Stretching of semiflexible polymers with elastic bonds

A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible polymer in a unified manner. The interplay between bond extension and external force can be described by an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length. We discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear response for weak stretching depends on the relative size of the contour length and the persistence length which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension relations are corroborated by transfer matrix and variational calculations.PACS: 87.15.-v Biomolecules: structure and physical properties - 87.15.Aa Theory and modeling; computer simulation - 87.15.La Mechanical properties     

Stacking interactions in denaturation of DNA fragments

A mesoscopic model for heterogeneous DNA denaturation is developed in the framework of the path integral formalism. The base pair stretchings are treated as one-dimensional, time-dependent paths contributing to the partition function. The size of the paths ensemble, which measures the degree of cooperativity of the system, is computed versus temperature consistently with the model potential physical requirements. It is shown that the ensemble size strongly varies with the molecule backbone stiffness providing a quantitative relation between stacking and features of the melting transition. The latter is an overall smooth crossover which begins from the adenine-thymine-rich portions of the fragment. The harmonic stacking coupling shifts, along the T -axis, the occurrence of the multistep denaturation but it does not change the character of the crossover. The methods to compute the fractions of open base pairs versus temperature are discussed: by averaging the base pair displacements over the path ensemble, we find that such fractions signal the multisteps of the transition in good agreement with the indications provided by the specific heat plots.     

A novel family of space-filling curves in their relation to chromosome conformation in eukaryotes

Spatial conformation of DNA chains during interphase in eukaryotic cell nucleus is relatively dense, yet unknotted and exhibits self-similar fractal properties. In this respect it resembles the space-filling curves of Hilbert, but differs in the experimentally accessible contact probability of distant loci. Here we construct space-filling curves with fractal domain boundaries of dimension close to that of the embedding space and show how these match the statistical properties and the contact probability of the DNA conformation. The present mathematical model should shed light on the statistical ensemble of unknotted dense polymers and ease the modeling of genome folding and related biological processes.     

Form of growing strings

Patterns and forms adopted by nature are often the results of simple dynamical paradigms. Here we show that a growing self-interacting string attached to a tracking origin, modeled to resemble nascent polypeptides in vivo, develops helical structures which are more pronounced at the growing end. We also show that the dynamic growth ensemble shares several features of an equilibrium ensemble in which the growing end of the polymer is under an effective stretching force. A statistical analysis of native states of proteins shows that the signature of this nonequilibrium phenomenon has been fixed by evolution at the C terminus, the growing end of a nascent protein. These findings suggest how evolution may have built on the properties of a generic nonequilibrium growth process in favoring helical structures in nascent chains.     

The secondary structure of RNA under tension

We study the force-induced unfolding of random disordered RNA or single-stranded DNA polymers. The system undergoes a second-order phase transition from a collapsed globular phase at low forces to an extensive necklace phase with a macroscopic end-to-end distance at high forces. At low temperatures, the sequence inhomogeneities modify the critical behaviour. We provide numerical evidence for the universality of the critical exponents which, by extrapolation of the scaling laws to zero force, contain useful information on the ground-state (f = 0) properties. This provides a good method for quantitative studies of scaling exponents characterizing the collapsed globule. In order to get rid of the blurring effect of thermal fluctuations, we restrict ourselves to the ground state at fixed external force. We analyze the statistics of rearrangements, in particular below the critical force, and point out its implications for force-extension experiments on single molecules. Received 18 June 2002 and Received in final form 23 September 2002 RID="a" ID="a"e-mail: muller@ipno.in2p3.fr     

Denaturation transition of stretched DNA

We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force. We demonstrate the existence of a force-induced DNA denaturation transition and obtain the temperature-force phase diagram. The transition is determined by the loop exponent c, for which we find the new value c = 4 nu-1/2 such that the transition is second order with c = 1.85 < 2 in d = 3. We show that a finite stretching force F destabilizes DNA, corresponding to a lower melting temperature T(F), in agreement with single-molecule DNA stretching experiments.     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Force response of a viscous liquid in a probe-tack geometry: Fingering versus cavitation

We perform traction experiments on viscous liquids highly confined between parallel plates, a geometry known as the probe-tack test in the adhesion community. Direct observation during the experiment coupled to force measurement shows the existence of several mechanisms for releasing the stress: while fingering is favored for low traction velocities, low confinement and low viscosity, nucleation of bubbles occurs in the opposite conditions. It is possible to quantitatively predict the transition between the two regimes and, in many respects, describe the shape of the force response. Using a model for purely viscous fluids, we also present a phase diagram for the different force peak regimes that remarkably accounts for the data. Our results show that conspicuous features of the traction curve commonly thought to be characteristic of soft viscoelastic solids like adhesives are already encountered in liquid materials.Received: 30 July 2004, Published online: 26 October 2004PACS: 82.35.Gh Polymers on surfaces; adhesion - 47.55.Bx Cavitation - 83.50.Jf Extensional flow and combined shear and extension     

