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Simple molecular networks that respond optimally to time-periodic stimulation.

Cournac A, Sepulchre JA - BMC Syst Biol (2009)

Bottom Line: We next show a mechanism by which average of oscillatory response can be maximized by bursting temporal patterns.The identified mechanisms are simple and based on known network motifs in the literature, so that that they could be embodied in existing organisms, or easily implementable by means of synthetic biology.Moreover we show that these designs can be studied in different contexts of molecular biology, as for example in genetic networks or in signaling pathways.

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Affiliation: Institut Non Linéaire de Nice, Université de Nice Sophia-Antipolis, CNRS, Valbonne, France. axel.cournac@inln.cnrs.fr

ABSTRACT

Background: Bacteria or cells receive many signals from their environment and from other organisms. In order to process this large amount of information, Systems Biology shows that a central role is played by regulatory networks composed of genes and proteins. The objective of this paper is to present and to discuss simple regulatory network motifs having the property to maximize their responses under time-periodic stimulations. In elucidating the mechanisms underlying these responses through simple networks the goal is to pinpoint general principles which optimize the oscillatory responses of molecular networks.

Results: We took a look at basic network motifs studied in the literature such as the Incoherent Feedforward Loop (IFFL) or the interlerlocked negative feedback loop. The former is also generalized to a diamond pattern, with network components being either purely genetic or combining genetic and signaling pathways. Using standard mathematics and numerical simulations, we explain the types of responses exhibited by the IFFL with respect to a train of periodic pulses. We show that this system has a non-vanishing response only if the inter-pulse interval is above a threshold. A slight generalisation of the IFFL (the diamond) is shown to work as an ideal pass-band filter. We next show a mechanism by which average of oscillatory response can be maximized by bursting temporal patterns. Finally we study the interlerlocked negative feedback loop, i.e. a 2-gene motif forming a loop where the nodes respectively activate and repress each other, and show situations where this system possesses a resonance under periodic stimulation.

Conclusion: We present several simple motif designs of molecular networks producing optimal output in response to periodic stimulations of the system. The identified mechanisms are simple and based on known network motifs in the literature, so that that they could be embodied in existing organisms, or easily implementable by means of synthetic biology. Moreover we show that these designs can be studied in different contexts of molecular biology, as for example in genetic networks or in signaling pathways.

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Response of the IFFL to periodic stimulation in function of σ. The average response <Z >T and the maximum of response Zmax are represented in function of the inter-pulse interval σ with a fixed τ for an IFFL motif (Fig 1.(c)) stimulated by a pulsatile signal. σ is in 1/α units, the concentration is in nM. σ0 is the minimal inter-pulse interval for the system to respond. The inter-pulse interval σ1 gives the optimum average response for the system. The numerical simulation was done with the equations (4–5) of the main text and with the following parameters: (a) for the case τ > τθ, τ = 2 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 200 min give σ0 ~20 min and σ1 ~2 hours. (b) for the case τ <τθ, τ = 1 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 100 min give σ0 ~15 min and σ1 ~1 hour.
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Figure 5: Response of the IFFL to periodic stimulation in function of σ. The average response <Z >T and the maximum of response Zmax are represented in function of the inter-pulse interval σ with a fixed τ for an IFFL motif (Fig 1.(c)) stimulated by a pulsatile signal. σ is in 1/α units, the concentration is in nM. σ0 is the minimal inter-pulse interval for the system to respond. The inter-pulse interval σ1 gives the optimum average response for the system. The numerical simulation was done with the equations (4–5) of the main text and with the following parameters: (a) for the case τ > τθ, τ = 2 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 200 min give σ0 ~20 min and σ1 ~2 hours. (b) for the case τ <τθ, τ = 1 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 100 min give σ0 ~15 min and σ1 ~1 hour.

Mentions: In this Section we show that when the IFFL network is periodically stimulated by a train of pulses, a new property appears regarding the optimization of observables ⟨Z⟩T and Zmax. As illustrated in Fig. 4 and Fig. 5, the average value ⟨Z⟩T, as well as Zmax can reach maximal values for specific choices of the pulse pattern (τ, σ). We will describe this phenomenon in more detail.


Simple molecular networks that respond optimally to time-periodic stimulation.

