Salt-bridge angle

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salt bridge : normal define ( short-range)

long rang salt-bridge : Centroids of the side-chain charged
                                    group is greater than 4 A


A pair of oppositely charged residues, Asp or Glu with Arg, His, or Lys, is considered an ion pair. The geometrical orientation of the side-chain charged groups in the ion-pairing residues with respect to each other is characterized in terms of
1) the distance (r) between the side-chain charged group centroids and
2) the angular orientation (θ) of the side-chain charged groups in the two ion-pairing residues.
This is the angle between two unit vectors. Each unit vector joins a C^α atom and a side-chain charged group centroid in a charged residue. Fig. 1 presents a schematic diagram.





Figure 1. A schematic diagram characterizing geometrical orientation of the side-chain charged residues in an ion pair. Ion pair geometry can be measured in terms of r and θ. r is the distance in angstroms between the centroids, C1 and C2, of the side-chain charged groups in the ion-pairing residues 1 and 2. θ, in degrees, is the angle between two unit vectors C1^αC1 and C2^αC2. Note that we actually take the supplemental angle.


 

Figure 3. The spatial orientations of side-chain charged groups in 1174 ion pairs in 14 NMR conformer ensembles. The number of unique ion pairs is 22. The ion pair types are color coded. Salt bridges are in blue, N_O bridges in green, and longer range ion pairs in red. 

The geometry of an ion pair can be characterized in terms of distance between its side-chain charged group centroids (r (Å)) and angular orientation of its side-chain charged groups (θ (°)). In this polar plot, radii of the concentric circles represent different r (Å) values. 

The dotted lines connecting the circles denote different θ (°) values. Additional details are given in Materials and Methods. Most of the ion pairs with r ≤ 5 Å are stabilizing. In contrast, most of the ion pairs with r > 5 Å are destabilizing.


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Salt Bridge Stability in Monomeric Proteins

The angular orientation of the side-chain charged groups in the two salt-bridging residues is computed as the angle between two unit vectors. Each unit vector joins a Ca atom and a side-chain charged group centroid in a salt- bridging residue. 

The angle between the vectors that join the Ca atoms and the side-chain charged group centroids is 46.3 度 , resulting in a very good bridge geometry.

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To resolve these different findings, we performed analysis of the geometries of salt bridges in a representative set of structures from the PDB and found that over 87% of all complex salt bridges anchored by Arg/Lys have a geometry such that the angle formed by their Cα atoms, Θ, is < 90°.

This preferred geometry is observed in the two reported instances when the energetics of complex salt bridge formation is cooperative, while in the reported anti-cooperative complex salt bridge, Θ is close to 160°. Based on these observations, we hypothesized that complex salt bridges are cooperative for Θ < 90° and anti-cooperative for 90° < Θ < 180°.






Cartoon representation of the spatial arrangement of complex salt bridges


 

Cartoon illustrating a possible source of cooperativity in complex salt bridges