The architecture of the chromatin fiber, which determines DNA accessibility for transcription and other template-directed biological processes, remains unknown. Here we investigate the internal organization of the 30-nm chromatin fiber, combining Monte Carlo simulations of nucleosome chain folding with EM-assisted nucleosome interaction capture (EMANIC). We show that at physiological concentrations of monovalent ions, linker histones lead to a tight 2-start zigzag dominated by interactions between alternate nucleosomes (i ± 2) and sealed by histone N-tails. Divalent ions further compact the fiber by promoting bending in some linker DNAs and hence raising sequential nucleosome interactions (i ± 1). Remarkably, both straight and bent linker DNA conformations are retained in the fully compact chromatin fiber as inferred from both EMANIC and modeling. This conformational variability is energetically favorable as it helps accommodate DNA crossings within the fiber axis. Our results thus show that the 2-start zigzag topology and the type of linker DNA bending that defines solenoid models may be simultaneously present in a structurally heteromorphic chromatin fiber with uniform 30 nm diameter. Our data also suggest that dynamic linker DNA bending by linker histones and divalent cations in vivo may mediate the transition between tight nucleosome packing within discrete 30-nm fibers and self-associated higher-order chromosomal forms.

We develop an efficient multiple time step (MTS) force splitting scheme for biological applications in the AMBER program in the context of the particle-mesh Ewald (PME) algorithm. Our method applies a symmetric Trotter factorization of the Liouville operator based on the position-Verlet scheme to Newtonian and Langevin dynamics. Following a brief review of the MTS and PME algorithms, we discuss performance speedup and the force balancing involved to maximize accuracy, maintain long-time stability, and accelerate computational times. Compared to prior MTS efforts in the context of the AMBER program, advances are possible by optimizing PME parameters for MTS applications and by using the position-Verlet, rather than velocity-Verlet, scheme for the inner loop. Moreover, ideas from the Langevin/MTS algorithm LN are applied to Newtonian formulations here. The algorithm’s performance is optimized and tested on water, solvated DNA, and solvated protein systems. We find CPU speedup ratios of over 3 for Newtonian formulations when compared to a 1 fs single-step Verlet algorithm using outer time steps of 6 fs in a three-class splitting scheme; accurate conservation of energies is demonstrated over simulations of length several hundred ps. With modest Langevin forces, we obtain stable trajectories for outer time steps up to 12 fs and corresponding speedup ratios approaching 5. We end by suggesting that modified Ewald formulations, using tailored alternatives to the Gaussian screening functions for the Coulombic terms, may allow larger time steps and thus further speedups for both Newtonian and Langevin protocols; such developments are reported separately.

The role of each histone tail in regulating chromatin structure is elucidated by using a coarse-grained model of an oligonucleosome incorporating flexible histone tails that reproduces the conformational and dynamical properties of chromatin. Specifically, a tailored configurational-bias Monte Carlo method that efficiently samples the possible conformational states of oligonucleosomes yields positional distributions of histone tails around nucleosomes and illuminates the nature of tail/core/DNA interactions at various salt milieus. Analyses indicate that the H4 histone tails are most important in terms of mediating internucleosomal interactions, especially in highly compact chromatin with linker histones, followed by H3, H2A, and H2B tails in decreasing order of importance. In addition to mediating internucleosomal interactions, the H3 histone tails crucially screen the electrostatic repulsion between the entering/exiting DNA linkers. The H2A and H2B tails distribute themselves along the periphery of chromatin fibers and are important for mediating fiber/fiber interactions. A delicate balance between tail-mediated internucleosomal attraction and repulsion among linker DNAs allows the entering/exiting linker DNAs to align perpendicular to each other in linker-histone deficient chromatin, leading to the formation of an irregular zigzag-folded fiber with dominant pair-wise interactions between nucleosomes i and i ± 4.