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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.

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.

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Input stimulation signal. The pulsatile signal is shown, the duration of the "on-phase" is denoted by t, the inter-pulse interval or the silent phase between the pulses, is denoted by σ. Thus the period of S(t) is given by T = τ + σ.
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Figure 2: Input stimulation signal. The pulsatile signal is shown, the duration of the "on-phase" is denoted by t, the inter-pulse interval or the silent phase between the pulses, is denoted by σ. Thus the period of S(t) is given by T = τ + σ.

Mentions: where R(X) is called the regulatory function. We consider regulatory functions bounded by 1. Typically R(X) has the form of a Hill function Xn/(Xn + θn) with some cooperativity n and an activation threshold θ but we will often use the logic approximation for R(X), where the latter is replaced by the unit step function H(X - θ) (with only two values H(X) = 0 if X <0, and H(X) = 1 otherwise). The parameters β and α are respectively the maximum synthesis rate of protein Y and the degradation parameter, including the possible dilution effect from cell growth. Whenever R(X) = 1 the system converges to a steady state κ = β/α. In the sequel X(t) is considered as a function of time, and one defines S(t) = R(X(t)). A class of signals S(t) which will be considered below is a periodic train of square pulses of amplitude 1, whose temporal pattern is characterized by the numbers (τ, σ) (cf. Fig. 2). The parameter τ describes the duration of the "on-phase" corresponding to the activation of transcription factor X binding gene Y. The inter-pulse interval, or the silent phase between the pulses, is denoted by σ. Thus the period of S(t) is given by T = τ + σ.


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

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

Input stimulation signal. The pulsatile signal is shown, the duration of the "on-phase" is denoted by t, the inter-pulse interval or the silent phase between the pulses, is denoted by σ. Thus the period of S(t) is given by T = τ + σ.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2666635&req=5

Figure 2: Input stimulation signal. The pulsatile signal is shown, the duration of the "on-phase" is denoted by t, the inter-pulse interval or the silent phase between the pulses, is denoted by σ. Thus the period of S(t) is given by T = τ + σ.
Mentions: where R(X) is called the regulatory function. We consider regulatory functions bounded by 1. Typically R(X) has the form of a Hill function Xn/(Xn + θn) with some cooperativity n and an activation threshold θ but we will often use the logic approximation for R(X), where the latter is replaced by the unit step function H(X - θ) (with only two values H(X) = 0 if X <0, and H(X) = 1 otherwise). The parameters β and α are respectively the maximum synthesis rate of protein Y and the degradation parameter, including the possible dilution effect from cell growth. Whenever R(X) = 1 the system converges to a steady state κ = β/α. In the sequel X(t) is considered as a function of time, and one defines S(t) = R(X(t)). A class of signals S(t) which will be considered below is a periodic train of square pulses of amplitude 1, whose temporal pattern is characterized by the numbers (τ, σ) (cf. Fig. 2). The parameter τ describes the duration of the "on-phase" corresponding to the activation of transcription factor X binding gene Y. The inter-pulse interval, or the silent phase between the pulses, is denoted by σ. Thus the period of S(t) is given by T = τ + σ.

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