Mickey Atwal, CSHL
$\mathbf{1}$. Estimate how many mutations in a 5ml culture of Escherichia coli that originally grew from a single bacterium.
$\mathbf{2}$. High-throughput screening assays, in the field of drug discovery, can typically test a library of millions of compounds to identify a few that are active. The challenge is to figure out how many assays do we need to perform before we can reliably identify a successful compound. Let’s assume that the success rate in these screens is one in ten thousand, $10^{−4}$ .
$\mathbf{3}$ . A neuron generates spikes at an average rate of $r$ spikes per second (Hertz). We can assume a homogeneous Poisson process to model the firing of spikes.
$\mathbf{4}$ . Let’s simulate a Poisson process with a constant rate $m$ in Python.
$\mathbf{5}$. Hemophilia is a disease associated with a recessive gene on the X chromosome. Since human males are XY, a male inheriting the mutant gene will always be affected. Human females, XX, with only one bad copy of the gene are simply carriers and are not affected, whereas females with two bad copies will be affected. Consider a woman with an affected brother. Her parents, her husband, and herself are all unaffected.
$\mathbf{6}$. A published study reported the micrarray expressions of a select number of genes in two kinds of tumors: those with BRCA1 mutations and those with BRCA2 mutations. The goal was to detect genes that showed differential expression across the two conditions. The data consists of the expression ratios of $3226$ genes on $n_1 = 7$ BRCA1 arrays and $n_2 = 8$ BRCA2 arrays.