Abstract
Protein backbones occupy diverse conformations, but compact metrics to describe such conformations and transitions between them have been missing. This report re-introduces the Ramachandran number (ℛ) as a residue-level structural metric that could simply the life of anyone contending with large numbers of protein backbone conformations (e.g., ensembles from NMR and trajectories from simulations). Previously, the Ramachandran number (ℛ) was introduced using a complicated closed form, which made the Ramachandran number difficult to implement. This report discusses a much simpler closed form of ℛ that makes it much easier to calculate, thereby making it easy to implement. Additionally, this report discusses how ℛ dramatically reduces the dimensionality of the protein backbone, thereby making it ideal for simultaneously interrogating large numbers of protein structures. For example, 200 distinct conformations can easily be described in one graphic using ℛ (rather than 200 distinct Ramachandran plots). Finally, a new Python-based backbone analysis tool—BackMAP—is introduced, which reiterates how ℛ can be used as a simple and succinct descriptor of protein backbones and their dynamics.
Highlights
Proteins are a class of biomolecules unparalleled in their functionality (Berg, Tymoczko & Stryer, 2010)
This paper shows how the Ramachandran number is both compact enough and informative enough to generate immediately useful graphs (MAPs) of a dynamic protein backbone
0.3 ala cys asp glu phe gly his ile lys leu met asn pro gln arg ser thr val trp tyr α helix share identical backbone connectivity, the analysis described below could be applied to both peptides and peptoids
Summary
Proteins are a class of biomolecules unparalleled in their functionality (Berg, Tymoczko & Stryer, 2010). It is evident that prolines dramatically modify the structure of an amino acid preceding it (compared to average behavior of amino acids in Fig. 7B), while residues following glycines have a higher prevalence of R > 0.5 conformations (both trends are indicated by small arrows) Such trends, while previously discovered (see text), would not be accessible when naïvely considering Ramachandran plots because one would require 400 (20 Â 20) distinct Ramachandran plots to compare. Amino acids following glycines appear to have their structures modified (Fig. 8D; upward arrow) Note that these results are not new, and it has already been confirmed that, for example, nearest neighbors affect the conformational behavior of an amino acid as witnessed within Ramachandran plots (Ting et al, 2010), and proline changes the backbone conformation of the preceeding residue (Gunasekaran et al, 1998; Ho & Brasseur, 2005). Select color scheme (color map) In addition to custom colormaps listed one can use traditional colormaps available at matplotlib.org (e.g., “Reds” or “Reds_r”)
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