On the appearance of carboxylates in electrostatic potential maps

Abstract

Electron microscopy can provide accurate, high‐resolution images of the distribution of electrostatic potential (ESP) in biological macromolecules. Careful examination of ESP maps that have been published for peptides and proteins at resolution ranging from 1.0 Å to 2.9 Å reveals that the negative charges of carboxylate groups have a profound effect on their appearance. It is clear that investigators must take the negative features in their experimental ESP maps into account when modeling the conformations of Asp and Glu side chains and those of the residues that surround them.

Introduction

Recent technological advances in electron microscopy (EM) have made it far easier to image macromolecules at atomic resolution than ever before.1, 2, 3 Superficially, EM images look like the electron density (ED) maps X‐ray crystallographers have been working with for decades, but they are not the same. Electron microscopes image the distribution of electrostatic potential (ESP) in macromolecules, rather than the distribution of electrons. ED distributions are everywhere positive, but while the ESP distributions of macromolecules are positive in most places, they can be negative in the vicinity of atoms carrying full or partial negative charges.4 Nonetheless, it appears that many EM investigators do not take negative features into account when interpreting ESP maps. As will be illustrated below, this can lead to incorrect assignment of the conformations of aspartic and glutamic acid residues. In addition, interference between negative and positive features makes the appearance of ESP maps much more sensitive to resolution than ED maps in regions that include negatively charged atoms.

Results

On the appearance of carboxylate side chains in ESP maps

Using the electron structure factors that have been published for isolated atoms, both neutral and ionized, it is easy to compute ESP maps for both Asp and Glu residues that show what they should look like in different states of ionization over a range of resolutions (see Methods).4 Figure 1 shows the results obtained for Asp residues at two different resolutions: 3.0 Å, and 2.0 Å. The three ionization states considered were: (1) fully protonated, (2) fully deprotonated with the negative charge distributed equally on the two oxygen atoms of the carboxylate group, and (3) fully deprotonated with the charge localized on one of the two O atoms. These simulations indicate that there should be positive density in ESP maps for the Cγ atom and the associated O atoms of any Asp that is fully protonated. If the Asp is deprotonated, and the negative charge distributed, there will be no positive density for the two O atoms, and little for Cγ. On the other hand, if the Asp is deprotonated and the charge localized on one O atom, there is likely to be some positive density for Cγ and the uncharged O atom, but none for the O atom that is carrying the charge. Supporting Information Figure S1 shows the simulated ESP density for Asp side chains with negative values included.

Figure 1.

Simulated ESP maps for Asp side chain in protonated state (A), deprotonated‐delocalized state (B), and deprotonated‐non‐delocalized state at 2.0 Å (top) and 3.0 Å resolution (bottom), contoured at +5.0σ (cyan), +10.0σ (gold), and/or +15.0σ (blue).

High‐resolution experimental ESP maps obtained by image reconstruction

How do these simulated ESP images compare with those obtained experimentally for Asp and Glu residues in the same resolution range? This question can be addressed by examining two recently published high‐resolution ESP maps: (1) the 1.80‐Å resolution map of glutamine dehydrogenase (GDH) (PDB‐5K12/EMBD‐8194) obtained by Merk et al., and the 2.20‐Å resolution map of β‐galactosidase (bGAL) (PDB‐5A1A/EMDB‐2984) produced by Bartesaghi and coworkers.5, 6 Both of these maps were obtained by image reconstruction, and thus should be unbiased by any prior knowledge about the structures of the proteins they represent.

With the exception of Asp163 [Fig. 2(A,B)], for which there is reasonably well‐defined side chain ESP density, there is very little side chain density for any of the Asp residues in the ESP map for GDH.5 Their appearance is about the same as that predicted for deprotonated Asp residues in which the negative charge is delocalized [Fig. 2(A)]. In the slightly lower resolution ESP map of bGAL,6 on the other hand, examples can be found of Asp and Glu residues that have side chain ESP distributions that resemble all those shown in Figure 1. The majority of them belong to the fully deprotonated‐delocalized group (Fig. 3). Asp411 is one of the few that appears to be fully protonated [Fig. 3(A)], and there are several residues on the borderline between the second group (deprotonated–delocalized), and the third group (deprotonated‐but‐localized).

Figure 2.

Experimental ESP maps at 1.80‐Å resolution for glutamine dehydrogenase (PDB‐5K12/EMBD‐8194)5 contoured at +3.0σ (salmon) and +6.0σ (blue). A: Two nearly orthogonal views for Asp163. B: The same as (A) but with additional sharpened ESP map using B = −30 Ų. C: Stereodigram for Asp68, Asp69, and Glu140. D: Stereodigram for Glu402 and Asp404.

Figure 3.

