Geometric description of self-interaction potential in symmetric protein complexes

Regular distance to the closest bounding aircraft (nDp) calculation

To review the results of level mutations on symmetric homomers, we outlined a novel structural descriptor primarily based on quaternary construction geometry. We known as this descriptor the “regular distance to the closest bounding aircraft”, or nDp. These strategies are expanded variations of descriptions in our associated work3.

We reasoned that for level mutations to behave synergistically within the creation of novel self-interacting interfaces, the affected residues on the floor of 1 copy of the homomer have to be altogether accessible to the floor of different copies of this oligomer. Bounding planes, that are orthogonal to symmetry axes, seize such info. The nDp measure thus describes the gap of a residue from the closest apex of a quaternary construction alongside a symmetry axis (Fig. 1). The decrease a residue’s nDp, the upper its potential to mediate interactions with one other copy of the homomer, and the extra probably it’s to set off a novel self-interacting interface upon mutation3. To calculate the nDp, a symmetry axis is taken into account as a unit (1 Å) vector s originating from the middle of mass of the meeting. Equally, the Cα of every residue i defines a vector ri originating from the middle of mass. For every symmetry axis a of the meeting, two bounding planes parallel to 1 one other are outlined. They’re orthogonal to the symmetry axis thought-about, and intersect on the maximal (da,max) and minimal (da,min) values of the dot product s · ri, contemplating all residues i of the quaternary construction. The measure nDp for a given residue i is calculated with respect to a selected axis because the minimal distance to both of its bounding planes a, as follows: nDpa,i = min(da,max − s · ri, s · ri − da,min)7.

Fig. 1Fig. 1

Precept of calculation of various variations of the traditional distance to the closest bounding aircraft (nDp) visualized on the dihedral construction of isoaspartyl dipeptidase. (a) Coloration of the organic meeting of isoaspartyl dipeptidase by subunits (PDB accession 1POK35). Symmetry axes seem in inexperienced (2-fold axes) and pink (Four-fold axis). (b) Residues are assigned to their closest bounding aircraft. For this D4 complicated, bounding planes originate from both 2- or Four-fold axes (gray and brown, respectively). (c) Visualization of the nDp-2-fold. (d) Visualization of the nDp-n-fold, the place n = Four within the case of this D4 complicated. (e) Visualization of the nDp, which is relative to all bounding planes of the meeting independently of axes folds.

Amongst cyclic complexes, which have a single axis of symmetry, there is no such thing as a ambiguity to calculate nDp with the formulation above. Nevertheless, homomers with dihedral symmetry have a number of axes of symmetry, so a number of nDp values may be computed for every residue (one for every symmetry axis). Right here, we contemplate three circumstances:


nDp relative to bounding planes originating from 2-fold axes, the place every residue is assigned the bottom nDp worth relative to all 2-fold axes (i.e. nDp-low-fold or nDp-2-fold, Fig. 1c),


nDp relative to bounding planes originating from the n-fold axis (i.e. nDp-high-fold or nDp-n-fold, Fig. 1d), and


nDp relative to all bounding planes originating from all axes, whereby every residue is assigned the bottom nDp worth relative to all axes (i.e. nDp, Fig. 1e). In our earlier study3, we employed this definition.

Importantly, D2 homomers have three 2-fold axes and so it’s not attainable to tell apart between axes’ folds. Thus, for these we solely make use of nDp definition quantity three.

Atmosphere stickiness calculation

In our earlier work, we noticed that areas with excessive geometric potential to set off self-assembly counterbalanced that potential by detrimental design consisting of a decrease than common chemical potential for self-assembly. We measured the chemical potential for self-assembly of a given floor patch by the “stickiness” of amino acids it accommodates, launched in our earlier work12 and described intimately beneath.

The stickiness of an amino acid is outlined because the log-ratio of its frequency at protein-protein interfaces relative to solvent-exposed surfaces (Fig. 2a). The stickiness scale thus quantifies the trade-off between the possibilities of discovering a given amino acid concerned in an interplay with one other protein versus being in a solvated setting (Fig. 2a)12. Its calculation relies on a set of 397 non-redundant protein constructions from E. coli. Floor and interface protein areas had been outlined utilizing the residues relative accessible solvent space within the complexed and unbound states (rASAc and rASAu, respectively)Four,12. If a residue has a rASAc worth superior to 25% and the delta between rASAc and rASAu is null, then this residue is assigned to the floor (ΔrASA = zero & rASAc > 25%). Interface residues had been outlined as these belonging to the interface core (ΔrASA > zero & rASAc < 25% & rASAu > 25%). The stickiness scale employed right here relies on E. coli proteins, however it’s sturdy to utilizing completely different units of proteins. For instance, deriving stickiness scales primarily based on proteins from S. cerevisiae and H. sapiens confirmed excessive correlation values (RE. coli−S. cere = zero.94, RE. coli−S. sapi = zero.97)12.

