A mathematical model of the metastatic bottleneck predicts patient outcome and response to cancer treatment

Szczurek, Ewa; Krüger, Tyll; Klink, Barbara; Beerenwinkel, Niko

doi:10.1371/journal.pcbi.1008056

Cited by 21 publications

(22 citation statements)

References 38 publications

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“…The terms “dissemination” and “seeding” are used interchangeably in this paper as we do not model the processes in between. For models regarding other parts of the metastatic cascade, see [ 36 , 37 ]. The primary and the single-clone-seeded metastatic tumor are detected until they reach size N , respectively.…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, here we do not model the circulatory phase of metastasis, a bottleneck that could confound the M-P divergence further. Unified mathematical models have been proposed to understand the full picture of this phase [ 36 , 37 , 63 ], which would aid the decomposition of the complexity of metastases. While our analysis here is applied to the specific case of metastatic progression, the usefulness of our approach extends to the case of comparing longitudinal tumor samples, as well.…”

Section: Discussionmentioning

confidence: 99%

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Elements and evolutionary determinants of genomic divergence between paired primary and metastatic tumors

Sun

Νικολακόπουλος

2021

PLoS Comput Biol

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Can metastatic-primary (M-P) genomic divergence measured from next generation sequencing reveal the natural history of metastatic dissemination? This remains an open question of utmost importance in facilitating a deeper understanding of metastatic progression, and thereby, improving its prevention. Here, we utilize mathematical and computational modeling to tackle this question as well as to provide a framework that illuminates the fundamental elements and evolutionary determinants of M-P divergence. Our framework facilitates the integration of sequencing detectability of somatic variants, and hence, paves the way towards bridging the measurable between-tumor heterogeneity with analytical modeling and interpretability. We show that the number of somatic variants of the metastatic seeding cell that are experimentally undetectable in the primary tumor, can be characterized as the path of the phylogenetic tree from the last appearing variant of the seeding cell back to the most recent detectable variant. We find that the expected length of this path is principally determined by the decay in detectability of the variants along the seeding cell’s lineage; and thus, exhibits a significant dependence on the underlying tumor growth dynamics. A striking implication of this fact, is that dissemination from an advanced detectable subclone of the primary tumor can lead to an abrupt drop in the expected measurable M-P divergence, thereby breaking the previously assumed monotonic relation between seeding time and M-P divergence. This is emphatically verified by our single cell-based spatial tumor growth simulation, where we find that M-P divergence exhibits a non-monotonic relationship with seeding time when the primary tumor grows under branched and linear evolution. On the other hand, a monotonic relationship holds when we condition on the dynamics of progressive diversification, or by restricting the seeding cells to always originate from undetectable subclones. Our results highlight the fact that a precise understanding of tumor growth dynamics is the sine qua non for exploiting M-P divergence to reconstruct the chronology of metastatic dissemination. The quantitative models presented here enable further careful evaluation of M-P divergence in association with crucial evolutionary and sequencing parameters.

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Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Elements and evolutionary determinants of genomic divergence between paired primary and metastatic tumors

Sun

Νικολακόπουλος

2021

PLoS Comput Biol

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“…To integrate newly discovered pathways, appropriate computational models are required to describe cell-to-cell interactions and protein expression dynamics. The conventional computational models include, but not limited to, mechanistic models [ 69 - 71 ], statistical models [ 72 , 73 ], and data-driven models [ 74 ].…”

Section: Discussionmentioning

confidence: 99%

Integrating single cell sequencing with a spatial quantitative systems pharmacology model spQSP for personalized prediction of triple-negative breast cancer immunotherapy response

