Journal articles: 'Worm-like chain model'

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Xu, Xin, and Ying Jiang. "Applications of worm-like chain model in polymer physics." International Journal of Modern Physics B 32, no. 18 (July 15, 2018): 1840006. http://dx.doi.org/10.1142/s0217979218400064.

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Saito, Takahashi and Yunoki developed the continuous version of worm-like chain (WLC) model that is very suitable for description of the polymer conformational properties affected by chain rigidity. By adjusting persistence length directly, the WLC model can depict the extensive range of chain conformations from flexible chains to rigid chains. It is widely accepted that more physical properties of real polymer can be obtained by utilizing coarse-grained model than Gaussian chain (GSC). This paper reviews the applications of the WLC model in the framework based on self-consistent field theory, which is an efficient method of theoretical exploration of phase separation in polymer system. It is noticed that the development of numerical schemes is in favor of solving modified diffusion equation that adjusts the probability distribution of polymers. In addition, we conclude the recent applications of the self-consistent field theory based on the WLC model as the following three points: phase transitions of liquid crystal polymer; the influences of surface curvature on polymer system that involves the chain orientation effects; self-assembly of worm-like block copolymer. These researches have been out of the range of the self-consistent field theory based on GSC model that has been used in a large number of theoretical studies. Finally, we present ideas of theoretical development in field theory simulations based on the WLC model in the future. It is universally acknowledged that chain rigidity is a key factor that influences the properties of structural stabilities in the meso-scale in articles. Theoretical researches determine the key physical mechanisms that play crucial roles in many experimental systems with attractively promising applications in practice, for systems such as liquid crystalline polymers and organic solar cell based on the conjugated polymers.

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Fu, Yi-Ben, Yu-Ru Liu, Peng-Ye Wang, and Ping Xie. "A revised worm-like chain model for elasticity of polypeptide chains." Journal of Polymer Science Part B: Polymer Physics 56, no. 4 (November 4, 2017): 297–307. http://dx.doi.org/10.1002/polb.24541.

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Hillgärtner, Markus, Kevin Linka, and Mikhail Itskov. "Worm-like chain model extensions for highly stretched tropocollagen molecules." Journal of Biomechanics 80 (October 2018): 129–35. http://dx.doi.org/10.1016/j.jbiomech.2018.08.034.

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Ogden, Ray W., Giuseppe Saccomandi, and Ivonne Sgura. "On worm-like chain models within the three-dimensional continuum mechanics framework." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2067 (December 19, 2005): 749–68. http://dx.doi.org/10.1098/rspa.2005.1592.

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In this paper, we review critically some basic models derived from the statistics of long-chain molecules and then discuss the status of such models within the three-dimensional nonlinear theory of elasticity. We draw attention to some deficiencies of certain worm-like chain (WLC) models when viewed within the three-dimensional continuum mechanics framework. Modifications of the WLC models motivated by such considerations and avoiding these deficiencies are then discussed and shown to correspond well with data generated by the exact WLC model.

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Xiao, Hongyi, Xinghua Zhang, and Dadong Yan. "A Local-Exchange Model of Folding Chain Surface of Polymer Crystal Based on Worm-Like Chain Model within Single-Chain in Mean-Field Theory." Polymers 12, no. 11 (October 30, 2020): 2555. http://dx.doi.org/10.3390/polym12112555.

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The structure of amorphous layer of folding surface controls the properties of the polymer lamellar crystal, which consists of chains with a loop conformation. The surface tension depends on the length and the distance between two injection points of the loop which involving the reptation motion and lateral exchange motion of the stems. In the present work, a local-exchange motion model based on the worm-like chain model is developed to investigate the effects of lateral motion of stems on the release the surface tension. The optimal distance between two injection points is determined by the balance of chain bending energy and conformational entropy. The numerical results provide evidences to the adjacent re-entry model for various loop lengths. A possible explanation involving density of injection points is proposed to interpret the mechanism.

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Ou, C. R. "WORM LIKE CHAIN MODEL - PROPOGATIONS OF THE DOMAIN WALLS AND THE STABILITIES ISSUES." Journal of Biomechanics 40 (January 2007): S734. http://dx.doi.org/10.1016/s0021-9290(07)70722-4.

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Chan, Yue, Richard G. Haverkamp, and James M. Hill. "Force-extension formula for the worm-like chain model from a variational principle." Journal of Theoretical Biology 262, no. 3 (February 2010): 498–504. http://dx.doi.org/10.1016/j.jtbi.2009.10.009.

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Liao, Xinyu, Prashant K. Purohit, and Arvind Gopinath. "Extensions of the worm-like-chain model to tethered active filaments under tension." Journal of Chemical Physics 153, no. 19 (November 21, 2020): 194901. http://dx.doi.org/10.1063/5.0025200.

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DING, YAN, and TIEJUN LI. "A NOTE ON THE ANALYSIS OF A HETEROGENEOUS ROD-LIKE CHAIN IN DNA MODELING." International Journal of Modern Physics B 22, no. 14 (June 10, 2008): 2213–24. http://dx.doi.org/10.1142/s0217979208039460.

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Two different results concerning the elastic behavior of the heterogeneous worm-like chain (WLC) [D. Bensimon et al., Europhys. Lett.42, 97 (1998)] and rod-like chain (RLC) [P. Nelson, Phys. Rev. Lett.80, 5810 (1998)] are compared. We argue that the RLC is a more suitable model for double-stranded (ds-) DNA. As the hetero-RLC is the basic model for studying sequence-dependent ds-DNA, a rigorous path integral analysis for the effective bending persistence length is performed in the weak disorder limit. The novelty of the paper is in analyzing a path integral on the Lie group SO(3) with random forcing, which supplies a rigorous basis for the analysis of RLC type models.

