Characterizing Changes in the Rate of Protein-Protein Dissociation upon Interface Mutation Using Hotspot Energy and Organization

<div><p>Predicting the effects of mutations on the kinetic rate constants of protein-protein interactions is central to both the modeling of complex diseases and the design of effective peptide drug inhibitors. However, while most studies have concentrated on the determination of association rate constants, dissociation rates have received less attention. In this work we take a novel approach by relating the changes in dissociation rates upon mutation to the energetics and architecture of hotspots and hotregions, by performing alanine scans pre- and post-mutation. From these scans, we design a set of descriptors that capture the change in hotspot energy and distribution. The method is benchmarked on 713 kinetically characterized mutations from the SKEMPI database. Our investigations show that, with the use of hotspot descriptors, energies from single-point alanine mutations may be used for the estimation of off-rate mutations to any residue type and also multi-point mutations. A number of machine learning models are built from a combination of molecular and hotspot descriptors, with the best models achieving a Pearson's Correlation Coefficient of 0.79 with experimental off-rates and a Matthew's Correlation Coefficient of 0.6 in the detection of rare stabilizing mutations. Using specialized feature selection models we identify descriptors that are highly specific and, conversely, broadly important to predicting the effects of different classes of mutations, interface regions and complexes. Our results also indicate that the distribution of the critical stability regions across protein-protein interfaces is a function of complex size more strongly than interface area. In addition, mutations at the rim are critical for the stability of small complexes, but consistently harder to characterize. The relationship between hotregion size and the dissociation rate is also investigated and, using hotspot descriptors which model cooperative effects within hotregions, we show how the contribution of hotregions of different sizes, changes under different cooperative effects.</p></div

Off-rate prediction model scatter plots.

<p>The relationship between experimental values for Δlog₁₀(<i>k_off</i>) and predicted values for Δlog₁₀(<i>k_off</i>) with (A) <i>RFSpot_KFC2_Off-Rate+MOL</i>, best performing off-rate prediction model combining hotspot and molecular descriptors. Hotspot descriptors for this model are generated using the <i>RFSpot_KFC2</i> hotspot prediction algorithm. (B) <i>RFSpot_KFC2_Off-Rate+MOL</i>, best performing off-rate prediction model using only hotspot descriptors. Hotspot descriptors for this model are again generated using the <i>RFSpot_KFC2</i> hotspot prediction algorithm. (C) <i>Molecular_Off-Rate</i>, off-rate prediction model using molecular descriptors. The addition of hotspot descriptors as observed in (A) to molecular descriptor model as shown in (B) notably improves the prediction of stabilizing mutants, which are all found in the lower left quadrant for <i>RFSpotKFC2_Off-Rate+MOL</i>.</p

Effects of conformational changes and off-rate prediction.

<p>Predictions of the original 13 regression models developed for off-rate prediction. The predictions are assessed separately (PCC with Δlog₁₀(<i>k_off</i>)) for mutations on complexes which undergo significant backbone conformational changes of I_RMSD >1.5 Å (dark green), notable conformational changes of I_RMSD >1 Å (light green) and little to no conformational changes I_RMSD <1 Å (dark blue). Predicted accuracy is directly related to the magnitude of conformational change and becomes highly dependent on the model at higher levels of conformational changes. I_RMSD values were extracted from our previous work on the construction of a protein-protein affinity database <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003216#pcbi.1003216-Kastritis2" target="_blank">[66]</a>.</p

Detection of rare complex stabilizing mutations using off-rate classification models.

<p>(A) Ranked list of 31 stabilizing mutations (Δlog₁₀(<i>k_off</i>) <−1) in SKEMPI off-rate dataset. The list is ranked according to the number of off-rate prediction classification models that detect the mutation in question as stabilizing. Detections per model (B) are highlighted in white, and non-detections highlighted in black. The lower portion of (A) is dominated by single-point mutations to alanine residues, which suggests that the stabilizing effects of these mutations, as opposed to their more common neutralizing/destabilizing effects, are much harder to characterize.</p

Effects of cooperativity on effective energetic contribution of hotregions.

<p>The summation of single-point alanine <i>ΔΔG</i>s of a hotregion may underestimate/overestimate its contribution if negative/positive cooperative effects are at play respectively. In this work, in order to account for potential cooperative effects, hotspot descriptors <i>HSEner_PosCoop</i>, <i>HSEner_NegCoop</i> apply linearly decreasing and increasing weights respectively to single-point alanine <i>ΔΔG</i>s within a hotregion. In turn <i>Int_HS_Energy</i>, based on the assumption the hotspot residues within the hotregion can be assumed to be additive, does not apply any weights. Here, the effects of accounting for cooperative/additive effects on the predicted hotspot and hotregions energies on all mutated complexes used in this work, is shown. (A) The mean hotspot energies for hotregion sizes of 1 to 8 hotspot residues. Each column shows the predictions of different hotspot predictors. (A) First row (blue), shows the raw mean hotspot energies, which essentially assumes all hotspots are additive within a hotregion. (A) Second row (red), assumes negative cooperativity within hotregions. To account for negative cooperativity, a linearly increasing weight is applied to the hotspot energies according to the size of the hotregion they are in (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003216#s3" target="_blank">Materials and Methods</a>). (A) Third row (green), assumes positive cooperativity within hotregions and a linearly decreasing weight is applied to the hotspot energies according to the size of hotregion. (B) is similar to (A) but values are now the mean of the total hotregion energy of the given size. Effectively, the additive hotspot energy assumption results in hotregions contributing in a linearly increasing manner according to their size, the negative cooperativity assumption results in hotregions contributing in an increasing exponential-like manner as the hotregions increase in size, and the positive cooperativity assumption results in hotregions reaching a maximum contribution at around a hotregion size of 5, with their contribution decreasing beyond.</p

Hotspot and molecular descriptors for estimating change in off-rate.

