A thermodynamic chromatin polymer model characterizes the epigenetic conditions for Hox collinearity.

Hox genes consist of four clusters, A, B, C, and D, each containing up to 13 paralogous genes. They are linearly arrayed on cluster regions in the same order as their expression timings along the anterior-posterior (A-P) axis development. This correspondence is known as temporal collinearity, and when the expression order of Hox genes is disrupted, the A-P axis is not accurately established. Although essential molecules and genomic regulatory elements for Hox collinearity have been identified, it remains unclear whether they act on individual genes or instead coordinate the cluster-wide sequential activation along the genomic order. To address this question, we developed a theoretical framework based on the statistical thermodynamics of chromatin modeled as a polymer, interpreting collinearity as a sequential opening of nucleosomes along the gene cluster. The model incorporates interactions between nucleosomes and DNA-binding factors, including transcription factors, represented by energy terms for binding and chromatin bridging. This formulation links the thermodynamic stability of chromatin states with the sequential opening process along the Hox clusters. Our model characterized key quantities that determine the order of chromatin opening and revealed intrinsic constraints that limit sequential opening of chromatin, underlying Hox collinearity. Significance statementHox collinearity, a remarkable correspondence between the genomic order and expression timing of Hox genes, provides cells with positional information on the anterior-posterior axis during development. Although essential molecules and genomic regulatory elements have been identified, the mechanism of sequential activation along the genomic order remains elusive. To address this question, we theoretically investigated the epigenetic states of chromatin using a chromatin polymer model in statistical thermodynamics. Our model provides a possible explanation for the sequential activation of the chromatin underlying Hox collinearity. This work bridges developmental genetics and statistical thermodynamics, offering a quantitative framework for understanding gene activation order along the genome.