A method for copying the methylation patterns of molecules of genomic DNA (MGD) during isothermal amplification of the MGD comprising obtaining MGD, copying the methylation patterns of the MGD using a DNA methylation-maintenance enzyme, while isothermally amplifying the MGD using a DNA polymerase with strand displacement activity, under conditions that simultaneously promote activity of the DNA methylation-maintenance enzyme and the DNA polymerase; a method for copying the methylation patterns in double-stranded DNA molecules during isothermal amplification of the DNA molecules comprising obtaining DNA molecules, contacting the DNA molecules with transposable elements and an enzyme, which can randomly insert the transposable elements into the DNA molecules, copying the methylation patterns of the DNA molecules using a DNA methylation-maintenance enzyme, while isothermally amplifying the DNA molecules using a DNA polymerase with strand displacement activity, under conditions that simultaneously promote activity of the DNA methylation-maintenance enzyme and the DNA polymerase; a buffer comprising a divalent ion, deoxynucleotide triphosphates (dNTPs), primers, and S-adenosyl-methionine (SAM); and a composition comprising a DNA methylation-maintenance enzyme, a DNA polymerase with strand displacement activity, and the buffer.