Concept: What Is Shannon’s Entropy in Sequence Alignment?

Shannon’s entropy measures the variability (uncertainty) at each position
(column) of a multiple sequence alignment.

The Shannon entropy formula is:

H = − Σ p_i log₂ p_i

• p_i = frequency of each nucleotide (A, C, G, T) in a column
• Entropy is measured in bits

Note: Total alignment entropy is calculated as the
sum of entropies of all columns.

Step-by-Step Solution

Column 1

A A A A

p(A) = 1

H₁ = − (1 × log₂ 1) = 0

Column 2

C C G G

p(C) = 0.5, p(G) = 0.5

H₂ = − [0.5 log₂(0.5) + 0.5 log₂(0.5)] = 1 bit

Column 3

T T T C

p(T) = 0.75, p(C) = 0.25

H₃ = − [0.75 log₂(0.75) + 0.25 log₂(0.25)]

H₃ ≈ 0.811 bits

Column 4

A G C T

p(A) = p(G) = p(C) = p(T) = 0.25

H₄ = − 4 × (0.25 log₂ 0.25) = 2 bits

Total Shannon’s Entropy of the Alignment

H_total = H₁ + H₂ + H₃ + H₄

H_total = 0 + 1 + 0.811 + 2 = 3.81 bits (approximately)

Correct Answer

✅ Shannon’s entropy = 3.81 bits (approximately)

Explanation of All Common Options

Option A: 0 bits ❌

This would indicate no variation across the alignment, which is incorrect
because multiple columns show nucleotide diversity.

Option B: 1 bit ❌

This value represents entropy of only one column with two equally frequent
nucleotides, not the entire alignment.

Option C: 0.95 bits ❌

This is the average entropy per column:

3.81 ÷ 4 ≈ 0.95

Incorrect unless the question explicitly asks for average entropy.

Option D: 3.81 bits ✅

This is the sum of entropies of all four columns and is the
correct answer.

Key Takeaway

• Highly conserved columns → low entropy
• Highly variable columns → high entropy
• Always check whether total or average entropy is asked

Final Answer

Shannon’s entropy of the alignment ≈ 3.81 bits