Dynamics of chain closure: Approximate treatment of nonlocal interactions

Abstract

The Wilemski-Fixman model of diffusion controlled-reactions [J. Chem. Phys. 58, 4009 (1973)] is combined with a generalized random walk description of chain conformations to predict the dependence of the closure time tau on the chain length N of polymers with reactive end groups and nonlocal interactions. The nonlocal interactions are modeled by a modification to the connectivity term in the Edwards continuum representation of the polymer. The modification involves a parameter h lying between 0 and 1 that is a measure of the extent of correlation between adjacent monomers on the chain backbone. Different choices of h correspond to chain conformations of different average radial dimensions. In particular, the values 1/3, 1/2 and 3/5 provide approximations to the statistics of polymers in poor, theta and good solvents, respectively. The closure time tau of such chains is calculated analytically for different N. In all cases, tau is found to vary as a power law in N, Nb, with b a function of h. For the special case h = 1/3, which models collapsed polymers and globular proteins, b is about 1.6-1.7.

Dynamics of end-to-end loop formation: A flexible chain in the presence of hydrodynamic interaction

“…All the theories of loop closing dynamics are approximate [5,8]. Although many theoretical and simulation attempts have been made to investigate the effect of flexibility [17], solvent quality [13] on the loop closing dynamics, not much theoretical investigation has been performed to shed light on the effects of hydrodynamic interaction on loop closing dynamics other than the renormalization group calculation by Freidman et al [22]. Hydrodynamic interaction which is essentially nonlocal in space has been shown to have profound effects on the dynamics of long chain molecules [23,24].…”

“…Dynamics of loop formation in long chain molecules has been a subject of immense interest to experimentalists [1][2][3][4] and theoreticians [5][6][7][8][9][10][11][12][13][14][15][16][17] for over a decade. Recently the dynamics of loop formation has found greater importance because of its relevance in biophysics.…”

Solvent-quality-dependent contact formation dynamics in proteins

“…By solving the reaction-diffusion equation with the heaviside sink, the diffusion-controlled mean time of contact formation was shown to follow a power law scaling τ D ∝ N β . The third and fourth columns of Table 1 present the values of the scaling exponent β obtained in this previous study 24 and in a recent Brownian dynamics simulations 21 respectively. These values have been obtained in good, theta and poor solvents in the absence of the hydrodynamic interactions (freely-draining chain).…”

“…24 The nonlocal interactions have been included by modifying the connectivity term in the Edwards continuum representation of the polymer. This involves introducing a parameter h, with values 1/3, 1/2 and 3/5, which correspond to the average size of the chain in poor, theta and good solvents respectively.…”

Reconfiguration dynamics in folded and intrinsically disordered protein with internal friction: Effect of solvent quality and denaturant

“…But the experimental conditions remain close to a good solvent rather than a θ solvent. There have been few theoretical studies to elucidate the effect of solvent quality on loop formation in single polymer chain [43][44][45] and unfortunately there exists almost no theoretical study to analyze the combined effect of sol-vent quality and internal friction on the ring closure dynamics in polymer chains other than the very recent simulation by Yu and Luo [46]. Apart from the solvent quality, denaturant concentration does play an important role in ring closure dynamics [31,47] of proteins as it profoundly affects the compactness of the protein and routinely used in experiments.…”