Beyond the Poisson-Boltzmann Model: Modeling Biomolecule-Water and Water-Water Interactions

We present an extension to the Poisson-Boltzmann model in which the solvent is modeled as an assembly of self-orienting dipoles of variable densities. Interactions between these dipoles are included implicitly using a Yukawa potential field. This model leads to a set of equations whose solutions give the dipole densities; we use the latter to study the organization of water around biomolecules. The computed water density profiles resemble those derived from molecular dynamics simulations. We also derive an excess free energy that discriminates correct from incorrect conformations of proteins.

Figure 1

Water radial density profiles near neutral oxygens, as a function of the distance to the center of the atom, for different strengths of the Yukawa field. Experimental values derived from x-ray crystallographic data [19] are shown as open circles.

Figure 2

Water radial density profiles as a function of the distance to the center of the atom, for all N, O, and C of the PARSE data set. The characteristic length defining the strength of the Yukawa field $l_Y$ is set to 7.0 Å. For clarity, the profiles are shown over one characteristic length. All curves converge to a value of 1 (i.e., bulk water) for large distances.

Figure 3

The excess free energies ${\mathcal{F}}_1$ of misfolded models compared to their native counterparts (in percent of the native free energies) are compared for two values of strength of the Yukawa field: $l_Y=0$ ($X$ axis) and $l_Y=7\AA$ ($Y$ axis). The original native-misfolded pairs of Novotny et al. [22, 23] are shown as +, while the set created by Holm and Sander [24] is shown as ○. Positive values indicate that the native conformation has a lower energy than its misfolded counterpart. Values above the diagonal indicate that the Yukawa field improves discrimination of the native fold.