Experimental ESP maps at 2.2‐Å resolution for β‐galactosidase (PDB‐5A1A/EMBD‐2984)6 contoured at +1.5σ (salmon), +3.0σ (blue), and +4.5σ (cyan) superimposed with EM‐derived model (green) and/or X‐ray derived model (gold). A: A protonated carboxylic acid, Asp411. B: D479 in two views. C: D224. D: D375 in two views. E: D144/D211 pair in a β‐sheet. F: D509 in two views. G: D869. H: D659. I: The D130/E131 loop.

In the case of the EM‐derived bGAL structure (PDB‐5A1A), there is an X‐ray structure (PDB‐4TTG)7 available to which it can be directly compared. Interestingly, in the neighborhood of nearly all carboxylate residues (as well as many other non‐carboxylate residues, data not shown), the experimental ESP map (EMBD‐2984)6 corresponds better to the X‐ray derived model than to the EM‐derived model (5A1A)6 (Fig. 3). Often the EM‐derived model puts one of the two Oδ atoms of an Asp into positive ESP density, while failing to do the same for the other, and sometimes even for the Cγ atom as well, for example, Asp479, Asp375, Asp224, Asp509, and Asp659 (Fig. 3). The X‐ray derived model does much better; it places both Oδ atoms in regions of negative or low potential in the ESP map, and invariably positions Cγ atoms in positive density (Fig. 3).

There are reasons to think that refinement of the EM model against the ESP map by maximization of the real‐space correlation coefficient (RSCC) between that map and an Asp model containing no charged atoms may be the source of these problems. When the ESP peaks for the Cα and Cβ atoms of an Asp residue are strong and positive, the torsion angle around Cα—Cβ bond in EM‐derived models often differs by about 90° relative to X‐ray models. This could easily happen if Oγ atoms carrying negative charge, which should be located in negative or low positive potential, were modeled as uncharged atoms that should, therefore, be situated in regions where the potential is positive, for example, Asp375, Asp479, and Asp224 (Fig. 3). When the ESP map has little density for the Cα and Cβ atoms of Asp residues, EM‐derived atomic models can be entirely misleading because refinement routines aimed at maximizing RSCC values may end up placing atoms in positive noise peaks, for example, Asp211, Asp869, and Asp659 (Fig. 3).

To test these inferences, RSCC values were computed to determine the degree of correspondence between the X‐ray‐derived model7 and the ESP map6 for 10 selected Asp residues, including Asp375, Asp479, Asp224, and Asp211. RSCC values vary from 0.90 to 0.95 if the model used assigns a half negative charge to both O atoms, but drop to 0.35 to 0.50 if the model treats those atoms are treated as uncharged.

ESP maps derived from electron diffraction data

While net charge has an effect on ESP maps at all resolution, it diminishes as resolution increases. For example, Sawaya et al.8 recently reported a structure for a small peptide they were able to solve by direct methods using measured electron diffraction amplitudes that extended to a resolution of 1.0 Å, even though direct method algorithms all assume that densities are everywhere positive, which they may not be in ESP maps. Others have solved ESP structures by molecular replacement starting X‐ray derived atomic models.9 Examination of ESP maps that have been deposited for these structures shows that they are largely consistent with what one would anticipate based on computer simulations done at the same resolutions. However, the ESP maps deposited for these structures are not purely experimental in origin because the phases used to compute them derive from models that did not take ionizations into account. Thus, it is hard to be sure how they should be interpreted. It would be interesting to reexamine these structures if the experimental diffraction intensities on which their maps are based were made available.

From this point of view, the ESP map at somewhat lower resolution has been reported for the α‐synuclein fragment peptide structure corresponding residues 47‐GVVHGVTTVA‐56 (PDB‐4ZNN) (1.41‐Å resolution) is quite interesting. It too was obtained from electron diffraction data,10 but its PDB entry contains both measured amplitudes and calculated structure factors (it remains far from clear whether intensity–amplitude relationship of I = F ² is valid for electron diffraction data whereas it is absolutely valid for conventional X‐ray diffraction data, and whether the same a prior knowledge of intensity distribution in treatment of weak and negative intensity that works well for X‐ray data can be applied to electron diffraction data). Using these data, two σ _A‐weighted maps were calculated for (see Methods), one corresponding to an F‐map, that is, an ESP map, and the other to a ΔF‐map, that is, a map of the differences between the data and the model.

The carboxylate group of the C‐terminal Ala56 interacts with both the terminal amine of a symmetry‐related Gly47 residue, and the side chain of a symmetry‐related His50 (Fig. 4). In the difference ESP map, there is significant negative density associated with both the O and OXT atoms of this carboxylate group [Fig. 4(A)], and in the corresponding ESP map, both atoms have much lower electrostatic potentials associated with them than the other atoms in that residue [Fig. 4(B,C)]. These observations indicate that both O atoms have negative charges. Additional evidence for this conclusion can be found in B‐factors assigned to the O and OXT atoms in PDB‐4ZNN, which are 50.34 Ų and 45.80 Ų, respectively. The B‐factors for the atoms to which they are covalently bonded, Cβ and Cα, are 18.64 Ų and 22.36 Ų. It appears that during refinement, the B‐factors for these O atoms became artificially inflated to compensate for the fact that their ESP peaks were weaker than the neutral‐atoms model used implied they should be.

