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Rsequence, Rfrequency, Excess Information at
Bacteriophage T7 promoters and the Evolution of Binding
Frederick, Laboratory of Experimental and Computational
Biology, Frederick, MD 21702-1201, toms@alum.mit.edu,
https://alum.mit.edu/www/toms/, www.fred.net/tds/work

Information required to find a set of binding sites in
a genome 16 positions: 1 site, log2 16/1 = 4 bits. 16
positions: 2 sites, log2 16/2 = 3 bits.

Information required to find a set of binding sites. G
= # of potential binding sites = genome size in some cases.
gamma = number of binding sites on genome. Rfrequency =
Hbefore = Hafter = log2 G - log2 gamma = -log2 gamma/G.

Hypothesis: The information in binding site patterns is
just sufficient for the sites to be found in the genome

Table: Binding Site Recognizer Total Pattern
Information = Rsequence (bits) Information needed to Locate
Site in Genome = Rfrequency (bits) Pattern Info Location
Info = Rsequence Rfrequency Spliceosome acceptor 9.35 ±
0.12 9.66 0.97 ± 0.01 Spliceosome donor 7.92 ± 0.09 9.66
0.82 ± 0.01 Ribosome λ cI/cro LexA TrpR LacI ArgR O (λ
Origin) Ara C 11.0 17.7 ± 1.6 21.5 ± 1.7 23.4 ± 1.9 19.2
± 2.8 16.4 20.9 19.3 10.6 1.0 19.3 0.9 ± 0.1 18.4 1.2 ±
0.1 20.3 1.2 ± 0.1 21.9 0.9 ± 0.1 18.4 0.9 19.9 1.0 19.3
1.0 AT T7 Promoter 35.4 16.5 2.1 IN T7 Promoter 18 ± 2
16.5 1.1 ± 0.1

Two sequence logos. 17 Bacteriophage T7 RNA polymerase
binding sites (about 35 bits). Pattern required by T7 RnA
polymerase to function (only 18 bits).

Evolution of Binding Sites * Rfrequency is fixed
relative to Rsequence * Can Rsequence evolve toward
Rfrequency? Setup: A population of

How A Weight Matrix Works Sequence matrix, s(b,l,j) for
sequence j has 4 rows (base b: ACGT) and -3 to 6 columns
(position l: CAGGTCTGCA). Each column has 3 zeros and a 1
corrsponding to that base. Individual information weight
matrix, Riw(b,l) has the same form as the sequence matrix
but has positive and negative numbers in it. Add the
numbers that correspond to 1's in the first matrix to get
the total. Sequence walker - a graphic 5' to 3' showing the
sequence and then the same letters but with heights
corresponding to the individual information weight matrix.
The letters are rotated 90 degrees counterclockwise to
represent the direction of the donor site shown.

A sequence from the ev program. A 266 base sequence is
marked every 10 bases. The first part of the sequence has
a 'gene' with parts marked by underlines. Each underline
has a letter and a number. The letters repeat A, C, G, T.
The numbers are computed from the two's complement notation
of the sequence coded as 00, 01, 10 and 11. the remainder
of the genome consists of sites marked with plus (for
functional) or minus for (non functional).

Evolution Cycle * EVALUATE each creature - translate
the recognizer gene into a weight matrix - scan the weight
matrix across the genome - count the number of mistakes: =
missing a site at the right places = finding a site at
wrong places - Sort the creatures by their mistakes *
REPLICATE: the best creatures are duplicated and replace
the worst ones * MUTATE all genomes randomly

a, Number of mistakes made by the organism with the
fewest mistakes is plotted against the generation number.
b, The information content at binding sites (Rsequence) of
the organism making the fewest mistakes is plotted against
generation number.

20 sequence logos of 16 evolving binding sites
generation 100 (-0.1 +/- 0.5 bits) to generation 2000 (5.2
+/- 0.5 bits).

16 evolving binding sites generation 2000 Rs = 5.2 +/-
0.5 bits

20 $Shannon Information Measure of Binding Site Patterns Information is measured as a decrease in uncertainty: $R = H_{before} - H_{after}$ (bits per symbol). Before binding there are 4 possible bases at each position $l$, so the uncertainty is: $H_{before}(l) = \log_2 4$ (bits per base) \approx 2 . After binding the uncertainty depends on the frequencies of bases $b$ at positions $l$ in a binding site, $f(b,l)$: $H_{after}(l) = -\sum b \in \{A,C,G,T\}$ $f(b,l) \log_2 f(b,l)$ (bits per base). The information at a position $l$} is: $\rsequence(l) & = & H_{before}(l) - H_{after}(l) & \approx & 2 - H_{after}(l)$ (bits \emph{per base}). The total site information is: $\rsequence & = & \sum_l \left( H_{before}(l) - H_{after}(l)\right) & \approx & 2l - H_{after}$ (bits \emph{per site}). As $H_{after} \downarrow$, $\rsequence \uparrow$$ 21

In the evening a Baryonx dinosaur standing in the pond
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