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

Ligand recognition by the human /{beta} T-cell antigen receptor (TCR) heterodimer protein, unlike the surface immunoglobulin (sIg) B-cell receptor, is not governed by relative binding affinity. Its interaction with the peptide (p) plus major histocompatibility complex (MHC) protein (abbrev. pMHC) likely involves some different molecular mechanism linking pMHC binding to T-cell functions. Recent analytical geometry of TCR:pMHC-II solved crystallographic structures (n = 40) revealed that each variable (V)-domain is bound in similar, yet mathematically unique orientations to its target pMHC groove. The relative position of the central cysteine of each V-domain was examined by multivariable calculus in spherical coordinates, where a simple volume element (dV) was found to describe clonotypic geometry with pMHC-II. Here, the study was expanded to include TCR:pMHC-I structures, and to model a physical mechanism, specifically involving the two directionally opposed inclined planes (IP) manifest by the two major -helices prominent in both MHC-I and MHC-II proteins. Calculations for rotational torque of each V-domain, together with acceleration up and down the slopes of both MHC -helices were used to estimate the time a given V-domain spends sliding down its cognate MHC IP. This V-domain rotation/sliding mechanism appears to be quantitatively unique for each TCR:pMHC V-domain (n = 40). However, there is an apparent and common dichotomy between the mobility of each V-domain with respect to the two classes of MHC proteins. Evolutionary motifs in the MHC helices support that the V-domains negotiate the opposed inclined planes of pMHC ligands in clonotypic fashion. Thus, this model is useful in understanding how mechanical forces are linked to TCR function.