Mix &amp; Match: Phenotypic coexistence as a key facilitator of solid tumour invasion

Strobl, Maximilian; Krause, Andrew L.; Damaghi, Mehdi; Gillies, Robert J.; Anderson, Alexander R.A.; Maini, Philip K.

doi:10.1101/750810

Cited by 3 publications

(1 citation statement)

References 53 publications

(83 reference statements)

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“…1 Introduction Since Fisher's famous work on waves of advantageous genes in a population (Fisher, 1937), the emergence of wave solutions in reaction-diffusion models in and beyond population ecology has been well studied (Ablowitz and Zeppetella, 1979;Dunbar, 1983Dunbar, , 1984Miller, 1997;Hosono, 1998;Grindrod, 1991;Hosono, 1998;Murray, 2003;Volpert and Petrovskii, 2009). Such solutions have been used to investigate invasion fronts (Lewis et al, 2016) of species which locally out-compete their native competitors, such as in the invasion of grey squirrels in Britain (Okubo et al, 1989;White et al, 2015), or in studying the invasive properties of cancer cells (Sherratt, 1993;Strobl et al, 2020). Many other ecologically relevant scenarios require the knowledge of how different kinds of dispersal mechanisms lead to different spreading speeds of a population, and reaction-diffusion systems have been a central model of study in such spreading processes.…”

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A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations

Krause

Gorder

2020

Bull Math Biol

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We study traveling waves in a non-local cross-diffusion type model, where organisms move along gradients in population densities. Such models are valuable for understanding waves of migration and invasion, and how directed motion can impact such scenarios. In this paper we demonstrate the emergence of traveling wave solutions, studying properties of both planar and radial wavefronts in one and two species variants of the model. We compute exact traveling wave solutions in the purely diffusive case, and then perturb these solutions to analytically capture the influence directed motion has on these exact solutions. Using linear stability analysis, we find that the minimum wavespeeds correspond to the purely diffusive case, but numerical simulations suggest that advection can in general increase or decrease the observed wavespeed substantially, which allows a single species to more rapidly move into unoccupied resource rich spatial regions, or modify the speed of an invasion for two populations. We also find interesting effects from the non-local interactions in the model, suggesting that single species invasions can be enhanced with stronger non-locality, but that invasion of a competitive species may be slowed due to this non-local effect. Finally we simulate pattern formation behind waves of invasion, showing that directed motion can have substantial impacts not only on wave speed but also on the existence and structure of emergent patterns, as predicted in the first part of our study (Taylor et al, 2020).

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A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations

Krause

Gorder

2020

Bull Math Biol

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A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns

et al. 2020

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We extend a spatially non-local cross-diffusion model of aggregation between multiple species with directed motion toward resource gradients to include many species and more general kinds of dispersal. We first consider diffusive instabilities, determining that for directed motion along fecundity gradients, the model permits the Turing instability leading to colony formation and persistence provided there are three or more interacting species. We also prove that such patterning is not possible in the model under the Turing mechanism for two species under directed motion along fecundity gradients, confirming earlier findings in the literature. However, when the directed motion is not along fecundity gradients, for instance if foraging or migration is sub-optimal relative to fecundity gradients, we find that very different colony structures can emerge. This generalization also permits colony formation for two interacting species. In the advection -dominated case, aggregation patterns are more broad and global in nature, due to the inherent non-local nature of the advection which permits directed motion over greater distances, whereas in the diffusion -dominated case, more highly localized pattens and colonies develop, owing to the localized nature of random diffusion. We also consider the interplay between Turing patterning and spatial heterogeneity in resources. We find that for small spatial variations, there will be a combination of Turing patterns and patterning due to spatial forcing from the resources, whereas for large resource variations, spatial or spatiotemporal patterning can be modified greatly from what is predicted on homogeneous domains. For each of these emergent behaviors, we outline the theoretical mechanism leading to colony formation, and then provide numerical simulations to illustrate the results. We also discuss implications this model has for studies of directed motion in different ecological settings.

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The Harsh Microenvironment in Early Breast Cancer Selects for a Warburg Phenotype

Damaghi

West

Robertson-Tessi

et al. 2020

Preprint

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The harsh microenvironment of ductal carcinoma in situ (DCIS) exerts strong evolutionary selection pressures on cancer cells. We hypothesize that the poor metabolic conditions near the ductal center foment the emergence of a Warburg Effect (WE) phenotype, wherein cells rapidly ferment glucose to lactic acid, even in normoxia. To test this hypothesis, we subjected pre-malignant breast cancer cells to different microenvironmental selection pressures using combinations of hypoxia, acidosis, low glucose, and starvation for many months, and isolated single clones for metabolic and transcriptomic profiling. The two harshest conditions selected for constitutively expressed WE phenotypes. RNA-seq analysis of WE clones identified the transcription factors NFB and KLF4 as potential inducers of the WE phenotype. NFB was highly phosphorylated in the glycolytic clones. In stained DCIS samples, KLF4 expression was enriched in the area with the harshest microenvironmental conditions. We simulated in vivo DCIS phenotypic evolution using a mathematical model calibrated from the in vitro results. The WE phenotype emerged in the poor metabolic conditions near the necrotic core. We propose that harsh microenvironments within DCIS select for a Warburg phenotype through constitutive transcriptional reprogramming, thus conferring a survival advantage and facilitating further growth and invasion.

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Mix & Match: Phenotypic coexistence as a key facilitator of solid tumour invasion

Cited by 3 publications

References 53 publications

A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations

A Non-local Cross-Diffusion Model of Population Dynamics II: Exact, Approximate, and Numerical Traveling Waves in Single- and Multi-species Populations

A Non-local Cross-Diffusion Model of Population Dynamics I: Emergent Spatial and Spatiotemporal Patterns

The Harsh Microenvironment in Early Breast Cancer Selects for a Warburg Phenotype

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