Epigenetic inheritance is a term that describes heritable changes in gene expression that are not caused by DNA sequence. Purine dimers, mismatched bases, and the coding regions of genes are all describe information that is contained within the DNA sequence. Histone methylation patterns, however, are not contained within the DNA. This heritable information has various effects on gene expression that is not due to the sequence of DNA, thus making it an example of epigenetic inheritance. Expression patterns based on histone methylation affect the accessibility of a DNA sequence and the ability of RNA polymerase to bind the sequence for transcription, silencing a gene without actually altering it.

Out of the choices, only methylation of histones is commonly associated with the silencing of genes. Proteins known as histone methyltransferases bind a methyl group to amino acids in the histone, most commonly lysine or arginine. The result is a change in chromatin structure, most commonly blocking transcription sites and preventing expression.

Acetylation of histones is often found in activated genes. Phosphorylation of histones has been seen in DNA regulation, but it is unclear whether or not this modification affects the expression of genes.

The correct answer is insulators. Insulators are regions of DNA that serve as boundary elements, preventing the formation of euchromatin from heterochromatin. Mediators and chromosomal looping promote transcription factor recruitment to the DNA and promoter-enhancer interactions. Nuclear lamins provide structure to the nuclear envelope.

Methylation is one of the most common epigenetic modifications that can be made to DNA sequences, and it typically results in repression of transcription at that site. This is typically achieved by modifying activity of the promoter region of a given gene. 

Acetylation induces a change directly to the histone; the histone is typically positively charged and thus has a high level of interaction with the negatively charged DNA. Acetylation makes the histone less positive, and therefore it is less attracted to the DNA. This reduced interaction reduces the tight coiling of DNA around the histones, and transcriptional machinery has more access to the strand to increase transcription of genes at those sites. 

By adding acetyl groups to the positively charged histone tails, the cell can loosen the binding of DNA to a histone since DNA is largely negatively charged. This DNA can now be accessed by transcription machinery such as RNA polymerase. In this way acetylation of histones promotes transcription of genes on that piece of DNA. Deacetylation does the opposite - replaces positive charges onto histones so that they can interact more tightly with the DNA, ultimately suppressing expression of the DNA. 

CpG (cytosine-phosphate-guanine) methylation is a common type of epigenetic change caused by this set of enzymes. In this case, the bees use this to create difference castes of bees out of the same shared genome.