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host range of their host pathogen. To date, our system is the first artificial system
to incorporate two inversion systems into a single circuit for controlled DNA
rearrangement. It is, also, perhaps, one of the first biological finite-state machine
encoding more than two sequential states, along with the hin based inversion
system used to solve a version of the burning pancake problem [25].
results and discussion
An informative idealization of invertase based
recombinatorics
Before delving into the experimental realization of our circuit we demonstrate an
aspect of the possible power of this approach through a quick series of calcula-
tions of scalability of designs with invertase activities as input and resulting DNA
sequence as the formal output or “state” of the system. In some cases it is pos-
sible to have a particular DNA configuration encode the expression of RNA and
this could then be an output as well. How the actual physical realization of such
circuits can affect the predictions of this idealization will be discussed briefly. In
fact, it is critical to the experimental results of our circuit described below. But
our goal in this work is not to create a biological computer but only to suggest
the power of using DNA read/write as a “stateful” element in synthetic biological
regulatory circuitry. Interestingly, an iGEM team from Davidson University has
already considered using the possible computational power of a single invertible
system as a means of solving a combinatorial problem [25]. As will become clear
below, the nature of recombination operations in DNA result in combinatorial
equations that describe both their configurations and operations. Thus, we call
the theory of design with recombinases “Recombinatorics”.
A more complete theory would include, among other things, the wide variety
of recombinase activities including excision, insertion and inversion of DNA seg-
ments into a target region of a replicon. Here we limit ourselves to invertases like
those in our experimental implementation. For the purposes of our arguments
here, we assume the following idealizations of invertase circuit dynamics, nearly
all of which are violated in some way by our own circuit but also all of which are
not beyond the ken of natural engineered inversion systems. First, we assume that
there is a single copy DNA target for the recombinases whose activity serves as
input to our system. Second, recombinases can only invert a target region once.
That is, they are irreversible flippers. This also limits the possible computational
power of the device quite a bit. Third, there is no interference among the recom-
binase inputs such that the ability of one recombinase to flip the region of DNA
between its target pair of sites is unaffected by the presence of other recombinases
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