Why do ten rows (Figure_1) correspond to 2 bits (Figure_2) in a sequence logo?

Question

Following this question, I'm confused with the computation of sequence logo

Following data comes from the book "Machine Learning - A Probabilistic Perspective (Figure_1)"

here is the corresponding sequence logo (Figure_2).

ten rows represent sequences of DNA (e.g. row 1 could be a human sequence, row 2 could be the equivalent mouse sequence etc.)

Each column corresponds to a particular position.

Why do ten rows (Figure_1) correspond to 2 bits (Figure_2)?

Answer 1

Bits are not frequencies. If a position only contains an A (position 3 for example) then you would need 2 questions (bits) to derive that information without a priori knowledge.

1. Is it a G or C? if no > then it is a A or T
2. Is it T? If no then it is an A

Position 1 can be derived by 1 question only:

1. is it a G or C? If no then it is an A or T

In this case the number of bits can be calculated using the frequenci)es.

For 4 bases, A only (100%):

4 * -0.25 * log2(0.25) - (-1 * log2(1)) = 2 (bits)

For 8 letters, A only (100%):

8 * -1/8 * log(1/8)- (-1 * log2(1)) = 3 (bits)

Mixed base possibility (A/T 50% each) with 4 bases:

4 * -0.25 * log2(0.25) - (-0.5 * log2(0.5)+-0.5 * log2(0.5)) = 1 (bit)

As mentioned in the comments, you can follow the wiki link for an example.

Or, an example with a little more explanation from the biology SE site.

sequence logo calcuation

Hopes this helps