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Branching Process Models of Cancer
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TLDR
This chapter uses multitype branching processes with mutation to model cancer, with cancer progression, resistance to therapy, and metastasis in mind, and investigates the time of the first type k mutation and the growth of the number of type k cells.Abstract:
In this chapter, we will use multitype branching processes with mutation to model cancer. With cancer progression, resistance to therapy, and metastasis in mind, we will investigate τ k , the time of the first type k mutation, and σ k , the time of the first type k mutation that founds a family line that does not die out, as well as the growth of the number of type k cells. The last three sections apply these results to metastasis, ovarian cancer, and tumor heterogeneity. Even though martingales and stable laws are mentioned, these notes should be accessible to a student who is familiar with Poisson processes and continuous time Markov chains.read more
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The mathematics of cancer: integrating quantitative models
TL;DR: The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance.
Journal ArticleDOI
Extremely high genetic diversity in a single tumor points to prevalence of non-Darwinian cell evolution
Shaoping Ling,Zheng Hu,Z.F. Yang,Fang Yang,Yawei Li,Pei Lin,Ke Chen,Lili Dong,Lihua Cao,Yong Tao,Lingtong Hao,Qingjian Chen,Qiang Gong,Dafei Wu,Wenjie Li,Wenming Zhao,Xiuyun Tian,Chunyi Hao,Eric A. Hungate,Daniel V.T. Catenacci,Richard R. Hudson,Wen-Hsiung Li,Xuemei Lu,Chung-I Wu,Chung-I Wu,Chung-I Wu +25 more
TL;DR: A single tumor is evaluated by sequencing or genotyping nearly 300 regions from the tumor and the number of coding region mutations was estimated to be greater than 100 million in this unexceptional tumor, suggesting non-Darwinian evolution should be heeded in cancer treatments even for microscopic tumors.
Journal ArticleDOI
Quantification of subclonal selection in cancer from bulk sequencing data.
Marc J Williams,Marc J Williams,Benjamin Werner,Timon Heide,Christina Curtis,Chris P. Barnes,Andrea Sottoriva,Trevor A. Graham +7 more
TL;DR: Application of the method to high-depth sequencing data from breast, gastric, blood, colon and lung cancer samples, as well as metastatic deposits, showed that detectable subclones under selection consistently emerged early during tumor growth and had a large fitness advantage.
Journal ArticleDOI
Minimal functional driver gene heterogeneity among untreated metastases
Johannes G. Reiter,Johannes G. Reiter,Alvin Makohon-Moore,Jeffrey M. Gerold,Alexander Heyde,Marc A. Attiyeh,Zachary A. Kohutek,Collin Tokheim,Alexia Brown,Rayne M. DeBlasio,Juliana Niyazov,Amanda Zucker,Rachel Karchin,Rachel Karchin,Kenneth W. Kinzler,Christine A. Iacobuzio-Donahue,Bert Vogelstein,Martin A. Nowak +17 more
TL;DR: Within individual patients, a large majority of driver gene mutations are common to all metastases, and a mathematical model of tumor evolution and metastasis formation provides an explanation for the observed driver gene homogeneity.
References
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TL;DR: The interim integrative analysis of DNA copy number, gene expression and DNA methylation aberrations in 206 glioblastomas reveals a link between MGMT promoter methylation and a hypermutator phenotype consequent to mismatch repair deficiency in treated gliobeasts, demonstrating that it can rapidly expand knowledge of the molecular basis of cancer.