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On the Mathematics of RNA Velocity I: Theoretical Analysis

On the Mathematics of RNA Velocity I: Theoretical Analysis
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Year:    2021

Author:    Tiejun Li, Jifan Shi, Yichong Wu, Peijie Zhou

CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 1 : pp. 1–55

Abstract

The RNA velocity provides a new avenue to study the stemness and lineage of cells in the development in scRNA-seq data analysis. Some promising extensions of it are proposed and the community is experiencing a fast developing period. However, in this stage, it is of prime importance to revisit the whole process of RNA velocity analysis from the mathematical point of view, which will help to understand the rationale and drawbacks of different proposals. The current paper is devoted to this purpose. We present a thorough mathematical study on the RNA velocity model from dynamics to downstream data analysis. We derived the analytical solution of the RNA velocity model from both deterministic and stochastic point of view. We presented the parameter inference framework based on the maximum likelihood estimate. We also derived the continuum limit of different downstream analysis methods, which provides insights on the construction of transition probability matrix, root and ending-cells identification, and the development routes finding. The overall analysis aims at providing a mathematical basis for more advanced design and development of RNA velocity type methods in the future.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.SO-2020-0001

CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 1 : pp. 1–55

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    55

Keywords:    RNA velocity stochastic model continuum limit kNN density estimate.

Author Details

Tiejun Li

Jifan Shi

Yichong Wu

Peijie Zhou

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