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A multi-functional synthetic gene network: a frequency multiplier, oscillator and switch.

Purcell O, di Bernardo M, Grierson CS, Savery NJ - PLoS ONE (2011)

Bottom Line: Analysis of the bifurcation structure also reveals novel, programmable multi-functionality; in addition to functioning as a frequency multiplier, the network is able to function as a switch or an oscillator, depending on the temporal nature of the input.Multi-functionality is often observed in neuronal networks, where it is suggested to allow for the efficient coordination of different responses.This network represents a significant theoretical addition that extends the capabilities of synthetic gene networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Mathematics, Bristol Centre for Complexity Sciences, University of Bristol, Bristol, United Kingdom. enoep@bristol.ac.uk

ABSTRACT
We present the design and analysis of a synthetic gene network that performs frequency multiplication. It takes oscillatory transcription factor concentrations, such as those produced from the currently available genetic oscillators, as an input, and produces oscillations with half the input frequency as an output. Analysis of the bifurcation structure also reveals novel, programmable multi-functionality; in addition to functioning as a frequency multiplier, the network is able to function as a switch or an oscillator, depending on the temporal nature of the input. Multi-functionality is often observed in neuronal networks, where it is suggested to allow for the efficient coordination of different responses. This network represents a significant theoretical addition that extends the capabilities of synthetic gene networks.

Show MeSH
Existence of a period-doubling bifurcation.A period-doubling is observed at an input period of  seconds ( hours). The period-doubling point is labelled as ‘PD’. Blue lines and red lines represent period-1 and period-2 solutions respectively. A. Relationship between input period and ‘output’ period, where output denotes the proteins R1 to R4. B. Relationship between input period and L2-Norm.
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pone-0016140-g007: Existence of a period-doubling bifurcation.A period-doubling is observed at an input period of seconds ( hours). The period-doubling point is labelled as ‘PD’. Blue lines and red lines represent period-1 and period-2 solutions respectively. A. Relationship between input period and ‘output’ period, where output denotes the proteins R1 to R4. B. Relationship between input period and L2-Norm.

Mentions: Continuations demonstrate that the frequency multiplier functionality is a consequence of a period-doubling bifurcation as the period of the input crosses a certain threshold. Figure 7A shows the period of the ‘output’ i.e. proteins R1 to R4, as a function of the input period. Prior to the period-doubling bifurcation the output period is equal to the input period (blue line). A period-doubling bifurcation occurs at seconds ( hours), after which (red line) the output period is twice the period of the input. Equivalently the output frequency is half the input frequency. The existence of a period doubling bifurcation is further confirmed in figure 7B, which shows the relationship between the input period, and the L2-Norm. As expected for a period-doubling bifurcation, the L2-Norm of the period-2 limit cycle is equal to the period-1 limit cycle at the bifurcation point.


A multi-functional synthetic gene network: a frequency multiplier, oscillator and switch.

Purcell O, di Bernardo M, Grierson CS, Savery NJ - PLoS ONE (2011)

Existence of a period-doubling bifurcation.A period-doubling is observed at an input period of  seconds ( hours). The period-doubling point is labelled as ‘PD’. Blue lines and red lines represent period-1 and period-2 solutions respectively. A. Relationship between input period and ‘output’ period, where output denotes the proteins R1 to R4. B. Relationship between input period and L2-Norm.
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Related In: Results  -  Collection

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pone-0016140-g007: Existence of a period-doubling bifurcation.A period-doubling is observed at an input period of seconds ( hours). The period-doubling point is labelled as ‘PD’. Blue lines and red lines represent period-1 and period-2 solutions respectively. A. Relationship between input period and ‘output’ period, where output denotes the proteins R1 to R4. B. Relationship between input period and L2-Norm.
Mentions: Continuations demonstrate that the frequency multiplier functionality is a consequence of a period-doubling bifurcation as the period of the input crosses a certain threshold. Figure 7A shows the period of the ‘output’ i.e. proteins R1 to R4, as a function of the input period. Prior to the period-doubling bifurcation the output period is equal to the input period (blue line). A period-doubling bifurcation occurs at seconds ( hours), after which (red line) the output period is twice the period of the input. Equivalently the output frequency is half the input frequency. The existence of a period doubling bifurcation is further confirmed in figure 7B, which shows the relationship between the input period, and the L2-Norm. As expected for a period-doubling bifurcation, the L2-Norm of the period-2 limit cycle is equal to the period-1 limit cycle at the bifurcation point.

Bottom Line: Analysis of the bifurcation structure also reveals novel, programmable multi-functionality; in addition to functioning as a frequency multiplier, the network is able to function as a switch or an oscillator, depending on the temporal nature of the input.Multi-functionality is often observed in neuronal networks, where it is suggested to allow for the efficient coordination of different responses.This network represents a significant theoretical addition that extends the capabilities of synthetic gene networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Engineering Mathematics, Bristol Centre for Complexity Sciences, University of Bristol, Bristol, United Kingdom. enoep@bristol.ac.uk

ABSTRACT
We present the design and analysis of a synthetic gene network that performs frequency multiplication. It takes oscillatory transcription factor concentrations, such as those produced from the currently available genetic oscillators, as an input, and produces oscillations with half the input frequency as an output. Analysis of the bifurcation structure also reveals novel, programmable multi-functionality; in addition to functioning as a frequency multiplier, the network is able to function as a switch or an oscillator, depending on the temporal nature of the input. Multi-functionality is often observed in neuronal networks, where it is suggested to allow for the efficient coordination of different responses. This network represents a significant theoretical addition that extends the capabilities of synthetic gene networks.

Show MeSH