Boolean logic links chromatin accessibility states to gene expression variability across cell types

Multiomic technologies have enabled simultaneous profiling of chromatin accessibility and gene expression, providing a rich foundation for decoding cis-regulatory logic. However, existing approaches emphasize pairwise correlations and overlook the combinatorial, multilocus accessibility states that govern gene regulation in a context-specific manner. We present ocrRBBR, a computational framework that infers interpretable Boolean rules from combinations of accessible open chromatin regions (OCRs) to explain gene expression variability across diverse cell types. These rules [e.g. $(\lnot OCR_A \wedge OCR_B)\ \text{or}\ (OCR_A \wedge OCR_B)$] capture regulatory logic ranging from synergistic to additive (redundant) enhancer interactions, revealing how OCR combinations drive cell-type-specific gene expression. Applying ocrRBBR to paired ATAC-RNA data, we uncover thousands of Boolean rules linked to both lineage-restricted and broadly expressed genes. We show that cell-type-specific genes rely on fewer but more selective Boolean rules that integrate signals from a larger number of OCRs, including distal enhancers. In contrast, housekeeping genes depend on more numerous, simpler rules that involve fewer OCRs, reflecting a modular and additive regulatory logic. Functional enrichment analysis reveals that genes regulated by cell-type-specific rules are enriched for lineage-defining pathways. Together, ocrRBBR offers a mechanistically interpretable and biologically grounded framework for decoding combinatorial cis-regulatory logic from multimodal genomic data.