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invertases will switch back and forth between the two states its activity connects.
Thus, the populations of these two DNA states in the plasmid population will
reach some steady-state ratio. This is important to understand because when state
0 is induced to state 1, both state 0 and 1 are present in the population (either as
mixed plasmids or cells). Ideally, if the reaction is allowed to go to steady state,
there will be a 50/50 mixture of the initial and final states, as FimB and Hin
are known to have the same forward and reverse rates. In our case, if FimB is
expressed at state 0, we will end up with a 50/50 mixture of states 0 and 1. Sub-
sequently, if FimB is removed, so that there are no further transitions between
state 0 and 1, then Hin is expressed and allowed to equilibrate, ½ of state 1 will
transition to state 3, and ½ of state 0 will transition to state 2. Thus, the overall
population will have ¼ state 0, ¼ state 1, ¼ state 2, and ¼ state 3. A similar result
ensues if we apply Hin and then FimB: only states 0, 1, 2, and 4 are populated.
Second, because the invertases are reversible it is possible to apply them more
than once in sequence. The sequences {Hin, FimB, Hin} and (FimB, Hin, FimB}
both result in 1/8 of the population reaching the fifth state of DNA (3
→
2
→
1)
mentioned above. Once state 5 is reached, the order information is lost, and the
system no longer remembers which states it had been, but rather simply that it
had seen both inputs.
Such mixture of states is not entirely desirable, but as there are no known
unidirectional, re-settable switches available so we can restart our system, and
having only one unidirectional switch (FimE) would unbalance our population
distribution, the mixtures were accepted as a compromise for demonstrating our
proof-of-principle circuit.
As should be clear from above, our device resembles an AND gate switch in
electronic and logic circuitry. An AND gate only outputs when both inputs are
present. This circuit, however, behaves differently than a regular AND gate. In-
stead of requiring that both inputs be present in order to have output, it remem-
bers the input order—that is, it remembers that inputs had been present at some
time in the past. The switch then outputs a different fluorescent protein, condi-
tioned on the sequence of inputs it had observed. A temporal memory switch like
this has many potential uses, such as in environmental sensors that can track two
different conditions occurring one after another, or as in vivo biosensors investi-
gating development or other temporally sensitive assays.
testing for the inversions
As many of the inversion states did not have fluorescent output, and because as
discussed below flipping events were rarer than expected, the inversion state was
assayed using “culture PCR” as described in the methods section. A culture PCR
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