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Hsu, Hsiao-Ping, Wolfgang Paul, and Kurt Binder. "Polymer chain stiffness vs. excluded volume: A Monte Carlo study of the crossover towards the worm-like chain model." EPL (Europhysics Letters) 92, no. 2 (October 1, 2010): 28003. http://dx.doi.org/10.1209/0295-5075/92/28003.

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CHEN, HU, HONGXIA FU, ZHEN ZHOU, and JIE YAN. "NON-HARMONIC DNA BENDING ELASTICITY IS REVEALED BY STATISTICS OF DNA MINICIRCLE SHAPES." International Journal of Modern Physics B 24, no. 28 (November 10, 2010): 5475–85. http://dx.doi.org/10.1142/s0217979210056682.

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Unusual DNA elasticity has been observed in a few recent experiments for DNA under tight bending conditions. Here we present new experimental evidence demonstrating unusual DNA bending elasticity by analyzing the atomic force microscope (AFM) images of DNA minicircles of sizes 189 and 378 base-pairs that are relaxed on 2D surface. The DNA shape distributions are found in disagreement with the canonical 50 nm persistence length based worm-like chain (WLC) model. Instead, they are found in agreement with the recently proposed flexible defect excitation model and linear subelastic chain (LSEC) model.

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Rittman, Martyn, Emma Gilroy, Hashem Koohy, Alison Rodger, and Adair Richards. "Is DNA a worm-like chain in Couette flow?: In search of persistence length, a critical review." Science Progress 92, no. 2 (July 2009): 163–204. http://dx.doi.org/10.3184/003685009x462205.

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Persistence length is the foremost measure of DNA flexibility. Its origins lie in polymer theory which was adapted for DNA following the determination of B-DNA structure in 1953. There is no single definition of persistence length used, and the links between published definitions are based on assumptions which may, or may not be, clearly stated. DNA flexibility is affected by local ionic strength, solvent environment, bound ligands and intrinsic sequence-dependent flexibility. This article is a review of persistence length providing a mathematical treatment of the relationships between four definitions of persistence length, including: correlation, Kuhn length, bending, and curvature. Persistence length has been measured using various microscopy, force extension and solution methods such as linear dichroism and transient electric birefringence. For each experimental method a model of DNA is required to interpret the data. The importance of understanding the underlying models, along with the assumptions required by each definition to determine a value of persistence length, is highlighted for linear dichroism data, where it transpires that no model is currently available for long DNA or medium to high shear rate experiments.

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Niu, Yingli, Xiangyu Bu, and Xinghua Zhang. "Single Chain Mean-Field Theory Study on Responsive Behavior of Semiflexible Polymer Brush." Materials 14, no. 4 (February 7, 2021): 778. http://dx.doi.org/10.3390/ma14040778.

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The application of single chain mean-field theory (SCMFT) on semiflexible chain brushes is reviewed. The worm-like chain (WLC) model is the best mode of semiflexible chain that can continuously recover to the rigid rod model and Gaussian chain (GC) model in rigid and flexible limits, respectively. Compared with the commonly used GC model, SCMFT is more applicable to the WLC model because the algorithmic complexity of the WLC model is much higher than that of the GC model in self-consistent field theory (SCFT). On the contrary, the algorithmic complexity of both models in SCMFT are comparable. In SCMFT, the ensemble average of quantities is obtained by sampling the conformations of a single chain or multi-chains in the external auxiliary field instead of solving the modified diffuse equation (MDE) in SCFT. The precision of this calculation is controlled by the number of bonds Nm used to discretize the chain contour length L and the number of conformations M used in the ensemble average. The latter factor can be well controlled by metropolis Monte Carlo simulation. This approach can be easily generalized to solve problems with complex boundary conditions or in high-dimensional systems, which were once nightmares when solving MDEs in SCFT. Moreover, the calculations in SCMFT mainly relate to the assemble averages of chain conformations, for which a portion of conformations can be performed parallel on different computing cores using a message-passing interface (MPI).

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Xiao, Ye, Zaixing Huang, Lei Qiang, and Jun Gao. "Elastic response of DNA molecules under the action of interfacial traction and stretching: An elastic thin rod model." Modern Physics Letters B 29, no. 31 (November 20, 2015): 1550193. http://dx.doi.org/10.1142/s0217984915501936.

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In a multivalent salt solution, a segment of DNA is modeled as an elastic rod subjected to the interfacial traction. The shooting method is used to calculate the equilibrium configurations of condensed DNA under the action of the longitudinal end-force and interfacial traction simultaneously. The results show that the shapes of DNA are mainly determined by the competition between the interfacial energy and elastic strain energy of stretching. The change of end-to-end distance with the longitudinal end-force is consistent with the worm-like chain (WLC) model. The higher the concentration is, the stronger the condensation of DNA.

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Aliev, M. A. "Influence of polydispersity on the isotropic-nematic boundary in melt of semiflexible diblock copolymer." Modern Physics Letters B 29, no. 35n36 (December 30, 2015): 1550240. http://dx.doi.org/10.1142/s0217984915502401.

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The analytical expressions have been obtained to describe the dependence of spinodal curve at which isotropic state of polydisperse melt of semiflexible diblock copolymer becomes unstable with respect to formation of nematic state on the polydispersity indices of the blocks, parameters of anisotropic interactions, and flexibility of blocks. The flexibility of blocks is taken into account within discrete worm-like chain model, lengths of blocks are assumed to be distributed by the Schulz–Zimm distribution. It is shown that increase of degree of polydispersity of blocks yields the increase of nematic spinodal temperature.

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I'Anson, K. J., V. J. Morris, P. R. Shewry, and A. S. Tatham. "Small-angle X-ray-scattering studies of the C hordeins of barley (Hordeum vulgare)." Biochemical Journal 287, no. 1 (October 1, 1992): 183–85. http://dx.doi.org/10.1042/bj2870183.

