Dataset Information

Point charges optimally placed to represent the multipole expansion of charge distributions.

ABSTRACT: 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 2x 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.

SUBMITTER: Anandakrishnan R

PROVIDER: S-EPMC3701554 | biostudies-literature | 2013

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Point charges optimally placed to represent the multipole expansion of charge distributions.

Anandakrishnan Ramu R Baker Charles C Izadi Saeed S Onufriev Alexey V AV

PloS one 20130704 7

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 ...[more]

PMID: 23861790

Similar Datasets

Project description:N-type inactivation is produced by the binding of a potassium channel's N-terminus within the open pore, blocking conductance. Previous studies have found that introduction of negative charges into N-terminal inactivation domains disrupts inactivation; however, the Aplysia AKv1 N-type inactivation domain contains two negatively charged residues, E2 and E9. Rather than being unusual, sequence analysis shows that this N-terminal motif is highly conserved among Kv1 sequences across many phyla. Conservation analysis shows some tolerance at position 9 for other charged residues, like D9 and K9, whereas position 2 is highly conserved as E2. To examine the functional importance of these residues, site directed mutagenesis was performed and effects on inactivation were recorded by two electrode voltage clamp in Xenopus oocytes. We find that inclusion of charged residues at positions 2 and 9 prevents interactions with non-polar sites along the inactivation pathway increasing the efficiency of pore block. In addition, E2 appears to have additional specific electrostatic interactions that stabilize the inactivated state likely explaining its high level of conservation. One possible explanation for E2's unique importance, consistent with our data, is that E2 interacts electrostatically with a positive charge on the N-terminal amino group to stabilize the inactivation domain at the block site deep within the pore. Simple electrostatic modeling suggests that due to the non-polar environment in the pore in the blocked state, even a 1 Å larger separation between these charges, produced by the E2D substitution, would be sufficient to explain the 65× reduced affinity of the E2D N-terminus for the pore. Finally, our studies support a multi-step, multi-site N-type inactivation model where the N-terminus interacts deep within the pore in an extended like structure placing the most N-terminal residues 35% of the way across the electric field in the pore blocked state.

Dataset Information

Point charges optimally placed to represent the multipole expansion of charge distributions.

Publications

Point charges optimally placed to represent the multipole expansion of charge distributions.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets