of torsional stress between the un-replicated and replicated regions in partially replicated molecules

DNA topology changes continuously as replication proceeds. Unwinding of the DNA duplex by helicases is favored by negative supercoiling but it causes the progressive accumulation of positive supercoiling ahead of the fork. This torsional stress must be removed for the fork to keep advancing. Elimination of this positive torsional stress may be accomplished by topoisomerases acting solely ahead of the fork or simultaneously in the un-replicated and replicated regions after diffusion of some positive torsional strain from the un-replicated to the replicated regions by swivelling of the replication forks. In any case, once replication is completed fully replicated molecules are known to be heavily catenated and this catenation derives from pre-catenanes formed during replication. Although there is still controversy as to whether fork swiveling redistributes this positive torsional stress continuously or only as termination approaches, the forces that cause fork rotation and the generation of pre-catenanes are still poorly characterized. Here we used a numerical simulation, based on the worm-like chain model and the Metropolis Monte Carlo method, to study the interchange of supercoiling and pre-catenation in a naked circular DNA molecule of 4,440 bp partially replicated in vivo and in vitro. We propose that a dynamic gradient of torsional stress between the un-replicated and replicated regions drives fork swiveling allowing the interchange of supercoiling and pre-catenation. Communicated by Ramaswamy H. Sarma

Kinetics of rare events for non-Markovian stationary processes and application to polymer dynamics

How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the first-passage time statistics to a target zone in phase space with lower occupation probability. Here, we present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories. We apply our method to polymer systems, to determine (i) the first time for a flexible polymer to reach a large extension, and (ii) the first closure time of a stiff inextensible wormlike chain. Our results are in excellent agreement with numerical simulations and provide explicit asymptotic laws for the mean first-passage times to rarely visited configurations.

Modelling the mechanical behaviors of double-network hydrogels

Double-network hydrogels (DN gels), consisting of a rigid, highly cross-linked short-chain network and a flexible, loosely cross-linked long-chain network, are a kind of promising soft and tough material with superior mechanical properties. In order to capture the mechanical behaviors of DN gels more accurately and with more physical depth than some existing models, a constitutive formulation is developed in this paper. The Helmholtz free energy function is decomposed into three parts accounting for the free energies of each network and the mixing of all the components. The eight-chain worm-like chain (WLC) based model is then employed to describe the deformation of each network with two network structure parameters: the chain density and the average chain length. Based on the existing experimental investigations of the internal fracture process of DN gels, a detailed and clear physical picture is illustrated. According to this damage picture, the two network structure parameters of the short-chain network are regarded as two internal variables. Within the framework of general thermodynamics, the energy dissipation is defined through the variation of the internal variables, which allows one to obtain the evolutions of internal variables from analyzing the macroscopic dissipated behaviors of DN gels. For the cases without energy dissipation, the network structure parameters are constant and can be determined directly through the stress-strain relation at one typical point on the stress-strain curve and the stored Helmholtz free energy of each state. These determined values of the parameters are then used to validate the mass conservation. For the cases with energy dissipation, the evolution equations of the two internal variables are determined through the analysis of the energy dissipation and the mass conservation. As a result, not only the unloading stress-stain curves but also the primary loading curve can be theoretically predicted by the constitutive formulation. The mechanical behaviors of both t-DN gels and c-DN gels before necking are analyzed. The comparisons of the theoretical results with the experimental data show sufficiently good agreements, demonstrating the ability and efficiency of the formulation to capture the Mullins effect of DN gels.

Dynamics of the Buckling Transition in Double-Stranded DNA and RNA

DNA under torsional strain undergoes a buckling transition that is the fundamental step in plectoneme nucleation and supercoil dynamics, which are critical for the processing of genomic information. Despite its importance, quantitative models of the buckling transition, in particular to also explain the surprising two-orders-of-magnitude difference between the buckling times for RNA and DNA revealed by single-molecule tweezers experiments, are currently lacking. Additionally, little is known about the configurations of the DNA during the buckling transition because they are not directly observable experimentally. Here, we use a discrete worm-like chain model and Brownian dynamics to simulate the DNA/RNA buckling transition. Our simulations are in good agreement with experimentally determined parameters of the buckling transition. The simulations show that the buckling time strongly and exponentially depends on the bending stiffness, which accounts for more than half the measured difference between DNA and RNA. Analyzing the microscopic conformations of the chain revealed by our simulations, we find clear evidence for a solenoid-shaped transition state and a curl intermediate. The curl intermediate features a single loop and becomes increasingly populated at low forces. Taken together, the simulations suggest that the worm-like chain model can account semiquantitatively for the buckling dynamics of both DNA and RNA.