Figure 4.

ESP map for the α‐synuclein fragment residue 47–56 (GVVHGVTTVA) (PDB‐4ZNN)10 from electron diffraction experiments at 1.41‐Å resolution. A: σ _A‐weighted ΔF map contoured at −2.0σ (red) for the C‐terminal Ala56 residue. B–D: σ _A‐weighted F‐map contoured at +1.5σ (blue), +1.0σ (salmon), and/or +0.5σ (blue). D: The C‐terminal Ala carboxylate makes interactions with the N‐terminal amine of a symmetry‐related G41 and the side chain of a symmetry‐related H50.

Variations in the B‐factors of the atoms in Asp and Glu residues that appear to be unrelated to structural disorder are by no means unique to 4ZNN. They are evident in nearly all the electron scattering‐derived structures that have been examined, and the lower the resolution, the worse the problem gets (Supporting Information Table S1).4, 6, 11 When refinements produce results like these, one has to be concerned that the conformations assigned to Asp and Glu side chains may be seriously in error.

Discussion

It is a major challenge to generate accurate descriptions of the ESP density distributions of macromolecules starting with X‐ray‐derived atomic models. There are many issues. For example, the H atoms in macromolecules, which make important contributions to their ESP distributions, are largely invisible in X‐ray structures. It is also true that ESP distributions are much more sensitive than ED distributions to bond polarity and ionizations, especially at the resolutions at which most macromolecule structures are solved. That said, the simple‐minded approach taken here for estimating the appearance of the ESP distributions for Asp and Glu residues, which takes no account whatever of the redistributions of valence electrons associated with the formation of specific covalent bonds, seems to have worked reasonably well. The ESP maps computed this way correspond well with what is observed experimentally.

What this study teaches is the critical importance of taking net negative charges into account when interpreting the ESP maps obtained for proteins. Failure to take proper account of net positive charge appears to have less damaging consequences because all it does is make peaks in ESP maps that would be positive if there were no charge even more positive (data not shown). As has already been pointed out elsewhere, negative changes also influences the appearance of the ESP maps of nucleic acids at about 2.9‐Å resolution.4

Two additional points might also be made. First, resolution issues aside, it is far from obvious that the EM‐derived atomic models for macromolecules reported so far are superior in quality to the X‐ray‐derived models for the same molecules. If more care were taken in addressing net charge issues, it is likely that their quality would improve significantly. Second, many believe that radiation‐induced decarboxylations account for the absence of density for the carboxylate groups of Asp and Glu residues in ESP maps. The observations reported here suggest that it would be wise to examine the negative density in the ESP maps of proteins before concluding that any given Asp or Glu has been decarboxylated.

Recommendations

It is recommended that the PDB require the deposition of experimental intensities for structures determined by electron diffraction. It would also be useful if Fourier shell correlation coefficient (FSCC) data as a function of resolution were deposited in the EMDB, and if different masks were used for image reconstruction and for FSCC calculations, those masks should be deposited as well.

This study as well as other recent studies4, 12 has shown that proper simulation of ESP density from atomic models requires information of coordinate (xyz), and atomic properties like occupancy (q), B‐factor (B), and partial charge (p). It is recommended that the PDB format include partial charge information in column 67–72 with two decimal points so that all the three atomic property parameters q, B, and p have the same format (3F6.2 in Fortran code). It is likely in near future that atomic partial charges can directly be extracted from high‐resolution experimental ESP density using the same procedure that has currently been done from theoretical ESP density obtained using condensed‐state quantum mechanics.13, 14

Methods

The ESP maps examined in this study were retrieved from PDB/EMDB without modifications unless otherwise stated. In a few instances they were recomputed following the addition of explicit H atoms to the model used for phasing. Experimental ESP maps were recalculated with B‐factor sharpening when necessary; σ _A‐weighted ED maps were rotated and translated to align with experimental ESP maps using the RAVE and CCP4 packages.15, 16 Both ED and ESP maps were visualized using the graphics program Coot.17 ESP maps were simulated as described elsewhere4 with resolution limits ranging from 0.5 to 5.0 Å, and with uniform B‐factors applied that ranged in value from 2 to 144 Ų, consistent with dependence of overall B‐factors on resolution that this author has determined using all the X‐ray data sets present in the PDB. The spherically averaged, isolated atom electron scattering factors used were taken from International Tables of Crystallography18 and from data reported by Peng et al.19, 20 RSCC value for selected residue was calculated using matrix improvement routine of the RAVE package. Figures were made using the program Pymol.21

Supporting information

Supporting Information