Tumor escape from immune elimination: simplified precursor bound cytotoxicity models

In this paper we present a series of models on cytotoxic T-cell activation derived, by successive simplifications, from the model for Tumor Escape from Immune Elimination of Grossman & Berke (1980). In their model Grossman & Berke (1980) investigate the "sneaking through" phenomenon, by which they mean that small tumors grow progressively, medium-sized tumors are rejected and large ones break through again. We define precursor bound cytotoxicity models as systems incapable of infinite proliferation. We show that sneaking through can occur in a broad class of very simple precursor bound cytotoxicity models due to the depletion of the precursor cells. The simplest process by which precursors can be depleted is long-lasting antigenic stimulation. We conclude that in precursor bound cytotoxicity models sneaking through does not need the rather intricate combination of counteracting feedback loops, memory and blocking described by Grossman & Berke (1980).