Specific Conformational Dynamics and Expansion Underpin a Multi-Step Mechanism for Specific Binding of p27 with Cdk2/Cyclin A

The protein p27, a prominent regulatory protein in eukaryotes and an intrinsically disordered protein (IDP), regulates cell division by causing cell cycle arrest when bound in ternary complex with cyclin-dependent kinase (Cdk2) and cyclins (e.g., Cdk2/Cyclin A). We present an integrative study of p27 and its binding to Cdk2/Cyclin A complex by performing single-molecule multiparameter fluorescence spectroscopy, stopped-flow experiments, and molecular dynamics simulations. Our results suggest that unbound p27 adopts a compact conformation and undergoes conformational dynamics across several orders of magnitude in time (nano-to milliseconds), reflecting a multi-step mechanism for binding Cdk2/Cyclin A. Mutagenesis studies reveal that the region D1 in p27 plays a significant role in mediating the association kinetics, undergoing conformational rearrangement upon initial binding. Additionally, FRET experiments indicate an expansion of p27 throughout binding. The detected local and long-range structural dynamics suggest that p27 exhibits a limited binding surface in the unbound form, and stochastic conformational changes in D1 facilitate initial binding to Cdk2/Cyclin A complex. Furthermore, the post-kinase inhibitory domain (post-KID) region of p27 exchanges between distinct conformational ensembles: an extended regime exhibiting worm-like chain behavior, and a compact ensemble, which may protect p27 against nonspecific interactions. In summary, the binding interaction involves three steps: (i) D1 initiates binding, (ii) p27 wraps around Cdk2/Cyclin A and D2 binds, and (iii) the fully-formed fuzzy ternary complex is formed concomitantly with an extension of the post-KID region. An understanding of how the IDP nature of p27 underpins its functional interactions with Cdk2/Cyclin A provides insight into the complex binding mechanisms of IDPs and their regulatory mechanisms.

Molecular chains under tension: Thermal and mechanical activation of statistically interacting extension and contraction particles.

This work introduces a methodology for the statistical mechanical analysis of polymeric chains under tension controlled by optical or magnetic tweezers at thermal equilibrium with an embedding fluid medium. The response of single bonds between monomers or of entire groups of monomers to tension is governed by the activation of statistically interacting particles representing quanta of extension or contraction. This method of analysis is capable of describing thermal unbending of the freely jointed or wormlike chain kind, linear or nonlinear contour elasticity, and structural transformations including effects of cooperativity. The versatility of this approach is demonstrated in an application to double-stranded DNA undergoing torsionally unconstrained stretching across three regimes of mechanical response including an overstretching transition. The three-regime force-extension characteristic, derived from a single free-energy expression, accurately matches empirical evidence.

How does stiffness of polymer chains affect their adsorption transition?

The adsorption transition and the structure of semiflexible adsorbed macromolecules are studied by a molecular dynamics simulation of a coarse-grained, bead-spring type model. Varying chain length N and stiffness κ (which is proportional to the persistence length ℓp in d = 3 dimensions) as well as the strength ϵwall of the adsorption potential, the adsorbed monomer fraction, orientational bond order parameter, and chain linear dimensions are studied. In the simulations, excluded volume interactions normally are included but can be "switched off," and thus, the influence of excluded volume (leading to deviations from predictions of the wormlike chain model) can be identified. It is shown that the variation in the adsorption threshold ϵwall cr with ℓp is compatible with the predicted law ϵwall cr∝ℓp -1/3. In the vicinity of the adsorption threshold, the coils are still three-dimensional, and for large ℓp, the effect of the excluded volume is almost negligible, while for strongly adsorbed chains it is always felt. Near the transition, the decay length of orientational correlations along the chain contour increases gradually from ℓp to 2ℓp. While the latter value is expected for strictly two-dimensional chains from the Kratky-Porod model, this model is inaccurate for the description of lateral chain dimensions of long, strongly adsorbed, semiflexible polymers due to its neglect of excluded volume. The significance of these findings for the interpretation of pertinent experiments is briefly discussed.

