6th ESACP Congress, Heidelberg, April 7-11, 1999

A147
MATHEMATICAL MODEL OF EXPRESSION OF THE ACTIVATION MOLECULES
Vassilyev OS 1, Glasko VB 2, Kazaryan P 2, Rodionov V 3

1) Central Institute of Traumatology and Orthopaedy, 2) Moscow State University, 3) State Scientific Center, Institute of Immunology, Moscow, Russia

Flow cytometry histograms of activation molecules (HLA-DR) on CD4 T-lymphocytes exhibit a high level of dispersion. The existing method of evaluation consists in counting the number of "positive cells", that is, to calculate the area under the histogram. Much useful information is lost in this way. A model for a more accurate way of evaluation of these complex histograms was developed. The key to the model is the function of the kinetics of loss of activation molecules on an average activated T-cell. Knowing this function, the processes of activation can be more precisely estimated from the histograms. In case of HLA-DR molecules on T-lymphocytes one observes in peripheral blood either few cells with high HLA-DR expression or many cells with lower HLA-DR expression. Furthermore high levels of HLA-DR expression occur in tissue lymphocytes as compared to peripheral blood T-lymphocytes. Based on experimental observations, the model for the loss of activation molecules can be formulated as an autonomous system: dn/dA = {[ L - k dF(A)/dt] / F(A)} n The solution, n=n(A), is corresponds to the "theoretical histogram". It can be calculated and be compared with the experimental histogram for each individual patient. By such comparisons, the state of a patient is characterized by the pair (k,F(A)), which under known conditions provides parameters for the dynamics of activation molecules on T-cell membranes as derived from the degree of dispersion of the flow cytometric cell clusters.