Answer:
1. If the gene is weakly activated, it likely lacks repressive histone modifications, but may also lack the presence of histone marks associated with strong transcriptional activation such as acetylation.
When the gene is strongly activated, it likely lacks repressive marks (such as H3K9me2/3 and H3K27me3 - both examples of repressive histone methylation) and might possess some activating histone acetylation marks, such as H3K4ac, and active histone methylation such as H3K4me3
<em>An aside: The pattern and presence of different histone modifications would depend on the gene, but based on the fact that it is a developmental gene, I would assume that H3K27me3 and H3K4me3 are at play (these are part of the Polycomb/Trithorax system)</em>
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After limb growth is complete, the gene is turned off. Repressive histone methylation marks would be associated with this state, such as the aforementioned H3K9me2/3 or H3K27me3.
2. Histone modifications are tightly linked to genome organisation. Histone methylation marks associated with repression such as H3K27me3 and H3K9me3 are associated with compact chromatin structures, which restrict the access of transcriptional machinery and other positive regulators. Conversely, histone marks associated with gene activation are associated with a more permissive chromatin environment that facilitates the binding of factors associated with gene expression. In the case of histone acetylation, the acetyl mark directly removes the positive charge of chromatin, relaxing its interaction with negatively charged DNA.
3. If the inappropriate activation of this gene caused a cancerous tumor, this gene would be referred to as an oncogene (or a proto-oncogene for the term before it is inappropriately activated).
Typically, there are two classes of genes that lead to cancer: tumor-suppressor genes and oncogenes. Tumor suppressor genes lead to cancer when their protective activity is reduced or demolished, leading to the production of cancer cells. Oncogenes lead to cancer when they become over active. Oncogenes are often genes associated positively with growth and proliferation, consistent with the gene in this example.