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Small angle X-ray scattering was used to study the solution conformation of the C hordeins of barley (Hordeum vulgare), a group of proteins whose primary structure consists predominantly of an octapeptide repeat motif. Measurements on the protein in 0.1 M-acetic acid at 25 degrees C are consistent with a model for the protein conformation of a stiff coil, the so-called ‘worm-like’ chain. The characteristic parameters (the Kuhn statistical segment length and the contour length) of the protein were calculated as 5.11 and 71.5 nm respectively.

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Yesudasan, Sumith, and Rodney D. Averett. "Multiscale Network Modeling of Fibrin Fibers and Fibrin Clots with Protofibril Binding Mechanics." Polymers 12, no. 6 (May 27, 2020): 1223. http://dx.doi.org/10.3390/polym12061223.

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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.

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Zhou, L. W., Yu-Qian Zhang, Xiao-Long Deng, and M. B. Liu. "ICCM2015(Paper ID:1148): DPD Simulation of the Movement and Deformation of Bioconcave Cells." International Journal of Computational Methods 13, no. 04 (July 4, 2016): 1641003. http://dx.doi.org/10.1142/s0219876216410036.

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This paper presents a dissipative particle dynamics (DPDs) method for investigating the movement and deformation of biconcave shape red blood cells (RBCs) with the worm-like chain (WLC) bead spring. First, the stretching of a RBC is modeled and the obtained shape evolution of the cell agrees well with experimental results. Second, the movement and deformation of a RBC in shear flows are investigated and three typical modes (tumbling, intermittent and tank-treading) are observed. Lastly, an illustrating example of multi-RBCs in Poiseuille flow in a tube is simulated. We conclude that the presented DPD method with WLC spring can effectively model the movement and deformation of bioconcave cells.

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Ehret, Alexander E., and Markus Böl. "Modelling mechanical characteristics of microbial biofilms by network theory." Journal of The Royal Society Interface 10, no. 78 (January 6, 2013): 20120676. http://dx.doi.org/10.1098/rsif.2012.0676.

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In this contribution, we present a constitutive model to describe the mechanical behaviour of microbial biofilms based on classical approaches in the continuum theory of polymer networks. Although the model is particularly developed for the well-studied biofilms formed by mucoid Pseudomonas aeruginosa strains, it could easily be adapted to other biofilms. The basic assumption behind the model is that the network of extracellular polymeric substances can be described as a superposition of worm-like chain networks, each connected by transient junctions of a certain lifetime. Several models that were applied to biofilms previously are included in the presented approach as special cases, and for small shear strains, the governing equations are those of four parallel Maxwell elements. Rheological data given in the literature are very adequately captured by the proposed model, and the simulated response for a series of compression tests at large strains is in good qualitative agreement with reported experimental behaviour.

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DONG, SHIJIN, HAITAO ZHANG, XUEJUN CUI, ZHENYING SUI, JIA XU, and HONGYAN WANG. "MESOSCOPIC SIMULATION ON THE PHASE STRUCTURE OF PLURONIC P105 AQUEOUS SOLUTION." Journal of Theoretical and Computational Chemistry 09, no. 04 (August 2010): 767–83. http://dx.doi.org/10.1142/s0219633610005955.

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The mesoscopic dynamic simulation (MesoDyn) has been carried out to investigate the phase structure and the aggregate properties of triblock copolymers (ethylene oxide)37 (propylene oxide)56 (ethylene oxide)37 (P105) in aqueous solution. A Gaussian chain model is successfully built according to the equivalent chain method and the Flory–Huggins interaction parameters, χ, used for determining the repulsions between different chain segments are computed. Simulation results show that P105 can form several microstructures including spherical micelles, ellipsoid micellar cluster, worm-like micelles, defective bicontinuous phase, and bicontinuous phase with increasing concentration. A special transition phase structure of P105 is found in the spherical micellar region. The dynamic evolution processes of spherical micelles are investigated by observing the induction time before phase separation and the changing of isosurface during phase separation. The influence of P105 concentration on the density of micelles at equilibrium state is also discussed, which shows that the increase of P105 concentration will lead to the decrease of micelles' amount. Two kinds of growth mechanisms during phase separation are discussed by MesoDyn simulation.

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Shon, Min Ju, Sang-Hyun Rah, and Tae-Young Yoon. "Submicrometer elasticity of double-stranded DNA revealed by precision force-extension measurements with magnetic tweezers." Science Advances 5, no. 6 (June 2019): eaav1697. http://dx.doi.org/10.1126/sciadv.aav1697.

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Submicrometer elasticity of double-stranded DNA (dsDNA) governs nanoscale bending of DNA segments and their interactions with proteins. Single-molecule force spectroscopy, including magnetic tweezers (MTs), is an important tool for studying DNA mechanics. However, its application to short DNAs under 1 μm is limited. We developed an MT-based method for precise force-extension measurements in the 100-nm regime that enables in situ correction of the error in DNA extension measurement, and normalizes the force variability across beads by exploiting DNA hairpins. The method reduces the lower limit of tractable dsDNA length down to 198 base pairs (bp) (67 nm), an order-of-magnitude improvement compared to conventional tweezing experiments. Applying this method and the finite worm-like chain model we observed an essentially constant persistence length across the chain lengths studied (198 bp to 10 kbp), which steeply depended on GC content and methylation. This finding suggests a potential sequence-dependent mechanism for short-DNA elasticity.

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Peters, Justin P., and L. James Maher. "DNA curvature and flexibility in vitro and in vivo." Quarterly Reviews of Biophysics 43, no. 1 (February 2010): 23–63. http://dx.doi.org/10.1017/s0033583510000077.

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AbstractIt has been more than 50 years since the elucidation of the structure of double-helical DNA. Despite active research and progress in DNA biology and biochemistry, much remains to be learned in the field of DNA biophysics. Predicting the sequence-dependent curvature and flexibility of DNA is difficult. Applicability of the conventional worm-like chain polymer model of DNA has been challenged. The fundamental forces responsible for the remarkable resistance of DNA to bending and twisting remain controversial. The apparent ‘softening’ of DNA measured in vivo in the presence of kinking proteins and superhelical strain is incompletely understood. New methods and insights are being applied to these problems. This review places current work on DNA biophysics in historical context and illustrates the ongoing interplay between theory and experiment in this exciting field.