et al. 2021

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Response to cancer immunotherapies depends on the complex and dynamic interactions between T cell recognition and killing of cancer cells that are counteracted through immunosuppressive pathways in the tumor microenvironment. Therefore, while measurements such as tumor mutational burden provide biomarkers to select patients for immunotherapy, they neither universally predict patient response nor implicate the mechanisms that underlie immunotherapy resistance. Recent advances in single-cell RNA sequencing technology measure cellular heterogeneity within cells of an individual tumor but have yet to realize the promise of predictive oncology. In addition to data, mechanistic multiscale computational models are developed to predict treatment response. Incorporating single-cell data from tumors to parameterize these computational models provides deeper insights into prediction of clinical outcome in individual patients. Here, we integrate whole-exome sequencing and scRNA-seq data from Triple-Negative Breast Cancer patients to model neoantigen burden in tumor cells as input to a spatial Quantitative System Pharmacology model. The model comprises a four-compartmental Quantitative System Pharmacology sub-model to represent a whole patient and a spatial agent-based sub-model to represent tumor volumes at the cellular scale. We use the high-throughput single-cell data to model the role of antigen burden and heterogeneity relative to the tumor microenvironment composition on predicted immunotherapy response. We demonstrate how this integrated modeling and single-cell analysis framework can be used to relate neoantigen heterogeneity to immunotherapy treatment outcomes. Our results demonstrate feasibility of merging single-cell data to initialize cell states in multiscale computational models such as the spQSP for personalized prediction of clinical outcomes to immunotherapy.

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“…This suggests that these genome level processes can be important in the invasion process as has also been implicated in the evolutionary ecology of invasive species (Bock et al, 2015;Mounger et al, 2021a). At the same time, bottleneck events shape the genomics and evolution of metastatic cancers (Loeb et al, 2003;Szczurek et al, 2020;Patel et al, 2021), and clonal diversity varies by cancer type and the recipient tissues of the metastases (Turajlic et al, 2018). All the progress in cancer genomics notwithstanding, the cancer research community has been unable to identify any common events that provide a universal predictor FIGURE 1 | A schematic figure that compares the steps of biological invasion in invasive species (adopted from Theoharides and Dukes, 2007) and cancers (adopted from Gatenby et al, 2009).…”

Section: Introductionmentioning

confidence: 98%

The Genomic Processes of Biological Invasions: From Invasive Species to Cancer Metastases and Back Again

et al. 2021

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The concept of invasion is useful across a broad range of contexts, spanning from the fine scale landscape of cancer tumors up to the broader landscape of ecosystems. Invasion biology provides extraordinary opportunities for studying the mechanistic basis of contemporary evolution at the molecular level. Although the field of invasion genetics was established in ecology and evolution more than 50 years ago, there is still a limited understanding of how genomic level processes translate into invasive phenotypes across different taxa in response to complex environmental conditions. This is largely because the study of most invasive species is limited by information about complex genome level processes. We lack good reference genomes for most species. Rigorous studies to examine genomic processes are generally too costly. On the contrary, cancer studies are fortified with extensive resources for studying genome level dynamics and the interactions among genetic and non-genetic mechanisms. Extensive analysis of primary tumors and metastatic samples have revealed the importance of several genomic mechanisms including higher mutation rates, specific types of mutations, aneuploidy or whole genome doubling and non-genetic effects. Metastatic sites can be directly compared to primary tumor cell counterparts. At the same time, clonal dynamics shape the genomics and evolution of metastatic cancers. Clonal diversity varies by cancer type, and the tumors’ donor and recipient tissues. Still, the cancer research community has been unable to identify any common events that provide a universal predictor of “metastatic potential” which parallels findings in evolutionary ecology. Instead, invasion in cancer studies depends strongly on context, including order of events and clonal composition. The detailed studies of the behavior of a variety of human cancers promises to inform our understanding of genome level dynamics in the diversity of invasive species and provide novel insights for management.

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A mathematical model of the metastatic bottleneck predicts patient outcome and response to cancer treatment

Cited by 21 publications

References 38 publications

Elements and evolutionary determinants of genomic divergence between paired primary and metastatic tumors

Elements and evolutionary determinants of genomic divergence between paired primary and metastatic tumors

Integrating single cell sequencing with a spatial quantitative systems pharmacology model spQSP for personalized prediction of triple-negative breast cancer immunotherapy response

The Genomic Processes of Biological Invasions: From Invasive Species to Cancer Metastases and Back Again

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