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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.

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Demonstration of switch function.In each case the system is allowed to reach equilibrium under a constant level of input. The concentrations of R1, R2, R3 and R4 are represented by pink, black, orange and green lines respectively. A. Switch from [R1 & R2 high, R3 & R4 low] to [R3 & R4 high, R1 & R2 low], at an input of 0.1 nM. B. Switch from [R3 & R4 high, R1 & R2 low] to [R1 & R2 high to R3 & R4 low], at an input of 0.1 nM. C. Switch from [R2 & R3 high, R1 & R4 low] to [R1 & R4 high, R2 & R3 low], at an input of 50 nM. D. Switch from [R1 & R4 high, R2 & R3 low] to [R2 & R3 high, R1 & R4 low], at an input of 50 nM. In A and C the switch is performed by increasing the  for R1 and R2 binding from  M to  M ( exactly) between the times  and  seconds. In B and D the switch is performed by increasing the  for R3 and R4 binding by the same amount and duration. Initial conditions of  nM,  nM for A and C, and  nM,  nM for B and D. Parameters from table 1 are used.
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pone-0016140-g008: Demonstration of switch function.In each case the system is allowed to reach equilibrium under a constant level of input. The concentrations of R1, R2, R3 and R4 are represented by pink, black, orange and green lines respectively. A. Switch from [R1 & R2 high, R3 & R4 low] to [R3 & R4 high, R1 & R2 low], at an input of 0.1 nM. B. Switch from [R3 & R4 high, R1 & R2 low] to [R1 & R2 high to R3 & R4 low], at an input of 0.1 nM. C. Switch from [R2 & R3 high, R1 & R4 low] to [R1 & R4 high, R2 & R3 low], at an input of 50 nM. D. Switch from [R1 & R4 high, R2 & R3 low] to [R2 & R3 high, R1 & R4 low], at an input of 50 nM. In A and C the switch is performed by increasing the for R1 and R2 binding from M to M ( exactly) between the times and seconds. In B and D the switch is performed by increasing the for R3 and R4 binding by the same amount and duration. Initial conditions of nM, nM for A and C, and nM, nM for B and D. Parameters from table 1 are used.

Mentions: The bifurcation structure also reveals that if the input is held constant between either the concentrations 0 to 0.4 nM or 9 to 60 nM, the network exhibits bi-stability. This allows the network to function as a toggle switch if the binding affinity of particular repressors is temporarily lowered. This can be done in vivo by small molecules termed ‘inducers’ [4]. This toggle switch behaviour can be achieved for a very low concentration (figures 8A and 8B) and a high concentration (figures 8C and 8D). It is likely that switching can be achieved for a range of constant input values far exceeding 60 nM. If we consider the network within E. coli, one can use the approximation that 1 molecule corresponds to a concentration of 1 nM. Then the low input range for switching is probably physically irrelevant as the concentration corresponds to less that a single molecule. However, in cells with larger volumes these lower concentrations will become more relevant.


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

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

Demonstration of switch function.In each case the system is allowed to reach equilibrium under a constant level of input. The concentrations of R1, R2, R3 and R4 are represented by pink, black, orange and green lines respectively. A. Switch from [R1 & R2 high, R3 & R4 low] to [R3 & R4 high, R1 & R2 low], at an input of 0.1 nM. B. Switch from [R3 & R4 high, R1 & R2 low] to [R1 & R2 high to R3 & R4 low], at an input of 0.1 nM. C. Switch from [R2 & R3 high, R1 & R4 low] to [R1 & R4 high, R2 & R3 low], at an input of 50 nM. D. Switch from [R1 & R4 high, R2 & R3 low] to [R2 & R3 high, R1 & R4 low], at an input of 50 nM. In A and C the switch is performed by increasing the  for R1 and R2 binding from  M to  M ( exactly) between the times  and  seconds. In B and D the switch is performed by increasing the  for R3 and R4 binding by the same amount and duration. Initial conditions of  nM,  nM for A and C, and  nM,  nM for B and D. Parameters from table 1 are used.
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pone-0016140-g008: Demonstration of switch function.In each case the system is allowed to reach equilibrium under a constant level of input. The concentrations of R1, R2, R3 and R4 are represented by pink, black, orange and green lines respectively. A. Switch from [R1 & R2 high, R3 & R4 low] to [R3 & R4 high, R1 & R2 low], at an input of 0.1 nM. B. Switch from [R3 & R4 high, R1 & R2 low] to [R1 & R2 high to R3 & R4 low], at an input of 0.1 nM. C. Switch from [R2 & R3 high, R1 & R4 low] to [R1 & R4 high, R2 & R3 low], at an input of 50 nM. D. Switch from [R1 & R4 high, R2 & R3 low] to [R2 & R3 high, R1 & R4 low], at an input of 50 nM. In A and C the switch is performed by increasing the for R1 and R2 binding from M to M ( exactly) between the times and seconds. In B and D the switch is performed by increasing the for R3 and R4 binding by the same amount and duration. Initial conditions of nM, nM for A and C, and nM, nM for B and D. Parameters from table 1 are used.
Mentions: The bifurcation structure also reveals that if the input is held constant between either the concentrations 0 to 0.4 nM or 9 to 60 nM, the network exhibits bi-stability. This allows the network to function as a toggle switch if the binding affinity of particular repressors is temporarily lowered. This can be done in vivo by small molecules termed ‘inducers’ [4]. This toggle switch behaviour can be achieved for a very low concentration (figures 8A and 8B) and a high concentration (figures 8C and 8D). It is likely that switching can be achieved for a range of constant input values far exceeding 60 nM. If we consider the network within E. coli, one can use the approximation that 1 molecule corresponds to a concentration of 1 nM. Then the low input range for switching is probably physically irrelevant as the concentration corresponds to less that a single molecule. However, in cells with larger volumes these lower concentrations will become more relevant.

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
Related in: MedlinePlus