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Wang, Qing, Nan Hu, and Junbo Duan. "Fitting of Atomic Force Microscopy Force Curves with a Sparse Representation Model." Mathematical Problems in Engineering 2021 (July 28, 2021): 1–7. http://dx.doi.org/10.1155/2021/1951456.

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Atomic force microscopy (AFM) is a high-resolution scanning technology, and the measured data are a set of force curves, which can be fitted with a piecewise curve model and be analyzed further. Most methods usually follow a two-step strategy: first, the discontinuities (or breakpoints) are detected as the boundaries of two consecutive pieces; second, each piece separated by the discontinuities is fitted with a parametric model, such as the well-known worm-like chain (WLC) model. The disadvantage of this method is that the fitting (the second step) accuracy depends largely on the discontinuity detection (the first step) accuracy. In this study, a sparse representation model is proposed to jointly detect discontinuities and fit curves. The proposed model fits the curve with a linear combination of parametric functions, and the estimation of the parameters in the model can be formulated as an optimization problem with ℓ 0 -norm constraint. The performance of the proposed model is demonstrated by the fitting of AFM retraction force curves with the WLC model. Results shows that the proposed method can segment the force curve and estimate the parameter jointly with better accuracy, and hence, it is promising for automatic AFM force curve processing.

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Harrington, Matthew J., S. Scott Wasko, Admir Masic, F. Dieter Fischer, Himadri S. Gupta, and Peter Fratzl. "Pseudoelastic behaviour of a natural material is achieved via reversible changes in protein backbone conformation." Journal of The Royal Society Interface 9, no. 76 (June 13, 2012): 2911–22. http://dx.doi.org/10.1098/rsif.2012.0310.

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The egg capsules of marine prosobranch gastropods, commonly know as whelks, function as a protective encapsulant for whelk embryos in wave-swept marine environments. The proteinaceous sheets comprising the wall of whelk egg capsules (WEC) exhibit long-range reversible extensibility with a hysteresis of up to 50 per cent, previously suggested to result from reversible changes in the structure of the constituent protein building blocks. Here, we further investigate the structural changes of the WEC biopolymer at various hierarchical levels using several different time-resolved in situ approaches. We find strong evidence in these biological polymers for a strain-induced reversible transition from an ordered conformational phase to a largely disordered one that leads to the characteristic reversible hysteretic behaviour, which is reminiscent of the pseudoelastic behaviour in some metallic alloys. On the basis of these results, we generate a simple numerical model incorporating a worm-like chain equation to explain the phase transition behaviour of the WEC at the molecular level.

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Menzel, Andreas, and Tobias Waffenschmidt. "A microsphere-based remodelling formulation for anisotropic biological tissues." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1902 (September 13, 2009): 3499–523. http://dx.doi.org/10.1098/rsta.2009.0103.

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Biological tissues possess the ability to adapt according to the respective local loading conditions, which results in growth and remodelling phenomena. The main goal of this work is the development of a new remodelling approach that, on the one hand, reflects the alignment of fibrous soft biological tissue with respect to representative loading directions. On the other hand, the continuum approach proposed is based on a sound micro-mechanically motivated formulation. To be specific, use of a worm-like chain model is made to describe the behaviour of long-chain molecules as present in, for instance, collageneous tissues. The extension of such a one-dimensional constitutive equation to the three-dimensional macroscopic level is performed by means of a microsphere formulation. Inherent with the algorithmic treatment of this type of modelling approach, a finite number of unit vectors is considered for the numerical integration over the domain of the unit sphere. As a key aspect of this contribution, remodelling is incorporated by setting up evolution equations for the referential orientations of these integration directions. Accordingly, the unit vectors considered now allow interpretation as internal variables, which characterize the material’s anisotropic properties. Several numerical studies underline the applicability of the model that, moreover, nicely fits into iterative finite element formulations so that general boundary value problems can be solved.

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Marin-Gonzalez, Alberto, Cesar L. Pastrana, Rebeca Bocanegra, Alejandro Martín-González, J. G. Vilhena, Rubén Pérez, Borja Ibarra, Clara Aicart-Ramos, and Fernando Moreno-Herrero. "Understanding the paradoxical mechanical response of in-phase A-tracts at different force regimes." Nucleic Acids Research 48, no. 9 (April 13, 2020): 5024–36. http://dx.doi.org/10.1093/nar/gkaa225.

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Abstract 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.

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Monsen, Robert C., Srinivas Chakravarthy, William L. Dean, Jonathan B. Chaires, and John O. Trent. "The solution structures of higher-order human telomere G-quadruplex multimers." Nucleic Acids Research 49, no. 3 (January 19, 2021): 1749–68. http://dx.doi.org/10.1093/nar/gkaa1285.

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Abstract Human telomeres contain the repeat DNA sequence 5′-d(TTAGGG), with duplex regions that are several kilobases long terminating in a 3′ single-stranded overhang. The structure of the single-stranded overhang is not known with certainty, with disparate models proposed in the literature. We report here the results of an integrated structural biology approach that combines small-angle X-ray scattering, circular dichroism (CD), analytical ultracentrifugation, size-exclusion column chromatography and molecular dynamics simulations that provide the most detailed characterization to date of the structure of the telomeric overhang. We find that the single-stranded sequences 5′-d(TTAGGG)n, with n = 8, 12 and 16, fold into multimeric structures containing the maximal number (2, 3 and 4, respectively) of contiguous G4 units with no long gaps between units. The G4 units are a mixture of hybrid-1 and hybrid-2 conformers. In the multimeric structures, G4 units interact, at least transiently, at the interfaces between units to produce distinctive CD signatures. Global fitting of our hydrodynamic and scattering data to a worm-like chain (WLC) model indicates that these multimeric G4 structures are semi-flexible, with a persistence length of ∼34 Å. Investigations of its flexibility using MD simulations reveal stacking, unstacking, and coiling movements, which yield unique sites for drug targeting.

