title: The Ramachandran Number: An Order Parameter for Protein Geometry.
abstract: Three-dimensional protein structures usually contain regions of local order, called secondary structure, such as α-helices and β-sheets. Secondary structure is characterized by the local rotational state of the protein backbone, quantified by two dihedral angles called ϕ and ψ. Particular types of secondary structure can generally be described by a single (diffuse) location on a two-dimensional plot drawn in the space of the angles ϕ and ψ, called a Ramachandran plot. By contrast, a recently-discovered nanomaterial made from peptoids, structural isomers of peptides, displays a secondary-structure motif corresponding to two regions on the Ramachandran plot [Mannige et al., Nature 526, 415 (2015)]. In order to describe such 'higher-order' secondary structure in a compact way we introduce here a means of describing regions on the Ramachandran plot in terms of a single Ramachandran number, [Formula: see text], which is a structurally meaningful combination of ϕ and ψ. We show that the potential applications of [Formula: see text] are numerous: it can be used to describe the geometric content of protein structures, and can be used to draw diagrams that reveal, at a glance, the frequency of occurrence of regular secondary structures and disordered regions in large protein datasets. We propose that [Formula: see text] might be used as an order parameter for protein geometry for a wide range of applications.
authors.affiliation: Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, United States of America.
authors.forename: Ranjan V
authors.initials: RV
authors.lastname: Mannige
authors.affiliation: Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, United States of America.
authors.forename: Joyjit
authors.initials: J
authors.lastname: Kundu
authors.affiliation: Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA, United States of America.
authors.forename: Stephen
authors.initials: S
authors.lastname: Whitelam
mesh_terms: D000465:Algorithms; D056004:Molecular Dynamics Simulation; D049329:Nanostructures / Q000737:chemistry; D034444:Peptoids / Q000737:chemistry; D017433:Protein Structure, Secondary; D011506:Proteins / Q000737:chemistry*
chemical_list: D034444:Peptoids; D011506:Proteins