Macromolecular Theory and Simulations Volume 5 issue 1 1996 [doi 10.1002 mats.1996.040050109] Arkady L. Kholodenko; Jack F. Douglas; Thomas A. Vilgis -- Electrostatic rigidity of polyelectrolytes from reparametrizati (original) (raw)

Electrostatic rigidity of polyelectrolytes from reparametrization invariance

Macromolecular Theory and Simulations, 1996

The persistence length I, of a polyelectrolyte chain can be represented as I, = I, + I, where I, is the bare persistence and I, is the electrostatic contribution coming from the effects of electrostatic chain self-interactions. Using a reparametrization-invariant path integral model of semiflexible polymers we find that I, depends on the ionic strength Z as I,-Z-"2. This result accords with experimental observations and recent Monte Carlo simulations. Reparametrization-invariance is apparently an essential constraint in selecting acceptable models of semiflexible polymers. The Kratky-Porod (K-P) model is widely utilized for the description of conformational properties of semiflexible chains ' 1. The basic feature of this model is that the tangent-tangent (t-t) correlator for the K-P chain is an exponential, exp (-I r I / l ,) , where T is the contour distance along the polymer chain and the "persistence length" I, is the rigidity correlation length. The second moment, i. e., the end-to-end distance (R2> of the K-P chain is determined by integrating the t-t to obtain the well known result, (R2> = 21: 01-1 + exp(-y)) wherey = N/Ip and N i s the total contour length of the chain. Not all conformational properties of semiflexible chains can be calculated using the K-P model however. For instance, there are no known closed form expressions for the moment generating function, the static scattering form factor S(k), etc. 2, Under these circumstances it is difficult to assess the adequacy of the K-P model for describing real polymers. Noticing that for y + 1 the limiting K-P result for (R2) = 21,Ncoincides with that known for fully flexible chains, it i s natural to assume that the K-P propagator describes simple random walk paths, at least in this limit. Following Polyakov's observation3) that "while in the bosonic case we have a Brownian path with its size R

A ug 2 00 5 A generalized theory of semiflexible polymers

2017

NA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biologically relevant length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific, illustrative model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics...

A generalized theory of semiflexible polymers

2005

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain (WLC) model, to DNA bending on biological length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific toy model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by the Renormalization Group. In particular, we show that either the WLC or our new model adequate describes force-extension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization J factors observed by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments.

Generalized theory of semiflexible polymers

Physical Review E, 2006

DNA bending on length scales shorter than a persistence length plays an integral role in the translation of genetic information from DNA to cellular function. Quantitative experimental studies of these biological systems have led to a renewed interest in the polymer mechanics relevant for describing the conformational free energy of DNA bending induced by protein-DNA complexes. Recent experimental results from DNA cyclization studies have cast doubt on the applicability of the canonical semiflexible polymer theory, the wormlike chain ͑WLC͒ model, to DNA bending on biologically relevant length scales. This paper develops a theory of the chain statistics of a class of generalized semiflexible polymer models. Our focus is on the theoretical development of these models and the calculation of experimental observables. To illustrate our methods, we focus on a specific, illustrative model of DNA bending. We show that the WLC model generically describes the long-length-scale chain statistics of semiflexible polymers, as predicted by renormalization group arguments. In particular, we show that either the WLC or our present model adequately describes forceextension, solution scattering, and long-contour-length cyclization experiments, regardless of the details of DNA bend elasticity. In contrast, experiments sensitive to short-length-scale chain behavior can in principle reveal dramatic departures from the linear elastic behavior assumed in the WLC model. We demonstrate this explicitly by showing that our toy model can reproduce the anomalously large short-contour-length cyclization J factors recently measured by Cloutier and Widom. Finally, we discuss the applicability of these models to DNA chain statistics in the context of future experiments.

Statistical Mechanics of Double-Stranded Semiflexible Polymers

Physical Review Letters, 1998

We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while at low temperatures they are different due to a twist structure. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin. 87.15By, 36.20Ey, 61.25Hq

Statistical Mechanics of Semiflexible Polymer Chains from a new Generating Function

Eprint Arxiv Cond Mat 0309626, 2003

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 P (k, p) = (I + ikDM) −1 D, 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-toend 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.

Statistical mechanics of semiflexible polymers

The European Physical Journal B, 2004

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 P (k, p) = (I + ikDM ) −1 D, 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-toend 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. 61.41.+e, 82.35.Gh

Macromolecular conformations in solutions. I. Model for chains with partial flexibility

Less-than fully flexible polymer chains in solution are considered. Each chain is represented by relatively rigid and with relatively low pervaded volume groupings of monomeric units called compact bundles, intercalated with extended bundles. A partition function for the system is constructed in terms of numbers of possible kinds of pairs of neighboring bundles, and of configurational energies. Results of the extremization of the partition function show an interplay of the interaction forces as decisive for the behavior of the system. The parameters characterizing the system are related to those in the Elory freevolume theory of liquids and solutions. The resulting equations enable evaluation of the relative concentration of compact bundles and of the numbers of pairs of neighboring bundles of different kinds. The model is related to some experimental evidence. Possible connections to structures of polymer-containing phases other than solutions are pointed out.

Persistence lengths of semiflexible chains — methods and approximations

Macromolecular Theory and Simulations, 1994

Several models and methods for stiff polymer chains are discussed. The basic idea is to develop approximate soIutions to the problem of the persistence length of stiff polymers. It turns out that the persistence length can be regarded as a measure for the quality of approximations. Mean-field methods for field theoretical calculations of the persistence length show similarities of 1 /d expansions in statistical physics (d being the space dimension) and saddle point approximations become reliable in various limits. Gaussian approximations becomeas well known for the king modelsimple extensions of random walks as trivial renormalisations of the Wiener-Edwards model for bosonic strings.

Semiflexible polymers: Dependence on ensemble and boundary orientations

Physical Review E, 2007

We show that the mechanical properties of a worm-like-chain (WLC) polymer, of contour length L and persistence length λ such that t = L/λ ∼ O(1), depend both on the ensemble and the constraint on end-orientations. In the Helmholtz ensemble, multiple minima in the free energy near t = 4 persists for all kinds of orientational boundary conditions. The qualitative features of projected probability distribution of end to end vector depend crucially on the embedding dimensions. A mapping of the WLC model, to a quantum particle moving on the surface of an unit sphere, is used to obtain the statistical and mechanical properties of the polymer under various boundary conditions and ensembles. The results show excellent agreement with Monte-Carlo simulations.