<p>The hotspot descriptors designed in this work are benchmarked against a set of 110 molecular descriptors; both in their ability to estimate Δlog₁₀(<i>k_off</i>) and in their ability to detect stabilizing mutations of <b>Δlog₁₀(</b><b><i>k_off</i></b><b>)</b> <−1. The performance measures shown here enable us to assess the raw predictive power of the descriptors independent of any learning models. Green and black bars highlight descriptors from the hotspot and molecular descriptor sets respectively. (A) Comparison of the distribution of the absolute PCC values for the hotspot descriptors designed in this work against that for the molecular descriptors. The related list of descriptor names and their respective PCCs is found in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003216#pcbi.1003216.s015" target="_blank">Text S5</a>. (B) Top 10 hotspot descriptors and top 10 molecular descriptor according to absolute PCC with experimental Δlog₁₀(<i>k_off</i>). (C) Mann Whitney U-Test rankings for all descriptors where values are ranked according to −log₁₀(pval) and represent the discrimination ability of the descriptors for the detection of stabilizing mutants (<b>Δlog₁₀(</b><b><i>k_off</i></b><b>)</b> <−1) from neutral to destabilizing mutants (<b>Δlog₁₀(</b><b><i>k_off</i></b><b>)</b> >0) (Referred to as CDS1). This dataset contains 31 stabilizing mutants and 503 neutral to destabilizing mutants. (D) Matthew's Correlation Coefficient (MCC) rankings for all descriptors on same dataset. (E) and (F) are identical to (C) and (D) except that results are for off-rates that satisfy |<b>Δlog₁₀(</b><b><i>k_off</i></b><b>)|</b> >1. This dataset contains 31 stabilizing mutants and 213 destabilizing mutants (referred to as CDS2).</p

Hotspot and molecular descriptor scatter plots.

<p>The relationship between experimental values for Δlog₁₀(<i>k_off</i>) and (A) hotspot descriptors showing highest correlation with Δlog₁₀(<i>k_off</i>) (SuppHSEnergy_KFC2a - changes in hotspot energies in the support region as predicted by KFC2a <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003216#pcbi.1003216-Zhu1" target="_blank">[30]</a>), (B) molecular descriptor showing highest correlation with Δlog₁₀(<i>k_off</i>) (AP_MPS - the DARS atomic potential <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003216#pcbi.1003216-Chuang1" target="_blank">[54]</a>), (C) top performing hotspot descriptor for the detection of stabilizing mutants (HSEner_PosCoop_RFSpot – changes in hotspot energies on accounting for positive cooperativity in hotregions) and (D) top performing molecular descriptor for the detection of stabilizing mutants (CP_TB – coarse grained protein-protein docking potential).</p

Stability regions, interface-area and complex-size.

<p>The changes in hotspot energies upon mutation are assessed at three interface regions, which enable us to explore changes in the distribution of stability for complexes of different size and interface-area. CORE, RIM and SUPP represent the PCCs of CoreHSEnergy/RimHSEnergy/SuppHSEnergy averaged for the 6 hotspot prediction algorithms with Δlog₁₀(<i>k_off</i>).(A) PCCs for mutants on Complexes with interface-area >1600 Ų (LIA). (B) PCCs for mutants on complexes with interface-area <1600 Ų (SIA). (C) PCCs for mutants on complexes with size <500 residues (SCS). (D) PCCs for mutants on complexes with size >500 residues (LCS). (E) LIA-SCS, (F) LIA-LCS, (G) SIA-SCS, (H) SIA-LCS. (I) Scatter plot of complex size vs. interface area for all complexes in off-rate mutant dataset. Here it is observed that complex stability is distributed across all three regions for small-size complexes (C, E and G), whereas the core becomes a localized region of stability for large-complex sizes (D, F, H). On analysis of the interface-area vs. complex-size subsets (E–H), the distribution of stability regions is affected primarily through complex-size irrespective of interface-area.</p

Relationship of off-rate changes upon mutation with change in binding free energy and change in interface hotspot energy.

<p>(A) The relationship between experimental values for Δlog₁₀(<i>k_off</i>) and <i>ΔΔG</i> for all the 713 mutations in the SKEMPI off-rate dataset. (B) The relationship between changes in interface hotspot energies, as predicted by <i>RFSpot_KFC2</i> hotspot predictor, and change in Δlog₁₀(<i>k_off</i>) for all the 713 mutations in the SKEMPI off-rate dataset. Note that 50% of off-rate mutants in this dataset involve mutations to non-alanine residues and include multi-point mutants. In turn <i>Int_HS_Energy</i> characterizes these changes with the use of single-point alanine <i>ΔΔG</i>s as highlighted in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003216#pcbi-1003216-g001" target="_blank">Figure 1</a>.</p

Pearson's Correlation Coefficient (PCC) of hotspot descriptors with experimental Δlog₁₀(<i>k_off</i>) for the 713 off-rate mutations in SKEMPI.

<p>Pearson's Correlation Coefficient (PCC) of hotspot descriptors with experimental Δlog₁₀(<i>k_off</i>) for the 713 off-rate mutations in SKEMPI.</p