Force-induced desorption and unzipping of semiflexible polymers

The thermally assisted force-induced desorption of semiflexible polymers from an adhesive surface or the unzipping of two bound semiflexible polymers by a localized force are investigated. The phase diagram in the force-temperature plane is calculated both analytically and by Monte Carlo simulations. Force-induced desorption and unzipping of semiflexible polymers are first order phase transitions. A characteristic energy barrier for desorption is predicted, which scales with the square root of the polymer bending rigidity and governs the initial separation process before a plateau of constant separation force is reached. This leads to activated desorption and unzipping kinetics accessible in single molecule experiments.     

Highly stretched single polymers: atomic-force-microscope experiments versus ab-initio theory

Experimental single-molecule stretching curves for three backbone architectures (single-stranded DNA, various types of peptides, polyvinylamine) are quantitatively compared with corresponding quantum-chemical (zero-temperature) ab-initio calculations in the high-force range of up to two nanonewtons. For high forces, quantitative agreement is obtained with the contour length of the polymers as the only fitting parameter. For smaller forces, the effects of chain fluctuations are accounted for by using recent theoretical results for the stretching response of a freely-rotating-chain model.     

Raman spectroscopy study of damage induced in fluorapatite by swift heavy ion irradiations

Raman spectroscopy was used to study the radiation damage of fluorapatite single crystals and sinters. Krypton and iodine ion irradiations were performed at high energies (∼1 MeV amu⁻¹) for fluences ranging between 1 × 10¹¹ and 5 × 10¹³ cm⁻². Evolution of the symmetric stretching mode of the PO₄³⁻ tetrahedral building blocks (strongest Raman mode observed at 965 cm⁻¹) versus ion fluence was investigated. After irradiation, this peak decreases in intensity and a second broader peak appears at lower wavenumber. The well‐resolved peak has been assigned to the crystalline phase, and the broader one to the amorphous phase. The integrated intensity ratios of these two peaks versus fluence are in good agreement with the damage fractions determined by X‐ray diffraction (XRD). Fits of the amorphous fraction versus fluence show that the amorphization mechanisms is dominated by a single‐impact process for iodine ions and by a double‐impact process for krypton ions in the case of single crystals and sinters. For both irradiations, complete amorphization could not be obtained. The amorphous fraction saturates at a maximum value of 88% for sinters and 72% for single crystals. This is attributed to a recrystallization effect which is more important in single crystals than in sinters. For both types of samples, the crystalline peak shifts slightly to a lower wavenumber with fluence, and then shifts back to its initial value for an amorphous fraction larger than 60%. This feature is attributed to a stress relaxation, as shown in the XRD data, which is accompanied by a decrease of the crystalline peak full‐width at half‐maximum. Copyright © 2011 John Wiley & Sons, Ltd.     

激光诱导等离子体对水OH伸缩振动受激拉曼散射的影响

利用532 nm脉冲激光进行水的受激拉曼散射研究,通过改变激光焦点与水-空气界面的距离,获得截然不同的OH伸缩振动受激斯托克斯和反斯托克斯谱线.焦点距水-空气界面大于20 mm时,只存在±3400cm-1的斯托克斯和反斯托克斯谱线;焦点距离水-空气界面小于20 mm时,存在±3000和±3400cm-1的斯托克斯和反斯托克斯谱线;继续缩小焦点与水-空气界面的距离,3000 cm-1谱线被增强,而3400 cm-1谱线被削弱.研究结果表明,激光诱导水产生的等离子体增强了局部水分子的氢键,导致OH伸缩振动红移,同时过剩电子增强了水的OH伸缩振动受激拉曼散射.     

Force-extension behavior of folding polymers

The elastic response of flexible polymers made of elements which can be either folded or unfolded, having different lengths in these two states, is discussed. These situations are common for biopolymers as a result of folding interactions intrinsic to the monomers, or as a result of binding of other smaller molecules along the polymer length. Using simple flexible-chain models, we show that even when the energy ε associated with maintaining the folded state is comparable to k _B T, the elastic response of such a chain can mimic usual polymer linear elasticity, but with a force scale enhanced above that expected from the flexibility of the chain backbone. We discuss recent experiments on single-stranded DNA, chromatin fiber and double-stranded DNA with proteins weakly absorbed along its length which show this effect. Effects of polymer semiflexiblity and torsional stiffness relevant to experiments on proteins binding to dsDNA are analyzed. We finally discuss the competition between electrostatic self-repulsion and folding interactions responsible for the complex elastic response of single-stranded DNA. Received 7 August 2002 and Received in final form 7 March 2003 / Published online: 15 April 2003 RID="a" ID="a"e-mail: jmarko@uic.edu     

