Scaling of gene transcriptional gradients with brain size across mouse development

The structure of the adult brain is the result of complex physical mechanisms acting in three-dimensional space through development. Consequently, the brain's spatial embedding plays a key role in its organization, including the gradient-like patterning of gene expression that encodes the molecular underpinning of functional specialization. However, we do not yet understand how changes in brain shape and size that occur across development influence the brain's transcriptional architecture. 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 transcriptional similarity decreases exponentially with separation distance across all developmental time points, with a correlation length scale that follows a power-law scaling relationship with a linear dimension of brain size. This scaling suggests that the mouse brain achieves a characteristic balance between local molecular similarity (homogeneous gene expression within a specialized brain area) and longer-range diversity (between functionally specialized brain areas) throughout its development. Extrapolating this mouse developmental scaling relationship to the human cortex yields a prediction consistent with the value measured from microarray data. We introduce 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 characterize an analogous exponential distance rule for transcriptional gradients that scales across mouse brain development, providing new understanding of spatial constraints on the brain's molecular patterning.