Inhomogeneous Forces in Semiflexible Biopolymers

Major developments in single-molecule experiments over the past few decades have permitted the manipulation of biomolecules and the study of their responses to force fields in unprecedented detail. These methods have led to the greater understanding of a wide range of biologically relevant processes, including the dynamics of cytoskeletal filaments, the stability of DNA double helix, or the formation of histone-DNA complexes. The wormlike chain model has been successfully applied to predict force-extension relations of semiflexible biopolymers. Despite these successes, the effects of inhomogeneous forces (for example effects of charge heterogeneity in a polyelectrolyte) are not well understood. In this work, we develop a new analytical model to understand the statistics of an inextensible polyelectrolyte chain under inhomogeneous tension. We show that an existing mean-field formalism that does not account for the inhomogeneity in the tension results in local over-stretching of the chain. We improve upon this approach by subdividing the chain into smaller segments over which the homogeneity assumption is only approximately valid. This technique can analytically impose inextensibility of the chain and help us study the statistical properties of the chain. We can also extend the theory to predict the protein-binding statistics in experiments that probe protein-DNA interactions under an external field, applicable to DNA wrapping around histone octamers. This proposed method may prove valuable to other biologically relevant problems involving inhomogeneities in actin bundles, semiflexible chains under shear flow or in the design of biomimetic materials.

Drawing Silicone Fiber Optics for Flexible Biosensors

In vivo fiber optic biosensing is limited by mechanical and chemical characteristics: fiber flexibility, permeability, biocompatibility and analyte sensitivity. We have developed a method for gravity-drawing silicone PDMS filaments with diameters on the order of a hundred micrometers, which directly address these limitations. We demonstrate that PDMS filaments are multimode fiber optics with reasonable losses for device applications (∼1.3dB/cm). Their flexibility relative to their glass and acrylic counterparts makes them attractive as biosensors, with a measured Young's modulus that is three to four orders of magnitude less stiff than glass/acrylic fiber optics. Additionally, a silicone fiber's transmission may be tuned to be solvent or gas sensitive, suggesting low-cost applications as both biological and environmental sensors. Kiessling, R., Rubin, S.J., Zehner, J., Barraugh, C., Snell, K., Fukushima, C., Mulligan, M., Keckley, M., Bosshardt, A., Cook, W. and Sanii, B., 2017. Gravity-Drawn Silicone Filaments: Production, Characterization, and Wormlike Chain Dynamics. ACS applied materials & interfaces, 9(46), pp.39916-39920. Snell, K., Lopez, I., Louie, B., Kiessling, R. and Sanii, B., 2019. Drawing and Hydrophobicity-patterning Long Polydimethylsiloxane Silicone Filaments. JoVE (Journal of Visualized Experiments), (143), p.e58826.

Histone-DNA Interactions in the Archaeon Methanocaldococcus Jannaschii

The requirement for DNA compaction is universal across all domains of life. Although the histone proteins of Archaea and Eukaryotes have low sequence homology, the core histone fold is well-conserved and structures are virtually identical. However, small structural differences mean that Archaeal nucleosomes might assemble into a continuous solenoid-like fiber: the ‘hypernucleosome’. Given that M. jannaschii thrives at 80oC and its genomic DNA is positively supercoiled (the opposite to mesophiles like us), the mechanism of DNA packaging may show interesting adaptations and diversity that will inform us about the biophysics of chromatin in general. Here, we have used magnetic tweezers to control the supercoiling of DNA while quantifying the kinetics and energetics of DNA-histone binding, wrapping and compaction. Using this technique, we have investigated the properties of M. jannaschii chromatin with its most abundant histone protein “A3”. We propose a model for the force-extension properties of Archaeal chromatin, analogous to that for Eukaryotic chromatin, and demonstrate that the force-extension properties are dependent upon protein concentration. We find that, under moderate load, histone binding confers stability to DNA by preventing base-pair unstacking when negative supercoiling is applied, and the chromatin fiber shows a sharp buckling transition between both positive and negative supercoiling regimes. At high load (>5pN), the chromatin fiber is disrupted and the force-extension diagram returns to the worm-like chain, typical of naked DNA. Our model suggests a mechanism by which DNA processing enzymes may shunt or displace nucleosomes, obviating the need for active chromatin remodeling enzymes.