Revisiting polymer statistical physics to account for the presence of long-range-correlated structural disorder in 2D...

We elaborate on a generalization of the 2D wormlike chain (WLC) model that accounts for the presence of long-range correlations (LRC) in the intrinsic curvature distribution of eukaryotic DNA. This model predicts some decrease of the DNA persistence length resulting from some large-scale intrinsic curvature induced by sequence-dependent persistent random distribution of local bending sites. When assisting exact analytical calculations by numerical DNA simulations, we show that the conjugated contributions of i) the thermal curvature fluctuations characterized by the "dynamic" persistence length ℓ(p)(d) = 2A, where A is the elastic bending modulus, and ii) the intrinsic LRC curvature disorder of amplitude σ(o) and Hurst exponent H > 1/2, characterized by a "static" persistence length ℓ(p)(H) = A(1/2H)σ(o)(-1/H) Γ(1/2H + 1), can be described by a continuum of generalized WLC (GWLC) models parametrized by the LRC exponent H. We use perturbation analysis to investigate the two limiting cases of weak static disorder (w(H) << 1 and weak dynamical fluctuations (1/w (H) << 1), where w(H) = l(p)(d)/l(p)(H) is a dimensionless parameter. From a quantitative point of view, our study demonstrates that even for a small value of the LRC (H approximately equal 0.6-0.8) static disorder amplitude σ(o) ~ 10(-2), as previously reported for genomic DNA, the decrease of the persistence length from the WLC prediction l(p)(d) can be very significant, up to twofold. The implications of these results on the first steps of compaction of DNA in eukaryotic cells are discussed.