Maximum entropy models for patterns of gene expression

TL;DR

This paper applies maximum entropy models, specifically the Ising model, to analyze high-dimensional gene expression data from single cells, providing a probabilistic framework that captures gene interactions and cell classification.

Contribution

It introduces a maximum entropy approach to model gene expression patterns, capturing pairwise correlations and enabling cell classification without traditional clustering.

Findings

The Ising model accurately predicts higher-order gene expression statistics.

Cell states have multiple local maxima, aiding in cell classification.

The approach supports the idea that cell classes emerge from gene interactions.

Abstract

New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering or low-dimensional projections. Here we use the principle of maximum entropy to obtain a probabilistic description that captures the observed presence or absence of mRNAs from hundreds of genes in cells from the mammalian brain. We construct the Ising model compatible with experimental means and pairwise correlations, and validate it by showing that it gives good predictions for higher-order statistics. We notice that the probability distribution of cell states has many local maxima. By labeling cell states according to the associated maximum, we obtain a cell classification that agrees well with previous results that use traditional clustering techniques. Our results provide quantitative descriptions of gene expression statistics and interpretable criteria for defining cell classes, supporting the hypothesis that cell classes emerge from the collective interaction of gene expression levels.