Abstract
The structure of the adult brain is the result of complex physical mechanisms acting through development. Accordingly, the brain’s spatial embedding plays a key role in its structural and functional organization, including the gradient-like patterning of gene expression that encodes the molecular underpinning of functional specialization. But we do not understand how this transcriptional heterogeneity is spatially organized across the major alterations in brain geometry that occur through development. Here we investigate the spatial embedding of transcriptional patterns of over 1800 genes across seven time points through mouse-brain development using data from the Allen Developing Mouse Brain Atlas. We find that the similarity of transcriptional patterns decreases exponentially with separation distance across all developmental time points, with a correlation length scale that satisfies a powerlaw scaling relationship with a linear dimension of brain size. This scaling suggests that the mouse brain achieves a characteristic spatial balance between local transcriptional similarity (within functionally specialized brain areas) and longer-range diversity (between functionally specialized brain areas) throughout its development. Extrapolating this mouse-developmental scaling relationship to predict the correlation length of gene expression in the human cortex yields a slight overestimate, consistent with the human cortex being more molecularly diverse and functionally specialized than the mouse brain. We develop a simple model of brain growth as spatially autocorrelated gene-expression gradients that expand through development, which captures key features of the mouse developmental data. Complementing the well-known exponential distance rule for structural connectivity, our findings thus characterize an exponential distance rule for transcriptional gradients that scales across mouse-brain development, providing new understanding of the molecular patterns underlying the functional specialization in the brain.
Competing Interest Statement
The authors have declared no competing interest.