The underlying assumption of the definition of the elbow angle is that the superposition of the VL onto VH as well as CL onto CH1 is predominantly a two-fold rotation. In this case, the directional cosine matrix resembles a pure two fold rotation with relatively small non-diagonal components and the Euler axis is dominated by a correspondingly large principal component. In more than 90% of Fabs we examined, the assumption of near-twofold superposition operations is justified, and the elbow angle concept applicable.
If additional rotational components become significant in the domain superpositions, the Euler axes can deviate from the 2-fold to a point where the two axes become non-opposing, and the calculated elbow angle is less than 90°. Even in these cases a complement (180 - a) can be interpreted as elbow angle, but such Fabs need to be individually examined to decide whether the elbow angle definition is still meaningful.
Please read the WARNING sections which are issued in case inconsistencies in the input are detected. During the calculation as described above, the program checks for format errors and issues warnings at several levels for unexpected or borderline behavior. Warnings include large coordinate r.m.s.d.’s on superposition (>3.5Å), significant deviations from pseudo-twofold rotation axes, and occurrence of parallel superposition axes. If the final H-chain sequence alignment drops below 30%, an erroneously swapped assignment of light and heavy chains should be suspected. For example, mouse Fab H-chains are around 90%, and human H-chains around 60% identical to 1BBD.
Although elbow angles tend to be reported to a precision of one decimal, the choice of domain limits and superposition procedure places limitations on the absolute accuracy of the elbow angles. The superposition results can vary depending how the domain limits are defined, and depend on the alignment procedure used. With default domain limits (VL ≤ L107 < CL and VH ≤ H113 < CH, residues in Kabat numbering), we compared the elbow angles obtained using Kabat renumbered Fab coordinates, and a fixed set of structurally conserved residues for the superposition (using the program OVRLAP) with those computed using our web application based on automated LGA alignments and original numbering from the PDB. The angles computed using the different methods (n=167) agreed with a mean of -0.12º and a standard deviation of no more than 1.1º. It is interesting to note that molecular dynamics simulations of Fab domain movement in solution show periodic hinge bending fluctuations, with a 2-3o root mean square deviation (r.m.s.d.) in elbow angle. Presence of such dynamic fluctuations indicates that the reported precision to a tenth of a degree in the elbow angles is indeed overly optimistic, whereas the differences in calculated elbow angles based on different domain superposition techniques are well within the range of the dynamic elbow flexibility. It would therefore seem consistent that a difference in elbow angles below about 2-3º should not be considered significant. In addition, to what degree crystal packing additionally affects or limits the elbow angles is uncertain. Several examples exist where multiple Fabs in the asymmetric crystallographic unit display significantly different elbow angles up to 40o ( 2GFB, 1JNH, 1CIC, 1D5B, 1NJ9 may serve as examples), with an average deviation of about 2.2o, again in agreement with our significance limit of about 2-3o. However, even within the limits of accuracy discussed above, the elbow angles are still useful as measures for significant hinge flexibility and for classification purposes.