Analysis of coupled genetic oscillators with delayed positive feedback interconnections

Genetic oscillators have a fundamental role in the regulation not only of intracellular, but also of intercellular functions: for instance, in the segmentation clock, the synchronised oscillation of neighbouring cells generates spatial travelling waves that induce segmentation of precursors of the vertebral column. To investigate this type of phenomena, we consider the behaviour of two genetic negative feedback oscillators, each operating in a different cell, coupled by an intercellular positive-feedback interconnection with delays. The two coupled systems are nominally identical, but can be different due to noise and cell-to-cell variability. When they can be different in general, we study the effect of positive-feedback and of delay in inducing an oscillatory behaviour. When they are identical, we study how the intercellular feedback delay affects the phase difference between the two oscillators.

[1]  Chih-Wen Shih,et al.  The kinetics in mathematical models on segmentation clock genes in zebrafish , 2018, Journal of mathematical biology.

[2]  Giulia Giordano,et al.  Design and analysis of a biomolecular positive-feedback oscillator , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[3]  Benjamin L Turner,et al.  Supporting Online Material Materials and Methods Som Text Figs. S1 to S3 Table S1 References Robust, Tunable Biological Oscillations from Interlinked Positive and Negative Feedback Loops , 2022 .

[4]  Abhyudai Singh,et al.  Conditional Moment Closure Schemes for Studying Stochastic Dynamics of Genetic Circuits , 2015, IEEE Transactions on Biomedical Circuits and Systems.

[5]  Franco Blanchini,et al.  Molecular Titration Promotes Oscillations and Bistability in Minimal Network Models with Monomeric Regulators. , 2016, ACS synthetic biology.

[6]  Yoshihiro Morishita,et al.  Traveling wave formation in vertebrate segmentation. , 2009, Journal of theoretical biology.

[7]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[8]  Yongqiang Wang,et al.  The collective oscillation period of inter-coupled Goodwin oscillators , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[9]  F. Blanchini,et al.  Homogeneous Time Constants Promote Oscillations in Negative Feedback Loops , 2018, ACS synthetic biology.

[10]  L. Tsimring,et al.  A synchronized quorum of genetic clocks , 2009, Nature.

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

[12]  Hanspeter Herzel,et al.  Tuning the phase of circadian entrainment , 2015, Journal of The Royal Society Interface.

[13]  Franco Blanchini,et al.  Design of a molecular clock with RNA-mediated regulation , 2014, 53rd IEEE Conference on Decision and Control.

[14]  J. Tyson,et al.  Design principles of biochemical oscillators , 2008, Nature Reviews Molecular Cell Biology.

[15]  Franco Blanchini,et al.  A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems , 2014, Bulletin of mathematical biology.

[16]  D. Ish-Horowicz,et al.  Transcript processing and export kinetics are rate-limiting steps in expressing vertebrate segmentation clock genes , 2013, Proceedings of the National Academy of Sciences.

[17]  Soo Bin Kwon,et al.  Noise in the Vertebrate Segmentation Clock Is Boosted by Time Delays but Tamed by Notch Signaling , 2018, Cell reports.

[18]  A. Ay,et al.  Short-lived Her proteins drive robust synchronized oscillations in the zebrafish segmentation clock , 2013, Development.

[19]  Chih-Wen Shih,et al.  A LATTICE MODEL ON SOMITOGENESIS OF ZEBRAFISH , 2012 .

[20]  Abhyudai Singh,et al.  Stochastic hybrid systems for studying biochemical processes , 2010, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  Md. Jahoor Alam,et al.  Measurement of phase synchrony of coupled segmentation clocks , 2011, Comput. Biol. Medicine.

[22]  Julian Lewis.  Autoinhibition with Transcriptional Delay A Simple Mechanism for the Zebrafish Somitogenesis Oscillator , 2003, Current Biology.

[23]  Francis J Doyle,et al.  A model of the cell-autonomous mammalian circadian clock , 2009, Proceedings of the National Academy of Sciences.

[24]  Frank Jülicher,et al.  Chemical event chain model of coupled genetic oscillators. , 2018, Physical review. E.

[25]  Franco Blanchini,et al.  Stability analysis of an artificial biomolecular oscillator with non-cooperative regulatory interactions , 2017, Journal of biological dynamics.

[26]  Didier Gonze,et al.  The Goodwin Model: Behind the Hill Function , 2013, PloS one.

[27]  M. A. Henson,et al.  A molecular model for intercellular synchronization in the mammalian circadian clock. , 2007, Biophysical journal.

[28]  Yoshihiro Morishita,et al.  Synchronized oscillation of the segmentation clock gene in vertebrate development , 2010, Journal of mathematical biology.

[29]  B. Goodwin.  Oscillatory behavior in enzymatic control processes. , 1965, Advances in enzyme regulation.

[30]  J. Ferrell,et al.  Modeling the Cell Cycle: Why Do Certain Circuits Oscillate? , 2011, Cell.

[31]  Eduardo D. Sontag,et al.  Synchronization of Interconnected Systems With Applications to Biochemical Networks: An Input-Output Approach , 2009, IEEE Transactions on Automatic Control.

[32]  Kwang-Hyun Cho,et al.  537 Short Report , 2022 .

[33]  L. Tsimring,et al.  Entrainment of a Population of Synthetic Genetic Oscillators , 2011, Science.

[34]  William M. Shih,et al.  Single-Molecule Clocks Controlled by Serial Chemical Reactions. , 2017, Nano letters.

[35]  Zhiyue Lu,et al.  Biophysical clocks face a trade-off between internal and external noise resistance , 2018, eLife.

[36]  Jakob Ruess,et al.  Shaping bacterial population behavior through computer-interfaced control of individual cells , 2017, Nature Communications.

[38]  L. G. Morelli,et al.  Information flow in the presence of cell mixing and signaling delays during embryonic development. , 2019, Seminars in cell & developmental biology.

[39]  D. Volfson,et al.  Delay-induced stochastic oscillations in gene regulation. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[40]  S. Leibler,et al.  Biological rhythms: Circadian clocks limited by noise , 2000, Nature.

[41]  Peng Feng,et al.  Modelling periodic oscillations during somitogenesis. , 2007, Mathematical biosciences and engineering : MBE.