Borrowing ecological theory to infer interactions between sensitive and resistant breast cancer cell populations

Susswein, Zachary; Sengupta, Surojeet; Clarke, Robert B.; Bansal, Shweta

doi:10.1101/2022.02.18.481041

“…Another predator-prey mathematical model showed evidence of reciprocal antagonism at play within competition dynamics of parental and radiation-resistant cell lines [24]. These models have also been applied to endocrine therapy [25] and doxorubicin therapy [26,27] in breast cancer cell lines. There is also evidence of the existence of positive or cooperative ecological interactions in cancer: one recent study indicated paracrine signaling as a mechanism for which the dominant cell line's growth is enhanced by the presence of a co-cultured second cell line [28].…”

Section: Measuring Effective Games In Oncologymentioning

confidence: 99%

Games and the Treatment Convexity of Cancer

Bayer,

West

2023

Dyn Games Appl

5

0

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Evolutionary game theory has been highly valuable in studying frequency-dependent selection and growth between competing cancer phenotypes. We study the connection between the type of competition as defined by properties of the game, and the convexity of the treatment response function. Convexity is predictive of differences in the tumor's response to treatments with identical cumulative doses delivered with different variances. We rely on a classification of 2 × 2 games based on the signs of 'dilemma strengths', containing information about the kind of selection through the game's equilibrium structure. With the disease starting in one game class, we map the type of effects treatment may have on the game depending on dosage and the implications of treatment convexity. Treatment response is a linear function of dose if the game is a prisoner's dilemma, coordination, or harmony game and does not change game class, but may be convex or concave for anti-coordination games. If the game changes class, there is a rich variety in response types including convex-concave and concave-convex responses for transitions involving anti-coordination games, response discontinuity in case of a transition out of coordination games, and hysteresis in case of a transition through coordination games.

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“…cell density can either increase or decrease the efficacy of antibiotics. Existing work such as (Kaznatcheev et al 2019), (Paczkowski et al 2021), (Emond et al 2021), (Susswein et al 2022), and (Farrokhian et al 2022) shows that interactions between drug sensitive and resistant cancerous cells can shape the population’s evolution of drug resistance. To analyze the role of density dependence, especially in drug resistance, we consider one of the first, classical mathematical models of density-dependent population dynamics, Verhulst’s logistic growth model (Verhulst 1838), which describes the dynamics of a homogeneous population in terms of its net growth rate: …”

Section: Introductionmentioning

confidence: 99%

Inferring Density-Dependent Population Dynamics Mechanisms through Rate Disambiguation for Logistic Birth-Death Processes

Huynh

¹

,

Scott

²

,

Thomas

³

2022

Preprint

0

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Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether it happens through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited data sets, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.Mathematics Subject Classifications60J27 · 92D25 · 62M10 · 60J25

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“…cell density can either increase or decrease the efficacy of antibiotics. Existing work such as (Kaznatcheev et al 2019), (Paczkowski et al 2021), (Emond et al 2021), (Susswein et al 2022), and (Farrokhian et al 2022) shows that interactions between drug sensitive and resistant cancerous cells can shape the population's evolution of drug resistance. To analyze the role of density dependence, especially in drug resistance, we consider one of the first, classical mathematical models of density-dependent population dynamics, Verhulst's logistic growth model (Verhulst 1838), which describes the dynamics of a homogeneous population in terms of its net growth rate:…”

Section: Introductionmentioning

confidence: 99%

Inferring Density-Dependent Population Dynamics Mechanisms through Rate Disambiguation for Logistic Birth-Death Processes

Huynh¹,

Scott²,

Thomas³

2022

Preprint

0

View full text Add to dashboard Cite

Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can manifest in birth processes, death processes, or both. Therefore, we utilize the mean and variance of cell number fluctuations to separately identify birth and death rates from time series that follow stochastic birth-death processes with logistic growth. Our method provides a novel perspective on stochastic parameter identifiability, which we validate by analyzing the accuracy in terms of the discretization bin size. We apply our method to the scenario where a homogeneous cell population goes through three stages: (1) grows naturally to its carrying capacity, (2) is treated with a drug that reduces its carrying capacity, and (3) overcomes the drug effect to restore its original carrying capacity. In each stage, we disambiguate whether it happens through the birth process, death process, or some combination of the two, which contributes to understanding drug resistance mechanisms. In the case of limited data sets, we provide an alternative method based on maximum likelihood and solve a constrained nonlinear optimization problem to identify the most likely density dependence parameter for a given cell number time series. Our methods can be applied to other biological systems at different scales to disambiguate density-dependent mechanisms underlying the same net growth rate.

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Borrowing ecological theory to infer interactions between sensitive and resistant breast cancer cell populations

Cited by 6 publications

References 49 publications

Games and the Treatment Convexity of Cancer

Games and the Treatment Convexity of Cancer

Inferring Density-Dependent Population Dynamics Mechanisms through Rate Disambiguation for Logistic Birth-Death Processes

Inferring Density-Dependent Population Dynamics Mechanisms through Rate Disambiguation for Logistic Birth-Death Processes

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