Crosslinking of membrane immunoglobulins and B-cell activation: a simple model based on percolation theory

In immune network models it is assumed that membrane immunoglobulin (mIg) crosslinking leads to B-cell activation. To analyse further the implications of this idea, a model of B-cell activation by ligand-induced mIg crosslinking in the absence of cell-to-cell interactions is proposed. The present model, based on a simple crosslinking mechanism previously proposed by other authors, assumes that activation of B-cells is possible once crosslinks of mIgs percolate and that percolation of crosslinks can only happen within a relatively short time tau. Given a lattice (regular or not), a molecular cluster is said to percolate or to become a percolating cluster if it spans the whole lattice (this is the case, for instance, of a polymer in a gel phase). From this model of B-cell activation we define the activation function fa (LK) as the fraction of B-cells activated after tau minutes of interaction with a ligand at concentration L and with affinity K. Numerical calculations show that, for current estimates of kinetic constants involved in the interaction of a given ligand with a B-cell clone, the activation function fa shifts when k-, the dissociation rate constant, is varied below 10(-3) s-1, this shift being linearly proportional to the variation of k-. This result contradicts and, therefore, challenges the assumption in immune network models that the activation function is identical for all ligands. This is important because the behaviour of at least some of those immune network models is quite sensitive to the relative values of the activation function thresholds.