CDR3 binding chemistry controls TCR V-domain rotational probability and germline CDR2 scanning of polymorphic MHC

Dichotomy in TCR V-domain dynamics binding the opposed inclined planes of pMHC-II and pMHC-I α-helices

“…The equation series used to calculate a particular V-domain torque (τ θ ) is shown in Figure 1B & D through Figure 4B & D, where the general equations are described below. Firstly, the basic parameters for each were measured from the appropriate PDB file in VMD (https://www.ks.uiuc.edu/) using fixed a.a. positions for each variable, as previously described [11,25]. Briefly, mass (M) was computed from the a.a. sequence of each V-domain starting at position-1 in the crystal structure through the F-G-R-G motif near the end of the 110 a.a. domain using the ExPASy ProtPram algorithm (https://web.expasy.org/).…”

“…Briefly, mass (M) was computed from the a.a. sequence of each V-domain starting at position-1 in the crystal structure through the F-G-R-G motif near the end of the 110 a.a. domain using the ExPASy ProtPram algorithm (https://web.expasy.org/). The distance rho (ρ) can be seen to specify the shape of a 'cone-slice' volume element (dV) in Figure 1 through Figure 4 (lime green cone slice), where the triple-integral equation [11] is shown in the captions to Table 1 and Table 2 (see also, Materials and Methods). Crucially, the distance, rho (in angstroms, Å), is used in the trigonometric determination of the radius (r) of each uniquely shaped V-domain cone: ൌ sin ߶ ሺߩሻ [ref.…”

“…‫݊݅ݏ‬ ݀ߩ ݀θ ݀ {7} # kDa (from V-domain a.a. sequence using ExPASy Protparam; http://web.expasy.org/protparam). 1 measured distance from MHC α-helix a.a. to V-domain C21/22/23, as described (in angstroms, Å) [11]. 2 measured angle from fixed MHC α-helix a.a. to V-domain C21/22/23, as described (in degrees, °) [11].…”

“…4 ࣘ ൌ 180°ԟ ߣ (degrees, °) [11]. 5 ൌ sin߶ ሺߩሻ (angstroms, Å) [11]. 6 ‫ܞ‬ θ ൌ π/4⋅ ‫/ݎ‬μs (Å/μs) 7 τθ ൌ ‫ܫ‬ ᇱ ⋅ ߥ θ (kDa⋅Å/μs 2 ) 8 τ ԡ ൌ ‫ߛ݊݅ݏ‬ ‫ݎ‪ሺ‬‬ ߛ ଶ ሻ⋅ τθ (kDa⋅Å/μs 2 ) {1} (which was not certified by peer review) is the author/funder.…”

“…A dichotomy was revealed by the calculations of these dynamics for Vα versus Vβ binding pMHC-I versus pMHC-II ligands. As such, a novel path forward is defined for understanding evolved T-cell functions; this theory entails with prevailing evidence that relative TCR binding affinity is not the mechanism of TCR antigen specificity [11,16,17,20,24].…”