Semiflexible polymer confined to a spherical surface

We develop a formalism for describing the kinematics of a wormlike chain confined to the surface of a sphere that simultaneously satisfies the spherical confinement and the inextensibility of the chain contour. We use this formalism to study the statistical behavior of the wormlike chain on a spherical surface. In particular, we provide an exact, closed-form expression for the mean square end-to-end distance that is valid for any value of chain length L, persistence length l(p), and sphere radius R. We predict two qualitatively different behaviors for a long polymer depending on the ratio R/l(p). For R/l(p)>4, the mean square end-to-end distance increases monotonically with the chain length, whereas for R/l(p)<4, a damped oscillatory behavior is predicted.     

On Continuous-Time Self-Avoiding Random Walk in Dimension Four

We study the distribution of the end-to-end distance of continuous-time self-avoiding random walks (CTRW) in dimension four from two viewpoints. From a real-space renormalization-group map on probabilities, we conjecture the asymptotic behavior of the end-to-end distance of a weakly self-avoiding random walk (SARW) that penalizes two-body interactions of random walks in dimension four on a hierarchical lattice. Then we perform the Monte Carlo computer simulations of CTRW on the four-dimensional integer lattice, paying special attention to the difference in statistical behavior of the CTRW compared with the discrete-time random walks. In this framework, we verify the result already predicted by the renormalization-group method and provide new results related to enumeration of self-avoiding random walks and calculation of the mean square end-to-end distance and gyration radius of continous-time self-avoiding random walks.     

Tracer studies on f-actin fluctuations

We present a study on the fluctuations of semiflexible actin filaments using fluorescence videomicroscopy, focusing on the end-to-end fluctuations of single filaments. In order to specifically measure the position of the polymer's ends, we developed a novel noninvasive method that consists of annealing short end tags to the filaments. This allows us to probe polymer fluctuations to a very high accuracy. We compared the distribution of the end-to-end distance with recent theoretical results, and found excellent agreement. We also studied the dynamics of the mean-square end-to-end distance deltaR2(t) and orientation of the ends, deltaTheta(2)(t), finding power laws t(3/4) and t(1/4), respectively. Scaling behavior for deltaR2(t) is observed over several decades in relaxation time in agreement with theoretical results.     

拉伸取向聚合物2H NMR谱的键涨落模型Monte Carlo模拟

采用三维键涨落模型（BFM）的Monte Carlo计算机模拟方法,模拟了两种分别具有高取向和低取向链微观结构的拉伸取向聚合物²H NMR谱. 讨论了排除体积效应与链的均方末端距分布对²H NMR谱线的影响. 结果表明,排除体积效应对高取向和低取向聚合物²H谱劈裂的影响是不同的,较小均方末端距的链决定²H谱劈裂,而较大均方末端距的链使²H谱产生长的拖尾. 采用BFM计算机模拟与²H NMR实验的结合是研究拉伸取向聚合物网络微观结构的有力手段.     

Thermal properties of a two-dimensional intrinsically curved semiflexible biopolymer

We study the behaviors of mean end-to-end distance and specific heat of a two-dimensional intrinsically curved semiflexible biopolymer with a hard-core excluded volume interaction. We find the mean square end-to-end distance R~2_N∝ N~βat large N, with N being the number of monomers. Both β and proportional constant are dependent on the reduced bending rigidity κ and intrinsic curvature c. The larger the c, the smaller the proportional constant, and 1.5 ≥β≥ 1. Up to a moderate κ = κ_c, or down to a moderate temperature T = T_c, β = 1.5, the same as that of a self-avoiding random walk, and the larger the intrinsic curvature, the smaller the κ_c. However, at a large κ or a low temperature, β is close to 1,and the conformation of the biopolymer can be more compact than that of a random walk. There is an intermediate regime with 1.5 β 1 and the transition from β = 1.5 to β = 1 is smooth. The specific heat of the system increases smoothly with increasing κ or there is no peak in the specific heat. Therefore, a nonvanishing intrinsic curvature seriously affects the thermal properties of a semiflexible biopolymer, but there is no phase transition in the system.     

