# CTFacTomo: Reconstructing 3D spatial structures of RNA tomography transcriptomes by collapsed tensor factorization

## TL;DR

CTFacTomo is a new method that reconstructs 3D gene expression patterns from RNA tomography data using tensor factorization, outperforming existing methods in accuracy and spatial coherence.

## Contribution

CTFacTomo introduces a novel collapsed tensor factorization approach to reconstruct 3D spatial gene expression from RNA tomography data.

## Key findings

- CTFacTomo outperforms benchmark methods in predicting ground-truth gene expressions from 1D spatial projections.
- The method successfully reconstructs 3D spatial gene expressions in zebrafish embryos and mouse olfactory mucosa.
- Reconstructed gene expressions show spatial coherence and consistency with ISH staining and external Stereo-seq data.

## Abstract

Cells are organized to form three-dimensional structures of complex tissues. To map the complete 3D organization of a tissue, technologies based on tissue microdissections provide deep bulk RNA sequencing of orthogonally arranged cryosections of a tissue, such that the full 3D spatial structure could be inferred from deeply sequenced transcriptomes in three views projected similarly as 3D tomography. Here, we introduce CTFacTomo to learn a Collapsed Tensor Factorization for RNA tomography data from cryosections to reconstruct 3D spatially resolved gene expressions. CTFacTomo combines tensor factorization with collapsing tensor entries to match the bulk gene expressions in each cryosection, enriched by a regularization of a product graph of protein-protein interaction network and spatial graphs. In the experiments, CTFacTomo is first validated on three datasets projected from fully profiled 3D spatial gene expressions to demonstrate that CTFacTomo significantly outperforms the benchmark methods for predicting the ground-truth gene expressions based on the projected 1D spatial gene expressions of three orthographic views. CTFacTomo is then applied to two RNA tomography datasets from zebrafish embryo and mouse olfactory mucosa, respectively. In both datasets, CTFacTomo detects 3D spatial expressions of several marker genes that are consistent with the developmental or functional regions in comparison to accompanying ISH staining images. In addition, a qualitative comparison between the reconstructed zebrafish embryo gene expressions with a matched external 3D Stereo-seq dataset also suggests that CTFacTomo reconstructs more spatially coherent patterns in the whole transcriptome with state-of-the-art performance.

In multicellular organisms, the three-dimensional organization of cells is fundamental to forming complex tissue architectures to support essential cellular functions such as cell movement, communication and interactions, and spatially varying gene expression. RNA tomography technology applies 1D transcriptomic profiling to consecutive slices along orthogonal spatial axes of tomography, and is particularly useful for capturing such 3D organization. CTFacTomo is a computational method based on collapsed tensor factorization for reconstructing 3D spatial gene expression from RNA tomography data. By learning a tensor decomposition from collapsed entries along three orthogonal views, CTFacTomo accurately identifies underlying 3D spatial transcriptomic patterns using the factorization model. CTFacTomo is first validated on three datasets projected from fully profiled 3D spatial gene expression data, demonstrating accurate recovery of ground-truth expressions from 1D projections of three orthogonal views. It is then applied to reconstruct 3D spatial gene expression in large-scale zebrafish embryo and mouse olfactory mucosa datasets, with results evaluated using ISH images and an external zebrafish Stereo-seq dataset. Together, these results demonstrate the superior performance of CTFacTomo for reconstructing 3D spatial gene expression from RNA tomography data.