Elasticity of flexible polymers under cylindrical confinement: appreciating the blob scaling regime in computer simulations

Abstract

Despite much renewed interest in cylindrically confined polymers with linear or nonlinear topology, often considered as model chromosomes, their scaling predictions, especially on chain elasticity and relaxation, have not been reconciled with numerical data. Of particular interest is their “effective spring constant” given in the scaling form of k_eff ∼ N^−αD^−γ, where N is the number of monomers and D the diameter of the cylindrical space. If the blob-scaling approach produces α = 1 and γ = 2 − 1/ν = 1/3 with ν = 3/5 the Flory exponent, a series of numerical studies indicate α ≈ 0.75 and unexpectedly large γ ≈ 0.9. Using computer simulations, we show that there exists a crossover from the formerly called unexpected to blob-scaling regime at a certain value of D ≈ 10 (in units of monomer sizes) for sufficiently large N (>N_cr). Our results suggest that N_cr ≈ 1000, if the farthermost distance is used as the chain size: a quantity relevant in single-chain manipulations or for ring polymers (e.g., bacterial chromosomes). Accordingly, chain relaxation dynamics is expected to show a similar crossover. Our results imply that the applicability of the blob scaling approach depends on how confined chains are characterized.