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Delay-induced degrade-and-fire oscillations in small genetic circuits.

ABSTRACT: Robust oscillations have recently been observed in a synthetic gene network composed of coupled positive and negative feedback loops. Here we use deterministic and stochastic modeling to investigate how a small time delay in such regulatory networks can lead to strongly nonlinear oscillations that can be characterized by "degrade-and-fire" dynamics. We show that the period of the oscillations can be significantly greater than the delay time, provided the circuit components possess strong activation and tight repression. The variability of the period is strongly influenced by fluctuations near the oscillatory minima, when the number of regulatory molecules is small.

SUBMITTER: Mather W

PROVIDER: S-EPMC2924583 | biostudies-literature | 2009 Feb

REPOSITORIES: biostudies-literature

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Delay-induced degrade-and-fire oscillations in small genetic circuits.

Mather William W Bennett Matthew R MR Hasty Jeff J Tsimring Lev S LS

Physical review letters 20090213 6

Robust oscillations have recently been observed in a synthetic gene network composed of coupled positive and negative feedback loops. Here we use deterministic and stochastic modeling to investigate how a small time delay in such regulatory networks can lead to strongly nonlinear oscillations that can be characterized by "degrade-and-fire" dynamics. We show that the period of the oscillations can be significantly greater than the delay time, provided the circuit components possess strong activat ...[more]

PMID: 19257639

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Project description:BackgroundInformation processing in neuronal networks relies on the network's ability to generate temporal patterns of action potentials. Although the nature of neuronal network activity has been intensively investigated in the past several decades at the individual neuron level, the underlying principles of the collective network activity, such as the synchronization and coordination between neurons, are largely unknown. Here we focus on isolated neuronal clusters in culture and address the following simple, yet fundamental questions: What is the minimal number of cells needed to exhibit collective dynamics? What are the internal temporal characteristics of such dynamics and how do the temporal features of network activity alternate upon crossover from minimal networks to large networks?Methodology/principal findingsWe used network engineering techniques to induce self-organization of cultured networks into neuronal clusters of different sizes. We found that small clusters made of as few as 40 cells already exhibit spontaneous collective events characterized by innate synchronous network oscillations in the range of 25 to 100 Hz. The oscillation frequency of each network appeared to be independent of cluster size. The duration and rate of the network events scale with cluster size but converge to that of large uniform networks. Finally, the investigation of two coupled clusters revealed clear activity propagation with master/slave asymmetry.Conclusions/significanceThe nature of the activity patterns observed in small networks, namely the consistent emergence of similar activity across networks of different size and morphology, suggests that neuronal clusters self-regulate their activity to sustain network bursts with internal oscillatory features. We therefore suggest that clusters of as few as tens of cells can serve as a minimal but sufficient functional network, capable of sustaining oscillatory activity. Interestingly, the frequencies of these oscillations are similar those observed in vivo.

Dataset Information

Delay-induced degrade-and-fire oscillations in small genetic circuits.

Publications

Delay-induced degrade-and-fire oscillations in small genetic circuits.

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