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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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The graph of extremum values of Y in function of σ for a simple activation process. The extremum values of Y in function of σ for a simple activation process (Fig 1. (a)) are plotted thanks to the equations (2) of the main text. Ymax is the maximum reached by the protein, <Y >T is the mean concentration of the protein averaged over one period T, Ymin is the minimal value reached by the protein,  (dotted line) represents the stationary state that the protein would attain if the stimulation was constant and YL (dashed line) is the asymptotic value reached by Ymax when the inter-pulse interval σ becomes very large. The parameters are: α = 0.01 min-1, β = 10 nM.min-1, τ = 100 min.
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Figure 3: The graph of extremum values of Y in function of σ for a simple activation process. The extremum values of Y in function of σ for a simple activation process (Fig 1. (a)) are plotted thanks to the equations (2) of the main text. Ymax is the maximum reached by the protein, <Y >T is the mean concentration of the protein averaged over one period T, Ymin is the minimal value reached by the protein, (dotted line) represents the stationary state that the protein would attain if the stimulation was constant and YL (dashed line) is the asymptotic value reached by Ymax when the inter-pulse interval σ becomes very large. The parameters are: α = 0.01 min-1, β = 10 nM.min-1, τ = 100 min.

Mentions: Fig. 3 shows an example of these functions when the inter-pulse σ is varied, for a fixed pulse duration τ. When σ increases from 0 the observables are all decreasing. The maximum Ymax stays within the interval [YL, κ], where YL is the asymptotic value reached by Ymax (dotted line on Fig. 3, obtained when the denominator of Ymax, eq.(2), equals 1). We note that this level can be controlled by choosing the pulse duration τ. This can be useful if Y is itself a transcription factor with respect to a target gene Z (see next Section).


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

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

The graph of extremum values of Y in function of σ for a simple activation process. The extremum values of Y in function of σ for a simple activation process (Fig 1. (a)) are plotted thanks to the equations (2) of the main text. Ymax is the maximum reached by the protein, <Y >T is the mean concentration of the protein averaged over one period T, Ymin is the minimal value reached by the protein,  (dotted line) represents the stationary state that the protein would attain if the stimulation was constant and YL (dashed line) is the asymptotic value reached by Ymax when the inter-pulse interval σ becomes very large. The parameters are: α = 0.01 min-1, β = 10 nM.min-1, τ = 100 min.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: The graph of extremum values of Y in function of σ for a simple activation process. The extremum values of Y in function of σ for a simple activation process (Fig 1. (a)) are plotted thanks to the equations (2) of the main text. Ymax is the maximum reached by the protein, <Y >T is the mean concentration of the protein averaged over one period T, Ymin is the minimal value reached by the protein, (dotted line) represents the stationary state that the protein would attain if the stimulation was constant and YL (dashed line) is the asymptotic value reached by Ymax when the inter-pulse interval σ becomes very large. The parameters are: α = 0.01 min-1, β = 10 nM.min-1, τ = 100 min.
Mentions: Fig. 3 shows an example of these functions when the inter-pulse σ is varied, for a fixed pulse duration τ. When σ increases from 0 the observables are all decreasing. The maximum Ymax stays within the interval [YL, κ], where YL is the asymptotic value reached by Ymax (dotted line on Fig. 3, obtained when the denominator of Ymax, eq.(2), equals 1). We note that this level can be controlled by choosing the pulse duration τ. This can be useful if Y is itself a transcription factor with respect to a target gene Z (see next Section).

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