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- Gerlee, Philip, 1980, et al.
(author)
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Autocrine signaling can explain the emergence of Allee effects in cancer cell populations
- 2022
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In: Plos Computational Biology. - : Public Library of Science (PLoS). - 1553-734X .- 1553-7358. ; 18:3
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Journal article (peer-reviewed)abstract
- In many human cancers, the rate of cell growth depends crucially on the size of the tumour cell population. Low, zero, or negative growth at low population densities is known as the Allee effect; this effect has been studied extensively in ecology, but so far lacks a good explanation in the cancer setting. Here, we formulate and analyze an individual-based model of cancer, in which cell division rates are increased by the local concentration of an autocrine growth factor produced by the cancer cells themselves. We show, analytically and by simulation, that autocrine signaling suffices to cause both strong and weak Allee effects. Whether low cell densities lead to negative (strong effect) or reduced (weak effect) growth rate depends directly on the ratio of cell death to proliferation, and indirectly on cellular dispersal. Our model is consistent with experimental observations from three patient-derived brain tumor cell lines grown at different densities. We propose that further studying and quantifying population-wide feedback, impacting cell growth, will be central for advancing our understanding of cancer dynamics and treatment, potentially exploiting Allee effects for therapy.
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| 3. |
- Gerlee, Philip, 1980, et al.
(author)
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Complexity and stability in growing cancer cell populations
- 2015
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In: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 112:21
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Journal article (other academic/artistic)abstract
- Evolutionary game theory (EGT) describes dynamics in populations in which individual fitness can change because of the interactions with others, called frequency-dependent selection (1). Interactions are driven by differences in phenotype. EGT has been proposed as a framework for evolutionary dynamics of tumors (2). An underlying assumption is that different cancer cell types within a tumor engage in different heritable behavior; thus, frequency-dependent selection acts. Until now there has been little direct empirical evidence for this. The study by Archetti et al. (3) demonstrates frequency-dependent growth rates of two phenotypically distinct cancer subclones. One clone produced the insulin-like growth factor (IGF)-II, the other did not. In a mix of producers and nonproducers, the growth rates of both clones varied with the frequency of producers. Because a similar effect was shown when varying the concentration of serum, the production of IGF-II could be viewed as a public goods game.
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| 4. |
- Gerlee, Philip, 1980, et al.
(author)
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Extinction rates in tumour public goods games
- 2017
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In: Journal of the Royal Society Interface. - : The Royal Society. - 1742-5689 .- 1742-5662. ; 14:134
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Journal article (peer-reviewed)abstract
- Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here showthat this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.
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| 5. |
- Gerlee, Philip, 1980, et al.
(author)
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Persistence of cooperation in diffusive public goods games
- 2019
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In: Physical Review E. - 2470-0045 .- 2470-0053. ; 99:6
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Journal article (peer-reviewed)abstract
- Diffusive public goods (PG) games are difficult to analyze due to population assortment affecting growth rates of cooperators (producers) and free-riders. We study these growth rates using spectral decomposition of cellular densities and derive a finite cell-size correction of the growth rate advantage which exactly describes the dynamics of a randomly assorted population and approximates the dynamics under limited dispersal. The resulting effective benefit-to-cost ratio relates the physical parameters of PG dynamics to the persistence of cooperation, and our findings provide a powerful tool for the analysis of diffusive PG games, explaining commonly observed patterns of cooperation. © 2019 American Physical Society.
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| 6. |
- Kimmel, G. J., et al.
(author)
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Neighborhood size-effects shape growing population dynamics in evolutionary public goods games
- 2019
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In: Communications Biology. - : Springer Science and Business Media LLC. - 2399-3642. ; 2:AAC RM, 1994, JOURNAL OF PUBLIC ECONOMICS, V54, P1
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Journal article (peer-reviewed)abstract
- An evolutionary game emerges when a subset of individuals incur costs to provide benefits to all individuals. Public goods games (PGG) cover the essence of such dilemmas in which cooperators are prone to exploitation by defectors. We model the population dynamics of a non-linear PGG and consider density-dependence on the global level, while the game occurs within local neighborhoods. At low cooperation, increases in the public good provide increasing returns. At high cooperation, increases provide diminishing returns. This mechanism leads to diverse evolutionarily stable strategies, including monomorphic and polymorphic populations, and neighborhood-size-driven state changes, resulting in hysteresis between equilibria. Stochastic or strategy-dependent variations in neighborhood sizes favor coexistence by destabilizing monomorphic states. We integrate our model with experiments of cancer cell growth and confirm that our framework describes PGG dynamics observed in cellular populations. Our findings advance the understanding of how neighborhood-size effects in PGG shape the dynamics of growing populations.
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| 7. |
- Kimmel, G. J., et al.
(author)
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Time scales and wave formation in non-linear spatial public goods games
- 2019
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In: PLoS Computational Biology. - : Public Library of Science (PLoS). - 1553-734X .- 1553-7358. ; 15:9
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Journal article (peer-reviewed)abstract
- The co-evolutionary dynamics of competing populations can be strongly affected by frequency- dependent selection and spatial population structure. As co-evolving populations grow into a spatial domain, their initial spatial arrangement and their growth rate differences are important factors that determine the long-term outcome. We here model producer and free-rider co-evolution in the context of a diffusive public good (PG) that is produced by the producers at a cost but evokes local concentration-dependent growth benefits to all. The benefit of the PG can be non-linearly dependent on public good concentration. We consider the spatial growth dynamics of producers and free-riders in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by the processes of birth, death and diffusion (cell movement and public good distribution). Typically, one population goes extinct, but the time-scale of this process varies with initial conditions and the growth rate functions. We establish that spatial variation is transient regardless of dimensionality, and that structured initial conditions lead to increasing times to get close to an extinction state, called ∈-extinction time. Further, we find that uncorrelated initial spatial structures do not influence this ∈-extinction time in comparison to a corresponding well-mixed (non-spatial) system. In order to estimate the ∈-extinction time of either free-riders or producers we derive a slow manifold solution. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated. Our results provide quantitative predictions for the transient spatial dynamics of cooperative traits under pressure of extinction. © 2019 Kimmel et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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