Bond fluctuation model of polymers in random media

Dua, Arti; Cherayil, Binny J.

doi:10.1063/1.477337

Cited by 4 publications

(6 citation statements)

References 29 publications

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“…However, other models, such as the Yamakawa model and the Marko-Siggia model, also fit into our general formulation. For the Kratky-Porod wormlike chain model, the stiffness matrix, chirality vector and constant term in (2) are defined as 28 (50) where χ is known as the stiffness parameter. The definitions of the stiffness matrix, chirality vector and constants for the Yamakawa model and Marko-Siggia models can be found in 28 .…”

Section: Examples and Discussionmentioning

confidence: 99%

Conformational Statistics of Semiflexible Macromolecular Chains with Internal Joints

Chirikjian

2006

Macromolecules

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Fluctuations in the bending angles at internal irregularities of DNA and RNA (such as symmetric loops, bulges, and nicks/gaps) have been observed from various experiments. However, little effort has been made to computationally predict and explain the statistical behavior of semiflexible chains with internal defects. In this paper, we describe the general structure of these macromolecular chains as inextensible elastic chains with one or more internal joints which have limited ranges of rotation, and propose a method to compute the probability density functions of the end-to-end pose of these macromolecular chains. Our method takes advantage of the operational properties of the non-commutative Fourier transform for the group of rigid-body motions in three-dimensional space, SE(3). Two representative types of joints, the hinge for planar rotation and the ball joint for spatial rotation, are discussed in detail. The proposed method applies to various stiffness models of semi-flexible chain-like macromolecules. Examples are calculated using the Kratky-Porod model with specified stiffness, angular fluctuation, and joint locations. Entropic effects associated with internal angular fluctuations of semi-flexible macromolecular chains with internal joints can be computed using this formulation. Our method also provides a potential tool to detect the existence of internal irregularities.

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Section: Examples and Discussionmentioning

confidence: 99%

Conformational Statistics of Semiflexible Macromolecular Chains with Internal Joints

Chirikjian

2006

Macromolecules

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“…where the expectation values can be calculated, as before, using the propagator (13) with the Green function (33). For calculation of the rotationally invariant quantity G(s, s ′ ) = G(s − s ′ ), however, the Green function ∆(s, s ′ ) + C must be just as good a Green function satisfying Neumann boundary conditions as ∆(s, s ′ ).…”

Section: Correlation Function Up To Four Loopsmentioning

confidence: 99%

“…. 0 are evaluated by performing all possible Wick contractions with the basic propagator (13) and the Green function (33) of the unperturbed action (37). The relevant loop integrals I i and H i are calculated with our regularization rules when necessary and are listed in Appendices A and B.…”

Section: Partition Function and All Moments Up To Four Loopsmentioning

confidence: 99%

“…Calculation schemes based on periodic boundary conditions were considered in Refs.. 26,27 Path integrals for modified wormlike chain models with softened inextensibility condition have been suggested in Refs.. [28][29][30][31] These models, however, can describe the behavior of the stiff polymer only roughly. Some conformational properties were calculated in Refs.. 32,33 Additional insights into the properties of the end-to-end distribution function of polymers with intermediate stiffness have also been provided recently by Refs.. 34,35 Despite a number of recent developments, the theoretical understanding of the statistical properties of a semiflexible chain in isolation remains much less developed than for the flexible chain, and experimental data are often interpreted within the theoretical framework established for random chains or rigid rods, respectively. It is therefore important to find an unified analytic approximation procedure which will yield a reliable end-to-end distribution over the entire range of stiffnesses.…”

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confidence: 99%

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Perturbation theory for path integrals of stiff polymers

Kleinert¹,

Chervyakov²

2006

J. Phys. A: Math. Gen.

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The wormlike chain model of stiff polymers is a nonlinear σ-model in one spacetime dimension in which the ends are fluctuating freely. This causes important differences with respect to the presently available theory which exists only for periodic and Dirichlet boundary conditions. We modify this theory appropriately and show how to perform a systematic large-stiffness expansions for all physically interesting quantities in powers of L/ξ, where L is the length and ξ the persistence length of the polymer. This requires special procedures for regularizing highly divergent Feynman integrals which we have developed in previous work. We show that by adding to the unperturbed action a correction term A corr , we can calculate all Feynman diagrams with Green functions satisfying Neumann boundary conditions. Our expansions yield, order by order, properly normalized end-to-end distribution function in arbitrary dimensions d, its even and odd moments, and the two-point correlation function.

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“…For some basic polymer models, ''closed-form'' path integral formulas have been derived for the probability distributions of loop length, 21 segmental orientations, 22 trajectories of a segment, 23 radius of gyration, 24 end-to-end position and distance, [25][26][27][28][29][30][31][32] and moments. 29,32,33 However, for sophisticated models, the evaluation of path integrals can be hard to handle, and usually requires extensive numerical calcula-tions. In previous work we showed that the probability density function ͑PDF͒ of the end-to-end relative position and orientation for the most general model of an inextensible semiflexible polymer chain can be obtained by either solving a diffusion equation or convolving PDFs for short segments of the chain.…”

Section: Introductionmentioning

confidence: 99%

Conformational statistics of bent semiflexible polymers

Yu¹,

Chirikjian²

2003

The Journal of Chemical Physics

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This paper extends previous methods for obtaining the probability distribution function of end-to-end distance for semiflexible polymers, and presents a general formalism that can generate conformational statistics of any continuum filament model of semiflexible chains with internal bends and twists. In particular, our focus is distribution functions for chains composed of straight or helical segments connected with discrete bends or twists. Prior polymer theories are not able to fully account for the effects of these internal shape discontinuities. We use the operational properties of the noncommutative Fourier transform for the group of rigid-body motions in three-dimensional space. This general method applies to various stiffness models of semiflexible chainlike macromolecules. Examples are given which apply the stiffness parameters defined in the Kratky-Porod model, Yamakawa helical wormlike chain model, and revised Marko-Siggia double-helix model to chains with intrinsic bends or twists in their undeformed ͑minimal energy͒ state. We demonstrate how the location and magnitude of internal bends in the chain affect the distribution of end-to-end distances for each of these models. This capability allows one to study the entropic effects of intrinsic shape changes ͑e.g., bend angle͒ in various models, and may lead to coarse-grained continuum mechanical models of processes that occur during transcription regulation.

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Bond fluctuation model of polymers in random media

Cited by 4 publications

References 29 publications

Conformational Statistics of Semiflexible Macromolecular Chains with Internal Joints

Conformational Statistics of Semiflexible Macromolecular Chains with Internal Joints

Perturbation theory for path integrals of stiff polymers

Conformational statistics of bent semiflexible polymers

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