Lymphocytes must proliferate and differentiate in response to low concentrations of a vast array of antigens. The requirements of broad specificity and sensitivity conflict because the former is met by low-affinity antigen receptors, which precludes achieving the latter with high-affinity receptors. Coligation of the membrane protein CD19 with the antigen receptor of B lymphocytes decreased the threshold for antigen receptor-dependent stimulation by two orders of magnitude. B lymphocytes proliferated when approximately 100 antigen receptors per cell, 0.03 percent of the total, were coligated with CD19. The B cell resolves its dilemma by having an accessory protein that enables activation when few antigen receptors are occupied.