Flexibility shifts upon protein-ligand binding investigated with Elastic Network Models and structural compliance

Elastic Network Models (ENMs) are a family of methods used to investigate the dynamic comportment of the proteins. These models use structural mechanics concepts to describe the conformational changes of proteins. The simple idea behind them is that a protein can be described as a set of particles connected by springs. The atoms are point masses while the interaction between them is modelled as springs. These models used in combination with normal mode analysis (NMA) describe protein’s intrinsic flexibility to study functional motions of proteins, to analyse transition pathway, and to investigate molecular docking mechanism. It is interesting to investigate the change in the dynamics of a protein because it is strictly related to the biological function of the protein. It is also important to investigate how the presence of a ligand modifies and influences the change in dynamics. When one or more ligands are included in the model it must be considered how to model the interaction between the protein and the ligand. Several methods have been proposed and, in this work, we used the model presented by Burak T. Kaynak an all. called RESPEC. It is a hybrid method because the protein residues are described only by the Ca instead the ligand is described by all the atoms. The interaction strength between the nodes is described by the coupling constant which have different values according to whether the interaction is between two residues or between a residue and a ligand atom. After implementing RESPEC framework in MATLAB, the present work focuses on the variation of structural compliance for the evaluation of the change in protein’s deformability between two different conformations. By analysing a protein with apo and holo conformation, there is a difference in the overall flexibility/rigidity of its structure reflected also in the compliance values. It is expected that the ligand would induce a decrease in compliance and an increase in rigidity in all the protein. A greater decrease of compliance is expected around the binding site. What is interesting to note is the increase of compliance values in regions distant from the binding site. That is a type of compensation between the residues which show a increase in compliance (far from the ligand site) and the residue with a decrease value of compliance (closed to the ligand site).