XXI.—The Statistical Theory of Stiff Chains

Abstract

SynopsisThe paper is concerned with the distributional properties of Markoff chains in two and three dimensions where the transition probability for the length of a step and its orientation relative to that of the previous step is specified.The discrete two-dimensional chain of n steps is first discussed, and by the use of moving axes an equation relating characteristic functions of the end-point distribution for successive values of n is obtained. The corresponding differential equation for the limiting chain with continuous first derivatives is given and asymptotic solutions for long chains are found.The three-dimensional chain is similarly treated in terms of moving axes, and the limiting continuous chain is again discussed. Finally the same methods are applied to the discrete chain of equal steps to obtain the asymptotic form of the end-point distribution for long chains.

Diffusion and segmental dynamics of rodlike molecules by fluorescence correlation spectroscopy

“…10,[31][32][33][34][35][36][37][38][39][40] There are a number of results confirming the usefulness of such an approach for structural 10,41,42 as well as dynamical properties. 9,14,16,17,20 ͑ii͒ To determine the structural properties of the Kratky-Porod wormlike chain, various approximation schemes have been applied [43][44][45][46][47] and a number of equilibrium properties have been obtained successfully. 5,7,44,48 The evaluation of the polymer dynamics requires other strategies.…”

Fluctuations of Stiff Polymers and Cell Mechanics

“…Since we are primarily interested in a qualitative discussion (rather than in numerically exact prefactors), we employ scaling arguments to find the asymptotic forceextension relation for the WLC. (Daniels, 1950;Yamakawa, 1971) (solid line), compared with Monte Carlo simulation data (from Wilhelm & Frey (1996) for ℓ p /L = 0.1, 0.2 and kindly provided by Sebastian Schöbl for ℓ p /L = 0.5, 1, 2; symbols).…”

Efficient simulation of semiflexible polymers

“…(The inextensible WLC model, its subsequent modifications [9][10][11][12], and recent analyses [13][14][15][16][17][18] have been very successful in describing static and mechanical properties of dsDNA, such as its force extension curve and the radial distribution function of its end-to-end distance.) Since the contour length of the polymer is constrained in the original inextensible WLC model, Lagrangian multipliers of a varying degree of sophistication have been introduced in its computer implementation in order to enforce a contour length that is either strictly fixed [19][20][21][22][23][24][25] or fixed on average [26,27].…”