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The motivation for this article is to present an easy to understand equation that illustrates how cancers can arise within a lifetime from relatively normal mutation and division rates.
An interesting observation is that the mutation frequency in a cancer genome is less than one mutation per 100,000 bases, which is consistent with relatively normal mutation and division rates [ 3].
First, in view of great intra-individual variability in mutation and division rates across organs, it would be more appropriate to compare cancer prevalence in each organ separately [ 20].
The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology.
Whereas the accumulation of sufficient numbers of driver mutations might be highly unlikely with normal mutation rates [ 38], new experimental data illustrate that colorectal cancer mutation frequencies are relatively low and consistent with normal mutation and division rates [ 3].
A more formal analysis of this equation was previously published [ 1], which predicted human colorectal cancers could arise with relatively normal mutation and division rates, and the current presentation is a simpler, algebraic version that may be easier to understand and manipulate.
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The key parameters in this probability model are the number of tumour cells at steady state, time that the tumour remains at steady state before treatment, initial rate of cell division, initial death rate of tumour cells, the rate of resistance mutations, and the division and death rates (r′ and d′, respectively) of sensitive cells under treatment, in the absence of density constraints [ 55].
A large (∼200) collection of strains carrying a metabolic mutation and a replication or division Ts mutation (apart the spontaneously isolated strains) was generated by transforming Ts cells with total DNA extracted from strains containing a labeled metabolic mutation.
The division, mutation, and death of individual cells results in an evolving set of cell populations that can be represented mathematically as a system of differential equations describing a Markov birth-death process.
Because (i) unbalanced metabolism might be sensed by cells as a stress, (ii) some nutritional stresses interfere with DNA replication [14], [15] and (iii) osmotic shocks can suppress Ts mutations in division and replication genes [29] [31], the effect of various stresses on the Ts phenotype of replication mutants was assessed.
Cancerous cells undergo frequent mutation, division and selection, ultimately leading to the fittest 'disregulated' phenotype.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com