Abstract
This paper develops a mathematical model describing the evolutionary dynamics of a unicellular, asexually replicating population exhibiting chromosomal instability. Chromosomal instability is a form of genetic instability characterized by the gain or loss of entire chromosomes during cell division. We assume that the cellular genome is divided into several homologous groups of chromosomes, and that a single functional chromosome per homologous group is required for the cell to have the wild-type fitness. If the fitness is unaffected by the total number of chromosomes in the cell, our model is analytically solvable, and yields a mean fitness at mutation-selection balance that is identical to the mean fitness when there is no chromosomal instability. If this assumption is relaxed and the total number of chromosomes in the cell is not allowed to increase without bound, then chromosomal instability leads to a reduction in mean fitness. The results of this paper provide a useful baseline that can inform both future theoretial and experimental studies of chromosomal instability.
Highlights
Living systems have evolved a range of mechanisms to ensure the accurate transmission of their genetic information from one generation to the [1]
Genetic instability is a hallmark feature of cancer cells, and generally comes in one of two different forms: (1) Microsatellite INstability, or MIN, tumors, are characterized by elevated pointmutation rates and the accumulation of sequences of DNA in their chromosomes [1,2,3,4]. (2) Chromosomal INstability, or CIN, tumors, are characterized by a breakdown in chromosomal segregation mechanisms during cell division, leading to the gain or loss of entire chromosomes [1,2,3,4]
We assume that the organismal genome is organized as follows: We let N denote the total number of homologous groups in the genome
Summary
Living systems have evolved a range of mechanisms to ensure the accurate transmission of their genetic information from one generation to the [1]. 3. mz i,3 denotes the number of functional chromosomes in homologous group i of the parent cell that exhibit instability, and send two functional daughters into the left daughter cell.
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