Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space

Heyrim Cho; Ya-Huei Kuo; Russell C. Rockne; Heyrim Cho; Ya-Huei Kuo; Russell C. Rockne

doi:10.3934/mbe.2022395

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 8: 8505-8536. doi: 10.3934/mbe.2022395

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Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space

1.
Department of Mathematics, University of California Riverside, Riverside, CA, USA
2.
Department of Hematologic Malignancies Translational Science, City of Hope, Duarte, CA, USA
3.
Department of Computational and Quantitative Medicine, Division of Mathematical Oncology, City of Hope, Duarte, CA, USA
4.
Interdisciplinary Center for Quantitative Modeling in Biology, University of California Riverside, Riverside, CA, USA
Academic editor: Xiaoqiang Sun

Received: 21 February 2022 Revised: 21 April 2022 Accepted: 19 May 2022 Published: 10 June 2022

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two cell state geometries for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; (i) by using partial differential equations on a graph representing intermediate cell states between known cell types, and (ii) by using the equations on a multi-dimensional continuous cell state-space. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell states during the pathogenesis of acute myeloid leukemia. We particularly focus on comparing the strength and weakness of the graph model and multi-dimensional model.
- next generation sequencing data,
- cell state evolution,
- phenotype structured models,
- partial differential equation,
- hematopoeisis
Citation: Heyrim Cho, Ya-Huei Kuo, Russell C. Rockne. Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space[J]. Mathematical Biosciences and Engineering, 2022, 19(8): 8505-8536. doi: 10.3934/mbe.2022395

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Abstract

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two cell state geometries for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; (i) by using partial differential equations on a graph representing intermediate cell states between known cell types, and (ii) by using the equations on a multi-dimensional continuous cell state-space. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell states during the pathogenesis of acute myeloid leukemia. We particularly focus on comparing the strength and weakness of the graph model and multi-dimensional model.

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