A molecular device for frequency doubling enabled by molecular sequestration

In engineering, a frequency multiplier is a device that processes an oscillatory input and produces an output signal with shorter period oscillations, whose output frequency is an integer multiple of its input frequency. A molecular frequency multiplier will enable us to adjust the period of synthetic biological oscillators in a simpler way without the need to redesign or retune the oscillatory network itself. In this work, we describe the rational design and analysis of a biomolecular device for doubling the frequency of an oscillatory input. The device is based on the use of molecular sequestration, which operates as an electronic diode with a tunable threshold, and only signals with amplitude larger than the device's threshold are able to produce an output. The device architecture is similar to full wave rectifier circuit: we use two modules in parallel produce the output, where the first device will only process a signal above the threshold and the second device only responds to a signal below the threshold. This results in an output with a frequency that is the double of the input frequency. We derive conditions for proper operation of the device, that specify required network parameters and input frequency; with simulations, we examine the input-output rating of the device and we find that frequency doubling is achieved in a range of realistic parameters as well as in a stochastic setting.

[1]  Huiyi Chen,et al.  Genome-wide study of mRNA degradation and transcript elongation in Escherichia coli , 2015, Molecular systems biology.

[2]  Ankit Gupta,et al.  Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks. , 2014, Cell systems.

[3]  Elisa Franco,et al.  A self-regulating biomolecular comparator for processing oscillatory signals , 2015, Journal of The Royal Society Interface.

[4]  Franco Blanchini,et al.  Molecular Titration Promotes Oscillations and Bistability in Minimal Network Models with Monomeric Regulators. , 2016, ACS synthetic biology.

[5]  Erik Clark,et al.  Evidence for the temporal regulation of insect segmentation by a conserved sequence of transcription factors , 2018, Development.

[6]  Elisa Franco,et al.  A Robust Molecular Network Motif for Period-Doubling Devices. , 2017, ACS synthetic biology.

[7]  Christian Cuba Samaniego,et al.  An ultrasensitive biomolecular network for robust feedback control , 2017 .

[8]  K. Jensen,et al.  The RNA chain elongation rate in Escherichia coli depends on the growth rate , 1994, Journal of bacteriology.

[9]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[10]  D. Y. Zhang,et al.  Engineering Entropy-Driven Reactions and Networks Catalyzed by DNA , 2007, Science.

[11]  Richard M. Murray,et al.  Negative autoregulation matches production and demand in synthetic transcriptional networks , 2013 .

[12]  Andreas Handel.  Cell Biology by the Numbers. By Ron Milo and Rob Phillips; illustrated by Nigel Orme. New York: Garland Science (Taylor & Francis Group). $49.95 (paper). xlii + 356 p.; ill.; index. ISBN: 978-0-8153-4537-4. 2016. , 2017 .

[13]  M. Khammash,et al.  Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks. , 2016, Cell systems.

[14]  Bert W O'Malley,et al.  A Cell-Autonomous Mammalian 12 hr Clock Coordinates Metabolic and Stress Rhythms. , 2017, Cell metabolism.

[15]  Nicolas E. Buchler,et al.  Molecular titration and ultrasensitivity in regulatory networks. , 2008, Journal of molecular biology.

[16]  Franco Blanchini,et al.  Structurally robust biological networks , 2011, BMC Systems Biology.

[17]  E. Winfree,et al.  Synthetic in vitro transcriptional oscillators , 2011, Molecular systems biology.

[18]  Domitilla Del Vecchio,et al.  A quasi-integral controller for adaptation of genetic modules to variable ribosome demand , 2018 .

[19]  Richard M. Murray,et al.  Synthetic circuit for exact adaptation and fold-change detection , 2014, Nucleic acids research.

[20]  E. Winfree,et al.  Construction of an in vitro bistable circuit from synthetic transcriptional switches , 2006, Molecular systems biology.

[21]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[22]  Han N. Lim,et al.  Direct comparison of small RNA and transcription factor signaling , 2012, Nucleic acids research.

[23]  Erik Clark,et al.  Odd-paired controls frequency doubling in Drosophila segmentation by altering the pair-rule gene regulatory network , 2016 .