Bulletin of Mathematical Biology

, Volume 73, Issue 11, pp 2678–2706 | Cite as

Autonomous Synchronization of Chemically Coupled Synthetic Oscillators

  • Moritz LangEmail author
  • Tatiana T. Marquez-LagoEmail author
  • Jörg Stelling
  • Steffen Waldherr
Original Article


Synthetic biology has recently provided functional single-cell oscillators. With a few exceptions, however, synchronization across a population has not been achieved yet. In particular, designing a cell coupling mechanism to achieve autonomous synchronization is not straightforward since there are usually several different design alternatives. Here, we propose a method to mathematically predict autonomous synchronization properties, and to identify the network structure with the best performance, thus increasing the feasibility for a successful implementation in vivo.

Our method relies on the reduction of ODE-based models for synthetic oscillators to a phase description, and the subsequent analysis of the phase model either in the spatially homogeneous or heterogeneous case. This analysis identifies three major factors determining if and when autonomous synchronization can be achieved, namely cell density, cell to cell variability, and structural design decisions. Moreover, when considering a spatially heterogeneous medium, we observe phase waves. These waves may hinder synchronization substantially, and their suppression should be considered in the design process.

In contrast to previous work, we analyze the synchronization process of models of experimentally validated synthetic oscillators in mammalian cells. Alternative designs for cell-to-cell communication via a quorum sensing mechanism differ in few mechanistic details, but these differences have important implications for autonomous synchronization. Our analysis suggests that not only the periodical transcription of the protein producing the signaling molecule, but also of the receptor protein is necessary to achieve good performance.


Synchronization Synthetic oscillators Kuramoto analysis Spatial waves 


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Supplementary material

11538_2011_9642_MOESM1_ESM.pdf (2.6 mb)
(PDF 2.626 kB)

AHL During Synchronization (MOV 14.525 kB)

Phases During Synchronization (MOV 3.338 kB)


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Copyright information

© Society for Mathematical Biology 2011

Authors and Affiliations

  1. 1.Department of Biosystems Science and Engineering, and Swiss Institute of BioinformaticsETH ZürichBaselSwitzerland
  2. 2.Institute for Systems Theory and Automatic ControlUniversity of StuttgartStuttgartGermany

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