A Structural Principle for Macroscopic Neural Dynamics Correlations

A central question in neuroscience is how the brains structural connectivity gives rise to its emergent, correlated dynamics. These large-scale dynamical correlations underlie functional networks that support cognitive functions. Here, we identify coupling correlation--the similarity between the input connectivity profiles of brain regions--as a key structural determinant of macroscopic neural dynamical correlation. Using dynamical mean-field theory (DMFT) and numerical simulations of random neural network models, we demonstrate that coupling correlation quantitatively governs dynamical correlation. The functional form of this structure-function mapping is dictated by the eigenvalue spectrum of the coupling correlation matrix: networks with bulk eigenspectra exhibit an exact linear relationship, whereas biologically plausible long-tailed spectra yield an approximately linear mapping except when the magnitude of coupling correlation approaches unity. Particularly, a long-tailed spectrum is necessary to reproduce the appropriate magnitude and size-invariance of coupling correlations observed in empirical data, thereby sustaining non-vanishing dynamical correlations that may support brain function in large systems. The theoretical prediction of approximate linearity is consistently validated using empirical datasets that include both structural coupling and neural dynamics in humans, mice, and Drosophila. Together, these results provide a mechanistic and quantitative framework linking macroscopic brain network structure to emergent neural dynamics--an essential step toward a theory of structure-function relationship in the brain. Significance StatementHow the brains wiring gives rise to its coordinated activity is a fundamental unsolved problem in neuroscience. Prior work has identified correlations between structural and functional connectivity, but these relationships lacked a mechanistic, first-principles explanation. Here, we derive an analytical framework using Dynamical Mean-Field Theory and random neural network models to show that a single structural statistic--coupling correlation, the similarity between the input connectivity profiles of brain regions--linearly and causally determines the magnitude of correlated neural dynamics. We further show that a long-tailed eigenvalue spectrum in biological structural connectivity is necessary to sustain the strong, size-invariant functional correlations observed across species. Validated in humans, mice, and Drosophila using multiple imaging and connectome modalities, this principle may provide a quantitative bridge between structural connectomics and emergent brain dynamics, with implications extending to a broad class of complex networked systems.