Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments

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

doi:10.1007/s00285-019-01441-5

Cited by 29 publications

(69 citation statements)

References 74 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 1 in Appendix A). This is consistent with the analytical results that we presented in Ardaševa et al (2019). < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > t t t < l a t e x i t s h a 1 _ b a s e 6 4 = " ( n u l l ) " > ( n u l l ) < / l a t e x i t > Fig.…”

Section: Constant Oxygen Inflowsupporting

confidence: 93%

“…Theorem 2 in Appendix A). This is in line with the analytical results presented in Ardaševa et al (2019).…”

Section: Periodic Oxygen Inflowsupporting

confidence: 92%

“…Here, the parameters γ and ζ are the maximum cell division rates of fully oxidative and fully glycolytic phenotypic variants, respectively. As we noted in Ardaševa et al (2019), definition (7) leads to a fitness function that is close to the approximate fitness landscapes which can be inferred from experimental data through regression techniques -see, for instance, equation (1) in Otwinowski and Plotkin (2014).…”

Section: Cell Dynamicsmentioning

confidence: 84%

“…Building upon the modelling framework that we presented in Ardaševa et al (2019), we describe the evolution of the two cell populations through the following system of conservation equations for the population density functions…”

Section: Cell Dynamicsmentioning

confidence: 99%

“…In this paper, we use a phenotype-structured model of evolutionary dynamics in time-varying but spatially homogeneous environments to elucidate the mechanisms that underpin the adaptation of cell populations to fluctuating oxygen inflow. Building upon the modelling framework that we presented in Ardaševa et al (2019), the model is defined in terms of a system of non-local parabolic partial differential equations (PDEs) for the evolution of the phenotype distributions of two competing cell populations that undergo heritable, spontaneous phenotypic variations at different rates. Similar PDEs modelling the evolutionary dynamics of populations structured by continuous traits in periodically-fluctuating environments have recently received increasing attention from the mathematical community Mirrahimi et al, 2015;Iglesias and Mirrahimi, 2018;Carrere and Nadin, 2019).…”

mentioning

confidence: 99%

See 4 more Smart Citations

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

Ardaševa

Gatenby

Anderson

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Constant Oxygen Inflowsupporting

confidence: 93%

“…Theorem 2 in Appendix A). This is in line with the analytical results presented in Ardaševa et al (2019).…”

Section: Periodic Oxygen Inflowsupporting

confidence: 92%

Section: Cell Dynamicsmentioning

confidence: 84%

Section: Cell Dynamicsmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

Ardaševa

Gatenby

Anderson

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

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

2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Evolutionary Dynamics in Vascularised Tumours under Chemotherapy: Mathematical Modelling, Asymptotic Analysis and Numerical Simulations

2020

Self Cite

View full text Add to dashboard Cite

We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of tumour cells, the concentration of oxygen and the concentration of a chemotherapeutic agent. In order to disentangle the impact of different evolutionary parameters on the emergence of intra-tumour phenotypic heterogeneity and the development of resistance to chemotherapy, we construct explicit solutions to the equation for the phenotypic distribution of tumour cells and provide a detailed quantitative characterisation of the long-time asymptotic behaviour of such solutions. Analytical results are integrated with numerical simulations of a calibrated version of the model based on biologically consistent parameter values. The results obtained provide a theoretical explanation for the observation that the phenotypic properties of tumour cells in vascularised tumours vary with the distance from the blood vessels. Moreover, we demonstrate that lower oxygen levels may correlate with higher levels of phenotypic variability, which suggests that the presence of hypoxic regions supports intra-tumour phenotypic heterogeneity. Finally, the results of our analysis put on a rigorous mathematical basis the idea, previously suggested by formal asymptotic results and numerical simulations, that hypoxia favours the selection for chemoresistant phenotypic variants prior to treatment. Consequently, this facilitates the development of resistance following chemotherapy.

show abstract

Evolutionary dynamics of competing phenotype-structured populations in periodically fluctuating environments

Cited by 29 publications

References 74 publications

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

A mathematical dissection of the adaptation of cell populations to fluctuating oxygen levels

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

Evolutionary Dynamics in Vascularised Tumours under Chemotherapy: Mathematical Modelling, Asymptotic Analysis and Numerical Simulations

Contact Info

Product

Resources

About