Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: A one-dimensional generalized Langevin equation treatment

Abstract

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t) identical with x(0)x(t). We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformational dynamics within single molecule proteins [Min et al., Phys. Rev. Lett. 94, 198302 (2005)].

Fluctuating Enzymes: Lessons from Single-Molecule Studies

“…Theoretically, however, we have recently proposed a microscopic model to account for the power law memory kernels based on the dynamics of a continuum semiflexible polymer chain. 49 …”

Correlations in a generalized elastic model: Fractional Langevin equation approach

“…Moreover, the expression (68) and the corresponding single-file's [19] provide a compact and elegant representation of the D-A distance correlation function, reproducing the results obtained formerly starting from the same Rouse's protein models [28,30].…”

“…The detected quantity was the autocorrelation function of the D-A distance ∆ D−A (t) that was shown to display an asymptotic Mittag-Leffler decay in accordance with the FLE prescription. In order to recover the experimental results, in Refs [28,29] and [30] the authors used a respectively continuous and discrete Rouse model accounting for the protein conformational dynamics: this, in turn, corresponds to take…”

“…According to [28] we define the ∆ D−A autocorrelation function as (54) which can be rewritten in term of the spatial positions of the donor and acceptor sites, h (x D , t) and h (x A , t) respectively, as…”

Anomalous Brownian motion discloses viscoelasticity in the ear’s mechanoelectrical-transduction apparatus

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