Where do Proteins Fit in the Structural Classification of Condensed Matter?

Abstract

In this work, we use Bond Orientational Order Parameters(BOOP)[1] as the universal descriptors of local packing in proteins. To classify proteins as a distinct family, this local view is combined with a global one which is portrayed by translational order parameters and the free volume distribution. We find that the organization of first coordination shells carries strong signatures of close packed crystalline order in BOOP space. We also show that proteins exhibit no icosahedral bond orientational order at the heavy-atom level and at coarse grained level where residue packing is considered. Close packedness is characterized by the space filling ratio of 0.74048 and is achieved through stacking of hexagonal arrays. Depending on stacking order, this creates Face Centered Cubic(FCC) and Hexagonal Close Packed(HCP) crystals as well as an infinite variety of FCC-HCP mixtures. Using radial distribution formalism, we show that protein-crystal correspondence is strictly local and it extends up-to second nearest neighbors. Due to local correspondence, arbitrarily stacked systems capture protein properties as accurate as ideal crystals.In passing from bulk crystals to proteins we propose a robust route which randomly distributes free volume pockets in a close packed lattice. Remarkably, our results suggests that such protein-like structures automatically possess an exponential size distribution of free volume. This is in accordance with Cohen-Turnbull theory of dense liquids and glasses[2]. We conclude that proteins constitute a unique glassy phase with no icosahedral order.1. Steinhardt, P.J., D.R. Nelson, and M. Ronchetti, Bond-orientational order in liquids and glasses. Physical Review B, 1983. 28(2): p. 784.2. Cohen, M.H. and D. Turnbull, Molecular Transport in Liquids and Glasses. Vol. 31. 1959: AIP. 1164-1169.