Using dynamic simulations and analytic methods, we study the elastic response of a helical filament subject to uniaxial tension over a wide range of bend and twist persistence length. A low-pitch helix at low temperatures exhibits a stretching instability and the force-extension curve consists of a sequence of spikes. At elevated temperature (i.e. small persistence lengths) the helix melts and a pronounced force plateau is obtained in the fixed-extension ensemble. The torque boundary condition significantly affects the resulting elastic properties.
We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to step-like contraction and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the…
We perform Monte Carlo simulations to study the elastic properties of the helix-coil worm-like chain model of alpha-helical polypeptides. In this model the secondary structure enters as a scalar (Ising like) variable that controls the local chain bending modulus. We compute numerically the bending and stretching compliances of this molecule as well as the nonlinear interaction between stretching and torque over a wide range of model parameters. The numerical results agree well with previous mean-field and perturbative calculations where they are expected to do so. The Monte Carlo simulations a…
We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri J, Manghi M and Destainville N 2007 Phys. Rev. Lett. 99 088103). Our Discrete Helical Wormlike Chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in …
Generic interactions e.g. the Coulomb or other long ranged radially symmetric repulsive interactions between monomers of bead-spring model of a semi-flexible polymer induce instabilities in a initially straight polymer chain to form long lived helical structures. This mechanism can explain the spontaneous emergence of helices in stiff (bio-)polymers as effective charge of the chain increases. The helix formation is independent of the chemistry and torsional potentials are not used. So this method can be used to synthesize helical springs at length scales of nm-10$μ$.
Force-induced reversible transformations between coiled and normal polymorphs of bacterial flagella have been observed in recent optical-tweezer experiment. We introduce a discrete elastic rod model with two competing helical states governed by a fluctuating spin-like variable that represents the underlying conformational states of flagellin monomers. Using hybrid Brownian dynamics Monte-Carlo simulations, we show that a helix undergoes shape transitions dominated by domain wall nucleation and motion in response to externally applied uniaxial tension. A scaling argument for the critical force …
The Slinky is a well-known example of a highly flexible helical spring, exhibiting large, geometrically nonlinear deformations from minimal applied forces. By considering it as a system of coils that act to resist axial, shearing, and rotational deformations, we develop a discretized model to predict the equilibrium configurations of a Slinky via the minimization of its potential energy. Careful consideration of the contact between coils enables this procedure to accurately describe the shape and stability of the Slinky under different modes of deformation. In addition, we provide simple geome…
I propose a variation of the standard worm--like chain model to account for internal order parameter (helix/coil) fields on the polymer chain. This internal order parameter field influences polymer conformational statistics by locally modifying the persistence length of the chain. Using this model, I make predictions for the bending and stretching response of an alpha-helical domain of a protein. In particular, I show that alpha-helical protein domains will buckle under applied torque. This highly nonlinear elastic behavior may be important in the understanding of allosteric control of biochem…
A simple force-probe setup is employed to study the mechanical properties of transcription activator-like effector (TALE) proteins in computer experiments. It is shown that their spring-like arrangement benefits superelastic behaviour which is manifested by large-scale global conformational changes along the helical axis, thus linking structure and dynamics in TALE proteins. As evidenced from the measured force-extension curves the dHax3 and PthXo1 TALEs behave like linear springs, obeying Hooke's law, for moderate global structural changes. For larger deformations, however, the proteins exhib…
Mechanical properties of DNA, in particular their stretch dependent extension and their loop formation characteristics, have been recognized as an effective probe for understanding the possible biochemical role played by them in a living cell. Single stranded DNA (ssDNA), which, till recently was presumed to be an simple flexible polymer continues to spring surprises. Synthetic ssDNA, like polydA (polydeoxyadenosines) has revealed an intriguing force-extension (FX) behavior exhibiting two plateaus, absent in polydT (polydeoxythymidines) for example. Loop closing time in polydA had also been fo…
We analyze the stretching elasticity of a wormlike chain with a tension discontinuity resulting from a Hookean spring connecting its backbone to a fixed point. The elasticity of isolated semiflexible filaments has been the subject in a significant body of literature, primarily because of its relevance to the mechanics of biological matter. In real systems, however, these filaments are usually part of supramolecular structures involving cross-linkers or molecular motors which cause tension discontinuities. Our model is intended as a minimal structural element incorporating such a discontinuity.…
We present an effective medium theory that includes bending as well as stretching forces, and we use it to calculate mechanical response of a diluted filamentous triangular lattice. In this lattice, bonds are central-force springs, and there are bending forces between neighboring bonds on the same filament. We investigate the diluted lattice in which each bond is present with a probability $p$. We find a rigidity threshold $p_b$ which has the same value for all positive bending rigidity and a crossover characterizing bending-, stretching-, and bend-stretch coupled elastic regimes controlled by…
Taking into account the nonequivalence of fixed-force and fixed-length ensembles in the weak-force regime, equations of state are derived that describe the equilibrium extension or compression of an ideal Gaussian polymer chain in response to an applied force in such a manner that the calculated unstretched scalar end-to-end separation is the random-coil size rather than zero. The entropy-spring model for a polymer chain is thereby modified so that for calculational purposes, the spring is of finite rather than zero unstretched length. These force laws are shown to be consistent with observati…
Using Langevin simulations, we find that simple 'generic' bead-and-spring homopolymer chains in a sufficiently bad solvent spontaneously develop helical order during the process of collapsing from an initially stretched conformation. The helix formation is initiated by the unstable modes of the straight chain, which drive the system towards a long-lived metastable transient state. The effect is most pronounced if hydrodynamic interactions are screened.
Shape enantiomerism in semi-rigid polymer liquid crystals
Laboratoire de Physique des Solides - UMR 8502, CNRS, Université Paris-Saclay（巴黎萨克雷大学固体物理实验室）；Institut Charles Sadron, Université de Strasbourg & CNRS（斯特拉斯堡大学夏尔·萨德龙研究所）
We study the emergence of helical structures subjected to a stretching force, demonstrating that the force transforms disk-shaped colloidal membranes into twisted chiral ribbons of predetermined handedness. Using an experimental technique that enforces torque-free boundary conditions we simultaneously measure the force-extension curve and quantify the shape of emergent ribbons. An effective theory that accounts for the membrane bending energy and uses geometric properties of the edge to model the internal liquid crystalline degrees of freedom explains both the measured force-extension curve an…
