A Markov model for the assembly of heterochromatic regions in position effect variegation

Here we give a mathematical model for the assembly of heterochromatic regions at the heterochromatin-euchromatin interface in position effect variegation. This probabilistic model predicts the proportions of cells in which a gene is active in cells with one and two variegating chromosomes. The association of heterochromatic proteins to form remodeled chromatin following DNA replication is mainly described by accumulation independent conditional probabilities. These probabilities are conditional on the boundary of the sites to which the proteins can bind; they give the relative attractiveness of the sites to a protein complex chosen at random from a pool of available complexes. The number of complexes available is assumed to be limited and rates of reaction are implicitly modeled by the conditional probabilities. In general, these conditional probabilities are not known, however, they can be experimentally determined. By comparing double variegation situations to single variegation, this model shows that there may be an effect on the expression of reporter genes located near the interfaces due to different sites competing for heterochromatic proteins. In addition, this model suggests that in some cases the attractiveness of sites may change in the presence of other chemical species. Consequently, the model distinguishes between two sorts of data obtained from competition experiments using position effect variegation. The two sorts of data differ as to whether there is a change in the attractiveness of sites in addition to an effect from different sites competing for the same constituents of heterochromatin. Subject to the fact that some of its parameters are not known precisely, this model replicates data from several experiments and can give predictions in other cases.