A comprehensive continuous-time model for the appearance of CGH signal due to chromosomal missegregations during mitosis

Abstract

Aneuploidy, the gain or loss of large regions of the genome, is a common feature in cancer cells. Irregularities in chromosomal copy number caused by missegregations of chromosomes during mitosis can be visualized by cytogenetic techniques including fluorescence in situ hybridization (FISH), spectral karyotyping (SKY) and comparative genomic hybridization (CGH). In the current work, we consider the propagation of irregular copy numbers throughout a cell population as the individual cells progress through ordinary mitotic cell cycles. We use an algebraic model to track the different copy numbers as states in a stochastic process, based on the model of chromosome instability of Gusev, Kagansky, and Dooley, and consider the average copy number of a particular chromosome within a cell population as a function of the cell division rate. We review a number of mathematical models for determining the length of the cell cycle, including the Smith-Martin transition probability model and the "sloppy size" model of Wheals, Tyson and Diekmann. The program MITOSIM simulates the growth of a population of cells using the aforementioned models of the cell cycle. MITOSIM allows the cell population to grow, with occasional resampling, until the average copy number of a given chromosome in the population reaches a preset threshold signifying a positive copy number alteration in this region. MITOSIM calculates the relationship between the missegregation rate and the growth rate of the cell population. This allows the user to test hypotheses regarding the effect chromosomal aberrations have upon the cell cycle, cell growth rates, and time to population dominance.

A Markov chain for numerical chromosomal instability in clonally expanding populations

“…This Markov chain has several advantages over the computational models used by Laughney et al . [ 4 ] and in the previous papers [ 9 , 10 ]. For example, it allows us to determine, without having to run lengthy computer simulations, the probability that a random cell after g generations has i of copies of a certain chromosome, for any given g , i and an initial distribution of karyotypes.…”

“…Finally, a continuous time model based on the one from Gusev et al . [ 9 , 24 ] was developed by Desper, Difilippantonio, Ried and Schäffer [ 10 ]. This model uses an exponential distribution for the time between cell divisions, and it allows to vary the cell division rates as a function of the number of copies of the chromosome.…”

“…[ 9 ] and later in a continuous time model by Desper et al . [ 10 ]. While helpful, these models neglected the observed phenomenon that having more copies of chromosomes encoding a higher fraction of oncogenes is advantageous for the cell, while having more copies of chromosomes encoding tumor suppressor genes increases its chances of dying [ 8 ].…”

Predicting CIN rates from single-cell whole genome sequencing data using anin silicomodel

“…These physiological restrictions form an important advance over prior models, which used much larger numbers (i.e. thousands) of generations for their simulations [26][27][28][29][30].…”

Proliferative advantage of specific aneuploid cells drives evolution of tumor karyotypes

“…While in healthy cells, aneuploidy causes a strong anti-proliferative response as a result of gene dosage imbalances (Santaguida et al, 2015) this response can be overcome in cancer cells, allowing the increased frequency of errors to promote aneuploid karyotype evolution and acceleration of tumor formation (Duijf & Benezra, 2013;van Jaarsveld & Kops, 2016). These ideas have emerged from extensive studies of aneuploidy in different systems including cell lines (Cimini et al, 2001;Thompson & Compton, 2008, 2011a, organoids (Bolhaqueiro et al, 2019;Drost & Clevers, 2018;Narkar et al, 2021), animal models (Bolton et al, 2016;Sheppard et al, 2012;Shoshani et al, 2021;Trakala et al, 2021), as well as theoretically (Araujo et al, 2013;Desper et al, 2005;Elizalde et al, 2018;Gusev et al, 2000Gusev et al, , 2001Laughney et al, 2015;Lynch et al, 2021). Yet, how the interplay between chromosome missegregation, cell proliferation and other processes drives long-term karyotype evolution is poorly understood.…”