Cournac A, Sepulchre JA - BMC Syst Biol (2009)

Response of the IFFL to periodic stimulation in function of σ. The average response <Z >T and the maximum of response Zmax are represented in function of the inter-pulse interval σ with a fixed τ for an IFFL motif (Fig 1.(c)) stimulated by a pulsatile signal. σ is in 1/α units, the concentration is in nM. σ0 is the minimal inter-pulse interval for the system to respond. The inter-pulse interval σ1 gives the optimum average response for the system. The numerical simulation was done with the equations (4–5) of the main text and with the following parameters: (a) for the case τ > τθ, τ = 2 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 200 min give σ0 ~20 min and σ1 ~2 hours. (b) for the case τ <τθ, τ = 1 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 100 min give σ0 ~15 min and σ1 ~1 hour.
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Related In: Results  -  Collection

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Figure 5: Response of the IFFL to periodic stimulation in function of σ. The average response <Z >T and the maximum of response Zmax are represented in function of the inter-pulse interval σ with a fixed τ for an IFFL motif (Fig 1.(c)) stimulated by a pulsatile signal. σ is in 1/α units, the concentration is in nM. σ0 is the minimal inter-pulse interval for the system to respond. The inter-pulse interval σ1 gives the optimum average response for the system. The numerical simulation was done with the equations (4–5) of the main text and with the following parameters: (a) for the case τ > τθ, τ = 2 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 200 min give σ0 ~20 min and σ1 ~2 hours. (b) for the case τ <τθ, τ = 1 1/α unit. For example, the parameters: α = 0.01 min-1, β = 10 nM.min-1, θ = 800 nM and τ = 100 min give σ0 ~15 min and σ1 ~1 hour.
Mentions: In this Section we show that when the IFFL network is periodically stimulated by a train of pulses, a new property appears regarding the optimization of observables ⟨Z⟩T and Zmax. As illustrated in Fig. 4 and Fig. 5, the average value ⟨Z⟩T, as well as Zmax can reach maximal values for specific choices of the pulse pattern (τ, σ). We will describe this phenomenon in more detail.

Bottom Line: We next show a mechanism by which average of oscillatory response can be maximized by bursting temporal patterns.The identified mechanisms are simple and based on known network motifs in the literature, so that that they could be embodied in existing organisms, or easily implementable by means of synthetic biology.Moreover we show that these designs can be studied in different contexts of molecular biology, as for example in genetic networks or in signaling pathways.

View Article: PubMed Central - HTML - PubMed

Affiliation: Institut Non Linéaire de Nice, Université de Nice Sophia-Antipolis, CNRS, Valbonne, France. axel.cournac@inln.cnrs.fr

ABSTRACT

Background: Bacteria or cells receive many signals from their environment and from other organisms. In order to process this large amount of information, Systems Biology shows that a central role is played by regulatory networks composed of genes and proteins. The objective of this paper is to present and to discuss simple regulatory network motifs having the property to maximize their responses under time-periodic stimulations. In elucidating the mechanisms underlying these responses through simple networks the goal is to pinpoint general principles which optimize the oscillatory responses of molecular networks.

Results: We took a look at basic network motifs studied in the literature such as the Incoherent Feedforward Loop (IFFL) or the interlerlocked negative feedback loop. The former is also generalized to a diamond pattern, with network components being either purely genetic or combining genetic and signaling pathways. Using standard mathematics and numerical simulations, we explain the types of responses exhibited by the IFFL with respect to a train of periodic pulses. We show that this system has a non-vanishing response only if the inter-pulse interval is above a threshold. A slight generalisation of the IFFL (the diamond) is shown to work as an ideal pass-band filter. We next show a mechanism by which average of oscillatory response can be maximized by bursting temporal patterns. Finally we study the interlerlocked negative feedback loop, i.e. a 2-gene motif forming a loop where the nodes respectively activate and repress each other, and show situations where this system possesses a resonance under periodic stimulation.

Conclusion: We present several simple motif designs of molecular networks producing optimal output in response to periodic stimulations of the system. The identified mechanisms are simple and based on known network motifs in the literature, so that that they could be embodied in existing organisms, or easily implementable by means of synthetic biology. Moreover we show that these designs can be studied in different contexts of molecular biology, as for example in genetic networks or in signaling pathways.

Show MeSH