Quantum communication through chains with diluted disorder

We investigate a single-qubit state transfer protocol along a channel featuring diagonal diluted disorder. In the regime where the source and destination sites are weakly coupled to the channel, we report the possibility of transmitting quantum states with high fidelity as well as establishing end-to-end entanglement in that sort of configuration. We further discuss how the performance of the protocol depends upon the availability of extended states within the disordered channel.     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Distribution functions, loop formation probabilities, and force-extension relations in a model for short double-stranded DNA molecules

We obtain, using transfer-matrix methods, the distribution function P(R) of the end-to-end distance, the loop formation probability, and force-extension relations in a model for short double-stranded DNA molecules. Accounting for the appearance of "bubbles," localized regions of enhanced flexibility associated with the opening of a few base pairs of double-stranded DNA in thermal equilibrium, leads to dramatic changes in P(R) and unusual force-extension curves. An analytic formula for the loop formation probability in the presence of bubbles is proposed. For short heterogeneous chains, we demonstrate a strong dependence of loop formation probabilities on sequence.     

A MODIFIED METHOD OF DETERMINING FRACTAL DIMENSIONS OF POLYMERS AND BIOPOLYMERS

A modified method of calculating the end-to-end distance of segments with a given number of units in a single polymer chain is presented and numerical studies of some fractals by using Havlin and Ben-Avraham's and our methods are given. The results show that our method can remove the fluctuations in the end-to-end distances of the segments arising in Havlin and Ben-Avraham's method.     

Relaxation dynamics of semiflexible polymers

We study the relaxation dynamics of a semiflexible chain by introducing a time-dependent tension. The chain has one of its ends attached to a large bead, and the other end is fixed. We focus on the initial relaxation of the chain that is initially strongly stretched. Using a tension that is self-consistently determined, we obtain the evolution of the end-to-end distance with no free parameters. Our results are in good agreement with single molecule experiments on double stranded DNA.     

End-to-end Distance Distribution in Fluorescent Derivatives of Bradykinin in Interaction with Lipid Vesicles

Cellular membranes have relevant roles in processes related to proteases like human kallikreins and cathepsins. As enzyme and substrate may interact with cell membranes and associated co-factors, it is important to take into account the behavior of peptide substrates in the lipid environment. In this paper we report an study based on energy transfer in two bradykinin derived peptides labeled with the donor-acceptor pair Abz/Eddnp (ortho-aminobenzoic acid/N-[2,4-dinitrophenyl]-ethylenediamine). Time-resolved fluorescence experiments were performed in phosphate buffer and in the presence of large unilamelar vesicles of phospholipids, and of micelles of sodium dodecyl sulphate (SDS). The decay kinetics were analyzed using the program CONTIN to obtain end-to-end distance distribution functions f(r). Despite of the large difference in the number of residues the end-to-end distance of the longer peptide (9 amino acid residues) is only 20?% larger than the values obtained for the shorter peptide (5 amino acid residues). The proline residue, in position 4 of the bradykinin sequence promotes a turn in the longer peptide chain, shortening its end-to-end distance. The surfactant SDS has a strong disorganizing effect, substantially broadening the distance distributions, while temperature increase has mild effects in the flexibility of the chains, causing small increase in the distribution width. The interaction with phospholipid vesicles stabilizes more compact conformations, decreasing end-to-end distances in the peptides. Anisotropy experiments showed that rotational diffusion was not severely affected by the interaction with the vesicles, suggesting a location for the peptides in the surface region of the bilayer, a result consistent with small effect of lipid phase transition on the peptides conformations.     

Hairpin formation and elongation of biomolecules

We introduce a model of thermalized conformations in space of RNA-or single stranded DNA-molecules, which includes the possibility of hairpin formation. This model contains the usual secondary structure information, but extends it to the study of one element of the ternary structure, namely the end-to-end distance. The computed force-elongation characteristics are in good agreement with some recent measurements on single stranded DNA molecules.     

Spatial disorder in a smectic A mesophase

Starting with the equations of motion for a stiff chain, a projection operator approach is utilized to develop diffusional equations for the dynamics of the end-to-end distance. The diffusion equation resulting has a spatial-dependent diffusion coefficient calculable from equilibrium properties of the chain, and a frequency-dependent part which requires dynamical information. The analysis is applied, in so far as the spatial dependence of D is determined, for three and four bond chains. A critique of this procedure is provided.     

