Is cell segregation like oil and water: Asymptotic versus transitory regime
Understanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumor progression. Steinberg proposed that separation of cells can be compared to the separation of two liquids. Such a separation is well described by the Cahn-Hilliard (CH) equations and the...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2022-09-01
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| Series: | PLoS Computational Biology |
| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9484667/?tool=EBI |
| _version_ | 1828733987709779968 |
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| author | Florian Franke Sebastian Aland Hans-Joachim Böhme Anja Voss-Böhme Steffen Lange |
| author_facet | Florian Franke Sebastian Aland Hans-Joachim Böhme Anja Voss-Böhme Steffen Lange |
| author_sort | Florian Franke |
| collection | DOAJ |
| description | Understanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumor progression. Steinberg proposed that separation of cells can be compared to the separation of two liquids. Such a separation is well described by the Cahn-Hilliard (CH) equations and the segregation indices exhibit an algebraic decay with exponent 1/3 with respect to time. Similar exponents are also observed in cell-based models. However, the scaling behavior in these numerical models is usually only examined in the asymptotic regime and these models have not been directly applied to actual cell segregation data. In contrast, experimental data also reveals other scaling exponents and even slow logarithmic scaling laws. These discrepancies are commonly attributed to the effects of collective motion or velocity-dependent interactions. By calibrating a 2D cellular automaton (CA) model which efficiently implements a dynamic variant of the differential adhesion hypothesis to 2D experimental data from Méhes et al., we reproduce the biological cell segregation experiments with just adhesive forces. The segregation in the cellular automaton model follows a logarithmic scaling initially, which is in contrast to the proposed algebraic scaling with exponent 1/3. However, within the less than two orders of magnitudes in time which are observable in the experiments, a logarithmic scaling may appear as a pseudo-algebraic scaling. In particular, we demonstrate that the cellular automaton model can exhibit a range of exponents ≤1/3 for such a pseudo-algebraic scaling. Moreover, the time span of the experiment falls into the transitory regime of the cellular automaton rather than the asymptotic one. We additionally develop a method for the calibration of the 2D Cahn-Hilliard model and find a match with experimental data within the transitory regime of the Cahn-Hilliard model with exponent 1/4. On the one hand this demonstrates that the transitory behavior is relevant for the experiment rather than the asymptotic one. On the other hand this corroborates the ambiguity of the scaling behavior, when segregation processes can be only observed on short time spans. Author summary Segregation of different cell types is a crucial process for the pattern formation in tissues, in particular during embryogenesis. Since the involved cell interactions are complex and difficult to measure individually in experiments, mathematical modelling plays an increasingly important role to unravel the mechanisms governing segregation. The analysis of these theoretical models focuses mainly on the asymptotic behavior at large times, in a steady regime and for large numbers of cells. Most famously, cell-segregation models based on the minimization of the total surface energy, a mechanism also driving the demixing of immiscible fluids, are known to exhibit asymptotically a particular algebraic scaling behavior. However, it is not clear, whether the asymptotic regime of the numerical models is relevant at the spatio-temporal scales of actual biological processes and in-vitro experiments. By developing a mapping between 2D cell-based models and experimental settings, we are able to directly compare previous experimental data to numerical simulations of cell segregation quantitatively. We demonstrate that the experiments are reproduced by the transitory regime of the models rather than the asymptotic one. Our work puts a new perspective on previous model-driven conclusions on cell segregation mechanisms. |
| first_indexed | 2024-04-12T22:40:20Z |
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| issn | 1553-734X 1553-7358 |
| language | English |
| last_indexed | 2024-04-12T22:40:20Z |
| publishDate | 2022-09-01 |
| publisher | Public Library of Science (PLoS) |
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| series | PLoS Computational Biology |
| spelling | doaj.art-3915d13a3b484f6ca0f0c9ad9a8031412022-12-22T03:13:45ZengPublic Library of Science (PLoS)PLoS Computational Biology1553-734X1553-73582022-09-01189Is cell segregation like oil and water: Asymptotic versus transitory regimeFlorian FrankeSebastian AlandHans-Joachim BöhmeAnja Voss-BöhmeSteffen LangeUnderstanding the segregation of cells is crucial to answer questions about tissue formation in embryos or tumor progression. Steinberg proposed that separation of cells can be compared to the separation of two liquids. Such a separation is well described by the Cahn-Hilliard (CH) equations and the segregation indices exhibit an algebraic decay with exponent 1/3 with respect to time. Similar exponents are also observed in cell-based models. However, the scaling behavior in these numerical models is usually only examined in the asymptotic regime and these models have not been directly applied to actual cell segregation data. In contrast, experimental data also reveals other scaling exponents and even slow logarithmic scaling laws. These discrepancies are commonly attributed to the effects of collective motion or velocity-dependent interactions. By calibrating a 2D cellular automaton (CA) model which efficiently implements a dynamic variant of the differential adhesion hypothesis to 2D experimental data from Méhes et al., we reproduce the biological cell segregation experiments with just adhesive forces. The segregation in the cellular automaton model follows a logarithmic scaling initially, which is in contrast to the proposed algebraic scaling with exponent 1/3. However, within the less than two orders of magnitudes in time which are observable in the experiments, a logarithmic scaling may appear as a pseudo-algebraic scaling. In particular, we demonstrate that the cellular automaton model can exhibit a range of exponents ≤1/3 for such a pseudo-algebraic scaling. Moreover, the time span of the experiment falls into the transitory regime of the cellular automaton rather than the asymptotic one. We additionally develop a method for the calibration of the 2D Cahn-Hilliard model and find a match with experimental data within the transitory regime of the Cahn-Hilliard model with exponent 1/4. On the one hand this demonstrates that the transitory behavior is relevant for the experiment rather than the asymptotic one. On the other hand this corroborates the ambiguity of the scaling behavior, when segregation processes can be only observed on short time spans. Author summary Segregation of different cell types is a crucial process for the pattern formation in tissues, in particular during embryogenesis. Since the involved cell interactions are complex and difficult to measure individually in experiments, mathematical modelling plays an increasingly important role to unravel the mechanisms governing segregation. The analysis of these theoretical models focuses mainly on the asymptotic behavior at large times, in a steady regime and for large numbers of cells. Most famously, cell-segregation models based on the minimization of the total surface energy, a mechanism also driving the demixing of immiscible fluids, are known to exhibit asymptotically a particular algebraic scaling behavior. However, it is not clear, whether the asymptotic regime of the numerical models is relevant at the spatio-temporal scales of actual biological processes and in-vitro experiments. By developing a mapping between 2D cell-based models and experimental settings, we are able to directly compare previous experimental data to numerical simulations of cell segregation quantitatively. We demonstrate that the experiments are reproduced by the transitory regime of the models rather than the asymptotic one. Our work puts a new perspective on previous model-driven conclusions on cell segregation mechanisms.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9484667/?tool=EBI |
| spellingShingle | Florian Franke Sebastian Aland Hans-Joachim Böhme Anja Voss-Böhme Steffen Lange Is cell segregation like oil and water: Asymptotic versus transitory regime PLoS Computational Biology |
| title | Is cell segregation like oil and water: Asymptotic versus transitory regime |
| title_full | Is cell segregation like oil and water: Asymptotic versus transitory regime |
| title_fullStr | Is cell segregation like oil and water: Asymptotic versus transitory regime |
| title_full_unstemmed | Is cell segregation like oil and water: Asymptotic versus transitory regime |
| title_short | Is cell segregation like oil and water: Asymptotic versus transitory regime |
| title_sort | is cell segregation like oil and water asymptotic versus transitory regime |
| url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9484667/?tool=EBI |
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