The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean network model that captures the bistability of the system and all of the biological steady states. In this paper, we model the wellknown arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system’s bistability. Finally, we compare the state space under synchronous and asynchronous update, and see that the former has several artificial cycles that go away under a general asynchronous update. Crowther Audrey audrey.crowther@huskers.unl.edu University of Nebraska-Lincoln 2017-03-12T11:02:47Z 2017-07-18T15:44:25Z

extracellular arabinose (high levels)

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AraC protein (unbound to arabinose)

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extracellular arabinose (at least medium levels)

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extracellular glucose

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mRNA of the transport genes (araEFGH)

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enzymes AraA, AraB, and AraD, coded for by the structural genes

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cAMP-CAP protein complex

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intracellular arabinose (medium levels)

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DNA loop

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transport proteins, coded for by the transport genes

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intracellular arabinose (high levels)

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arabinose-bound AraC protein

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mRNA of the structural genes (araBAD)

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Ara+ in conjunction with C activates MT.

cAMP-CAP (C) stimulates the operon's promoter. This is needed for the transcription of the transport genes (MT).

The AraC protein (Ara+) is an inducer of the arabinose operon. This is needed for the transcription of the transport genes (MT).

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MS activates E.

After the structural genes' mRNA is produced, it is translated to make the enzymes needed for arabinose metabolism (AraA, AraB, and AraD).

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Ge inhibits C.

cAMP-CAP complex (C) is produced as a result of the absence of external glucose (Ge).

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Ae activates Am. Aem in conjunction with T activates Am.

Extracellular arabinose at mediumm levels (Aem) is transported into the cell by transport proteins (T).

Extracellular arabinose at mediumm levels (Aem) is transported into the cell by transport proteins (T).

Extracellular arabinose at high levels (Ae) is sufficient for at least medium levels in intracellular arabinose (Am) by means of passive transport.

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Ara- activates L. Ara+ inhibits L and is dominant to Ara-.

AraC protein not bound to arabinose (Ara-) binds to the operon in such a way (specifically to the I1 and O2 elements) to form an inhibitory DNA loop (L).

AraC protein bound to arabinose (Ara+) binds to the operon in such a way ( specifically to the adjacent I1 and I2 elements) that does not favor the DNA loop (L) formation.

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MT activates T.

The mRNA for the transport genes (MT) is translated to produce the transport proteins (T).

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Ae in conjunction with T activates A.

Extracellular arabinose at high levels (Ae) is transported into the cell by transport proteins (T).

Extracellular arabinose at high levels (Ae) is transported into the cell by transport proteins (T).

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Ara- in conjunction with A or Am activates Ara+.

The arabinose-bound form of the AraC protein (Ara+) requires the presence of the unbound form of the protein (Ara-) as well intracellular arabinose at either high (A) or medium (Am) levels. Arabinose binds to the arabinose-binding pocket located on AraC.

The arabinose-bound form of the AraC protein (Ara+) requires the presence of the unbound form of the protein (Ara-) as well intracellular arabinose at either high (A) or medium (Am) levels. Arabinose binds to the arabinose-binding pocket located on AraC.

The arabinose-bound form of the AraC protein (Ara+) requires the presence of the unbound form of the protein (Ara-) as well intracellular arabinose at either high (A) or medium (Am) levels. Arabinose binds to the arabinose-binding pocket located on AraC.

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Ara+ in conjunction with C activates MS. L inhibits MS and is dominant over Ara+.

cAMP-CAP (C) stimulates the operon's promoter. This is needed to initiate the transcription of the structural genes (MS).

The AraC protein (Ara+) is an inducer of the arabinose operon. This is needed for to initiate the transcription of the structural genes (MS).

Formation of a DNA loop (L) prevents RNA polymerase from binding and thus inhibits transcription of the structural genes (MS).

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