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rr_examples.nb
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(* Content-type: application/mathematica *)
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First note that without repressor interaction (\[Omega]=1) the possible logic \
functions are extremely limited:\
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This means than independent repressor binding can only generate SIG, SLOPE or \
asym-SLOPE logic. This could result in apparent AND logic if the repression \
by each was so strong as to lower it below background. We therefore focus on \
the solution to the interaction term \[Omega] and its relationship to logic \
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To consider the case of symmetric repression, we take c1=c2=c, or \
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From this function, it is clear that the most AND-like logic (largest l) for \
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Specifically, the best AND gates will have a large r.\
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The logic function of a symmetric RR-promoter depends on the binding constant \
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In the case of balanced repression it is easy to calculate the repression \
constant and interaction term given the logic type and regulatory range. This \
function shows that an RR-promoter cannot generate OR logic becuase as a \
symmetric gate (a=0) becomes more OR-like (l\[Rule]0), the necessary \
cooperativity explodes. This means that RR-promoters cannot generate \
symmetric OR logic. For example, for a 10-fold regulated OR gate:\
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