Rigidity Strengthening: A Mechanism for Protein–Ligand Binding

Abstract

Protein-ligand binding is essential to almost all life processes. The understanding of protein-ligand interactions is fundamentally important to rational drug and protein design. Based on large scale data sets, we show that protein rigidity strengthening or flexibility reduction is a mechanism in protein-ligand binding. Our approach based solely on rigidity is able to unveil a surprisingly apparently long-range contribution of apparently four residue layers to protein-ligand binding, which has ramifications for drug and protein design. Additionally, the present work reveals that among various pairwise interactions, the short-range ones within the distance of the van der Waals diameter are most important. It is found that the present approach outperforms all other state-of-the-art scoring functions for protein-ligand binding affinity predictions of two benchmark test sets.

A review of mathematical representations of biomolecular data

“…Consequently, we ended up with various element-specific subgraphs taking care of different types of physical interactions, such as hydrophilic, hydrophobic, hydrogen bonds. 17,102 As a result, the predicted accuracy for protein B-factors by our multiscale weighted colored graphs is over 40% higher than GNM models. 17 The success of multiscale weighted colored graph models on B-factor prediction encouraged us to design graph-based scoring functions to predict protein-ligand binding affinities.…”

“…These new graph theory methods are found to be some of the most powerful descriptors of macromolecules. 17,96,102 How biomolecules assume complex structures and intricate shapes and why biomolecular complexes admit convoluted interfaces between different parts can be naturally described by differential geometry, a mathematical subject drawing on differential calculus, integral calculus, algebra, and differential equation to study problems in geometry or differentiable manifolds. Einstein used this approach to formulate his general theory of relativity.…”

“…In fact, µ G i (η kk ) is the generalized form of our successful rigidity index model for protein-ligand binding affinity prediction in the previous work. 102 it is noticed that the WCS for the protein-ligand system is bipartite since each of its edges presents the interaction between one atom in the protein and another protein in the ligand. With that design, a variety of physical and biological properties such as electrostatics, van der Waals interactions, hydrogen bonds, polarization, hydrophilicity, hydrophobicity can be successfully encoded in our WCS representations.…”

Flexibility and rigidity index for chromosome packing, flexibility and dynamics analysis

“…Especially, MWCG based FRI has set a new accuracy benchmark for protein flexibility analysis. More interestingly, FRI model has been applied to protein-ligand binding affinity prediction in drug design (Nguyen et al, 2017). The results from the FRI based machine learning model has significantly outperformed all traditional models.…”

“…The results from the FRI based machine learning model has significantly outperformed all traditional models. This reveals that the rigidity strengthening can be a potential mechanism for protein-ligand binding (Nguyen et al, 2017). More recently, a virtual particle based FRI model is proposed for analyzing the dynamics of extremely large-sized biomolecular complexes and organelles, especially the ones from Electron Microscopy Data Bank (EMDB) Xia et al, 2018).…”