Interdependent random network: a model of protein-protein interaction

Proteins are complex biomolecules that are responsible for gene encoding. These encoding happen through nucleotide transcription. The sequence of amino acids defines the various types of proteins. Proteins differ by the nucleotide sequence of their genes. Gene expression usually results in proteins folding into a specific 3D structure that determines their activity. We propose a novel model for protein folding based on complex networks that enable us to understand umpteen facets of the experimental process that causes conformational states. We chose an ensemble of nonlinear oscillators embedded in a complex network. A complex network following a random topology has been proficient of producing the largest plausibile conformation states. Also, statistical measures of the complex network capture the essence of the substates. We perform analysis on the basis of the average energy of the molecule, here an ensemble of oscillators. The model encompasses the averaged solvent-molecule interaction that assists the osmotic exchange of ions. Two models of nonlinear oscillators are studied under the chosen framework. Note that the fluctuations from equilibrium correspond to the oscillations of bond angles. We chose a relaxation oscillator and a damped harmonic oscillator to study the nuances of protein folding. Numerical studies are based on the averaged energy of the network. We also tune the density of linkers in the network to elucidate the feature of the shape factor. We remark that this model could mimic the protein data structure obtained by the solution nuclear magnetic resonance method.