This model is from the article:
Queueing up for enzymatic processing: correlated signaling through coupled degradation.
Natalie A Cookson, William H Mather, Tal Danino, Octavio Mondragón-Palomino, Ruth J Williams, Lev S Tsimring, & Jeff Hasty Molecular Systems Biology2011; 7:561; DOI:10.1038/msb.2011.94
Abstract:
High-throughput technologies have led to the generation of complex wiring diagrams as a post-sequencing paradigm for depicting the interactions between vast and diverse cellular species. While these diagrams are useful for analyzing biological systems on a large scale, a detailed understanding of the molecular mechanisms that underlie the observed network connections is critical for the further development of systems and synthetic biology. Here, we use queueing theory to investigate how ‘waiting lines’ can lead to correlations between protein ‘customers’ that are coupled solely through a downstream set of enzymatic ‘servers’. Using the E. coli ClpXP degradation machine as a model processing system, we observe significant cross-talk between two networks that are indirectly coupled through a common set of processors. We further illustrate the implications of enzymatic queueing using a synthetic biology application, in which two independent synthetic networks demonstrate synchronized behavior when common ClpXP machinery is overburdened. Our results demonstrate that such post-translational processes can lead to dynamic connections in cellular networks and may provide a mechanistic understanding of existing but currently inexplicable links.

Note:
Individual stochastic trajectories for a queueing system in three different conditions, 1) Underloaded, 2) Balanced and 3) Overloaded, demonstrate correlation resonance. The parameter values in this model correspond to the Balanced Condition.

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