Uthsav Chitra, Spatial Transcriptomics

Algorithms for modeling the spatial and network organization of biological systems

Spatially resolved transcriptomics

Technologies: 10x Visium, MERFISH, etc

High throughput: e.g. 10x Visium measures unique molecular identifiers (UMIs) of 20000 genes at 1000-5000 spatial locations

Applications:

• Spatial organization of cell types
• Transcripts with spatially varying expression

Low sequence coverage Sparse matrix: 75%

How to overcome sparsity by incorporating spatial information?

Most algorithms use local models: nearby spots have similar cell type / expression.

• Hidden Markov Random Field: BayesSpace, SPICEMIX, Giotto
• Gaussian Processes: SpatialDE, SPARK
• Graph Neural networks (GNN): SpaGCN, STAGATE

Uthsav is trying to develop new models to address these challenges.

Consider a simple layered tissues, where the gene expression is constant along y-axis. That is, the cell types are parallel. Piecewise linear function models expression gradients. Pool sparse expression along y-axis.

But, how to consider curved boundaries? They are using conformal maps and harmonic functions. A conformal map \(\Phi : D \subset C \rightarrow C\) locally preserves angles between curves.

Layered tissue problem formulation. Input are the spot coordinates, transcript count matrix and number of layers.

Topography of gene expression \(\rightarrow\) isodepth

• Isodepth: contours of equal potential
• Generalizes relative depth from Belayer
• Gene expression function

Idea: Use trendfiltering on graphs!