Abstract
Cryo-electron microscopy (cryo-EM) directly images the distribution of electrostatic potential (ESP) within macromolecules, and thus can provide much more information about atomic charge than X-ray crystallography. The electron-scattering length of an isolated ion is quite different from that of the corresponding neutral atom. The difference is very large at small scattering angles where the effects of electron distributions are largest, but becomes smaller at high scattering angles where nuclear charge determines outcomes. For this reason, in cryo-EM maps that have been solved at resolutions lower than ∼2.5 Å, peaks corresponding to anions will always be less prominent than those of cations, and may even be negative. Furthermore, if a map of this kind is smeared computationally after the fact, which reduces its effective resolution, anion peaks will diminish in size, cation peaks will grow and peaks that represent uncharged atoms will remain about the same. These effects can be used to determine the sign of the charges carried by the ions associated with a macromolecule and even estimate their magnitudes. The ESP value for a cation in a cation-anion pair is smaller than the value of the cation in isolation, but the ESP value for the anion in the ionic pair is greater than the value of the anion in isolation. The experimental range of ESP values for Mg2+ relative to that of the closest C1' atom is found to be between 0.57 and 1.27.
Highlights
Even though the electron-density (ED) distributions of macromolecules do respond to differences in atomic charges, their effects are so small that they are hard to detect in ED maps with resolutions worse than 1 A
We show how the appearance of peaks corresponding to ions vary with the magnitude of the ÁB factor applied to the Fourier transforms of electrostatic potential (ESP) maps after the fact, either to sharpen or blur them, and demonstrate that these effects can be used to determine the signs and the magnitudes of the charges carried by ions
Disorder, such as that caused by the thermal motion of atoms, affects their appearance in the ED maps obtained by X-ray crystallography; it smears them out, and it has the same effect on the ESP maps obtained by Cryo-electron microscopy (cryo-electron microscopy (EM))
Summary
Even though the electron-density (ED) distributions of macromolecules do respond to differences in atomic charges, their effects are so small that they are hard to detect in ED maps with resolutions worse than 1 A. We show how the appearance of peaks corresponding to ions vary with the magnitude of the ÁB factor applied to the Fourier transforms of ESP maps after the fact, either to sharpen or blur them, and demonstrate that these effects can be used to determine the signs and the magnitudes of the charges carried by ions. Species such as OHÀ, H2O, Na+ and Mg2+, which are almost indistinguishable in crystallographic ED maps because they contain the same number of electrons, should be easy to differentiate in ESP maps with modest resolutions. As Mott demonstrated in 1930, the spherically averaged scattering length of an isolated atom
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