The Ramachandran Number: An Order Parameter for Protein Geometry

PLoS One. 2016 Aug 4;11(8):e0160023. doi: 10.1371/journal.pone.0160023. eCollection 2016.

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.

MeSH terms

  • Algorithms*
  • Molecular Dynamics Simulation
  • Nanostructures / chemistry
  • Peptoids / chemistry
  • Protein Structure, Secondary
  • Proteins / chemistry*

Substances

  • Peptoids
  • Proteins

Grants and funding

RVM and SW were supported by the Defense Threat Reduction Agency under contract no. IACRO-B0845281. This work was done at the Molecular Foundry at Lawrence Berkeley National Laboratory (LBNL), supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.