Velde: constructing cell potential landscapes by RNA velocity vector field decomposition
arxiv(2023)
摘要
The Waddington landscape serves as a metaphor illustrating the developmental
process of cells, likening it to a small ball rolling down various trajectories
into valleys. Constructing an epigenetic landscape of this nature aids in
visualizing and gaining insights into cell differentiation. Development
encompasses intricate processes involving both cell differentiation and cell
cycles. However, current landscape methods solely focus on constructing a
potential landscape for cell differentiation, neglecting the accompanying cell
cycle. This paper introduces a novel method that simultaneously constructs two
types of potential landscapes using single-cell RNA sequencing data.
Specifically, it presents the natural Helmholtz-Hodge decomposition (nHHD) of a
continuous vector field within a bounded domain in n-dimensional Euclidean
space. This decomposition uniquely breaks down the vector field into a gradient
field, a rotation field, and a harmonic field. Utilizing this approach, the RNA
velocity vector field is separated into a curl-free component representing cell
differentiation and a curl component representing the cell cycle. By
calculating the corresponding potential functions, potential landscapes for
both cell differentiation and the cell cycle are obtained. Finally, the
efficacy of this method is demonstrated through its application to synthetic
and real datasets.
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