Decoding cell signaling via optimal transport and information theory

Cellular signal processing performs reliably despite molecular noise. Mutual information (MI) is widely used to quantify signaling fidelity, capturing how well outputs discriminate input states. However, it fails to capture whether the output preserves the statistical structure of the input, a property crucial in morphogen patterning and dose-dependent signaling. To address this gap, we introduce the 2-Wasserstein (2-WD) distance, which provides a geometric basis for comparing input and output distributions. We define MI as informational fidelity (INF) and the inverse of the 2-WD as geometric fidelity (GMF). Applying this dual-fidelity framework to canonical regulatory motifs under Gaussian channel approximation reveals topology-dependent trade-offs: coherent feed-forward loops can perform well in both dimensions, whereas feedback architectures sacrifice INF to enhance GMF. Experimental analysis of tumor necrosis factor signaling supports the predicted role of feedback regulation. Analysis of RAS-MAPK signaling shows that intracellular signal relay is better described by a balance between INF and GMF than by information transmission alone. Our results demonstrate that reliable signaling need not maximize information alone, but can arise from balancing information transmission with distributional correspondence. Thus, GMF represents a distinct dimension of signaling fidelity and provides a framework for analyzing natural networks and designing task-specific synthetic circuits.