Browsing by Author "Izadi, Saeed"
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- Optimal Point Charge Approximation: from 3-Atom Water Molecule to Million-Atom Chromatin FiberIzadi, Saeed (Virginia Tech, 2016-07-13)Atomistic modeling and simulation methods enable a modern molecular approach to bio-medical research. Issues addressed range from structure-function relationships to structure-based drug design. The ability of these methods to address biologically relevant problems is largely determined by their accurate treatment of electrostatic interactions in the target biomolecular structure. In practical molecular simulations, the electrostatic charge density of molecules is approximated by an arrangement of fractional "point charges" throughout the molecule. While chemically intuitive and straightforward in technical implementation, models based exclusively on atom-centered charge placement, a major workhorse of the biomolecular simulations, do not necessarily provide a sufficiently detailed description of the molecular electrostatic potentials for small systems, and can become prohibitively expensive for large systems with thousands to millions of atoms. In this work, we propose a rigorous and generally applicable approach, Optimal Point Charge Approximation (OPCA), for approximating electrostatic charge distributions of biomolecules with a small number of point charges to best represent the underlying electrostatic potential, regardless of the distance to the charge distribution. OPCA places a given number of point charges so that the lowest order multipole moments of the reference charge distribution are optimally reproduced. We provide a general framework for calculating OPCAs to any order, and introduce closed-form analytical expressions for the 1-charge, 2-charge and 3-charge OPCA. We demonstrate the advantage of OPCA by applying it to a wide range of biomolecules of varied sizes. We use the concept of OPCA to develop a different, novel approach of constructing accurate and simple point charge water models. The proposed approach permits a virtually exhaustive search for optimal model parameters in the sub-space most relevant to electrostatic properties of the water molecule in liquid phase. A novel rigid 4-point Optimal Point Charge (OPC) water model constructed based on the new approach is substantially more accurate than commonly used models in terms of bulk water properties, and delivers critical accuracy improvement in practical atomistic simulations, such as RNA simulations, protein folding, protein-ligand binding and small molecule hydration. We also apply our new approach to construct a 3-point version of the Optimal Point Charge water model, referred to as OPC3. OPCA can be employed to represent large charge distributions with only a few point charges. We use this capability of OPCA to develop a multi-scale, yet fully atomistic, generalized Born approach (GB-HCPO) that can deliver up to 2 orders of magnitude speedup compared to the reference MD simulation. As a practical demonstration, we exploit the new multi-scale approach to gain insight into the structure of million-atom 30-nm chromatin fiber. Our results suggest important structural details consistent with experiment: the linker DNA fills the core region and the H3 histone tails interact with the linker DNA. OPC, OPC3 and GB-HCPO are implemented in AMBER molecular dynamics software package.
- Point Charges Optimally Placed to Represent the Multipole Expansion of Charge DistributionsAnandakrishnan, Ramu; Baker, Charles; Izadi, Saeed; Onufriev, Alexey V. (PLOS, 2013-07-04)We propose an approach for approximating electrostatic charge distributions with a small number of point charges to optimally represent the original charge distribution. By construction, the proposed optimal point charge approximation (OPCA) retains many of the useful properties of point multipole expansion, including the same far-field asymptotic behavior of the approximate potential. A general framework for numerically computing OPCA, for any given number of approximating charges, is described. We then derive a 2-charge practical point charge approximation, PPCA, which approximates the 2-charge OPCA via closed form analytical expressions, and test the PPCA on a set of charge distributions relevant to biomolecular modeling. We measure the accuracy of the new approximations as the RMS error in the electrostatic potential relative to that produced by the original charge distribution, at a distance the extent of the charge distribution–the mid-field. The error for the 2-charge PPCA is found to be on average 23% smaller than that of optimally placed point dipole approximation, and comparable to that of the point quadrupole approximation. The standard deviation in RMS error for the 2-charge PPCA is 53% lower than that of the optimal point dipole approximation, and comparable to that of the point quadrupole approximation. We also calculate the 3-charge OPCA for representing the gas phase quantum mechanical charge distribution of a water molecule. The electrostatic potential calculated by the 3-charge OPCA for water, in the mid-field (2.8 Å from the oxygen atom), is on average 33.3% more accurate than the potential due to the point multipole expansion up to the octupole order. Compared to a 3 point charge approximation in which the charges are placed on the atom centers, the 3-charge OPCA is seven times more accurate, by RMS error. The maximum error at the oxygen-Na distance (2.23 Å ) is half that of the point multipole expansion up to the octupole order.