Allele Frequency Spectrum in a Cancer Cell Population

Hisashi Ohtsuki, Hideki Innan

 

Abstract

A cancer grows from a single cell, thereby constituting a large cell population. In this work, we are interested in how mutations accumulate in a cancer cell population. We provide a theoretical framework of the stochastic process in a cancer cell population and obtain near exact expressions of allele frequency spectrum or AFS (only continuous approximation is involved) from both forward and backward treatments under a simple setting; all cells undergo cell division and die at constant rates, b and d, respectively, such that the entire population grows exponentially. This setting means that once a parental cancer cell is established, in the following growth phase, all mutations are assumed to have no effect on b or d (i.e., neutral or passengers). Our theoretical results show that the difference from organismal population genetics is mainly in the coalescent time scale, and the mutation rate is defined per cell division, not per time unit (e.g., generation). Except for these two factors, the basic logic are very similar between organismal and cancer population genetics, indicating that a number of well established theories of organismal population genetics could be translated to cancer population genetics with simple modifications.

doi: http://biorxiv.org/content/early/2017/01/30/104158 

 

 

Heterogeneity in the tumour size dynamics differentiates Vemurafenib, Dabrafenib and Trametinib in metastatic melanoma

Hitesh Mistry, David Orrell, Raluca Eftimie

 

Abstract

Molecular heterogeneity in tumours leads to variability in drug response both between patients and across lesions within a patient. These sources of variability could be explored through analysis of routinely collected clinical trial imaging data. We applied a mathematical model of tumour growth to analyse both within and between patient variability in tumour size dynamics to clinical data from three drugs, Vemurafenib, Dabrafenib and Trametinib, used in the treatment of metastatic melanoma. The analysis revealed: 1) existence of homogeneity in drug response and resistance development within a patient; 2) tumour shrinkage rate does not relate to rate of resistance development; 3) Vemurafenib and Dabrafenib, two BRAF inhibitors, have different variability in tumour shrinkage rates. Overall these results show how analysis of the dynamics of individual lesions can shed light on the within and between patient differences in tumour shrinkage and resistance rates, which could be used to gain a macroscopic understanding of tumour heterogeneity.

Keywords: heterogeneity, vemurafenib, dabrafenib, trametinib, melanoma, metastasis 

doi: http://biorxiv.org/content/early/2017/01/26/103366

 

 

Microenvironmental cooperation promotes early spread and bistability of a Warburg-like phenotype

Jorge Fernandez-de-Cossio-Diaz, Andrea De Martino, Roberto Mulet

(Submitted on 24 Jan 2017)

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Such a behaviour turns out to be linked to the re-cycling of overflow products by non-aberrant cells. Quantitative insight on the overall emerging picture is provided by a spatially homogeneous version of the model.

link: https://arxiv.org/abs/1701.06781