DNA sometimes has chemical groups attached, called methyl groups, that affect gene expression. Suppose that, during each hour, first a fraction m of unmethylated locations on the DNA become methylated, and then a fraction u of methylated locations become unmethylated. Find a recursion for the fraction f of the DNA molecule that is methylated.

f = m - u

Explanation:

DNA methylation is an important epigenetic modification associated with the regulation of gene expression. As such, the analysis of DNA methylation marks and the dynamics of this process may shed light on the genes that are being expressed at a given time in a given cell type/tissue. In the example above described, f is defined as the fraction of the DNA molecule that is methylated after one (1) hour, whose value can be estimated by subtracting u fraction (i.e., fraction of methylated locations that become unmethylated) from m fraction (i.e., fraction of unmethylated locations that become methylated).

In consequence, the equation is

f = m - u

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