Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Abstract

Ewald summation, which has become the de facto standard for computing electrostatic interactions in biomolecular simulations, formally requires that the simulation box is neutral. For non-neutral systems, the Ewald algorithm implicitly introduces a uniform background charge distribution that effectively neutralizes the simulation box. Because a uniform distribution of counter charges typically deviates from the spatial distribution of counterions in real systems, artifacts may arise, in particular in systems with an inhomogeneous dielectric constant. Here, we derive an analytical expression for the effect of using an implicit background charge instead of explicit counterions, on the chemical potential of ions in heterogeneous systems, which (i) provides a quantitative criterium for deciding if the background charge offers an acceptable trade-off between artifacts arising from sampling problems and artifacts arising from the homogeneous background charge distribution, and (ii) can be used to correct this artifact in certain cases. Our model quantifies the artifact in terms of the dif ference in charge density between the non-neutral system with a uniform neutralizing background charge and the real neutral system with a physically correct distribution of explicit counterions. We show that for inhomogeneous systems, such as proteins and membranes in water, the artifact manifests itself by an overstabilization of ions inside the lower dielectric by tens to even hundreds kilojoules per mole. We have tested the accuracy of our model in molecular dynamics simulations and found that the error in the calculated free energy for moving a test charge from water into hexadecane, at different net charges of the system and different simulation box sizes, is correctly predicted by the model. The calculations further confirm that the incorrect distribution of counter charges in the simulation box is solely responsible for the errors in the PMFs. ■ INTRODUCTIONMolecular dynamics (MD) simulations have come of age. Since the first applications of MD on protein systems more than three decades ago, 1,2 advances in computer power, algorithmic developments, and improvements in the accuracy of the applied interaction functions have established MD as an important predictive technique to study dynamic processes at atomic resolution. 3,4 An important improvement in accuracy is achieved by the use of lattice summation methods for the evaluation of the Coulombic interactions in simulation boxes subject to periodic boundary conditions. In such approaches, the Coulomb interactions between all pairs of charged particles are accounted for, including interactions between the charges in the central box and their periodic images,where we used Gaussian units, as in the remainder of this article. Here, N is the number of charged particles in the central simulation box, n = (n x , n y , n z ) is the box index vector. The prime indicates that if i = j the term n = 0 should be omitted. The distance r ij,n is the real distance between the charg...

Molecular Mechanism of Binding between 17β-Estradiol and DNA

“…In ongoing work we are working with colleagues to develop a more accurate force field to represent specific DNA sequences. We predict that this intercalation will alter the structure of the DNA duplex, and therefore have the potential to affect the biological functions of DNA including the inhibition of transcription, replication, and DNA repair processes [40]. Therefore, excess E2 has the potential to exert some serious side effects such as disruption of ER-DNA binding, DNA damage and possibly the initiation of cancer.…”

“…Our simulations do not have explicit ions in the system rather a neutralizing background charge is applied [40]. We examine the effect of neutralizing background charge by simulating one of the bound complexes of E2 to erDNA with 34 explicit Na + ions.…”

Potentials of mean force in acidic proton transfer reactions in constrained geometries

“…Long ranged forces (Coulomb interactions) were handled by Ewald sum techniques [62], using a uniform neutralizing background charge in all cases. This is satisfactory enough for a system including a small charge as the lone proton, whereas in extended systems such as proteins of membranes in water, it has been reported that the use of a counterion would be in order [63].…”

Population reversal driven by unrestrained interactions in molecular dynamics simulations: A dialanine model

“…The dipole moment values of dialanine prepared with additional charges span the intervals (4,14), (9,21) and (19,38) D for the cases with ±0.3 e, ±0.5 e and ±1.0 e, respectively. Note that a dipole moment of 9 D (the average value for the case with ±0.3 e) or, equivalently, a moment of 0.9 D per heavy atom, is a value not far from the average for the structures in the PDB.…”

“…This is not allowed when doing the usual one-protein simulation with Ewald, since a change in protein-protein distance is strictly forbidden. Ewald artifacts (inaccuracies created by the use of artificial periodicity) were studied before, [4][5][6] but it was Weber and McCammon 7 who specifically studied the problem presented here: due to the computational power available at the time, it was difficult to clearly distinguish between the different minima in the dialanine free energy space, hence leading to the neglect of the effects of this particular issue.…”