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POELERT, SANDER L., HARRIE H. WEINANS, and AMIR A. ZADPOOR. "FINITE ELEMENT MODELING OF THE THERMAL FLUCTUATIONS OF A SINGLE ANISOTROPIC POLYMER." Journal of Mechanics in Medicine and Biology 13, no. 04 (July 7, 2013): 1350056. http://dx.doi.org/10.1142/s0219519413500565.

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Thermal fluctuations of microtubules (MTs) and other cytoskeletal filaments govern to a great extent the complex rheological properties of the cytoskeleton in eukaryotic cells. In recent years, much effort has been put into capturing the dynamics of these fluctuations by means of analytical and numerical models. These attempts have been very successful for, but also remain limited to, isotropic polymers. To correctly interpret experimental work on (strongly) anisotropic semiflexible polymers, there is a need for a numerical modeling tool that accurately captures the dynamics of polymers with anisotropic material properties. In the current study, we present a finite element (FE) framework for simulating the thermal dynamics of a single anisotropic semiflexible polymer. First, we demonstrated the accuracy of our framework by comparison of the simulated mean square displacement (MSD) of the end-to-end distance with analytical predictions based on the worm-like chain model. Then, we implemented a transversely isotropic material model, characteristic for biopolymers such as MTs, and studied the persistence length for various ratios between the longitudinal shear modulus, G12, and corresponding Young's modulus, E1. Finally, we put our findings in context by addressing a recent experimental work on grafted transversely isotropic MTs. In that research, a simplified static mechanical model was used to deduce a very high level of MT anisotropy to explain the observation that the persistence length of grafted MTs increases as contour length increases. We showed, by means of our FE framework, that the anisotropic properties cannot account for the reported length-dependent persistence length.

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Errington, Wesley J., Bence Bruncsics, and Casim A. Sarkar. "Mechanisms of noncanonical binding dynamics in multivalent protein–protein interactions." Proceedings of the National Academy of Sciences 116, no. 51 (November 27, 2019): 25659–67. http://dx.doi.org/10.1073/pnas.1902909116.

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Protein multivalency can provide increased affinity and specificity relative to monovalent counterparts, but these emergent biochemical properties and their mechanistic underpinnings are difficult to predict as a function of the biophysical properties of the multivalent binding partners. Here, we present a mathematical model that accurately simulates binding kinetics and equilibria of multivalent protein–protein interactions as a function of the kinetics of monomer–monomer binding, the structure and topology of the multidomain interacting partners, and the valency of each partner. These properties are all experimentally or computationally estimated a priori, including approximating topology with a worm-like chain model applicable to a variety of structurally disparate systems, thus making the model predictive without parameter fitting. We conceptualize multivalent binding as a protein–protein interaction network: ligand and receptor valencies determine the number of interacting species in the network, with monomer kinetics and structural properties dictating the dynamics of each species. As predicted by the model and validated by surface plasmon resonance experiments, multivalent interactions can generate several noncanonical macroscopic binding dynamics, including a transient burst of high-energy configurations during association, biphasic equilibria resulting from interligand competition at high concentrations, and multiexponential dissociation arising from differential lifetimes of distinct network species. The transient burst was only uncovered when extending our analysis to trivalent interactions due to the significantly larger network, and we were able to predictably tune burst magnitude by altering linker rigidity. This study elucidates mechanisms of multivalent binding and establishes a framework for model-guided analysis and engineering of such interactions.

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Travers, Timothy, William K. Kanagy, Rachael A. Mansbach, Elton Jhamba, Cedric Cleyrat, Byron Goldstein, Diane S. Lidke, Bridget S. Wilson, and S. Gnanakaran. "Combinatorial diversity of Syk recruitment driven by its multivalent engagement with FcεRIγ." Molecular Biology of the Cell 30, no. 17 (August 2019): 2331–47. http://dx.doi.org/10.1091/mbc.e18-11-0722.

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Syk/Zap70 family kinases are essential for signaling via multichain immune-recognition receptors such as tetrameric (αβγ2) FcεRI. Syk activation is generally attributed to cis binding of its tandem SH2 domains to dual phosphotyrosines within FcεRIγ-ITAMs (immunoreceptor tyrosine-based activation motifs). However, the mechanistic details of Syk docking on γ homodimers are unresolved. Here, we estimate that multivalent interactions for WT Syk improve cis-oriented binding by three orders of magnitude. We applied molecular dynamics (MD), hybrid MD/worm-like chain polymer modeling, and live cell imaging to evaluate relative binding and signaling output for all possible cis and trans Syk–FcεRIγ configurations. Syk binding is likely modulated during signaling by autophosphorylation on Y130 in interdomain A, since a Y130E phosphomimetic form of Syk is predicted to lead to reduced helicity of interdomain A and alter Syk’s bias for cis binding. Experiments in reconstituted γ-KO cells, whose γ subunits are linked by disulfide bonds, as well as in cells expressing monomeric ITAM or hemITAM γ-chimeras, support model predictions that short distances between γ ITAM pairs are required for trans docking. We propose that the full range of docking configurations improves signaling efficiency by expanding the combinatorial possibilities for Syk recruitment, particularly under conditions of incomplete ITAM phosphorylation.

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Viader-Godoy, Xavier, Maria Manosas, and Felix Ritort. "Sugar-Pucker Force-Induced Transition in Single-Stranded DNA." International Journal of Molecular Sciences 22, no. 9 (April 29, 2021): 4745. http://dx.doi.org/10.3390/ijms22094745.

