Scaling of gene transcriptional gradients with brain size across mouse development

Abstract

The structure of the adult brain is the result of complex physical mechanisms acting through development. These physical processes, acting in threedimensional space, mean that the brains 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 the dramatic changes in brain shape and size that occur in early development influence the brains transcriptional architecture. Here we investigate the spatial embedding of transcriptional patterns of over 1800 genes across seven time points through mousebrain 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 powerlaw 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 brains molecular patterning.