Abstract
Since the pioneering works of Berg and Purcell, discriminating between diffusion followed by binding has played a central role in understanding cell signaling. B-cell receptors (BCR) and antibodies (Ab) challenge that simplified view as binding to antigen follows after a chain of diffusion and rotations, including whole molecule rotation, and independent tilts and twists of their Fab arms due to their Y-shaped structure and flexibility. In this paper, we combine analytical calculations with Brownian simulations to derive the first-passage times due to these three rotations positioning the Fab paratopes at a proper distance and orientation required for antigen binding. Applying these estimations and those for 2-dimensional (2D) and 3D translational diffusion of, respectively, BCRs and Abs, we evidence that measuring Ab-Ag effective kinetic binding rates using experimental methods in which the analyte is in solution gives values proportional to the intrinsic binding rates, k+ and k−, only for values of k+ up to 109 s−1, beyond which a plateau of the effective 3D on rate between 108 M−1s−1 and 109 M−1s−1 is attained. Moreover, for BCR-Ag interactions, the effective 2D on and off binding rates can be inferred from the corresponding effective 3D on and off rates only for values of effective 3D on rates lower than 106 M−1s−1. This is highly relevant when one seeks to relate BCR-antigen binding strength and B cell response, particularly during germinal center reactions. Thus, there is an urgent need to revisit our current understanding of the BCR-antigen kinetic rates in germinal centers using state-of-the-art experimental assays for BCR-Ag interactions.
Significance Statement In germinal centers, binding between BCRs and antigen (Ag) tethered on the membrane of follicular dendritic cells occurs via two-dimensional (2D) membrane-to-membrane interactions. In contrast, in in vitro assays antibody (Ab)-antigen interactions occur with one component in solution. Structurally, there are large qualitative and quantitative differences between BCR-Ag 2D and Ab-Ag 3D translational and rotational diffusion processes, with the 2D translational diffusion being about 1000-fold lower than the 3D one. Moreover, the effective binding kinetics of both BCR-Ag and Ab-Ag interactions strongly deviate from the intrinsic molecular on and off rates. Here we expose this mismatch and, performing numerical and analytical calculations, quantify the ranges for which the experimental in-vitro data is informative on the BCR-Ag binding strength.
Competing Interest Statement
The authors have declared no competing interest.
Footnotes
New figures 3 and 4. New “inverse” method to quantify the range of validity of SPR experiments and its relevance to BCR-Ag in germinal centers. New table 2. Extended supplementary material. Extensive rewriting.
