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Abstract Key functions of antibodies, such as viral neutralisation, depend on high-affinity binding. However, viral neutralisation poorly correlates with antigen affinity for reasons that have been unclear. Here, we use a new mechanistic model of bivalent binding to study  >45 patient-isolated IgG1 antibodies interacting with SARS-CoV-2 RBD surfaces. The model provides the standard monovalent affinity/kinetics and new bivalent parameters, including the molecular reach: the maximum antigen separation enabling bivalent binding. We find large variations in these parameters across antibodies, including reach variations (22–46 nm) that exceed the physical antibody size (~15 nm). By using antigens of different physical sizes, we show that these large molecular reaches are the result of both the antibody and antigen sizes. Although viral neutralisation correlates poorly with affinity, a striking correlation is observed with molecular reach. Indeed, the molecular reach explains differences in neutralisation for antibodies binding with the same affinity to the same RBD-epitope. Thus, antibodies within an isotype class binding the same antigen can display differences in molecular reach, substantially modulating their binding and functional properties. 

T cells use their T cell receptors (TCRs) to discriminate between lower-affinity self and higher-affinity non-self peptides presented on major histocompatibility complex (pMHC) antigens. Although the discriminatory power of the TCR is widely believed to be near-perfect, technical difficulties have hampered efforts to precisely quantify it. Here, we describe a method for measuring very low TCR/pMHC affinities and use it to measure the discriminatory power of the TCR and the factors affecting it. We find that TCR discrimination, although enhanced compared with conventional cell-surface receptors, is imperfect: primary human T cells can respond to pMHC with affinities as low as K D ∼ 1 mM. The kinetic proofreading mechanism fit our data, providing the first estimates of both the time delay (2.8 s) and number of biochemical steps (2.67) that are consistent with the extraordinary sensitivity of antigen recognition. Our findings explain why self pMHC frequently induce autoimmune diseases and anti-tumour responses, and suggest ways to modify TCR discrimination.