Solvent reaction field potential inside an uncharged globular protein: a bridge between implicit and explicit solvent models?

Abstract

The solvent reaction field potential of an uncharged protein immersed in simple point charge/extended explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560 ns of simulation time. A finite, positive potential of 13-24 kbTec(-1) (where T=300 K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0 A from the solute surface, on average 0.008 ec/A3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99.

Figure 1

(Color online.) Solvent reaction field potential due to SPC/E explicit solvent charge density around the uncharged protein. This particular slice cuts through the centroid of the protein. Potential values as low as −70 k_bTe_c⁻¹ (T = 300K) are present, but the color scale has been adjusted for greater detail at more common values. As a guide, the protein’s solvent-accessible surface, measured with a 1.4 Å probe, is shown as a black outline.

Figure 2

(Color online.) Solvent reaction field potential due to SPC/E explicit solvent charge density around the charged protein. The charge density due to the protein, though present in simulations with SPC/E water, was omitted during the calculation of this potential grid. As in Figure 1, the slice depicted cuts through the centroid of the protein. Potential values as low as −800 k_bTe_c⁻¹ and as high as +400k_bTe_c⁻¹ (T = 300K) are present, but the color scale has been adjusted for greater detail between these extremes. As a guide, the protein’s solvent-accessible surface, measured with a 1.4 Å probe, and the outlines of charged side-chain head groups and polypeptide chain termini are shown in a black outline.

Figure 3

Properties of the solvent (denoted by text inset in each panel) as a function of distance r from the uncharged protein van der-Waals surface (VDWS, x-axis). Solid lines show mean values of each property, dashed lines show the mean ± one standard deviation. In these plots, “0 Å” means that the center of a solvent atom is 0.0Å from the protein’s van-der Waals surface; an oxygen that comes within 1.0 Å of the VDWS of a protein nitrogen atom, for example, means that oxygen and nitrogen atoms are really 2.5Å apart.

Figure 4

Properties of the solvent (denoted by text inset in each panel) as a function of the distance r from the charged protein van der-Waals surface (VDWS, x-axis). Solid lines show mean values of each property, dashed lines show the mean ± one standard deviation. In the top two panels, a dotted line is a guide to show the mean value of the corresponding property from simulations of the uncharged protein. See Figure 3 for an explanation of what it means for solvent atoms to be very close to the protein VDWS.

Figure 5

(Color online.) Average interaction energy of a water molecule located at 1.7 Å (black, solid line), 4.4 Å (red, dashed line), and 7.0 Å (blue, dotted line) from the surface of the uncharged protein with nearby water molecules at other distances from the protein van der-Waals surface as indicated by the x-axis. These graphs show the local interaction characteristics of the first and second solvation shells, and deep solution, respectively.

Figure 6

(Color online.) Average interation energy of a water molecule located 1.7 Å (black, solid line), 4.4 A (red, dashed line), and 7.0 Å (blue, dotted line) from the surface of the charged protein with nearby water molecules at other distances from the protein van der-Waals surface as indicated by the x-axis. These graphs correspond to those in Figure 5 describing water:water interaction energies around the uncharged protein.

Figure 7

Comparison of protein atom electrostatic energies for the charged protein due to the solvent reaction field potential predicted by different implicit solvent models (y-axis) plotted against those generated by an explicit solvent model (x-axis). $U_i^{(\text{Q})}$ refers to per-atom energies in the explicit solvent reaction field, $G_i^{(\text{Q})}$ to per-atom energies in the implicit solvent reaction field, and $G_i^{(\text{Q},\text{Opt}\text{.})}$ to per-atoms energies in an implicit solvent reaction field obtained a solute volume definition optimized to fit the results of free-energy perturbation experiments. A ~ denotes implicit energies adjusted by the energy $U_i^{(\text{no Q})}$, the energy of atomic charges in the solvent reaction field potential created by the uncharged protein. Dots and crosses represent positively and negatively charged atoms, respectively. The black lines show y = x.