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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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Related in: MedlinePlus

1-dimensional sketch summarising the bifurcation structure.The three main features are two simultaneous saddle-node bifurcations, a Hopf bifurcation and a pitchfork bifurcation. These occur at input concentrations of 0.4 nM, 7 nM and 9 nM respectively. The analysis covers the input concentration range 0–60 nM, and traces out three branches of equilibria, A, B and C. The structure can be divided into four dynamical regions corresponding to labels 1–4. The dynamics at each label are shown in the set of simulations above. At position 1 and 4 two stable equilibria exist simultaneously. In all simulation panels the horizontal axis is time (seconds) and the vertical axis is concentration. All simulations are for  seconds. The concentration range on the vertical axis in panels 1 and 1, 2, 3 and 4 and 4, are 0–150 nM, 0–90 nM, 0–140 nM and 0–180 nM respectively. Simulation panels 4 and 4 used initial conditions  nM,  nM. All other panels used initial conditions  nM,  nM. Panels 1 and 1, 2, 3 and 4 and 4 use a constant input concentration   nM, 5 nM, 7.5 nM and 10 nM (4 and 4) respectively. All simulations use table 1 parameters. Red dashed lines delineate the oscillatory region, which lies in between two stable regions in which trajectories decay to equilibrium levels. This diagram is intended to convey the qualitative aspects of the phase portrait. As such there is no scale on the vertical axis.
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pone-0016140-g005: 1-dimensional sketch summarising the bifurcation structure.The three main features are two simultaneous saddle-node bifurcations, a Hopf bifurcation and a pitchfork bifurcation. These occur at input concentrations of 0.4 nM, 7 nM and 9 nM respectively. The analysis covers the input concentration range 0–60 nM, and traces out three branches of equilibria, A, B and C. The structure can be divided into four dynamical regions corresponding to labels 1–4. The dynamics at each label are shown in the set of simulations above. At position 1 and 4 two stable equilibria exist simultaneously. In all simulation panels the horizontal axis is time (seconds) and the vertical axis is concentration. All simulations are for seconds. The concentration range on the vertical axis in panels 1 and 1, 2, 3 and 4 and 4, are 0–150 nM, 0–90 nM, 0–140 nM and 0–180 nM respectively. Simulation panels 4 and 4 used initial conditions nM, nM. All other panels used initial conditions nM, nM. Panels 1 and 1, 2, 3 and 4 and 4 use a constant input concentration nM, 5 nM, 7.5 nM and 10 nM (4 and 4) respectively. All simulations use table 1 parameters. Red dashed lines delineate the oscillatory region, which lies in between two stable regions in which trajectories decay to equilibrium levels. This diagram is intended to convey the qualitative aspects of the phase portrait. As such there is no scale on the vertical axis.

Mentions: Six continuation of equilibria experiments were performed, using automatic branch switching where appropriate. Initial estimates of the model equilibria were obtained through numerical integration in MATLAB (The Mathworks, Natick, MA) and the numerical solvers in MAPLE (Maplesoft, Waterloo, ON) and are summarised in table 2. Two stable equilibria (‘’ and ‘’) are characterised by zero concentrations of R1 and R2 () or R3 and R4 () respectively, while equilibrium ‘’ is characterised by low concentrations of all repressors except R3. Figure 5 depicts a 1-dimensional schematic bifurcation diagram summarising the results of all the continuation runs.


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

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

1-dimensional sketch summarising the bifurcation structure.The three main features are two simultaneous saddle-node bifurcations, a Hopf bifurcation and a pitchfork bifurcation. These occur at input concentrations of 0.4 nM, 7 nM and 9 nM respectively. The analysis covers the input concentration range 0–60 nM, and traces out three branches of equilibria, A, B and C. The structure can be divided into four dynamical regions corresponding to labels 1–4. The dynamics at each label are shown in the set of simulations above. At position 1 and 4 two stable equilibria exist simultaneously. In all simulation panels the horizontal axis is time (seconds) and the vertical axis is concentration. All simulations are for  seconds. The concentration range on the vertical axis in panels 1 and 1, 2, 3 and 4 and 4, are 0–150 nM, 0–90 nM, 0–140 nM and 0–180 nM respectively. Simulation panels 4 and 4 used initial conditions  nM,  nM. All other panels used initial conditions  nM,  nM. Panels 1 and 1, 2, 3 and 4 and 4 use a constant input concentration   nM, 5 nM, 7.5 nM and 10 nM (4 and 4) respectively. All simulations use table 1 parameters. Red dashed lines delineate the oscillatory region, which lies in between two stable regions in which trajectories decay to equilibrium levels. This diagram is intended to convey the qualitative aspects of the phase portrait. As such there is no scale on the vertical axis.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3040778&req=5

pone-0016140-g005: 1-dimensional sketch summarising the bifurcation structure.The three main features are two simultaneous saddle-node bifurcations, a Hopf bifurcation and a pitchfork bifurcation. These occur at input concentrations of 0.4 nM, 7 nM and 9 nM respectively. The analysis covers the input concentration range 0–60 nM, and traces out three branches of equilibria, A, B and C. The structure can be divided into four dynamical regions corresponding to labels 1–4. The dynamics at each label are shown in the set of simulations above. At position 1 and 4 two stable equilibria exist simultaneously. In all simulation panels the horizontal axis is time (seconds) and the vertical axis is concentration. All simulations are for seconds. The concentration range on the vertical axis in panels 1 and 1, 2, 3 and 4 and 4, are 0–150 nM, 0–90 nM, 0–140 nM and 0–180 nM respectively. Simulation panels 4 and 4 used initial conditions nM, nM. All other panels used initial conditions nM, nM. Panels 1 and 1, 2, 3 and 4 and 4 use a constant input concentration nM, 5 nM, 7.5 nM and 10 nM (4 and 4) respectively. All simulations use table 1 parameters. Red dashed lines delineate the oscillatory region, which lies in between two stable regions in which trajectories decay to equilibrium levels. This diagram is intended to convey the qualitative aspects of the phase portrait. As such there is no scale on the vertical axis.
Mentions: Six continuation of equilibria experiments were performed, using automatic branch switching where appropriate. Initial estimates of the model equilibria were obtained through numerical integration in MATLAB (The Mathworks, Natick, MA) and the numerical solvers in MAPLE (Maplesoft, Waterloo, ON) and are summarised in table 2. Two stable equilibria (‘’ and ‘’) are characterised by zero concentrations of R1 and R2 () or R3 and R4 () respectively, while equilibrium ‘’ is characterised by low concentrations of all repressors except R3. Figure 5 depicts a 1-dimensional schematic bifurcation diagram summarising the results of all the continuation runs.

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