An n log n Generalized Born Approximation.

Molecular dynamics (MD) simulations based on the generalized Born (GB) model of implicit solvation offer a number of important advantages over the traditional explicit solvent based simulations. Yet, in MD simulations, the GB model has not been able to reach its full potential partly due to its computational cost, which scales as ∼n(2), where n is the number of solute atoms. We present here an ∼n log n approximation for the generalized Born (GB) implicit solvent model. The approximation is based on the hierarchical charge partitioning (HCP) method (Anandakrishnan and Onufriev J. Comput. Chem. 2010 , 31 , 691 - 706 ) previously developed and tested for electrostatic computations in gas-phase and distant dependent dielectric models. The HCP uses the natural organization of biomolecular structures to partition the structures into multiple hierarchical levels of components. The charge distribution for each of these components is approximated by a much smaller number of charges. 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. To apply the HCP concept to the GB model, we define the equivalent of the effective Born radius for components. The component effective Born radius is then used in GB computations for points that are distant from the component. This HCP approximation for GB (HCP-GB) is implemented in the open source MD software, NAB in AmberTools, and tested on a set of representative biomolecular structures ranging in size from 632 atoms to ∼3 million atoms. For this set of test structures, the HCP-GB method is 1.1-390 times faster than the GB computation without additional approximations (the reference GB computation), depending on the size of the structure. Similar to the spherical cutoff method with GB (cutoff-GB), which also scales as ∼n log n, the HCP-GB is relatively simple. However, for the structures considered here, we show that the HCP-GB method is more accurate than the cutoff-GB method as measured by relative RMS error in electrostatic force compared to the reference (no cutoff) GB computation. MD simulations of four biomolecular structures on 50 ns time scales show that the backbone RMS deviation for the HCP-GB method is in reasonable agreement with the reference GB simulation. A critical difference between the cutoff-GB and HCP-GB methods is that the cutoff-GB method completely ignores interactions due to atoms beyond the cutoff distance, whereas the HCP-GB method uses an approximation for interactions due to distant atoms. Our testing suggests that completely ignoring distant interactions, as the cutoff-GB does, can lead to qualitatively incorrect results. In general, we found that the HCP-GB method reproduces key characteristics of dynamics, such as residue fluctuation, χ1/χ2 flips, and DNA flexibility, more accurately than the cutoff-GB method. As a practical demonstration, the HCP-GB simulation of a 348 000 atom chromatin fiber was used to refine the starting structure. Our findings suggest that the HCP-GB method is preferable to the cutoff-GB method for molecular dynamics based on pairwise implicit solvent GB models.