Subdiffusive motion of a polymer composed of subdiffusive monomers

Abstract

We use Brownian dynamics simulations and analytical theory to investigate the physical principles underlying subdiffusive motion of a polymer. Simulations of a single circular polymer reveal that relaxation of the elastic Rouse modes dominates monomer motion, even under strong confinement. Thus, we incorporate two anomalous diffusion models into the theoretical framework of the Rouse model for polymer dynamics. First, a polymer is considered moving within a viscoelastic fluid, in which monomers experience frictional memory described by fractional Brownian motion. Second, we examine a polymer whose monomers are subjected to random pausing events according to the continuous time random walk model. We derive scaling laws for the mean square displacement of a monomer within a polymer, as well as the velocity autocorrelation function. Unlike particles, which exhibit the same ensemble-averaged behavior regardless of subdiffusive mechanism, subdiffusive monomer motion leads to widely varying behavior for a polymer depending on the root cause of the monomer subdiffusion. Our results can be applied directly to experiments as diagnostic tools for determining the dominant physical mechanism underlying anomalous subdiffusive polymer dynamics.

Short-time movement of E. coli chromosomal loci depends on coordinate and subcellular localization

“…First, individual loci 'subdiffuse', that is, explore space slower than Brownian motion, as reflected by a power law scaling of MSD with time with an exponent o1. This behaviour appears to be universal, in the sense that it has been observed for different loci of both E. coli and Caulobacter, and with different drug treatments 20 , and the value cannot be explained by simple polymer models 4,27 . The authors surmised that this kind of motion could depend on viscoelastic properties of the surrounding cytosol.…”

“…20), which can be rationalized as a finite-size effect of limited length loci tracks (see ref. 27). The mean exponent agrees with that of the ensemble averages.…”

“…We analysed the simulated distributions and checked if the exponent 0.4 (which points to non-trivial physical organization 4,27 ) could be distinguished from 0.5, which corresponds to more conventional 'Rouse' subdiffusion of polymer solutions 32 . Comparison of the ensemble-averaged MSD and the single-track a exponent histograms from experiment and simulation ( Supplementary Fig.…”

Disentangling Random Motion and Flow in a Complex Medium

“…In principle, this technique could be extended to particles moving through a viscoelastic medium by taking the discrete Fourier transform of the known velocity correlation function for such motion (35). The BNEW method, however, provides a related but more general approach, using wavelet analysis instead of Fourier transforms to perform the high-pass filtering of particle trajectories.…”

Encounter dynamics of a small target by a polymer diffusing in a confined domain

“…Previous studies of polymer in confined domains focused on their static properties 5,6 , translocation [7][8][9] , reptation 10 through a cylindrical tube and their dynamics 11 . During translocation, the polymer is threaded through a pore and diffuses until it exits the other side.…”