Structural and Functional Analysis of Proteins Using Rigidity Theory

Abstract

Over the past two decades, we have witnessed an unprecedented explosion in available biological data. In the age of big data, large biological datasets have created an urgent need for the development of bioinformatics methods and innovative fast algorithms. Bioinformatics tools can enable data-driven hypothesis and interpretation of complex biological data that can advance biological and medicinal knowledge discovery. Advances in structural biology and computational modelling have led to the characterization of atomistic structures of many biomolecular components of cells. Proteins in particular are the most fundamental biomolecules and the key constituent elements of all living organisms, as they are necessary for cellular functions. Proteins play crucial roles in immunity, catalysis, metabolism and the majority of biological processes, and hence there is significant interest to understand how these macromolecules carry out their complex functions. The mechanical heterogeneity of protein structures and a delicate mix of rigidity and flexibility, which dictates their dynamic nature, is linked to their highly diverse biological functions. Mathematical rigidity theory and related algorithms have opened up many exciting opportunities to accurately analyse protein dynamics and probe various biological enigmas at a molecular level. Importantly, rigidity theoretical algorithms and methods run in almost linear time complexity, which makes it suitable for high-throughput and big-data style analysis. In this chapter, we discuss the importance of protein flexibility and dynamics and review concepts in mathematical rigidity theory for analysing stability and the dynamics of protein structures. We then review some recent breakthrough studies, where we designed rigidity theory methods to understand complex biological events, such as allosteric communication, large-scale analysis of immune system antibody proteins, the highly complex dynamics of intrinsically disordered proteins and the validation of Nuclear Magnetic Resonance (NMR) solved protein structures.

Mechanistic insights into the nickel-dependent allosteric response of the Helicobacter pylori NikR transcription factor

“…To learn more about allosteric networks of residues or pathways that may connect the nickel binding residues to Lys64 and Lys140 at the MBD/DBD interface, rigidity-transmission allostery (RTA) computational analysis was performed ( 67 , 68 ). RTA methods utilize mathematical rigidity theory and graph algorithms ( 69 , 70 , 71 ) to analyze allosteric networks within protein structures ( 72 , 73 ). This approach provides a mechanistic view of allostery by analyzing how local perturbation of rigidity and conformational degrees of freedom propagates from one site to modify rigidity at distant sites across the protein.…”

“…The method FIRST, which uses mathematical rigidity theory to analyze protein flexibility, was used to decompose HpNikR into flexible and rigid clusters ( 69 , 71 ). As shown in Fig.…”

“…An extension of the method FIRST ( 69 , 71 ) was utilized to perform rigidity theory-based structural analysis. Starting with a crystal structure, FIRST was used to create a geometric molecular framework, whose underlying network (graph) consists of atoms (nodes) and edges ( i.e ., constraints representing covalent bonds, hydrogen bonds, electrostatic interactions, and hydrophobic contacts).…”

Low pH structure of heliorhodopsin reveals chloride binding site and intramolecular signaling pathway

“…Allostery was analyzed using the rigidity-transmission allostery (RTA) algorithms 42 , 43 , 67 . The RTA method is based on mathematical rigidity theory 42 , 68 . Starting with TaHeR (PDB ID 7u55) and HeR 48C12 (PDB ID 6su4) dimers, a constrained network representation of protein structure was generated with the method FIRST 44 , which consists of nodes (atoms) and edges representing covalent and non-covalent interactions.…”

“…To probe the dynamical features of TaHeR and HeR 48C12, we have applied a constrained geometric Monte Carlo simulation, based on methodology Framework Rigidity Optimized Dynamics Algorithm New (FRODAN) 68 – 70 . This approach, which can be regarded as a low computational complexity alternative to MD simulations, utilizes a coarse-grained molecular mechanics potential and rigidity theory to explore the wide regions of conformational space, probing the conformational ensemble well outside the starting structure.…”