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 $H_{after}
\downarrow$, $\rsequence \uparrow$

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