Abstract
This paper explicates a solution to the problem of building correspondences between molecular-scale transcriptomics and tissue-scale atlases. The central model represents spatial transcriptomics as generalized functions encoding molecular position and high-dimensional transcriptomic-based (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling each atlas compartment as a homogeneous random field with unknown transcriptomic feature distribution. The algorithm presented solves simultaneously for the minimizing geodesic diffeomorphism of coordinates and latent atlas transcriptomic feature fractions by alternating LDDMM optimization for coordinate transformations and quadratic programming for the latent transcriptomic variables. We demonstrate the universality of the algorithm in mapping tissue atlases to gene-based and cell-based MERFISH datasets as well as to other tissue scale atlases. The joint estimation of diffeomorphisms and latent feature distributions allows integration of diverse molecular and cellular datasets into a single coordinate system and creates an avenue of comparison amongst atlas ontologies for continued future development.
Competing Interest Statement
Under a license agreement between AnatomyWorks and the Johns Hopkins University, Dr. Miller and the University are entitled to royalty distributions related to technology described in the study discussed in this. Dr. Miller is a founder of and holds equity in AntomyWorks. This arrangement has been reviewed and approved by the Johns Hopkins University in accordance with its conflict of interest policies. The remaining authors declare no conflicts of interest.