Ordered appearance of antigenic variants of African trypanosomes explained in a mathematical model based on a stochastic switch process and immune-selection against putative switch intermediates.

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Abstract
Antigenic variation of African trypanosomes results from the periodic activation of a single new variant cell surface glycoprotein (VSG) gene out of a repertoire of about a 1000 VSG genes. In spite of the apparently random genetic basis of the process of antigenic variation, the relapsing parasitemias are characterized by an as yet unexplained order of appearance of major VSG variants. Here we mathematically test hypotheses concerning the blood-based parasitemia. In our model the antigenic switches occur at random at the DNA level. A variable proportion of the switches has a short intermediate phase in which two different VSGs simultaneously occur on the cell surface. We show that, in a theoretical population of 230 single expressor variants in an immunocompetent or in an immunodeficient host, it is not possible to explain the ordered appearance of variants by affecting the growth coefficients of single expressors or double expressors or by affecting the antigen switch probabilities. Rather, a realistic parasitemia can be obtained if the majority of switches has a double expressor switch-intermediate phase and if the double expressors have a differential susceptibility to the immune control. This study is significant in providing a theoretical basis for the ordered appearance of variants and in explaining previously unresolved discrepancies between the rate of appearance of new variants in culture and in vivo. In addition, testable predictions as to the development of the infections, switch rate of variants, fraction of double expressors, and parasite mortality coefficients are generated.