Gene Gradients Reveal Directed Structural Connectivity Across Species

Studying the brain's inter-regional structural connectivity (SC) has transformed neuroscience, yet noninvasive neuroimaging remains blind to the directionality of neural wiring. Structural directionality must influence observed brain dynamics, but estimating edge-level directionality from brain function is ill-posed and underdetermined. Here, we show that gene co-expression gradients define a low-dimensional biological manifold that locally biases brain regions to act as network sources or sinks. Embedding gene gradients into a linear, higher-order network diffusion model defines a gene-structure-function relationship that recovers ground-truth directionality in C. elegans (r=0.70), mouse (r=0.57), and macaque (r=0.46). Applying this framework to 770 healthy young adults from the Human Connectome Project yields subject-specific directed connectomes that reproduce established corticothalamic asymmetries and reveal distinct gene ontologies associated with network sources and sinks. Furthermore, integrating directed structure with observed functional covariance enables us to derive a principled measure of directed functional connectivity, termed "angular flow" (AF), related to probability angular momentum in non-equilibrium statistical mechanics. Regional AF recapitulates the principal unimodal--multimodal gradient of functional connectivity, suggesting that this macroscale functional hierarchy emerges from a source--sink organization of signal flow through the brain. This framework resolves a long-standing limitation in connectomics and opens new opportunities to study structural directionality and non-equilibrium brain dynamics in health and disease.