The clustering of B-cell receptor (BCR) molecules and the formation of the protein segregation structure known as the "immunological synapse" at the contact region between B cells and antigen presenting cells appears to precede antigen (Ag) uptake by B cells. The mature B-cell synapse is characterized by a central cluster of BCR/Ag molecular complexes surrounded by a ring of LFA-1/ICAM-1 complexes. In this study, we investigate the biophysical mechanisms that drive immunological synapse formation in B cells by means of Monte Carlo simulation. Our approach simulates individual reaction and diffusion events on cell surfaces in a probabilistic manner with a clearly defined mapping between our model's probabilistic parameters and their physical equivalents. Our model incorporates the bivalent nature of the BCR as well as changes in membrane shape due to receptor-ligand binding. We find that differences in affinity and bond stiffness between BCR/Ag and LFA-1/ICAM-1 are sufficient to drive synapse formation in the absence of membrane deformation. When significant membrane deformation occurs as a result of receptor-ligand binding, our model predicts the affinity-dependent mechanism needs to be complemented by a BCR signaling-driven shift in LFA-1 affinity from low to high in order for synapses to form.