Statistical mechanics of semiflexible polymers

We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, 1/(k ²/3 + p), through the matrix , where D and M are related to the spectrum of the quantum rigid rotator, and considers an appropriate matrix element of the expression under consideration. The present work provides also the framework to study polymers in external fields, and problems including the tangents of semiflexible polymers. We study the structure factor of the polymer, the transversal fluctuations of a free end of the polymer with fixed tangent of another end, and the localization of a semiflexible polymer onto an interface. We obtain the partition function of a semiflexible polymer in half space with Dirichlet boundary condition in terms of the end-to-end distribution function of the free semiflexible polymer, study the behaviour of a semiflexible polymer in the vicinity of a surface, and adsorption onto a surface.Received: 23 March 2004, Published online: 23 July 2004PACS: 36.20.-r Macromolecules and polymer molecules - 61.41. + e Polymers, elastomers, and plastics - 82.35.Gh Polymers on surfaces; adhesion     

Peeling model for cell detachment

In many experimental situations, the adhesion of cells to solid substrates is due to non-covalent chemical bonds. It is the thesis of this paper that many phenomena occurring in cell detachment experiments, such as in I (E. Decavé, G. Garriver, Y. Brechet, B. Fourcade, F. Bruckert, Biophys. J. 82, 2383 (2002)), result from the static and dynamic properties of the adhesive bridges at the extreme margin of the cell. This region defines the adhesive belt where the distribution of connected bonds crosses over to zero where the membrane leaves the substrate. The theoretical model we introduce in this paper discusses the threshold force together with the peeling velocity in the same theoretical framework. In this one-dimensional model, the threshold force results from a non-homogeneous distribution of anchor proteins along the membrane so that the adhesive belt increases its capacity to resist motion with increasing the external force. Analyzing the kinetics of the the contact line motion, we derive the characteristic relationship speed versus external force and we describe the non-equilibrium state of the adhesive belt as a function of the speed. We discuss our model in view of the experimental results obtained with D. discoideum for hydrodynamic shear experiments. Our results could be also confronted to single-cell observations. Received 14 January 2002     

Mechanochemical Coupling of Kinesin Studied with a Neck-Linker Swing Model

A neck-linker swing model has been proposed in this work to investigate the mechanochemical coupling of kinesin. The difference between force-velocity curves given by force clamp and fixed trap respectively has been satisfactorily interpreted by this model. The study implies that ADP releasing and ATP hydrolysis are much less forcedependent in force clamp experiments than that in fixed trap experiments in the regime of moderate loading force, which might be a consequence of the delayed response of servo system in force clamp experiments.     

L-阿拉伯糖指纹区太赫兹光谱和拉曼光谱的研究

为了解生物体内L-阿拉伯糖在代谢过程中的合成与降解机制,采用太赫兹和拉曼光谱系统,对其指纹区的振动进行检测。结果表明,L-阿拉伯糖太赫兹图谱在频率49.5和72.2 cm-1分别检测出了振动吸收,其中72.2 cm-1的振动为首次检出。该振动频率与其折射率图谱反常色散的频率基本一致,故这两个振动吸收可以作为L-阿拉伯糖的特征吸收。最为重要的是,在该频域内,检测得到图谱的波型与三种异构体理论值简单叠加后波型极为相似,故可以初步判定样品含有三种构象异构体(α-型、β-型和l-型结构),非单一组分,而是混合组分;对于拉曼图谱而言,其特点简洁而明晰,一般将指纹区的振动,从高到低分为四个区域：吡喃环结构的伸缩振动、亚甲基的摇摆振动、环上羟基的扭曲振动及环骨架扭曲和畸变振动。同时也根据密度泛函理论B3LYP/6-311G**基组,分别对L-阿拉伯糖的三种构象异构体的振动进行模拟计算,利用势能分布对这些振动进行归属和指认。与理论值相比,振动频率检测值有不同程度的红移,即振动频率向低频发生了偏移,其原因是样品内不同分子间相互影响所致。     

Simulating the vapour–liquid equilibria of large cyclic alkanes

Self-adapting fixed endpoint configurational-bias Monte Carlo simulations in the Gibbs ensemble were carried out to determine the vapour–liquid coexistence curves of cyclic alkanes from c-pentane to c-octadecane. In general, the critical temperatures and densities of the cyclic alkanes are substantially higher than those of their linear counterparts. Furthermore, the simulation data point to a maximum in the critical density for cyclic alkanes with about eight carbon atoms as also observed for the linear alkanes.