Synchrony in a Population of Hysteresis-Based Genetic Oscillators

Oscillatory behavior has been found in different specialized genetic networks. Pre- vious work has demonstrated nonsynchronous, erratic single-cell oscillations in a genetic network composed of nonspecialized regulatory components and based entirely on negative feedback. Here, we present the construction of a more robust, hysteresis-based genetic relaxation oscillator and pro- vide a theoretical analysis of the conditions necessary for single-cell and population synchronized oscillations. The oscillator is constructed by coupling two subsystems that have previously been im- plemented experimentally. The first subsystem is the toggle switch, which consists of two mutually repressive genes and can display robust switching between bistable expression states and hysteresis. The second subsystem is an intercell communication system involved in quorum-sensing. This sub- system drives the toggle switch through a hysteresis loop in single cells and acts as a coupling between individual cellular oscillators in a cell population. We demonstrate the possibility of both population synchronization and suppression of oscillations (cluster formation), depending on diffusion strength and other parameters of the system. We also propose the optimal choice of the parameters and small variations in the architecture of the gene regulatory network that substantially expand the oscillatory region and improve the likelihood of observing oscillations experimentally.

[1]  L. Abbott,et al.  On the behavior of a neural oscillator electrically coupled to a bistable element , 1998 .

[2]  M. Ehrenberg,et al.  Noise in a minimal regulatory network: plasmid copy number control , 2001, Quarterly Reviews of Biophysics.

[3]  M. L. Simpson,et al.  Whole-cell biocomputing. , 2001, Trends in biotechnology.

[4]  M. Fussenegger,et al.  Artificial mammalian gene regulation networks-novel approaches for gene therapy and bioengineering. , 2002, Journal of biotechnology.

[5]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[6]  Ertugrul M. Ozbudak,et al.  Regulation of noise in the expression of a single gene , 2002, Nature Genetics.

[7]  S. Basu,et al.  Spatiotemporal control of gene expression with pulse-generating networks. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[8]  P. Swain,et al.  Intrinsic and extrinsic contributions to stochasticity in gene expression , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[9]  J. Collins,et al.  Programmable cells: interfacing natural and engineered gene networks. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Jeff Hasty,et al.  Engineered gene circuits , 2002, Nature.

[11]  E. P. Greenberg,et al.  Conversion of the Vibrio fischeriTranscriptional Activator, LuxR, to a Repressor , 2000, Journal of bacteriology.

[12]  Bjarke Bak Christensen,et al.  gfp-Based N-Acyl Homoserine-Lactone Sensor Systems for Detection of Bacterial Communication , 2001, Applied and Environmental Microbiology.

[13]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[14]  Nancy Kopell,et al.  Synchronization and Transient Dynamics in the Chains of Electrically Coupled Fitzhugh--Nagumo Oscillators , 2001, SIAM J. Appl. Math..

[15]  M K Winson,et al.  Construction and analysis of luxCDABE-based plasmid sensors for investigating N-acyl homoserine lactone-mediated quorum sensing. , 1998, FEMS microbiology letters.

[16]  Belykh,et al.  Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  A. Pikovsky,et al.  Resolving clusters in chaotic ensembles of globally coupled identical oscillators. , 2001, Physical review letters.

[18]  S. Sørensen,et al.  Presence of N-Acyl Homoserine Lactones in Soil Detected by a Whole-Cell Biosensor and Flow Cytometry , 2003, Microbial Ecology.

[19]  Ron Weiss,et al.  Engineered Communications for Microbial Robotics , 2000, DNA Computing.

[20]  M. Elowitz,et al.  Combinatorial Synthesis of Genetic Networks , 2002, Science.

[21]  R. Weiss,et al.  Programmed population control by cell–cell communication and regulated killing , 2004, Nature.

[22]  E. Greenberg,et al.  Signalling: Listening in on bacteria: acyl-homoserine lactone signalling , 2002, Nature Reviews Molecular Cell Biology.

[23]  Mads Kaern,et al.  The engineering of gene regulatory networks. , 2003, Annual review of biomedical engineering.

[24]  L. Perko.  Differential Equations and Dynamical Systems , 1991 .

[25]  A. Ninfa,et al.  Development of Genetic Circuitry Exhibiting Toggle Switch or Oscillatory Behavior in Escherichia coli , 2003, Cell.

[26]  J. Hasty,et al.  Synchronizing genetic relaxation oscillators by intercell signaling , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  R. Weiss,et al.  Directed evolution of a genetic circuit , 2002, Proceedings of the National Academy of Sciences of the United States of America.