Hierarchical bounds on RNA–chromatin statistical dependence across cellular states in paired single-cell multiome data

Abstract Understanding how transcriptional output and chromatin accessibility coordinate across cellular states remains a central challenge in multimodal single-cell biology. Here, we establish explicit hierarchical empirical bounds on RNA–chromatin statistical dependence using a strictly falsification-driven, information-theoretic analysis of paired RNA-seq and ATAC-seq data. Our contribution is not to assert universal coupling, but to quantify the maximum intra-state coupling that survives adversarial nulls , thereby converting qualitative intuition into empirical bounds. Leveraging unimodal latent representations and adversarial null models, we quantify both the existence and the limits of cross-modal dependence across organizational scales. At the population level, global RNA–ATAC mutual information is strong and reproducible across donors, but is shown to be overwhelmingly dominated by cell-type composition rather than fine-grained regulatory coordination. When cellular state is explicitly controlled, intra-state RNA–ATAC coupling collapses to null expectations in the majority of populations, directly falsifying the hypothesis of a universal within-state regulatory channel. Despite this collapse, a weak but statistically robust residual coupling persists in a restricted subset of highly dynamic states, including erythroid differentiation compartments, activated T cells, and NK cells. This residual signal survives stringent local permutation tests and conditional mutual information analysis, demonstrating that it cannot be reduced to compositional mixing alone. Quantitatively, residual within-state dependence is consistently an order of magnitude smaller than global dependence, placing an empirical upper bound on within-state RNA–ATAC coordination in this dataset. Donor-resolved ratios ρ = I(R;A|S)/I(R;A) indicate that most of the global dependence is removed by conditioning on state; operationally, we refer to the removed fraction (1−ρ) as composition-dominated dependence. Throughout, “state-contingent statistical dependence” is used strictly as an operational descriptor rather than a causal claim: mutual information and conditional mutual information quantify statistical dependence only, not directionality or mechanism. This framing constrains downstream mechanistic interpretation and future multimodal modeling.