Degranulation of Human Basophils: Quantitative Analysis of Histamine Release and Desensitization, Due to a Bivalent Penicilloyl Hapten

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Abstract
We present a quantitative model of histamine release from human basophils due to the symmetric bivalent hapten, Bis benzylpencilloyl 1,6 diaminohexane, (BPO)2. The major elements of model are: 1) The histamine content of basophils is divided into a large number of discrete and quasi-independent “quanta.” 2) A certain fraction of the quanta in a population of basophils are nonreleasable. 3) Release of the contents of a quanta is a stochastic event. 4) The binding and cross-linking reaction between (BPO)2 and cell surface IgE approaches thermal equilibrium on a time scale that is very short compared to the time scale of histamine release from or desensitization of basophils. 5) The probability per unit time of the release event, PR, is a function of the extracellular calcium concentration [Ca]ex, and of the number of cross-linked IgE molecules per cell, Xpoly. In addition, the functional dependence of PR on Xpoly for fixed [Ca]ex is sigmoid, and the dependence of PR on [Ca]ex is such that PR → 0 as [Ca]ex → 0 for all values of Xpoly. 6) Antigen-specific IgE molecules and/or their associated Fc receptors are inactivated at a rate that is a saturable function of Xpoly. Furthermore, this process of inactivation is not dependent on the extracellular calcium concentration. The model is tested by carrying out a detailed fitting to histamine release data obtained by using cells from a single donor. Good agreement between theory and experiment is obtained, and all the parameters of the model are determined. The ways in which the model can be extended to include systems more complex than the (BPO)2 system are briefly discussed.