Algorithmic Thinking in Bioinformatics End Term: 1 September 2024, Set QDB3 (May 2024 term)

Consider a system of 6 genes that regulate each other as follows:

• $G_1$ regulates $G_2$, $G_3$ and $G_4$.
• $G_5$ is regulated by $G_3$ and $G_2$.
• $G_2$ regulates $G_3$.
• $G_3$ regulates $G_4$.
• $G_6$ is regulated by $G_4$.

If we need 1 Byte to store a boolean value (i.e., 0 or 1), then how many Bytes are required to store the adjacency matrix of the underlying gene regulatory network?

In an alien world, mutations occur in every 10 million years only. A ultrametric tree is constructed on some of these alien species. If the height of the tree (defined as the maximum number of edges from the root to a leaf node in the tree) is 5, then calculate the age of the root node (in million years) of this ultrametric tree. (Hint: The distance between two nodes in consecutive levels is given in the question.)