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These devices may be more than memory even under these restrictive as-
sumptions. With proper placement of “active” elements such as promoters,
terminators, and even genes within the device, the system can have active out-
put at chosen states of the device. While a full treatment of how to place such
elements within a device is beyond this paper, Figure 1C shows an example
that we implement experimentally below. In this case, two promoters and a
bi-directional terminator have each been placed in a separate DNA region.
Under the operation of the two input recombinases, A and B, the regions
containing these elements are rearranged. Only the two “end” states of the
graph have an arrangement such that the promoters point away from the ter-
minator and transcription may proceed outside the device boundaries. While
the RNA produced might itself be an input to a downstream device, more
classically genes may be placed to the left and right of the device and be dif-
ferentially expressed based on whether the sequence A and then B occurred or
the reverse. These genes could be recombinases that drive this device or other
devices encoded into other regions of DNA or could be hooks into other more
classical synthetic biological circuits. If we allow genes to be placed internal to
the device, then all four states could have different output activity. How this
ability scales to larger devices remains to be seen and affects how powerful a
computer one could build with such a system if one were so motivated.
All this analysis concerns ideal systems however. If flipping is reversible, for
example, our device in Figure 1C has an addition state with DNA configuration
(3
→
2
→
1), that is reachable from the end states by action of either invertase A or
B. While our fifth assumption above prevents us from reaching this state, revers-
ibility means that the ordered input sequence {A,B} leads first to a probability of
being in state 0 or state 1 when A is input, then to a probability of being in state
0, 1, 2 or 3 when B is input. What the ratio is of these probabilities is dependent
on the kinetics of the forward and reverse flipping rates of the two invertases and
the time they are allowed to be active. In this case, one only gets a probability of
state 3 if A and then B and one only gets a probability of state 4 if B and then A
so it is still possible, statistically, to determine the order in which inputs were seen
from DNA sequence. Each member of a population of cells exposed to conditions
that activated invertases A or B in a given order will hold one state of the DNA
sequence, and a particular configuration can be read out by PCR or by a screen-
able output from the device. Violation of the other assumptions above leads to
other interesting phenomena which may be either good or bad for specific appli-
cations. All the implications of such violations are beyond the scope of the paper
other than the fact that in our experimental construct the effects end up being
important.
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