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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