A Quaternion Model For Single Cell Transcriptomics

Abstract

Quaternions have a wide range of applications in the field of computer graphics and in the field of biomedicine. Quaternions are mainly used to solve problems related to the orientation and structure of biomolecules, such as chromatin structure formation and protein folding. In my study, a model that maps unigrams/positions to quaternions and applies them to scRNA-seq/ST datasets is described. The model assumes that the biologically important orientation of scRNA-seq/ST has multiple advantages for data analysis, and that the dataset is preserved in 3D reconstruction of non-standardised counts. Firstly, it facilitates new ways of visualising scRNA-seq/ST data that capture the ambiguity of cellular states. Second, the model shows that changes in cell state can be viewed as 3D rotations, which use rotational quaternions as a comparable representation. The ability to interpret these rotational quaternions as cells opens up new ways of describing cell state changes, with pseudotemporal studies being particularly relevant to ordered trajectories. This quaternion-based modelling strategy provides new tools and per spectives for understanding and interpreting cellular states in scRNA-seq/ST datasets, and may lead to a deeper understanding of cell development and functional studies.