pH Dependence of Charge Multipole Moments in Proteins

Abstract

Electrostatic interactions play a fundamental role in the structure and function of proteins. Due to ionizable amino acid residues present on the solvent-exposed surfaces of proteins, the protein charge is not constant but varies with the changes in the environment-most notably, the pH of the surrounding solution. We study the effects of pH on the charge of four globular proteins by expanding their surface charge distributions in terms of multipoles. The detailed representation of the charges on the proteins is in this way replaced by the magnitudes and orientations of the multipole moments of varying order. Focusing on the three lowest-order multipoles-the total charge, dipole, and quadrupole moment-we show that the value of pH influences not only their magnitudes, but more notably and importantly also the spatial orientation of their principal axes. Our findings imply important consequences for the study of protein-protein interactions and the assembly of both proteinaceous shells and patchy colloids with dissociable charge groups.

Figure 1

Sketch of the model showing a rendering of the surface structure of human serum albumin (PDB: 1E7H), superimposed onto a circumscribed sphere with projected multipole expansion of the surface charge distribution (up to ℓ_max = 12). AA residues that are charged at pH 7 are highlighted in the structure, with colors pertaining to the red spectrum indicating positive charges, and colors in the blue spectrum indicating negative charges. The same color scheme applies to the projection of the charge distribution onto the sphere. The protein structure was rendered with UCSF Chimera (53). To see this figure in color, go online.

Figure 2

Magnitudes of the monopole (q), dipole (μ_z), and quadrupole (Q_ii) components of the surface charge distributions of lysozyme (PDB: 2LYZ) and human serum albumin (PDB: 1E7H), shown as a function of pH. Cysteine acidity is not considered. To see this figure in color, go online.

Figure 3

Quadrupole ratio |Q_xx/Q_zz| as a function of pH for all the proteins studied; cysteine acidity is not considered. The ratio determines whether the quadrupole distribution is axial (|Q_xx/Q_zz| = 0.5 and |Q_xx/Q_zz| = 2), planar (|Q_xx/Q_zz| = 1), or somewhere in-between. For additional geometrical interpretation of the quadrupole ratio, see Figs. S2 and S3. To see this figure in color, go online.

Figure 4

Multipole expansion of the surface charge distribution of β-lactoglobulin (PDB: 2BLG) in the original coordinate system up to (a) ℓ_max = 6 and (b) ℓ_max = 2. Shown also are the (c) dipole and (d) quadrupole distributions in the original (reference) system. The distributions are mapped from a sphere to a plane using the Mollweide projection. Black diamonds show the orientation of the z axis of the dipole, and black squares show the orientation of the z axis of the quadrupole. Gray stars show the coordinate axes of the original coordinate system. Cysteine acidity is not considered, and all the plots are drawn at pH 7.0. To see this figure in color, go online.

Figure 5

Multipole expansion of the surface charge distribution of lysozyme (PDB: 2LYZ) up to ℓ = 6 in the original coordinate system, shown for three different values of pH = 3, 7, 11. The distributions are mapped from a sphere to a plane using the Mollweide projection. Black diamonds show the orientation of the z axis of the dipole, and black squares show the orientation of the z axis of the quadrupole. Gray stars show the coordinate axes of the original coordinate system. Cysteine acidity is not considered. To see this figure in color, go online.

Figure 6

(a–d) Orientation of dipole and quadrupole principal z axes (denoted by diamonds and squares, respectively) as a function of pH (in steps of 0.2 pH unit). The pH increase from 0 to 14 is shown with a color gradient, with blue hues denoting acidic pH < 7 and red hues denoting basic pH > 7. In addition, we explicitly indicate the positions at pH values of 0, 7, and 14. The orientations of the axes are mapped from the circumscribed sphere of the protein onto a plane using the Mollweide projection; the gray stars show the coordinate axes of the original coordinate system of the protein, which is kept fixed. The pH dependence of the multipoles’ orientation is shown side by side for all four proteins included in our study. Cysteine acidity is not considered. To see this figure in color, go online.