CROSS-LINKING OF MEMBRANE IMMUNOGLOBULINS AND B-CELL ACTIVATION - A SIMPLE-MODEL BASED ON PERCOLATION THEORY

In immune network models it is assumed that membrane immunoglobulin (m Ig) crosslinking leads to B-cell activation. To analyse further the im plications of this idea, a model of B-cell activation by ligand-induce d mIg crosslinking in the absence of cell-to-cell interactions is prop osed. The present model, based on a simple crosslinking mechanism prev iously proposed by other authors, assumes that activation of B-cells i s possible once crosslinks of mIgs percolate and that percolation of c rosslinks 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 f(a)(LK) as th e fraction of B-cells activated after tau minutes of interaction with a ligand at concentration L and with affinity K. Numerical calculation s show that, for current estimates of kinetic constants involved in th e interaction of a given ligand with a B-cell clone, the activation fu nction f(a) shifts when k-, the dissociation rate constant, is varied below 10(-3) s-1, this shift being linearly proportional to the variat ion of k-. This result contradicts and, therefore, challenges the assu mption in immune network models that the activation function is identi cal for all ligands. This is important because the behaviour of at lea st some of those immune network models is quite sensitive to the relat ive values of the activation function thresholds.