Quantitative study of the control of HIV-1 gene expression

The biochemical processes that together determine the expression of a human immunodeficiency virus (HIV) provirus integrated into the genome of a host cell are translated into mathematical form to give a dynamic model that can be examined quantitatively. The model includes the contribution of cellular enhancers to transcription of the provirus, the subsequent splicing of the full length transcript, the nuclear export of transcripts and the translation of tat and rev mRNA to produce viral control proteins. The model is completed by the formulation of the feedback effects of Tat protein on transcription and translation and the feedback effect of Rev protein on nuclear export. Initial parameter values are estimated from available experimental data. The model is a formalization of a commonly accepted scheme, but one that has only previously been considered qualitatively. Quantification requires more explicit assumptions, but then allows the precise determination of resultant model behaviour and the stringent comparison of behaviour with experimental observation. Least squares matching of model behaviour to the observed appearance of mRNA in infected H9 cells gives very close agreement and, in particular, supports recent proposals concerning multimerization of the Rev protein. General quantitative characteristics of dynamic and steady-state behaviour of the model are determined and discussed; their possible contribution to the latency of HIV infection is considered.