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The binding of multiple transcription factors (TFs) to genomic enhancers drives gene expression in mammalian cells 1 . However, the molecular details that link enhancer sequence to TF binding, promoter state and transcription levels remain unclear. Here we applied single-molecule footprinting 2,3 to measure the simultaneous occupancy of TFs, nucleosomes and other regulatory proteins on engineered enhancer-promoter constructs with variable numbers of TF binding sites for both a synthetic TF and an endogenous TF involved in the type I interferon response. Although TF binding events on nucleosome-free DNA are independent, activation domains recruit cofactors that destabilize nucleosomes, driving observed TF binding cooperativity. Average TF occupancy linearly determines promoter activity, and we decompose TF strength into separable binding and activation terms. Finally, we develop thermodynamic and kinetic models that quantitatively predict both the enhancer binding microstates and gene expression dynamics. This work provides a template for the quantitative dissection of distinct contributors to gene expression, including TF activation domains, concentration, binding affinity, binding site configuration and recruitment of chromatin regulators., Competing Interests: Competing interests: W.J.G. is a consultant and equity holder for 10x Genomics, Guardant Health, Quantapore and Ultima Genomics, co-founder of Protillion Biosciences and is named on patents describing ATAC–seq. L.B. is a co-founder of Stylus Medicine and a member of its scientific advisory board. All other authors declare no competing interests., (© 2024. The Author(s), under exclusive licence to Springer Nature Limited.)

Genome-wide association studies (GWAS) have identified thousands of noncoding loci that are associated with human diseases and complex traits, each of which could reveal insights into the mechanisms of disease 1 . Many of the underlying causal variants may affect enhancers 2,3 , but we lack accurate maps of enhancers and their target genes to interpret such variants. We recently developed the activity-by-contact (ABC) model to predict which enhancers regulate which genes and validated the model using CRISPR perturbations in several cell types 4 . Here we apply this ABC model to create enhancer-gene maps in 131 human cell types and tissues, and use these maps to interpret the functions of GWAS variants. Across 72 diseases and complex traits, ABC links 5,036 GWAS signals to 2,249 unique genes, including a class of 577 genes that appear to influence multiple phenotypes through variants in enhancers that act in different cell types. In inflammatory bowel disease (IBD), causal variants are enriched in predicted enhancers by more than 20-fold in particular cell types such as dendritic cells, and ABC achieves higher precision than other regulatory methods at connecting noncoding variants to target genes. These variant-to-function maps reveal an enhancer that contains an IBD risk variant and that regulates the expression of PPIF to alter the membrane potential of mitochondria in macrophages. Our study reveals principles of genome regulation, identifies genes that affect IBD and provides a resource and generalizable strategy to connect risk variants of common diseases to their molecular and cellular functions.