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 proper analogues from simpler condensed matter systems. In most cases, sphere-packing arguments provide a straightforward route for structural comparison, as they successfully characterize a wide array of materials such as close packed crystals, dense liquids, and structural glasses. 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 proteins. It is shown that a minimalistic set of ground 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 until a predetermined residue concentration is achieved. All generated structures are checked for residue connectivity such that a path exists between any two residues. Two additional sets are prepared from the initial structures via random relaxation and a reverse Monte Carlo simulated annealing (RMC-SA) 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 via the proposed method closely resemble real residue networks. The broad correspondence established this way indicates a non-superficial link between the residue networks and the defect laden cubic crystalline order. The presented approach of  identifying a minimalistic set of operations performed on a target lattice such that each resulting cluster possess structural characteristics largely indistinguishable from that of a coarse-grained globular protein  opens up new venues in structural characterization, native state recognition, and rational design of proteins.