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The accurate knowledge of the elastic properties of single-stranded DNA (ssDNA) is key to characterize the thermodynamics of molecular reactions that are studied by force spectroscopy methods where DNA is mechanically unfolded. Examples range from DNA hybridization, DNA ligand binding, DNA unwinding by helicases, etc. To date, ssDNA elasticity has been studied with different methods in molecules of varying sequence and contour length. A dispersion of results has been reported and the value of the persistence length has been found to be larger for shorter ssDNA molecules. We carried out pulling experiments with optical tweezers to characterize the elastic response of ssDNA over three orders of magnitude in length (60–14 k bases). By fitting the force-extension curves (FECs) to the Worm-Like Chain model we confirmed the above trend:the persistence length nearly doubles for the shortest molecule (60 b) with respect to the longest one (14 kb). We demonstrate that the observed trend is due to the different force regimes fitted for long and short molecules, which translates into two distinct elastic regimes at low and high forces. We interpret this behavior in terms of a force-induced sugar pucker conformational transition (C3′-endo to C2′-endo) upon pulling ssDNA.

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Underhill, Patrick T., and Patrick S. Doyle. "Alternative spring force law for bead-spring chain models of the worm-like chain." Journal of Rheology 50, no. 4 (July 2006): 513–29. http://dx.doi.org/10.1122/1.2206713.

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Liu, Yi, Wenpeng Cao, Wenjing Cao, X. Long Zheng, and Xiaohui Zhang. "Binding of Gpibα to VWF A2 Domain Alters Mechanical Unraveling of the A2 Domain." Blood 136, Supplement 1 (November 5, 2020): 24–25. http://dx.doi.org/10.1182/blood-2020-143275.

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Background: Von Willebrand factor (VWF), is a large, multimeric plasma glycoprotein that plays a critical role in hemostasis. VWF is synthesized and secreted as ultra large (UL) multimers that contain up to 100 protomers. If not processed by ADAMTS13, a plasma metalloprotease, ULVWF may initiate the spontaneous formation of life-threatening thrombi, as seen in thrombotic thrombocytopenic purpura (TTP). The cleavage site is buried under the central β-sheet within the VWF-A2 domain and tensile force is required to expose the cleavage site for ADAMTS13. Our prior studies demonstrate that several VWF-binding proteins, including coagulation factor VIII, apoB100/LDL, as well as the ectodomains of platelet glycoprotein Iba (GPIba), appear to function as cofactors that facilitate the proteolytic cleavage of VWF by ADAMTS13 under shear. However, the mechanism underlying GPIba enhancing effect on ADAMTS13-mediated VWF proteolysis is yet to be determined. Methods: Recombinant human GPIbα was purchased from Sino Biological. The recombinant VWF-A2 domain fragment with a SpyTag on the N-terminus and an AviTag-HisTag on the C-terminus was expressed in the HEK 293T cells and affinity-purified by the Ni-NTA affinity chromatography. Biotinylation was performed in vitro using a biotin-labeling kit. The binding between VWF-A2 and GPIbα was studied by a custom-built atomic force microscope (AFM) using our established single-molecule binding study protocol. MicroScale Thermophoresis was conducted by a Monolith device to detect the binding affinity between the VWF-A2 and GPIbα. A dual-beam mini-tweezers instrument was utilized to characterize the force-induced conformational changes of the A2 domain in the absence and presence of GPIbα with a pulling speed of 200 nm/s. Results: AFM results indicated that specific binding interactions occurred between GPIbα and VWF-A2. Monolith MST assay revealed a strong binding affinity (Kd of ~20 nM) between GPIbα and the VWF-A2 fragment. In the optical tweezer study, pulling on a single VWF-A2 resulted in an unfolding event at 10-30 pN with an extension ranging from 30 to 40 nm (Fig. 1A). Gaussian fits of the unfolding extension distributions revealed a most probable force-induced extension of 34.87 ± 2.2 nm (mean ± SEM) (Fig. 1B). Addition of 100 nM of GPIbα led to a noticeable decrease in both unfolding force and extension of VWF-A2 (Fig. 1A). The most probable unfolding extension reduced to 16.05 ± 0.2 nm in the presence of 100 nM of GPIbα (Fig. 1B), indicating the binding of GPIbα may influence mechanical unfolding of VWF-A2. Further, the unfolding results were analyzed by a worm-like chain model fit, which yielded a contour length for the initially folded structure of VWF-A2 at 58.83 ± 2.0 nm (mean ± SEM) and 24.53 ± 0.2 nm in the absence and presence of GPIbα, respectively (Fig. 1C), indicating that the specific interactions between GPIbα and A2 domain may partially unfold the A2 domain. Conclusions: These results demonstrate for the first time that binding of GPIbα to VWF-A2 may alter the force-induced conformational changes in the A2 domain. Under physiological conditions, the glycocalicin (or soluble GP1bα) may bind the VWF-A2 and cause A2 partial unfolding, which may result in excessive cleavage of VWF by ADAMTS13, thus regulating hemostasis. Figure legend: Fig.1. GPIbα influences the mechanical unfolding of the A2 domain of VWF. (A) Typical optical tweezer pulling traces of A2 domain in the absence (red) and presence (blue) of GPIbα (100 nM). The arrows point to the unfolding events. The pulling speed is 200 nm/s. (B) The histograms of the unfolding extension of pulling VWF-A2 in the absence (red) or presence (blue) of 100 nM of GPIbα at 200 nm/s. Solid lines are Gaussian fits to the distributions. (C) The relationship between unfolding force (pN) and unfolding extension (nm) of pulling the VWF-A2 in the absence (red) or presence (blue) of 100 nM of GPIbα. The data are fitted to the worm-like chain model (solid lines). Horizontal and vertical error bars are one standard deviation for force and half width of the half bin width for extension, respectively. Figure Disclosures Cao: Ivygen: Consultancy; Bayer: Research Funding. Zheng:Sanofi: Consultancy, Speakers Bureau; Clotsolution: Other: Co-Founder; Alexion: Consultancy, Speakers Bureau; Takeda: Consultancy, Speakers Bureau.

