Intracellular delay limits cyclic changes in gene expression.

Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kappaB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding and mRNA production. This description of natural variability for delays introduces a transition from a stable steady state to limit cycle oscillations and then a second transition back to a stable steady state which has not been observed in previously published models. We demonstrate our approach for two models. The first model describes Hes1 autorepression with equations for Hes1 mRNA production and Hes1 protein translation. The second model describes Hes1 repression by the protein complex Gro/TLE1/Hes1, where Gro/TLE1 is activated by Hes1 phosphorylation. Finally, we discuss our analytical and numerical results in relation to experimental data.

[1]  M. Ehrenberg,et al.  Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Andreas Thiel,et al.  Complex dynamics is abolished in delayed recurrent systems with distributed feedback times , 2003, Complex..

[3]  Julian Lewis,et al.  The vertebrate segmentation clock. , 2004, Current opinion in genetics & development.

[4]  V. Liebscher,et al.  Modelling the Hes 1 Oscillator During Somitogenesis , 2005 .

[5]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  Andrea Ciliberto,et al.  Steady States and Oscillations in the p53/Mdm2 Network , 2005, Cell cycle.

[7]  Advances in Solid State Physics , 2009 .

[8]  Lorenz Fahse,et al.  Distributed delays stabilize ecological feedback systems. , 2005, Physical review letters.

[9]  J. Timmer,et al.  Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Marcel Abendroth,et al.  Biological delay systems: Linear stability theory , 1990 .

[11]  D. A. Baxter,et al.  Frequency selectivity, multistability, and oscillations emerge from models of genetic regulatory systems. , 1998, American journal of physiology. Cell physiology.

[12]  Stefan Zeiser,et al.  Number of active transcription factor binding sites is essential for the Hes7 oscillator , 2006, Theoretical Biology and Medical Modelling.

[13]  J. Mahaffy.  Periodic solutions for certain protein synthesis models , 1980 .

[14]  Andre Levchenko,et al.  Comment on "Oscillations in NF-κB Signaling Control the Dynamics of Gene Expression" , 2005, Science.

[15]  D. A. Baxter,et al.  Effects of macromolecular transport and stochastic fluctuations on dynamics of genetic regulatory systems. , 1999, The American journal of physiology.

[16]  Svetoslav Nikolov,et al.  An alternative approach to investigating a time delay model of JAK-STAT signalling pathway , 2005 .

[17]  Uri Alon,et al.  Dynamics of the p53-Mdm2 feedback loop in individual cells , 2004, Nature Genetics.

[18]  I. Cherevko,et al.  On approximation of systems with delay and their stability , 2004 .

[19]  A. Hoffmann,et al.  The I (cid:1) B –NF-(cid:1) B Signaling Module: Temporal Control and Selective Gene Activation , 2022 .

[20]  P. Swain,et al.  Gene Regulation at the Single-Cell Level , 2005, Science.

[21]  U Alon,et al.  Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Galit Lahav,et al.  The Strength of Indecisiveness: Oscillatory Behavior for Better Cell Fate Determination , 2004, Science's STKE.

[23]  N. Monk.  Oscillatory Expression of Hes1, p53, and NF-κB Driven by Transcriptional Time Delays , 2003, Current Biology.

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

[25]  E O Voit,et al.  Approximation of delays in biochemical systems. , 2005, Mathematical biosciences.

[26]  M. Mackey,et al.  Modelling transcriptional feedback loops: the role of Gro/TLE1 in Hes1 oscillations , 2006, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[27]  K. Sneppen,et al.  Sustained oscillations and time delays in gene expression of protein Hes1 , 2003, FEBS letters.

[28]  John J. Tyson,et al.  The Dynamics of Feedback Control Circuits in Biochemical Pathways , 1978 .

[29]  J. Mallet-Paret,et al.  The Poincare-Bendixson theorem for monotone cyclic feedback systems , 1990 .

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

[31]  H. Hirata,et al.  Oscillatory Expression of the bHLH Factor Hes1 Regulated by a Negative Feedback Loop , 2002, Science.

[32]  D. E. Nelson,et al.  Oscillations in transcription factor dynamics: a new way to control gene expression. , 2004, Biochemical Society transactions.

[33]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[34]  James R. Johnson,et al.  Oscillations in NF-κB Signaling Control the Dynamics of Gene Expression , 2004, Science.

[35]  Douglas B. Kell,et al.  Response to Comment on "Oscillations in NF-κB Signaling Control the Dynamics of Gene Expression" , 2005, Science.

[36]  M. Mackey,et al.  Sufficient conditions for stability of linear differential equations with distributed delay , 2001 .