Multipole fit quality for ovalbumin at an ionic strength of I = 150 mM as a function of pH. Fit quality χ is defined by the difference of the target APBS field Ψ to the multipole field Φ via Eq. (14) . Shown in descending order are the fits for ℓMAX = 0, 1, 2, …, 8.
Multipole fit quality for human serum albumin (left) and lysozyme (right) at I = 150 mM. Figure labels are the same as Fig. 1 .
Stacked area plots of the multipole coefficients α of the original field (top) and the multipole coefficients of the effective charges β (bottom) of ovalbumin. For comparison purposes across different pH values, the vectors have been normalized to unity. Starting from the bottom, each color is a different value of ℓ with the lighter shades representing the values of m (red → ℓ = 0, green → ℓ = 1, blue → ℓ = 2, …). While there is some uncertainty near the isoelectric point (pH = 4.4), the effective charges do a good job at capturing the multipole moments.
(Top) Quality of fit χ (Eq. (14) ) of the original field to the field generated by 12 effective charges for ovalbumin at I = 150 mM as a function of pH. The error is shown on a log scale, with the red dashed line indicating a 10% error. The solid line indicates the quality of fit for a corresponding multipole generated field which essentially acts as a lower bound to the error. (Bottom, left and right) Quality of fit χ for human serum albumin and lysozyme, respectively. Axes labels and scales are the same for all plots.
Logarithmic dependence of the average error at fixed ℓMAX = 8 for a variable number of effective charges N. The error is the same as Figure 4 , only averaged over all pH values.
(Top) Locations of the charged residues for human serum albumin at its isoelectric point pH ≈ 4.6. Positive/negative charges are shown in blue/red, and the volume of the illustrated sphere is proportional to the charge magnitude. Secondary structure is shown in the gray cartoon model. (Bottom) Best fit effective charge model N = 12, ℓMAX = 8 at the same pH. Not all 12 charges can be shown simultaneously for any fixed orientation.
(Top) Locations of the charged residues for lysozyme at its isoelectric point pH ≈ 11.4. (Bottom) Effective charge model. Representation is the same as Figure 6 .
(Top) Locations of the charged residues for ovalbumin at its isoelectric point pH ≈ 4.3. (Bottom) Effective charge model. Representation is the same as Figure 6 .
Interaction energy ΔΔU ϕ of two identical molecules separated by a distance of 1.25σ along the x-axis. The effective charges were computed from a single molecule. The interaction energy calculated from APBS, shown as dashed black line, was computed from Eq. (22) took several hours per configuration. In contrast, the computational cost of the effective charge model was negligible. Even at the isoelectric point where monopole moment vanishes, the effective charges do a good job of reproducing the interaction potential.
Scaled electrostatic contribution to the second virial coefficient B 22/B HS for the three studied molecules. Values at one signify no excess electrostatic contribution to the integral. The calculations were performed at ionic strength I = 150 mM using N = 12, ℓMAX = 8. The isoelectric points are marked with a solid dash for each molecule.
Article metrics loading...
Full text loading...