AtomicChargeCalculator
Conformationally Dependent Atomic Charges of Quantum Mechanics Quality

We calculated atomic charges in PG1 using ACC (coordinates from NMR model 1 of the PDB entry 1PG1). The total molecular charge was +7, owing to the many ARG residues. The EEM parameter set used was EX-NPA_6-31Gd_gas, which covered the NPA charge definition at the HF/6-31G* level of theory, and was developed for proteins. However, it was necessary to add to this set EEM parameters for deuterium (D), because this element was present in the input file. The EEM parameters for D were identical to the parameters for H. The full EEM matrix was solved in double precision. The computation took less than 1s.

PG1 contains 18 residues, and rather than analyzing atomic charges, we analyzed the residue charges, which are also reported by ACC (in all tabs, select the grouping Residues). PG1 is special because of its high positive charge. It contains 6 ARG residues. However, not all have the same charge. In particular, ARG at positions 4 and 9 have the least positive charge (around +0.5e), whereas the rest have much higher positive charge (over +0.8e). Such results suggest that mutations of ARG into a neutral residue at positions 4 or 9 would have a lower effect than mutations at positions 1, 10, 11 or 18.

A quick literature search reveals that many mutants of PG1 have been studied. Indeed, Ostberg and Kastnessis found that the mutation of ARG 4 into a neutral residue alters the antimicrobial activity against C. albicans significantly less than the mutation of ARG 10. Such biologically relevant insight can be gained by analyzing the residue charges on a single structure of PG1.

Necessarily, the proteasome undergoes large conformational changes during its operation. However, due to its size, such changes are very difficult to study. Recent work by Unverdorben et. al in the field of cryo-electron microscopy has lead to the discovery of intermediate conformers during the initial binding of ubiquitylated substrates. While the conformational changes in the regulatory particle are easily distinguishable, the changes in the catalytic particle are very subtle, due to the fact that all studied conformers refer to the initial phase of substrate binding.

Using ACC, we calculated atomic charges in the 3 conformers of the 26S proteasome that are available in the Protein Data Bank (PDB IDs 4CR2, 4CR3, 4CR4). The default ACC settings were used. Specifically, the total molecular charge was considered neutral for all conformers. The EEM parameter set used was EX-NPA_6-31Gd_gas, which covered the NPA charge definition at the HF/6-31G* level of theory, and was developed for proteins. The computation method was EEM Cutoff Cover, with a cutoff radius of 12Å. The computation took 130s.

The calculation produced 3 sets of atomic charges, one for each conformer. Since the proteasome is very large, we analyzed the residue charges, which are also reported by ACC, and subsequently the charges for the various subunits that make up the proteasome. Note that information about the subunits is given in the COMPND records of the PDB entries used here. Residues with the chain identifier 1-7 correspond to subunits beta 1-7. Residues with the chain identifier A-G correspond to subunits alpha 1-7. Finally, residues with the chain identifier H-Z correspond to regulatory subunits. Therefore, the total charge for a specific subunit or particle can be obtained as the sum of the charges for the residues with the corresponding chain identifiers. We thus followed the change in total charge for the regulatory particle, the catalytic particle, then separately for the alpha and beta rings.

The first observation was that, during the conformational changes from state 1, to state 2, and then to state 3, a significant amount of electron density is transferred between the catalytic particle and the regulatory particle. This suggests that, even though there is no significant movement observed for the catalytic particle, allosteric information is exchanged with the catalytic particle, and this information can be tracked at the electrostatic level. The next observation is that significant information is disseminated not only horizontally (within the alpha ring, or within the beta ring), but also vertically. In the overall transition it appears that the alpha ring loses electron density to the regulatory particle. By checking the intermediate state 2 it is possible to see that there is also transfer between the alpha ring and beta ring. This vertical shuttling of electron density within the catalytic particle suggests that the activity of alpha and beta subunits may cross-correlate. Such phenomena have indeed been reported.

For example, O'Hara et. al found that subunits alpha5 and beta1 may translocate together, while Cron et. al found that knockdown of alpha1 leads to loss of chymotrypsin activity associated with beta5. Further analysis can even yield the residues involved in the allosteric regulation, as those residues which exhibit a high variation in total charge (e.g., approximately 10 sites on the Rpn-13 regulatory subunit). This case study shows how a brief calculation using only a crude structural approximation can give insight regarding allosteric regulation in large biomolecular complexes.