Theory of Active Chromatin Remodeling

Abstract

Nucleosome positioning controls the accessible regions of chromatin and plays essential roles in DNA-templated processes. ATP driven remodeling enzymes are known to be crucial for its establishment in vivo, but their nonequilibrium nature has hindered the development of a unified theoretical framework for nucleosome positioning. Using a perturbation theory, we show that the effect of these enzymes can be well approximated by effective equilibrium models with rescaled temperatures and interactions. Numerical simulations support the accuracy of the theory in predicting both kinetic and steady-state quantities, including the effective temperature and the radial distribution function, in biologically relevant regimes. The energy landscape view emerging from our study provides an intuitive understanding for the impact of remodeling enzymes in either reinforcing or overwriting intrinsic signals for nucleosome positioning, and may help improve the accuracy of computational models for its prediction in silico.

FIG. 1.

Illustration of the kinetic model for nucleosome positioning that includes diffusion (top), ATP-driven single-nucleosome remodeling (middle), and ATP-driven remodeling for a pair of nucleosomes (bottom). The DNA is drawn as a black ladder, with nucleosomes shown in blue oval and the two enzymes drawn in yellow and green respectively. The rates for an elementary step of different dynamics are shown above the arrows.

FIG. 2.

Comparison between simulated and theoretical values of D_eff and T_eff for type one enzymes. (a) Dependence of D_eff on the enzyme rate k₁ and step size l. (b) T_eff determined as the fluctuation-dissipation ratio at l = 1, 2, 3, 5, 7 bp and k₁ = 1 s⁻¹. Error bars measured as standard deviation of the mean are comparable to the size of the symbols.

FIG. 3.

Comparison between radial distribution functions obtained from non-equilibrium simulations (empty circles) and from theoretical predictions of the effective equilibrium model (cyan lines) for type one enzymes with various step sizes.

FIG. 4.

Comparison between simulated and theoretical values of D_eff and T_eff for type two enzymes. (a) Dependence of D_eff on the enzyme rate k₂ and step size l. (b) T_eff determined as the fluctuation-dissipation ratio at l = 1, 2, 3 bp and k₂ = 0.08 s⁻¹. Error bars measured as standard deviation of the mean are comparable to the size of the symbols.

FIG. 5.

Comparison between radial distribution functions obtained from non-equilibrium simulations (empty circles) and from theoretical predictions of the effective equilibrium model (cyan lines) for type two enzymes with various step sizes. The red line for l = 3 bp was obtained from numerical simulations of the effective equilibrium model.