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Rappaport, S. M., and Y. Rabin. "Differential geometry of polymer models: worm-like chains, ribbons and Fourier knots." Journal of Physics A: Mathematical and Theoretical 40, no. 17 (April 11, 2007): 4455–66. http://dx.doi.org/10.1088/1751-8113/40/17/003.

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Ding, Wan, Qiang Ruan, and Yan-an Yao. "Design and locomotion analysis of a novel deformable mobile robot with two spatial reconfigurable platforms and three kinematic chains." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 8 (March 29, 2016): 1481–99. http://dx.doi.org/10.1177/0954406216641453.

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A novel five degrees of freedom deformable mobile robot composed of two spatial reconfigurable platforms and three revolute–prismatic–spherical kinematic chains acting in parallel to link the two platforms is proposed to realize large deformation capabilities and multiple locomotion modes. Each platform is an improved deployable single degrees of freedom three-plane-symmetric Bricard linkage. By taking advantage of locomotion collaborating among platforms and kinematic chains, the mobile robot can fold into stick-like shape and possess omnidirectional rolling and worm-like motions. The mechanism design, kinematics, and locomotion feasibility are the main focus. Through kinematics and gait planning, the robot is analyzed to have the capabilities of rolling and turning. Based on its deformation, the worm-like motion performs the ability to overcome narrow passages (such as pipes, holes, gaps, etc.) with large range of variable size. Dynamic simulations with detailed three-dimensional model are carried out to verify the gait planning and provide the variations of essential motion and dynamic parameters in each mode. An experimental robotic system with servo and pneumatic actuation systems is built, experiments are carried out to verify the validity of the theoretical analysis and the feasibility of the different locomotion functions, and its motion performances are compared and analyzed with collected data.

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Tan, Sisi, and Mingze Xu. "Numerical Studies of Shape Recovery of a Red Blood Cell Using Dissipative Particle Dynamics." International Journal of Computational Methods 17, no. 07 (June 13, 2019): 1950032. http://dx.doi.org/10.1142/s0219876219500324.

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A biological cell exhibits viscoelastic behavior mainly because its components (membrane and cytoplasm) are viscoelastic, and this is clearly seen when it is stretched and released. The present work numerically studied the shape recovery of a red blood cell (RBC) based on a viscoelastic model at the meso-scale using Dissipative Particle Dynamics (DPD) method. In this model, the RBC membrane is represented by a triangular network of worm-like chains, while the cytoplasm is replaced by a system of DPD particles. This viscoelastic model is validated by examining the stretching deformation of an RBC and comparing with the existing experimental data. Viscoelastic properties of the RBC are then analyzed by stretching an RBC under a 20 pN stretching force, and allowing it to relax. The time to recover its shape upon removal of the stretching force is measured to be 111 and 92.6[Formula: see text]ms for an RBC with and without cytoplasm, and the corresponding membrane viscosity is [Formula: see text] and [Formula: see text] [Formula: see text], respectively. These values, for an RBC with cytoplasm, are closer to experimental data than those for an RBC without cytoplasm, lending support to the model with cytoplasm. Finally, parametric studies are conducted on the membrane elastic and bending moduli. The results show that the shape recovery time decreases with increasing the membrane elastic and bending moduli.

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Chow, Andrea W., Steven P. Bitler, Paul E. Penwell, and James F. Wolfe. "Synthesis and Dilute Solution Characterization of Extended Chain Poly(Benzazoles)." MRS Proceedings 134 (1988). http://dx.doi.org/10.1557/proc-134-173.

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ABSTRACTThis paper reports the synthesis method for polymerizaing poly(2,6-benzothiazole) (ABPBT) and poly(2,5-benzoxazole) (ABPBO), and their dilute solution properties using low angle light scattering and viscometry. Our data indicate that the Mark-Houwink-Sakurada exponents for these extended-chain polymers are near unity, suggesting a semi-rigid conformation in dilute solutions. The solution properties agree well with the Yamakawa-Fujii worm-like chain model when persistence lengths of 130 Å and 90 Å are assumed for ABPBT and ABPBO, respectively. These values of persistence length are also in good agreement with those predicted by Flory's virtual bond model using information on the molecular geometries taken from x-ray crystallographic data on oriented fibers of ABPBT and ABPBO.

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Kothari, Konik, Yuhang Hu, Sahil Gupta, and Ahmed Elbanna. "Mechanical Response of Two-Dimensional Polymer Networks: Role of Topology, Rate Dependence, and Damage Accumulation." Journal of Applied Mechanics 85, no. 3 (January 24, 2018). http://dx.doi.org/10.1115/1.4038883.

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The skeleton of many natural and artificial soft materials can be abstracted as networks of fibers/polymers interacting in a nonlinear fashion. Here, we present a numerical model for networks of nonlinear, elastic polymer chains with rate-dependent crosslinkers similar to what is found in gels. The model combines the worm-like chain (WLC) at the polymer level with the transition state theory for crosslinker bond dynamics. We study the damage evolution and the force—displacement response of these networks under uniaxial stretching for different loading rates, network topology, and crosslinking density. Our results suggest a complex nonmonotonic response as the loading rate or the crosslinking density increases. We discuss this in terms of the microscopic deformation mechanisms and suggest a novel framework for increasing toughness and ductility of polymer networks using a bio-inspired sacrificial bonds and hidden length (SBHL) mechanism. This work highlights the role of local network characteristics on macroscopic mechanical observables and opens new pathways for designing tough polymer networks.

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Deng, Yichen, and Steven W. Cranford. "Tunable Toughness of Model Fibers With Bio-Inspired Progressive Uncoiling Via Sacrificial Bonds and Hidden Length." Journal of Applied Mechanics 85, no. 11 (July 17, 2018). http://dx.doi.org/10.1115/1.4040646.