Fig. 2Fig. 2

Workflow used to calculate the ‘setting stickiness’ of a residue illustrated on the dihedral construction of isoaspartyl dipeptidase (PDB accession 1POK). (a) Calculation of the ‘stickiness’ scale. Floor and interface areas are outlined for every protein of the dataset4. The stickiness of an amino acid is then outlined because the log-ratio of its frequency at protein-protein interfaces relative to solvent-exposed surfaces12. (b) The setting of a residue of curiosity is outlined by floor residues inside a 400 Å2 patch centered on the Cα of the residue of curiosity12. The central residue is excluded from the calculation. (c) Projection of the setting stickiness on isoaspartyl dipeptidase. Residues protected by low interplay propensity environments seem in blue.

Subsequent, the ‘setting stickiness’ of a residue of curiosity is calculated primarily based on its surrounding floor residues, by averaging their stickiness values (Fig. 2b)12. The residue on the heart of the patch is excluded since we concentrate on quantifying the buffering results within the residue’s neighborhood. The reasoning behind this strategy is that residues in additional sticky environments are anticipated to have a better likelihood of triggering protein-protein interfaces upon mutation to extra sticky or extra hydrophobic residues12. Surrounding floor residues are outlined as these whose Cα is positioned inside a 400 Å2 patch centered on the Cα of the residue of curiosity (i.e. a most Cα-Cα distance of 11.28 Å). The floor area outlined for the setting stickiness calculation are related to a rASAc > 25%, with out contemplating any delta between rASAc and rASAu. All buried residues (rASAc < 25%) are ignored and no stickiness is computed for these.

Organic relevance of homomers

The biologically related quaternary construction (QS) of a protein is just not available from its X-ray crystallographic construction, which offers the atomic coordinates of the uneven unit (ASU) solely. Certainly, the QS could also be shaped by components of a number of ASUs or be a sub-part of 1 ASU. The problem is, due to this fact, to tell apart fortuitous crystal contacts from organic ones forming the QS16,17. Quite a few approaches resembling PISA18 and EPPIC19 have been developed to foretell QS info from X-ray crystallographic constructions. On this dataset we offer predictions primarily based on the combination of PISA and EPPIC approaches along with novel ones we just lately developed, named QSalign/anti-QSalign and QSbio20. These strategies are summarized from descriptions in our associated work20.

QSalign employs evolutionary conservation of quaternary construction geometry as proof of organic significance20. Quaternary construction conservation is inferred following the structural superposition of full homomers utilizing Kpax21 and is quantified by a multichain model of the TM-score22. Anti-QSalign takes a complementary strategy the place the absence of QS of homologues is predictive of a monomeric state.

Lastly, QSbio scores the relevance of a QS primarily based on the predictions from three strategies (PISA18, EPPIC19, QSalign/anti-QSalign20) and offers a confidence estimate per meeting within the type of a likelihood for the QS to be incorrect20. These chances are estimated primarily based on a benchmark (Fig. three), and are given within the desk of assemblies descriptors (protein_assemblies_description.csv.tar.gz15).

Fig. threeFig. 3

Benchmark of particular person strategies and of their integration into QSbio. ROC curves are proven for every technique with their respective space below the curve (AUC) values; individually for monomers, dimers and bigger oligomers. The benchmark was carried out as earlier20, utilizing the manually curated PiQSi database as a gold-standard dataset.

Different descriptors acquisition

Assemblies descriptors had been retrieved from the 3DComplex database23: variety of subunits, molecular weight, decision, symmetry sorts, symmetry axes and Uniprot24 accession codes (protein_assemblies_description.csv.tar.gz15). Concerning residue descriptors, absolute and relative accessible floor space (ASA) had been calculated utilizing CCP425 Areaimol26,27. Relative ASA values initially superior to 100 had been corrected to 100. For comfort, stickiness scale values from Levy et al.12 had been additionally included for every residue entry.

Datasets development

As a place to begin to construct the datasets of assemblies we current on this paper, we interrogated the 3DComplex database23 to retrieve assemblies that: (i) don’t break into separated sub-structures when ignoring subunit-subunit contacts of lower than 5 residues per chain on common, (ii) have at the very least one area outlined in both SCOP28, Pfam28,29 or ECOD30, (iii) don’t include superposed chains, and (iv) don’t solely include Cα info (low decision constructions). This course of allowed us to retrieve 165,916 proposed organic assemblies from the PDB13 for which all descriptors cited on this research are supplied15.

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