= Solution
For each alignment column, ignore gaps, form the <empirical distribution> of its <amino acids>, and calculate its <Shannon entropy> in bits. The requested <alignment column information content> is
$$
\boxed{R_i=\log_2(20)-H_i
=\sum_{a:p_{ia}>0}p_{ia}\log_2(20p_{ia}).}
$$
Thus it is the <relative entropy> from the column distribution to the uniform distribution on twenty <amino acids>, not the ordinary <Shannon entropy> itself. A column containing one residue type has the maximum value $\log_2(20)=4.321928$ bits.
``
information = []
for j in range(A.shape[1]):
counts, n = emission_counts(A[:, j])
p = np.array(list(counts.values()), dtype=float) / n
H = -np.sum(p * np.log2(p))
information.append(float(np.log2(20) - H))
print(np.round(information, 4))
``
\b[The values for all 79 alignment columns are as follows], in bits. Each line lists its one-based column interval followed by the corresponding values in order:
``
01–10: 1.9025, 1.5964, 1.9025, 3.8187, 1.9025, 1.5964, 1.9025, 3.5577, 1.9025, 1.9025
11–20: 2.4420, 3.3355, 1.5964, 4.3219, 3.8187, 1.6803, 3.0975, 3.3355, 3.0975, 2.4420
21–30: 2.5692, 2.8219, 3.5106, 3.3219, 4.3219, 4.3219, 2.8000, 2.0703, 2.6574, 1.8003
31–40: 2.1938, 1.9163, 3.7784, 3.2606, 1.6803, 1.6803, 2.6642, 2.5692, 2.8753, 2.2631
41–50: 2.8753, 3.3355, 1.6803, 2.9703, 3.3355, 2.7914, 2.2086, 2.5692, 4.3219, 1.3742
51–60: 2.2631, 4.3219, 4.3219, 3.8187, 4.3219, 3.5577, 2.8753, 1.9025, 2.7914, 2.0409
61–70: 3.3355, 2.7370, 2.4309, 2.4309, 2.5692, 2.0409, 2.5692, 3.3355, 2.9298, 3.5577
71–79: 1.9025, 1.8187, 4.3219, 2.2631, 3.8187, 2.4309, 1.9025, 1.9025, 1.9025
``
A high score indicates conservation among the observed nongap letters, but does not itself imply low <gap fraction>. For example, an insertion column represented by only one observed nongap residue has maximal information by this calculation; its tiny sample size still makes that estimate uncertain.
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