‘Monte Carlo’ computer simulation of chain molecules III. Simulation of n-alkane molecules

Considering a realistic model for isolated n-alkane molecules, their configurational behaviour has been explored employing a ‘Monte Carlo’ method. The present study shows that the behaviour of the short molecules is unlike that of the longer molecules in regard to the variation with temperature of the mean-square end-to-end distance and radius of gyration. For the short molecules the mean-square end-to-end distance and the radius of gyration are decreasing functions of temperature, but they increase with temperature in the case of the longer molecules. The macromolecules assume random-walk behaviour at approximately 600 K. The computed heat capacity versus temperature curves disclose configurational transitions in the chains.     

Modular entanglement

We introduce and discuss the concept of modular entanglement. This is the entanglement that is established between the end points of modular systems composed by sets of interacting moduli of arbitrarily fixed size. We show that end-to-end modular entanglement scales in the thermodynamic limit and rapidly saturates with the number of constituent moduli. We clarify the mechanisms underlying the onset of entanglement between distant and noninteracting quantum systems and its optimization for applications to quantum repeaters and entanglement distribution and sharing.     

Effective temperature scaled dynamics of a flexible polymer in an active bath

Langevin dynamics simulations are employed to study the dynamical properties of a flexible polymer in an active bath. The diffusion of the centre of mass and end-to-end distance fluctuation are particularly analysed. We modulate both active force and active particle size to probe the activity-induced facilitation of polymer dynamics. Results indicate diffusivity and chain relaxation time can be well scaled by the effective temperature of the active bath. In addition, diffusion dynamics demonstrates an anomalous superdiffusive behaviour in short time scales, which becomes more prominent with increasing active particle size. Lastly, we extract the effective viscosity experienced by the probed chain, showing a sharp decrease with increment of effective temperature. The attenuation of effective viscosity due to activity might be responsible for the facilitated polymer dynamics.     

Dissipative Particle Dynamics Simulation of Microscopic Properties in Diblock Copolymer Films

利用耗散粒子动力学模拟方法研究了两嵌段共聚高分子薄膜中的一些微观性质. 结果表明：薄膜中共聚高分子链的均方根末端距2_e>^1/2、均方根回旋半径2_g>^1/2与薄膜厚度l、不同粒子间的相互作用强度a_ij、粒子与薄膜边界间的排斥作用强度a_pb均呈线性关系,而均方键长与a_ij、a_pb呈线性关系,随l增加则呈现出波浪形趋势. 2_e>^1/2与2_g>^1/2的变化趋势可以相互对应. 任一组分在薄膜中的密度分布可以通过其与薄膜边界间的相互作用来有效控制与调节.     

Determination of the equilibrium charge distribution for polyampholytes of different compactness in a single computer experiment

The conformational properties of charge-balanced polyampholytes described by the end-to-end distance or radius of gyration depend on parameters such as the temperature and pH as well as on the detailed charge distribution along the backbone. In this work we present a method to determine the charge distribution along a semi-stiff polyampholyte backbone which will result in a thermodynamically stable structure for the compactness of interest, from several loops to an uncoiled structure, performed in a single computer experiment.     

Effect of a force-free end on the mechanical property of a biopolymer——A path integral approach

We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point(i.e.,the origin) to the forced point in the biopolymer,with arclength L_f.The second part consists of the segment counted from the forced point to the force-free end with arclength △L.We apply the path integral technique to find the relationship between these two parts.At finite temperature and without any constraint at the end,we show exactly that if we focus on the quantities related to the first part,then we can ignore the second part completely.Monte Carlo simulation confirms this conclusion.In contrast,the effect for the quantities related to the second part is dependent on what we want to observe.A force-free end has little effect on the relative extension,but it affects seriously the value of the end-to-end distance if △L is comparable to L_f.     

Stretching instability of helical springs

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 steplike 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 region of parameters in which the deformation is continuous from that in which stretching instabilities occur.