Maximum entropy models for patterns of gene expression*

The expression level of the genes in a cell determines at least in part its state and behavior. Recent advances in experimental techniques allow to count with high precision the copies of several species of labeled MRNAs in many cells at the same time. The cell-to-cell correlations of these expressions are typically used to cluster cells into classes and subclasses.

We use the available data to write models for the number of copies of mRNAs and then study the statistical properties of the resulting distribution. In particular, following a maximum entropy approach, we can write the most general distribution compatible with some chosen constraints and check its goodness by comparing unconstrained quantities. Under some hypotheses, we get a multimodal distribution with different attraction basins. We compare these basins with the results of traditional cell clusterization.