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Molecular dynamics (MD) simulations based on the implicit solvent generalized Born (GB) models can provide significant computational advantages over the traditional explicit solvent simulations. However, the standard GB becomes prohibitively expensive for all-atom simulations of large structures; the model scales poorly, ∼n 2 , with the number of solute atoms. Here we combine our recently developed optimal point charge approximation (OPCA) with the hierarchical charge partitioning (HCP) approximation to present an ∼n log n multiscale, yet fully atomistic, GB model (GB-HCPO). The HCP approximation exploits the natural organization of biomolecules (atoms, groups, chains, and complexes) to partition the structure into multiple hierarchical levels of components. OPCA approximates the charge distribution for each of these components by a small number of point charges so that the low order multipole moments of these components are optimally reproduced. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. We show that GB-HCPO can deliver up to 2 orders of magnitude speedup compared to the standard GB, with minimal impact on its accuracy. For large structures, GB-HCPO can approach the same nominal speed, as in nanoseconds per day, as the highly optimized explicit-solvent simulation based on particle mesh Ewald (PME). The increase in the nominal simulation speed, relative to the standard GB, coupled with substantially faster sampling of conformational space, relative to the explicit solvent, makes GB-HCPO a suitable candidate for MD simulation of large atomistic systems in implicit solvent. As a practical demonstration, we use GB-HCPO simulation to refine a ∼1.16 million atom structure of 30 nm chromatin fiber (40 nucleosomes). The refined structure suggests important details about spatial organization of the linker DNA and the histone tails in the fiber: (1) the linker DNA fills the core region, allowing the H3 histone tails to interact with the linker DNA, which is consistent with experiment; (2) H3 and H4 tails are found mostly in the core of the structure, closer to the helical axis of the fiber, while H2A and H2B are mostly solvent exposed. Potential functional consequences of these findings are discussed. GB-HCPO is implemented in the open source MD software NAB in Amber 2016.

Implicit Solvent Model for Million-Atom Atomistic Simulations: Insights into the Organization of 30-nm Chromatin Fiber