  Spatial transcriptomics is a modern sequencing technology that allows the
measurement of the activity of thousands of genes in a tissue sample and map
where the activity is occurring. This technology has enabled the study of the
so-called spatially expressed genes, i.e., genes which exhibit spatial
variation across the tissue. Comprehending their functions and their
interactions in different areas of the tissue is of great scientific interest,
as it might lead to a deeper understanding of several key biological
mechanisms. However, adequate statistical tools that exploit the newly spatial
mapping information to reach more specific conclusions are still lacking.
  In this work, we introduce SpaRTaCo, a new statistical model that clusters
the spatial expression profiles of the genes according to the areas of the
tissue. This is accomplished by performing a co-clustering, i.e., inferring the
latent block structure of the data and inducing two types of clustering: of the
genes, using their expression across the tissue, and of the image areas, using
the gene expression in the spots where the RNA is collected. Our proposed
methodology is validated with a series of simulation experiments and its
usefulness in responding to specific biological questions is illustrated with
an application to a human brain tissue sample processed with the 10X-Visium
protocol.
