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Modeling Single-Cell Dynamics Using Unbalanced Parameterized Monge Maps

View ORCID ProfileLuca Vincent Eyring, View ORCID ProfileDominik Klein, View ORCID ProfileGiovanni Palla, Soeren Becker, View ORCID ProfilePhilipp Weiler, Niki Kilbertus, View ORCID ProfileFabian J. Theis
doi: https://doi.org/10.1101/2022.10.04.510766
Luca Vincent Eyring
1Institute of Computational Biology, Helmholtz Center Munich, Germany
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Dominik Klein
1Institute of Computational Biology, Helmholtz Center Munich, Germany
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Giovanni Palla
3Institute of Computational Biology, Helmholtz Center Munich, School of Life Sciences Weihenstephan, Technical University of Munich Germany
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Soeren Becker
4Helmholtz AI, Munich, Germany
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Philipp Weiler
5Institute of Computational Biology, Helmholtz Center Munich, Department of Mathematics, Technical University of Munich Germany
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Niki Kilbertus
6Helmholtz AI, Munich, Technical University of Munich, Germany
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Fabian J. Theis
7Institute of Computational Biology, Helmholtz Center Munich, School of Life Sciences Weihenstephan, Department of Mathematics, Technical University of Munich Germany
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  • For correspondence: fabian.theis@helmholtz-munich.de
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Abstract

Optimal Transport (OT) has proven useful to infer single-cell trajectories of developing biological systems by aligning distributions across time points. Recently, Parameterized Monge Maps (PMM) were introduced to learn the optimal map between two distributions. Here, we apply PMM to model single-cell dynamics and show that PMM fails to account for asymmetric shifts in cell state distributions. To alleviate this limitation, we propose Unbalanced Parameterised Monge Maps (UPMM). We first describe the novel formulation and show on synthetic data how our method extends discrete unbalanced OT to the continuous domain. Then, we demonstrate that UPMM outperforms well-established trajectory inference methods on real-world developmental single-cell data.

Competing Interest Statement

Fabian J. Theis consults for Immunai Inc., Singularity Bio B.V., CytoReason Ltd, and Omniscope Ltd, and has ownership interest in Dermagnostix GmbH and Cellarity.

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 October 05, 2022.
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Modeling Single-Cell Dynamics Using Unbalanced Parameterized Monge Maps
Luca Vincent Eyring, Dominik Klein, Giovanni Palla, Soeren Becker, Philipp Weiler, Niki Kilbertus, Fabian J. Theis
bioRxiv 2022.10.04.510766; doi: https://doi.org/10.1101/2022.10.04.510766
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Modeling Single-Cell Dynamics Using Unbalanced Parameterized Monge Maps
Luca Vincent Eyring, Dominik Klein, Giovanni Palla, Soeren Becker, Philipp Weiler, Niki Kilbertus, Fabian J. Theis
bioRxiv 2022.10.04.510766; doi: https://doi.org/10.1101/2022.10.04.510766

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