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Nature has a proven track record of advanced materials with outstanding mechanical properties, which has been the focus of recent research. A well-known trade-off between ultimate strength and toughness is one of the main challenges in materials design. Progress has been made by mimicking tough biological fibers by applying the concepts of (1) sacrificial bond and (2) hidden length, providing a so-called “safety-belt” for biological materials. Prior studies indicate a relatively common behavior across scales, from nano- to macro-, suggesting the potential of a generalized theoretical mechanistic framework. Here, we undertake molecular dynamics (MD) based simulation to investigate the mechanical properties of model nanoscale fibers. We explore representative models of serial looped or coiled fibers with different parameters—specifically number of loops, loop radii, cross-link strength, and fiber stiffness—to objectively compare strength, extensibility, and fiber toughness gain. Observing consistent saw-tooth like behavior, and adapting worm-like chain (WLC) mechanics (i.e., pseudo-entropic elasticity), a theoretical scaling relation which can describe the fiber toughness gain as a function of the structural factors is developed and validated by simulation. The theoretical model fits well with the simulation results, indicating that engineering the mechanical response based on controlled structure is possible. The work lays the foundation for the design of uniaxial metamaterials with tunable and predictable tensile behavior and superior toughness.

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Chen, Bin, and Chenling Dong. "Modeling Deoxyribose Nucleic Acid as an Elastic Rod Inlaid With Fibrils." Journal of Applied Mechanics 81, no. 7 (April 1, 2014). http://dx.doi.org/10.1115/1.4026988.

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A classical view of the double-stranded deoxyribose nucleic acid (DNA) as an isotropic elastic rod fails to explain its high flexibility manifested in the formation of sharp loops that are essential in gene regulation and DNA storage. Since the basic structure of DNA can be divided into the external highly polar backbone and the internal hydrophobic bases, here we model DNA as an elastic rod inlaid with fibrils. If the fibrils are much stiffer than the rod, we find that the persistence length of short DNA can be much smaller than that of long DNA with an adapted shear lag analysis. Consequently, the cyclization rate for short DNA is found to be much higher than the previous prediction of the worm-like chain model, which is interestingly in consistency with experiments. Our analysis suggests that the bending of short DNAs can be facilitated if there exists a specific structural heterogeneity.

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Liu, Yujiong, and Pinhas Ben-Tzvi. "A New Extensible Continuum Manipulator Using Flexible Parallel Mechanism and Rigid Motion Transmission." Journal of Mechanisms and Robotics 13, no. 3 (March 15, 2021). http://dx.doi.org/10.1115/1.4050097.

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Abstract An extensible continuum manipulator (ECM) has specific advantages over its nonextensible counterparts. For instance, in certain applications, such as minimally invasive surgery or pipe inspection, the base motion might be limited or disallowed. The additional extensibility provides the robot with more dexterous manipulation and a larger workspace. Existing continuum robot designs achieve extensibility mainly through artificial muscle/pneumatic, extensible backbone, concentric tube, and base extension, etc. This article proposes a new way to achieve this additional motion degree-of-freedom by taking advantage of the rigid coupling hybrid mechanism concept and a flexible parallel mechanism. More specifically, a rack and pinion set is used to transmit the motion of the i-th subsegment to drive the (i+1)-th subsegment. A six-chain flexible parallel mechanism is used to generate the desired spatial bending and one extension mobility for each subsegment. This way, the new manipulator can achieve tail-like spatial bending and worm-like extension at the same time. Simplified kinematic analyses are conducted to estimate the workspace and the motion nonuniformity. A proof-of-concept prototype was integrated to verify the mechanism’s mobility and to evaluate the kinematic model accuracy. The results show that the proposed mechanism achieved the desired mobilities with a maximum extension ratio of 32.2% and a maximum bending angle of 80 deg.

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"Nanomechanical Characterization of Apolipoprotein A-I Amyloid Fibrils." Issue 2 2020, no. 2 (2020). http://dx.doi.org/10.26565/2312-4334-2020-2-11.

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Amyloid fibrils represent a special type of protein aggregates that are currently receiving enormous attention due to their strong implication in molecular etiology of a wide range of human disorders. Amyloid fibrils represent highly ordered self-assemblies sharing a core cross-β-sheet structure. Such organization of the fibrils is responsible for amyloid insolubility and exceptional mechanical properties. The remarkable rigidity of the protein fibrillar aggregates is due to intra- and interstrand hydrogen bonds which stabilize the β-strand scaffold of amyloid fibrils. Increasing evidence indicates that physical properties of amyloid assemblies, especially their mechanical characteristics, play essential role in determining their cytotoxic action. This highlights the necessity of deciphering the correlation between the elastic properties of amyloid aggregates and their cytotoxicity. In the present paper we utilized the atomic force microscopy (AFM) to visualize and analyze the amyloid fibrils of G26R/W@8 mutant of N-terminal fragment of human apolipoprotein A-I (apoA-I). The examination of AFM images revealed the existence of two polymorphic forms of apoA-I fibrils – twisted ribbon and helical ribbon. The quantitative analysis of apoA-I elastic properties was performed within the framework of worm-like model of polymer chain using the Easyworm software. The Easyworm package analyzes the images of individual polymer chains obtained by the atomic force microscopy and allows calculation of the persistent length of a chain in three regimes depending on the ratio between the contour and persistent lengths of the polymer. The set of evaluated parameters included the Young’s modulus, persistent length, bending rigidity and the second moment of inertia. All parameters calculated for the helical ribbon conformation were higher than those of the twisted ribbon. These findings suggest that helical ribbon represents a more rigid and mechanically stable configuration. The results obtained may prove of importance for a deeper understanding the mechanics-driven pathological activities of amyloid fibrils.

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Hillgärtner, Markus, Kevin Linka, and Mikhail Itskov. "Comparative study of worm‐like chain models for collagen molecules." PAMM 18, no. 1 (December 2018). http://dx.doi.org/10.1002/pamm.201800111.

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Journal articles on the topic 'Worm-like chain model'

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