Could network structures generated with simple rules imposed on a cubic lattice reproduce the structural descriptors of globular proteins?

A direct way to spot structural features that are universally shared among proteins is to find analogues from simpler condensed matter systems. In the current study, the feasibility of creating ensembles of artificial structures that can automatically reproduce a large number of geometrical and topological descriptors of globular proteins is investigated. Towards this aim, a simple cubic (SC) arrangement is shown to provide the best background lattice after a careful analysis of the residue packing trends from 210 globular proteins. It is shown that a minimalistic set of rules imposed on this lattice is sufficient to generate structures that can mimic real proteins. In the proposed method, 210 such structures are generated by randomly removing residues (beads) from clusters that have a SC lattice arrangement such that all the generated structures have single connected components. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing algorithm, which targets the average radial distribution function (RDF) of 210 globular proteins. The initial and relaxed structures are compared to real proteins via RDF, bond orientational order parameters and several descriptors of network topology. Based on these features, results indicate that the structures generated with 40% occupancy closely resemble real residue networks. The structure generation mechanism automatically produces networks that are in the same topological class as globular proteins and reproduce small-world characteristics of high clustering and small shortest path lengths. Most notably, the established correspondence rules out icosahedral order as a relevant structural feature for residue networks in contrast to other amorphous systems where it is an inherent characteristic. The close correspondence is also observed in the vibrational characteristics as computed from the Anisotropic Network Model, therefore hinting at a non-superficial link between the proteins and the defect laden cubic crystalline order.