EXPLANATION OF THE REACTION OF MONOCLONAL ANTIBODIES WITH CANDIDA ALBICANS CELL SURFACE IN TERMS OF COMPOUND POISSON PROCESS

Abstract

Surprisingly, still very little is known about the mathematical modeling of peaks in the binding affinities distribution function. In general, it is believed that the peaks represent antibodies directed towards single epitopes. In this paper, we refer to fluorescence flow cytometry experiments and show that even monoclonal antibodies can display multi-modal histograms of affinity distribution. This result take place when some obstacles appear in the paratope–epitope reaction such that the process of reaching the specific epitope ceases to be a point Poisson process. A typical example is the large area of cell surface, which could be unreachable by antibodies leading to the heterogeneity of the cell surface repletion. In this case the affinity of cells to bind the antibodies should be described by a more complex process than the pure-Poisson point process. We suggested to use a doubly stochastic Poisson process, where the points are replaced by a binomial point process resulting in the Neyman distribution. The distribution can have a strongly multinomial character, and with the number of modes depending on the concentration of antibodies and epitopes. All this means that there is a possibility to go beyond the simplified theory, one response towards one epitope. As a consequence, our description provides perspectives for describing antigen–antibody reactions, both qualitatively and quantitavely, even in the case when some peaks result from more than one binding mechanism.