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Bridging genetic networks and queueing theory

Author

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  • Arazi, Arnon
  • Ben-Jacob, Eshel
  • Yechiali, Uri

Abstract

One of the main challenges facing biology today is the understanding of the joint action of genes, proteins and RNA molecules, interwoven in intricate interdependencies commonly known as genetic networks. To this end, several mathematical approaches have been introduced to date. In addition to developing the analytical tools required for this task anew, one can utilize knowledge found in existing disciplines, specializing in the representation and analysis of systems featuring similar aspects. We suggest queueing theory as a possible source of such knowledge. This discipline, which focuses on the study of workloads forming in a variety of scenarios, offers an assortment of tools allowing for the derivation of the statistical properties of the inspected systems. We argue that a proper adaptation of modeling techniques and analytical methods used in queueing theory can contribute to the study of genetic regulatory networks. This is demonstrated by presenting a queueing-inspired model of a genetic network of arbitrary size and structure, for which the probability distribution function is derived. This model is further applied to the description of the lac operon regulation mechanism. In addition, we discuss the possible benefits stemming for queueing theory from the interdisciplinary dialogue with molecular biology—in particular, the incorporation of various dynamical behaviours into queueing networks.

Suggested Citation

  • Arazi, Arnon & Ben-Jacob, Eshel & Yechiali, Uri, 2004. "Bridging genetic networks and queueing theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 585-616.
    • Handle: RePEc:eee:phsmap:v:332:y:2004:i:c:p:585-616
    DOI: 10.1016/j.physa.2003.07.009
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    Citations

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    Cited by:

    1. Addabbo, Tommaso & Kocarev, Ljupco, 2009. "Periodic dynamics in queuing networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2178-2192.
    2. Arnon Arazi & Eshel Ben-Jacob & Uri Yechiali, 2005. "Controlling an oscillating Jackson-type network having state-dependent service rates," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 453-466, December.
    3. D. Anderson & J. Blom & M. Mandjes & H. Thorsdottir & K. Turck, 2016. "A Functional Central Limit Theorem for a Markov-Modulated Infinite-Server Queue," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 153-168, March.

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