Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments

Ardaševa, Aleksandra; Anderson, Alexander R.A.; Gatenby, Robert A.; Byrne, Helen M.; Maini, Philip K.; Lorenzi, Tommaso

doi:10.1103/physreve.102.042404

Cited by 17 publications

(14 citation statements)

References 55 publications

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“…Furthermore, although well suited to modeling the dynamics of large cell populations, PDE models like that considered here cannot capture adaptive phenomena that are driven by stochasticity in the evolutionary paths of single cells. Therefore, it would also be interesting to complement the results of our study with numerical simulations of corresponding individual-based models which track the evolutionary trajectories of single cells across a space of discrete phenotypic states, as similarly done in [7,21,23,89]. This would make it possible to have a more precise description of the phenotypic evolution of tumor cells in cases where cell numbers are relatively low and, therefore, stochastic fluctuations in single-cell phenotypic properties will have a stronger impact on intratumor phenotypic heterogeneity.…”

Section: Conclusion and Research Perspectivesmentioning

confidence: 99%

Modeling the Emergence of Phenotypic Heterogeneity in Vascularized Tumors

Villa¹,

Chaplain²,

Lorenzi³

2021

SIAM J. Appl. Math.

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We present a mathematical study of the emergence of phenotypic heterogeneity in vascularized tumors. Our study is based on formal asymptotic analysis and numerical simulations of a system of nonlocal parabolic equations that describes the phenotypic evolution of tumor cells and their nonlinear dynamic interactions with the oxygen, which is released from the intratumoral vascular network. Numerical simulations are carried out both in the case of arbitrary distributions of intratumor blood vessels and in the case where the intratumoral vascular network is reconstructed from clinical images obtained using dynamic optical coherence tomography. The results obtained support a more in-depth theoretical understanding of the eco-evolutionary process which underpins the emergence of phenotypic heterogeneity in vascularized tumors. In particular, our results offer a theoretical basis for empirical evidence indicating that the phenotypic properties of cancer cells in vascularized tumors vary with the distance from the blood vessels, and establish a relation between the degree of tumor tissue vascularization and the level of intratumor phenotypic heterogeneity.

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Section: Conclusion and Research Perspectivesmentioning

confidence: 99%

Modeling the Emergence of Phenotypic Heterogeneity in Vascularized Tumors

Villa¹,

Chaplain²,

Lorenzi³

2021

SIAM J. Appl. Math.

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“…Our purpose is to provide a numerical validation of the existence and stability of the endemic equilibrium solution predicted by the theory. The analysis of finite size effects on the system goes beyond the scope of the present manuscript, although it is straightforward to perform once the agent-based codes are set up 64 . Details of the numerical simulations can be found in the Supplementary Material.…”

Section: Methodsmentioning

confidence: 99%

Evolutionary epidemiology consequences of trait-dependent control of heterogeneous parasites

Miele

Evans

Cunniffe

et al. 2021

Preprint

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Optimising the use of chemical pesticide is required in order to reduce the inevitable environmental and economic costs related to it. The consequences of chemical control are particularly tricky to foresee in the presence of pathogens, displaying heterogeneous traits involved in their life cycle, because its effect will likely differ across the population. In this work, we investigate the effects of trait-dependent pesticide on heterogeneous plant pathogens, by means of a minimal model connecting evolutionary and agricultural states of the system. We model a pathogen population displaying continuous levels of virulence and transmission. Control strategies are modelled by the quantity of pesticide released and its degree of correlation with the pathogen’s heterogeneous traits. We show that the pathogen population can adapt towards opposite evolutionary states, that may be reversed by chemical control due to its heterogeneous selective pressure. This dual behaviour triggers saturating effects in yield production, with respect to pesticide use. As a consequence, we show that maximising yield production and minimising pesticide application are conflicting objectives. We identify Pareto-efficient solutions, where the optimal pesticide type depends on the applied quantity. Our results provide a theoretical framework to explore how to harness heterogeneity in pathogen populations to our advantage.

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“…Since the analytical results we have obtained can accommodate parameter values for a wide range of SI systems and a variety of infectious diseases, from an application point of view it would be interesting to apply these results to specific datasets in order to test the validity of the explicit condition for the spread of infection that we have derived. Moreover, building upon previous work on the derivation of deterministic continuum models for the evolution of populations structured by phenotypic traits from stochastic individual-based models (Chisholm et al 2016;Stace et al 2020;Ardaševa et al 2020;Champagnat et al 2002Champagnat et al , 2006, another track to follow to further enrich the present study would be to develop a stochastic individual-based model corresponding to the deterministic continuum model presented here. This would make it possible to explore the impact of stochastic fluctuations in phenotypic properties of single individuals on the spread of infections.…”

Section: μ(T) −→ ϕ(Imentioning

confidence: 98%

Evolutionary dynamics in an SI epidemic model with phenotype-structured susceptible compartment

2021

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We present an SI epidemic model whereby a continuous structuring variable captures variability in proliferative potential and resistance to infection among susceptible individuals. The occurrence of heritable, spontaneous changes in these phenotypic characteristics and the presence of a fitness trade-off between resistance to infection and proliferative potential are explicitly incorporated into the model. The model comprises an ordinary differential equation for the number of infected individuals that is coupled with a partial integrodifferential equation for the population density function of susceptible individuals through an integral term. The expression for the basic reproduction number R 0 is derived, the disease-free equilibrium and endemic equilibrium of the model are characterised and a threshold theorem involving R 0 is proved. Analytical results are integrated with the results of numerical simulations of a calibrated version of the model based on the results of artificial selection experiments in a host-parasite system. The results of our mathematical study disentangle the impact of different evolutionary parameters on the spread of infectious diseases and the consequent phenotypic adaption of susceptible individuals. In particular, these results provide a theoretical basis for the observation that infectious diseases exerting stronger selective pressures on susceptible individuals and being characterised by higher infection rates are more likely to spread. Moreover, our results indicate that heritable, spontaneous phenotypic changes in proliferative potential and resistance to infection can either promote or prevent the spread of infectious diseases depending on the strength of selection acting on susceptible individuals prior to infection. Finally, we demonstrate that, when an endemic equilibrium is established, higher levels of resistance to infection and lower degrees of phenotypic heterogeneity among susceptible individuals are to be expected in the presence of infections which are characterised by lower rates of death and exert stronger selective pressures.

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Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments

Cited by 17 publications

References 55 publications

Modeling the Emergence of Phenotypic Heterogeneity in Vascularized Tumors

Modeling the Emergence of Phenotypic Heterogeneity in Vascularized Tumors

Evolutionary epidemiology consequences of trait-dependent control of heterogeneous parasites

Evolutionary dynamics in an SI epidemic model with phenotype-structured susceptible compartment

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