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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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Response of the double DIFFL to a bursting signal. The motif of double DIFFL (Fig. 1(f)) is stimulated with 3 different periodic input signals X(t) (on the left). The 3 graphs on the right give the response of the output W (t). The numerical simulations were done with the following parameters τ1 = 100 s and τ2 = 10000 s are fixed. The other parameters are: α1 = 0.01 sec-1, β1 = 10 nM.sec-1, α2 = 0, 006 min-1 β2 = 6 min-1, θ1 = θ5 = 700 nM, θ2 = θ6 = 800 nM, θ3 = θ4 = 50 nM. (a) with σ1 = 0 s, σ2 = 100 min (b) with σ1 = 60 s, σ2 = 0 min (c) σ1 = 60 s, σ2 = 100 min. For practical reasons, the representations of the pulsatile signals are not at real scale.
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Figure 8: Response of the double DIFFL to a bursting signal. The motif of double DIFFL (Fig. 1(f)) is stimulated with 3 different periodic input signals X(t) (on the left). The 3 graphs on the right give the response of the output W (t). The numerical simulations were done with the following parameters τ1 = 100 s and τ2 = 10000 s are fixed. The other parameters are: α1 = 0.01 sec-1, β1 = 10 nM.sec-1, α2 = 0, 006 min-1 β2 = 6 min-1, θ1 = θ5 = 700 nM, θ2 = θ6 = 800 nM, θ3 = θ4 = 50 nM. (a) with σ1 = 0 s, σ2 = 100 min (b) with σ1 = 60 s, σ2 = 0 min (c) σ1 = 60 s, σ2 = 100 min. For practical reasons, the representations of the pulsatile signals are not at real scale.

Mentions: When the network represented in Fig. 1(f) is stimulated by the signal S(t) described above, it has the property to selectively recognize temporal patterns of bursting oscillations, allowing the target gene to be maximally transcribed in some conditions. To illustrate this point Fig. 8 shows the time-evolution of W in response to various periodic stimulations S(t). When the system is submitted to periodic trains of square waves without bursting (Fig. 8(a), σ1 = 0), the gene W is not expressed. Likewise if the stimulation consists of a long train of spikes without any quiescent period (Fig. 8(b)), the average level of W remains negligible. However, if we stimulate the motif with a specific bursting signal (Fig. 8(c)), the system gives a non-zero response. More generally, the striking feature of the network of Fig. 1(f) is to exhibit a non vanishing response only in a given range of pulse patterns. Moreover, if the time intervals τ1 and τ2 are fixed, the system possesses a set of maxima for some optimal values of (σ1, σ2). In view of of Fig. 8(a–c), the system behaves as it filtered out low as well as high frequencies. But this conclusion is misleading since when high and low frequencies are mixed in the same input signal in the form of bursting oscillations, the system displays a non zero response in the evolution of W, with the possibility of optimizing the average level of W over one period.


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

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

Response of the double DIFFL to a bursting signal. The motif of double DIFFL (Fig. 1(f)) is stimulated with 3 different periodic input signals X(t) (on the left). The 3 graphs on the right give the response of the output W (t). The numerical simulations were done with the following parameters τ1 = 100 s and τ2 = 10000 s are fixed. The other parameters are: α1 = 0.01 sec-1, β1 = 10 nM.sec-1, α2 = 0, 006 min-1 β2 = 6 min-1, θ1 = θ5 = 700 nM, θ2 = θ6 = 800 nM, θ3 = θ4 = 50 nM. (a) with σ1 = 0 s, σ2 = 100 min (b) with σ1 = 60 s, σ2 = 0 min (c) σ1 = 60 s, σ2 = 100 min. For practical reasons, the representations of the pulsatile signals are not at real scale.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Response of the double DIFFL to a bursting signal. The motif of double DIFFL (Fig. 1(f)) is stimulated with 3 different periodic input signals X(t) (on the left). The 3 graphs on the right give the response of the output W (t). The numerical simulations were done with the following parameters τ1 = 100 s and τ2 = 10000 s are fixed. The other parameters are: α1 = 0.01 sec-1, β1 = 10 nM.sec-1, α2 = 0, 006 min-1 β2 = 6 min-1, θ1 = θ5 = 700 nM, θ2 = θ6 = 800 nM, θ3 = θ4 = 50 nM. (a) with σ1 = 0 s, σ2 = 100 min (b) with σ1 = 60 s, σ2 = 0 min (c) σ1 = 60 s, σ2 = 100 min. For practical reasons, the representations of the pulsatile signals are not at real scale.
Mentions: When the network represented in Fig. 1(f) is stimulated by the signal S(t) described above, it has the property to selectively recognize temporal patterns of bursting oscillations, allowing the target gene to be maximally transcribed in some conditions. To illustrate this point Fig. 8 shows the time-evolution of W in response to various periodic stimulations S(t). When the system is submitted to periodic trains of square waves without bursting (Fig. 8(a), σ1 = 0), the gene W is not expressed. Likewise if the stimulation consists of a long train of spikes without any quiescent period (Fig. 8(b)), the average level of W remains negligible. However, if we stimulate the motif with a specific bursting signal (Fig. 8(c)), the system gives a non-zero response. More generally, the striking feature of the network of Fig. 1(f) is to exhibit a non vanishing response only in a given range of pulse patterns. Moreover, if the time intervals τ1 and τ2 are fixed, the system possesses a set of maxima for some optimal values of (σ1, σ2). In view of of Fig. 8(a–c), the system behaves as it filtered out low as well as high frequencies. But this conclusion is misleading since when high and low frequencies are mixed in the same input signal in the form of bursting oscillations, the system displays a non zero response in the evolution of W, with the possibility of optimizing the average level of W over one period.

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