Population dynamics of multiple ecDNA types (2411.14588v3)

Abstract: Extrachromosomal DNA (ecDNA) can drive oncogene amplification, gene expression and intratumor heterogeneity, representing a major force in cancer initiation and progression. The phenomenon becomes even more intricate as distinct types of ecDNA present within a single cancer cell. While exciting as a new and significant observation across various cancer types, there is a lack of a general framework capturing the dynamics of multiple ecDNA types theoretically. Here, we present novel mathematical models investigating the proliferation and expansion of multiple ecDNA types in a growing cell population. By switching on and off a single parameter, we model different scenarios including ecDNA species with different oncogenes, genotypes with same oncogenes but different point mutations and phenotypes with identical genetic compositions but different functions. We analyse the fraction of ecDNA-positive and free cells as well as how the mean and variance of the copy number of cells carrying one or more ecDNA types change over time. Our results showed that switching does not play a role in the fraction and copy number distribution of total ecDNA-positive cells, if selection is identical among different ecDNA types. In addition, while cells with multiple ecDNA cannot be maintained in the scenario of ecDNA species without extra fitness advantages, they can persist and even dominate the ecDNA-positive population if switching is possible.

• The paper introduces novel mathematical models using both deterministic ODEs and stochastic simulations to capture the dynamics of multiple ecDNA types.
• It demonstrates that fitness discrepancies and switching probabilities significantly affect ecDNA distribution and influence tumor evolution.
• The findings highlight the need for tailored cancer therapies targeting ecDNA maintenance and switching mechanisms to combat treatment resistance.

Dynamics of Multiplicity in ecDNA Types

Introduction

The paper "Population dynamics of multiple ecDNA types" (2411.14588) explores the intricate dynamics of extrachromosomal DNA (ecDNA) in cancer cells, presenting novel mathematical models that describe the proliferation and evolution of multiple ecDNA types within a cell population. The study expands on existing models of single ecDNA type dynamics, providing a framework accounting for genetic and phenotypic variations that can influence cancer progression.

Modeling Framework

A core component of this study is its flexible modeling framework (Figure 1), which accommodates different ecDNA types through parameters dictating their interactions.

Figure 1: A general framework for modeling two ecDNA types.

The framework allows for modeling distinct species, genotypes with mutations, and phenotypes arising from epigenetic variations or switching. Switching mechanisms are represented via transition probabilities $p_y$ and $p_r$, illustrating genetic arrangement variabilities or phenotypical changes. The transition probabilities influence whether cells evolve to carry different types of ecDNA, impacting the evolutionary dynamics.

Deterministic and Stochastic Dynamics

Two mathematical methods are used to model ecDNA dynamics: deterministic ordinary differential equations (ODEs) and a stochastic framework (Figure 2). These approaches elucidate the density changes within cellular subpopulations — those carrying ecDNA and those that do not — and how these changes relate to parameters like reproduction rates ($s_y$, $s_r$) and switching probabilities.

Figure 2: ecDNA copy distribution among either identical or non-identical fitness scenarios.

For cells with identical fitness for both ecDNA types, the study finds that type-switching probabilities do not affect ecDNA-positive cells' distribution or ecDNA-free cells' fraction, while fitness discrepancies break this independence.

Analytical and Numerical Insights

The paper discusses analytical solutions aligning with stochastic simulations (Figure 3), particularly focusing on the implications of switching mechanisms on maintaining heterogeneous ecDNA types within a cellular population under different selection scenarios.

Figure 3: Weighted first moment dynamics for ecDNA species.

EcDNA-positive cells maintain different kinetics under identical selective pressures compared to distinct selection strengths. More specifically, one-way and two-way switching impact mean copy numbers differently, evident in the model's results depicting growth dynamics rooted in evolutionary advantages gained through ecDNA's genetic or phenotypic flexibility.

Two-Way Switching's Influence

When examining two-way switching scenarios, the paper's results (Figure 4) suggest that such dynamics encourage a balance between pure and mix cell populations, with switching facilitating greater ecDNA type mixing.

Figure 4: Weighted first moment dynamics in the neutral case for ecDNA geno-/pheno-types, two-way switching.

Switching contributes to sustaining a diverse ecDNA repertoire, thus influencing tumor evolutionary paths and potentially complicating treatment as several ecDNA types may confer differential responses to therapy.

Discussion and Implications

This study provides significant insights into ecDNA dynamics, positing that both genetic mutations and phenotypic state changes significantly influence cancer cell evolution and therapy resistance. The models suggest strategic implications for cancer treatment, underscoring the need for interventions targeting ecDNA maintenance mechanisms and switching pathways to preemptively address potential resistance developments.

Conclusion

The models proposed in this study serve as significant advancements in understanding ecDNA dynamics, incorporating an analytical approach backed by empirical simulation. This framework reveals ecDNA's contribution to cancer's genetic diversity and resistance capabilities, highlighting the necessity of tailored strategies addressing ecDNA-induced heterogeneity in therapeutic contexts.