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PDE-constrained optimization for estimating population dynamics over cell cycle from static single cell measurements

View ORCID ProfileKarsten Kuritz, Alain R Bonny, View ORCID ProfileJoão Pedro Fonseca, Frank Allgöwer
doi: https://doi.org/10.1101/2020.03.30.015909
Karsten Kuritz
1Institute for Systems Theory and Automatic Control, University of Stuttgart, Stuttgart, 70569, Germany
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  • For correspondence: karsten.kuritz@ist.uni-stuttgart.de
Alain R Bonny
2Department of Biochemistry and Biophysics, California Institute for Quantitative Biosciences, University of California, San Francisco, CA 94158, USA
3Chan Zuckerberg Biohub, San Francisco, CA 94158, USA
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João Pedro Fonseca
2Department of Biochemistry and Biophysics, California Institute for Quantitative Biosciences, University of California, San Francisco, CA 94158, USA
3Chan Zuckerberg Biohub, San Francisco, CA 94158, USA
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Frank Allgöwer
1Institute for Systems Theory and Automatic Control, University of Stuttgart, Stuttgart, 70569, Germany
4Stuttgart Research Center Systems Biology, University of Stuttgart, Stuttgart, 70569, Germany
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Abstract

Motivation Understanding how cell cycle responds and adapts dynamically to a broad range of stresses and changes in the cellular environment is crucial for the treatment of various pathologies, including cancer. However, measuring changes in cell cycle progression is experimentally challenging, and model inference computationally expensive.

Results Here, we introduce a computational framework that allows the inference of changes in cell cycle progression from static single-cell measurements. We modeled population dynamics with partial differential equations (PDE), and derive parameter gradients to estimate time- and cell cycle position-dependent progression changes efficiently. Additionally, we show that computing parameter sensitivities for the optimization problem by solving a system of PDEs is computationally feasible and allows efficient and exact estimation of parameters. We showcase our framework by estimating the changes in cell cycle progression in K562 cells treated with Nocodazole and identify an arrest in M-phase transition that matches the expected behavior of microtubule polymerization inhibition.

Conclusions Our results have two major implications: First, this framework can be scaled to high-throughput compound screens, providing a fast, stable, and efficient protocol to generate new insights into changes in cell cycle progression. Second, knowledge of the cell cycle stage- and time-dependent progression function allows transformation from pseudotime to real-time thereby enabling real-time analysis of molecular rates in response to treatments.

Availability MAPiT toolbox (Karsten Kuritz 2020) is available at github: https://github.com/karstenkuritz/MAPiT.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC 4.0 International license.
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Posted March 31, 2020.
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PDE-constrained optimization for estimating population dynamics over cell cycle from static single cell measurements
Karsten Kuritz, Alain R Bonny, João Pedro Fonseca, Frank Allgöwer
bioRxiv 2020.03.30.015909; doi: https://doi.org/10.1101/2020.03.30.015909
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PDE-constrained optimization for estimating population dynamics over cell cycle from static single cell measurements
Karsten Kuritz, Alain R Bonny, João Pedro Fonseca, Frank Allgöwer
bioRxiv 2020.03.30.015909; doi: https://doi.org/10.1101/2020.03.30.015909

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