Protein electrostatic potential Fourier maps calculated using the transferable aspherical atom model and the independent atom model across resolutions

Abstract

Electrostatic potential maps of proteins are calculated at various resolutions using the transferable aspherical atom model (TAAM) to determine the relations between the electrostatic potential and resolution for different atom types.

Common sense tells us that experimental maps of lower (worse) resolution obtained from cryogenic electron microscopy or three-dimensional electron diffraction convey less information than maps of higher (better) resolution. However, information regarding the presence of charged moieties is more visible at lower resolutions. To investigate this phenomenon from a theoretical perspective, we analyzed the effects of truncation of data from the high-resolution end (from 1 Å to 8 Å) on theoretical Fourier images of the electrostatic potential of protein crystals, using both the popular independent atom model (IAM) of scattering factors and the more accurate transferable aspherical atom model (TAAM) combined with the UBDB/MATTS data bank. We compared our findings with those obtained for theoretical Fourier images of electron density maps associated with X-ray diffraction. Strikingly, when IAM is applied, there is almost no qualitative difference between the Fourier maps of electrostatic potential and electron density, regardless of their resolution. In contrast, the Fourier electrostatic potential maps calculated with TAAM, when of lower resolution, strongly differ from the electron density maps at the positions of charged moieties. Comparing TAAM and IAM, in the case of Fourier electrostatic potential maps, the relative difference between them is usually greatest at lower resolution maps, with a noticeable dependence on atom type and charge. In the case of Fourier electron density maps, this relative difference is much smaller and becomes more apparent in higher resolution maps. Thus, the use of accurate scattering factors is much more important for lower resolution data than for higher resolution data if one wants to investigate charged systems.