The ability to learn and respond to recurrent events depends on the capacity to remember transient biological signals received in the past. Moreover, it may be desirable to remember or ignore these transient signals conditioned upon other signals that are active at specific points in time or in unique environments. Here, we propose a simple genetic circuit in bacteria that is capable of conditionally memorizing a signal in the form of a transcription factor concentration. The circuit behaves similarly to a “data latch” in an electronic circuit, i.e. it reads and stores an input signal only when conditioned to do so by a “read command.” Our circuit is of the same size as the well-known genetic toggle switch (an unconditional latch) which consists of two mutually repressing genes, but is complemented with a “regulatory front end” involving protein heterodimerization as a simple way to implement conditional control. Deterministic and stochastic analysis of the circuit dynamics indicate that an experimental implementation is feasible based on well-characterized genes and proteins. It is not known, to which extent molecular networks are able to conditionally store information in natural contexts for bacteria. However, our results suggest that such sequential logic elements may be readily implemented by cells through the combination of existing protein–protein interactions and simple transcriptional regulation.
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We assume no direct interaction between the DNA-bound repressors. This assumption is conservative, since cooperative interactions would only help to make the bistability of the circuit more pronounced.
We assume the same degradation rate for protein monomers and dimers, i.e. no cooperative stability (Buchler et al. 2005).
In our model, dimerization occurs always prior to operator binding. This pathway is consistent with typical parameter values for bacterial transcription factors.
Note that we could equally well assume that the transcription of R, S is constant, but their dimerization or their DNA-binding activity is time-dependent, e.g. due to regulation by ligand binding or phosphorylation. However, none of our conclusions are sensitive to the detailed mechanism that in one way or another controls the total concentrations of active R and S proteins.
For simplicity, we do not include the possible homodimerization of S in our model (434 repressor and its mutant 434R[α3(P22R)] can both homodimerize (Hollis et al. 1988)). Allowing S2 dimer formation only reduces the effective concentration of S available for heterodimerization and can be compensated for by increasing the expression rate of S.
We define the apparent binding threshold as the concentration of transcription factor, that is needed to reduce the promoter activity to 50% of its maximal value. It is not necessarily equal to the equilibrium dissociation constant K, but rather depends on the explicit expression of the promoter activity function.
We allow for a relaxation time of 60 min after the end of the read pulse and then determine the error fraction. Since the rate of spontaneous flipping is very low, the result depends only very weakly on the precise value of the relaxation time, provided it is not too short.
Note that while the time to reach the steady state concentration only depends on the degradation rate, the time to reach a certain threshold concentration also depends on the synthesis rate.
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We thank W. Hillen and G. Koudelka for providing useful information on TetR and 434 repressor. GF is grateful to J. Timmer (University of Freiburg) for guidance and support during his diploma thesis. NB acknowledges a Burroughs-Wellcome Fund CASI award, TH acknowledges support by the NSF through Grant No. MCB-0417721 and PFC-sponsored Center for Theoretical Biological Physics (Grants No. PHY-0216576 and PHY-0225630), and UG acknowledges an Emmy Noether grant of the Deutsche Forschungsgemeinschaft. Author contributions: GF performed the simulations. All authors designed the research and wrote the paper.
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Fritz, G., Buchler, N.E., Hwa, T. et al. Designing sequential transcription logic: a simple genetic circuit for conditional memory. Syst Synth Biol 1, 89–98 (2007). https://doi.org/10.1007/s11693-007-9006-8