Distance-based reconstruction of protein quaternary structures from inter-chain contacts

Abstract

Predicting the quaternary structure of protein complex is an important problem. Inter-chain residue-residue contact prediction can provide useful information to guide the ab initio reconstruction of quaternary structures. However, few methods have been developed to build quaternary structures from predicted inter-chain contacts. Here, we develop the first method based on gradient descent optimization (GD) to build quaternary structures of protein dimers utilizing inter-chain contacts as distance restraints. We evaluate GD on several datasets of homodimers and heterodimers using true/predicted contacts and monomer structures as input. GD consistently performs better than both simulated annealing and Markov Chain Monte Carlo simulation. Starting from an arbitrarily quaternary structure randomly initialized from the tertiary structures of protein chains and using true inter-chain contacts as input, GD can reconstruct high-quality structural models for homodimers and heterodimers with average TM-score ranging from 0.92 to 0.99 and average interface root mean square distance from 0.72 Å to 1.64 Å. On a dataset of 115 homodimers, using predicted inter-chain contacts as restraints, the average TM-score of the structural models built by GD is 0.76. For 46% of the homodimers, high-quality structural models with TM-score ≥ 0.9 are reconstructed from predicted contacts. There is a strong correlation between the quality of the reconstructed models and the precision and recall of predicted contacts. Only a moderate precision or recall of inter-chain contact prediction is needed to build good structural models for most homodimers. Moreover, GD improves the quality of quaternary structures predicted by AlphaFold2 on a Critical Assessment of Techniques for Protein Structure Prediction-Critical Assessments of Predictions of Interactions dataset.

Keywords: distance-based modeling; gradient descent optimization; inter-chain contact prediction; protein complex; protein quaternary structure modeling.

FIGURE 1

The superposition of the native structure of 1XDI and the models reconstructed by three methods (i.e., green and orange denoting the true dimer structure and blue and red the reconstructed dimer structure): (A) GD, (B) MC, and (C) CNS. TM‐score, RMSD, f_nat, I_RMSD, L_RMSD of the model predicted by GD are 0.99, 0.56 Å, 94.52%, 0.24 Å, and 0.74 Å, respectively. TM‐score, RMSD, f_nat, I_RMSD, L_RMSD of the model predicted by MC are 0.99, 0.61 Å, 93.15%, 0.45 Å, and 1.29 Å, respectively. TM‐score, RMSD, f_nat, I_RMSD, L_RMSD of the model predicted by CNS are 0.88, 2.25 Å, 74.79%, 1.49 Å, and 5.18 Å, respectively. CNS, crystallography and NMR system; GD, gradient descent optimization; MC, Markov chain; RMSD, root mean square distance

FIGURE 2

TM‐score and I_RMSD of quaternary structure models for a homodimer 1Z3A before applying GD and after applying GD during 20 runs. The 20 start models are initialized from the true tertiary structure of the monomer in the dimer before GD is applied. GD is then used to reconstruct the quaternary structures from predicted inter‐chain contacts. The x‐axis denotes the quality (TM‐score or I_RMSD) of 20 initial quaternary structure models and y‐axis the quality of 20 final models built by GD from the initial models. In 19 out of 20 cases, GD improves the TM‐score of the models. In all 20 cases, GD reduces the I_RMSD of the models. GD, gradient descent optimization; RMSD, root mean square distance

FIGURE 3

TM‐scores and root mean square distance (RMSD) of the models versus the inter‐chain contact density of 73 heterodimers

FIGURE 4

The superposition of the native structure of 1C6X and the models generated by three methods (i.e., green and orange representing the true dimer structure, blue, and red the generated models): (A) GD, (B) MC, and (C) CNS. TM‐score, RMSD, f_nat, I_RMSD, L_RMSD of the model predicted by GD are 0.99, 0.4 Å, 84.61%, 0.4 Å, and 0.91 Å, respectively. TM‐score, RMSD, f_nat, I_RMSD, L_RMSD of the model predicted by MC are 0.98, 0.6 Å, 78.84%, 0.6 Å, and 1.6 Å, respectively. TM‐score, RMSD, f_nat, I_RMSD, L_RMSD of the model predicted by CNS are 0.86, 2.02 Å, 41.6%, 2.14 Å, and 5.68 Å, respectively. CNS, crystallography and NMR system; GD, gradient descent optimization; MC, Markov chain; RMSD, root mean square distance

FIGURE 5

The plot of TM‐score and percent of native contacts of the models (f_nat) against the precision of predicted contacts on Homo115 dataset. (A) Pearson's correlation between TM‐score and precision is 0.78. (B) Pearson's correlation between f_nat and precision is .94

FIGURE 6

TM‐score and percent of native contacts of the predicted models (f_nat) reconstructed by GD versus the recall of the predicted inter‐chain contacts on the Homo115 dataset. (A) Pearson's correlation between TM‐score and recall is 0.78. (B) Pearson's correlation between f_nat and recall is 0.93. GD, gradient descent optimization

FIGURE 7

The average root mean square distance (RMSD) and TM‐score of models reconstructed for homodimers in the Homo115 dataset versus the cut‐off probability of selecting predicted inter‐chain contacts as restraints