Characterizing emerging features in cell dynamics using topological data analysis methods

Madeleine Dawson; Carson Dudley; Sasamon Omoma; Hwai-Ray Tung; Maria-Veronica Ciocanel; Madeleine Dawson; Carson Dudley; Sasamon Omoma; Hwai-Ray Tung; Maria-Veronica Ciocanel

doi:10.3934/mbe.2023143

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3023-3046. doi: 10.3934/mbe.2023143

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Characterizing emerging features in cell dynamics using topological data analysis methods

1.
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA
2.
Department of Mathematics, Duke University, Durham, NC 27708, USA
3.
Department of Biology, Duke University, Durham, NC 27708, USA

Academic Editor: Carlo Cattani

Received: 01 September 2022 Revised: 04 November 2022 Accepted: 16 November 2022 Published: 01 December 2022

Filament-motor interactions inside cells play essential roles in many developmental as well as other biological processes. For instance, actin-myosin interactions drive the emergence or closure of ring channel structures during wound healing or dorsal closure. These dynamic protein interactions and the resulting protein organization lead to rich time-series data generated by using fluorescence imaging experiments or by simulating realistic stochastic models. We propose methods based on topological data analysis to track topological features through time in cell biology data consisting of point clouds or binary images. The framework proposed here is based on computing the persistent homology of the data at each time point and on connecting topological features through time using established distance metrics between topological summaries. The methods retain aspects of monomer identity when analyzing significant features in filamentous structure data, and capture the overall closure dynamics when assessing the organization of multiple ring structures through time. Using applications of these techniques to experimental data, we show that the proposed methods can describe features of the emergent dynamics and quantitatively distinguish between control and perturbation experiments.
- topological data analysis,
- ring channel,
- actomyosin dynamics,
- persistent homology,
- filtration methods
Citation: Madeleine Dawson, Carson Dudley, Sasamon Omoma, Hwai-Ray Tung, Maria-Veronica Ciocanel. Characterizing emerging features in cell dynamics using topological data analysis methods[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3023-3046. doi: 10.3934/mbe.2023143

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Abstract

Filament-motor interactions inside cells play essential roles in many developmental as well as other biological processes. For instance, actin-myosin interactions drive the emergence or closure of ring channel structures during wound healing or dorsal closure. These dynamic protein interactions and the resulting protein organization lead to rich time-series data generated by using fluorescence imaging experiments or by simulating realistic stochastic models. We propose methods based on topological data analysis to track topological features through time in cell biology data consisting of point clouds or binary images. The framework proposed here is based on computing the persistent homology of the data at each time point and on connecting topological features through time using established distance metrics between topological summaries. The methods retain aspects of monomer identity when analyzing significant features in filamentous structure data, and capture the overall closure dynamics when assessing the organization of multiple ring structures through time. Using applications of these techniques to experimental data, we show that the proposed methods can describe features of the emergent dynamics and quantitatively distinguish between control and perturbation experiments.

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