Normal mode analysis and beyond

Abstract

Normal mode analysis provides a powerful tool in biophysical computations. Particularly, we shed light on its application to protein properties because they directly lead to biological functions. As a result of normal mode analysis, the protein motion is represented as a linear combination of mutually independent normal mode vectors. It has been widely accepted that the large amplitude motions throughout the entire protein molecule can be well described with a few low-frequency normal modes. Furthermore, it is possible to represent the effect of external perturbations, e.g., ligand binding, hydrostatic pressure, as the shifts of normal mode variables. Making use of this advantage, we are able to explore mechanical properties of proteins such as Young's modulus and compressibility. Within thermally fluctuating protein molecules under physiological conditions, tightly packed amino acid residues interact with each other through heat and energy exchanges. Since the structure and dynamics of protein molecules are highly anisotropic, the flow of energy and heat should also be anisotropic. Based on the harmonic approximation of the heat current operator, it is possible to analyze the communication map of a protein molecule. By using this method, the energy transfer pathways of photoactive yellow protein were calculated. It turned out that these pathways are similar to those obtained via the Green-Kubo formalism with equilibrium molecular dynamics simulations, indicating that normal mode analysis captures the intrinsic nature of the transport properties of proteins.

An Effective MM/GBSA Protocol for Absolute Binding Free Energy Calculations: A Case Study on SARS-CoV-2 Spike Protein and the Human ACE2 Receptor

“…Entropy calculation plays a key role in characterizing the absolute binding free energy within MM/PB(GB)SA methods [ 38 ]. Normal-mode analysis (NMA) [ 39 ] is a widely used method with promising convergence in calculating configurational entropy [ 28 ]. The main drawback of this method is the computational cost, which becomes intractable for large structures due to the expensive calculation of the covariance matrix of internal coordinates for all degrees of freedom.…”

Modeling Coronavirus Spike Protein Dynamics: Implications for Immunogenicity and Immune Escape

“…Fluctuations obtained via NMA can explore a small radius of movements around the equilibrium position within a protein's free energy landscape (46). For structured proteins, or those with flexible regions, this radius can characterize representative, biologically-accessible protein motions (46). Indeed, studies show that the linear combination of low frequency modes is adequate to characterize collective motions and intrinsically favored dynamic patterns of functional units of membrane proteins and large systems like ion channels (43,47), receptors (43,55,56), and transporters (43,46,57).…”

“…Although this approach is not as robust as, for example, molecular dynamics simulation using a more complex protein potential, it is able to produce accurate, large-scale protein motions around a starting structure (43,44). Fluctuations obtained via NMA can explore a small radius of movements around the equilibrium position within a protein's free energy landscape (46). For structured proteins, or those with flexible regions, this radius can characterize representative, biologically-accessible protein motions (46).…”

“…For structured proteins, or those with flexible regions, this radius can characterize representative, biologically-accessible protein motions (46). Indeed, studies show that the linear combination of low frequency modes is adequate to characterize collective motions and intrinsically favored dynamic patterns of functional units of membrane proteins and large systems like ion channels (43,47), receptors (43,55,56), and transporters (43,46,57). Additionally, other recent studies show that this is a valid method for describing realistic fluctuations of open and closed state S proteins, as well as for studying their nanomechanical properties (34,45).…”

“…This method is useful for investigating protein motions around an equilibrium starting structure (43,44), where fluctuations obtained through NMA characterize a large fraction of the biologicallyaccessible movements experienced by structured proteins and proteins that contain flexible regions (43,44). This is a wellaccepted method for describing biologically-relevant fluctuations of proteins, successfully applied to investigations of mechanically-driven deformations, energy transport properties, studies of large molecular complexes, and ligand-gated ion channels (34,(45)(46)(47). We apply these models to systematically analyze local protein domain dynamics of S protein systems, as well as their thermal stability, to characterize structural and dynamical variability among different variants.…”