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3.1 Overview
We develop semi-parametric Bayesian inference for data obtained from a human phage
display experiment. The experiment is carried out to learn about preferential binding
of proteins in certain organs. The long-term goal is to exploit such knowledge to
develop targeted therapies that could deliver a drug to specific tissues and limit side
effects such as toxicity (Kolonin et al., 2006; Arap et al., 2006). A phage library
is a collection of millions of phages, each displaying different peptide sequences. In
a bio-panning experiment the phage display library is exposed to a target. Phages
with proteins that do not bind to the target are washed away, leaving only those
with proteins that are binding specifically to the target. A critical limitation of the
described experiment is the lack of any amplification. Suppose that the peptide A
binds to the tissue T with high affinity. In addition, suppose that we are using a
library that contains a small amount of peptide A among a large number of different
peptides. We may observe only a small count of the peptide A in the tissue T
and therefore, we may not detect this binding behavior. To mitigate this limitation
Kolonin et al. (2006) proposed to perform multistage phage display experiment, that
is, to perform successive stages of panning (usually three or four) to enrich peptides
that bind to the targets. This procedure allows for the counts of peptides like A
referred above to increase in every stage and, therefore, it increases the chance of
detecting their binding behavior.
Kolonin et al. (2006) use a Bayesian beta-binomial model to make a list of the
peptides with relatively large increases from the first to the third stages. The outcome
of this first step is a list of peptide∕tissue pairs with the highest posterior probability of
increasing frequencies over the three stages. In a next step, for each peptide A tissue
T in this list, they compare the count of peptide A in tissue T in the last (third)
stage, versus the count of peptide A in the unselected library (a representative draw
from the peptide library injected into the first stage of the phage display experiment).
They consider a two-by-two table with counts in tissue T in the first row and counts