Mathematical models of the fate of lymphoma B cells after antigen receptor ligation with specific antibodies.

We formulate models of the mechanism(s) by which B cell lymphoma cells stimulated with an antibody specific to the B cell receptor (IgM) become quiescent or apoptotic. In particular, we aim to reproduce experimental results by Marches et al. according to which the fate of the targeted cells (Daudi) depends on the levels of expression of p21(Waf1) (p21) cell-cycle inhibitor. A simple model is formulated in which the basic ingredients are p21 and caspase activity, and their mutual inhibition. We show that this model does not reproduce the experimental results and that further refinement is needed. A second model successfully reproduces the experimental observations, for a given set of parameter values, indicating a critical role for Myc in the fate decision process. We use bifurcation analysis and objective sensitivity analysis to assess the robustness of our results. Importantly, this analysis yields experimentally testable predictions on the role of Myc, which could have therapeutic implications.