Noise-limited frequency signal transmission in gene circuits.

To maintain normal physiology, cells must properly process diverse signals arising from changes in temperature, pH, nutrient concentrations, and other factors. Many physiological processes are controlled by temporal aspects of oscillating signals; that is, these signals can encode information in the frequency domain. By modeling simple gene circuits, we analyze the impact of cellular noise on the fidelity and speed of frequency-signal transmission. We find that transmission of frequency signals is "all-or-none", limited by a critical frequency (f(c)). Signals with frequencies f(c) are severely corrupted or completely lost in transmission. We argue that f(c) is an intrinsic property of a gene circuit and it varies with circuit parameters and additional feedback or feedforward regulation. Our results may have implications for understanding signal processing in natural biological networks and for engineering synthetic gene circuits.

[1]  J. Rossant,et al.  Notch1 is required for the coordinate segmentation of somites. , 1995, Development.

[2]  L. You,et al.  Evolutionary design on a budget: robustness and optimality of bacteriophage T7. , 2006, Systems biology.

[3]  D. Wettstein,et al.  The Notch ligand, X-Delta-2, mediates segmentation of the paraxial mesoderm in Xenopus embryos. , 1997, Development.

[4]  M. Savageau.  Comparison of classical and autogenous systems of regulation in inducible operons , 1974, Nature.

[5]  T. Mak,et al.  Disruption of the mouse RBP-Jκ gene results in early embryonic death , 1995 .

[6]  D B Kell,et al.  Oscillations in NF-kappaB signaling control the dynamics of gene expression. , 2004, Science.

[7]  U. Alon,et al.  Negative autoregulation speeds the response times of transcription networks. , 2002, Journal of molecular biology.

[8]  O. Pourquié,et al.  Notch signalling is required for cyclic expression of the hairy-like gene HES1 in the presomitic mesoderm. , 2000, Development.

[9]  Hao Song,et al.  A synthetic biology challenge: making cells compute. , 2007, Molecular bioSystems.

[10]  C. Rao,et al.  Control, exploitation and tolerance of intracellular noise , 2002, Nature.

[11]  G. Richardson.  The human circadian system in normal and disordered sleep. , 2005, The Journal of clinical psychiatry.

[12]  O. Pourquié,et al.  When body segmentation goes wrong , 2001, Clinical genetics.

[13]  Lucy Shapiro,et al.  Oscillating Global Regulators Control the Genetic Circuit Driving a Bacterial Cell Cycle , 2004, Science.

[14]  David Ish-Horowicz,et al.  Notch signalling and the synchronization of the somite segmentation clock , 2000, Nature.

[15]  Tobias Lang,et al.  Model-Based Design of Growth-Attenuated Viruses , 2006, PLoS Comput. Biol..

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

[17]  J. Raser,et al.  Noise in Gene Expression: Origins, Consequences, and Control , 2005, Science.

[18]  W. Almers,et al.  Rhythmic exocytosis stimulated by GnRH-induced calcium oscillations in rat gonadotropes. , 1993, Science.

[19]  Alexander van Oudenaarden,et al.  Amplitude control of cell-cycle waves by nuclear import , 2004, Nature Cell Biology.

[20]  R. Weiss,et al.  Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[21]  P A de Boer,et al.  Rapid pole-to-pole oscillation of a protein required for directing division to the middle of Escherichia coli. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[22]  Wouter-Jan Rappel,et al.  Division accuracy in a stochastic model of Min oscillations in Escherichia coli. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[23]  Robert R. Klevecz,et al.  Dynamic architecture of the yeast cell cycle uncovered by wavelet decomposition of expression microarray data , 2000, Functional & Integrative Genomics.

[24]  Ovidiu Lipan,et al.  The use of oscillatory signals in the study of genetic networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[25]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[26]  M. Thattai,et al.  Intrinsic noise in gene regulatory networks , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[27]  S. Kay,et al.  Molecular bases of circadian rhythms. , 2001, Annual review of cell and developmental biology.

[28]  M. Berridge.  Unlocking the secrets of cell signaling. , 2005, Annual review of physiology.

[29]  M. Berridge.  The AM and FM of calcium signalling , 1997, Nature.

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

[31]  H. Othmer,et al.  A stochastic analysis of first-order reaction networks , 2005, Bulletin of mathematical biology.

[32]  L. Lopez-Molina,et al.  The Transcription Factor DBP Affects Circadian Sleep Consolidation and Rhythmic EEG Activity , 2000, The Journal of Neuroscience.

[33]  J. Paulsson.  Summing up the noise in gene networks , 2004, Nature.

[34]  Roger Y. Tsien,et al.  Cell-permeant caged InsP3 ester shows that Ca2+ spike frequency can optimize gene expression , 1998, Nature.

[35]  O. Pourquié,et al.  Avian hairy Gene Expression Identifies a Molecular Clock Linked to Vertebrate Segmentation and Somitogenesis , 1997, Cell.

[36]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[37]  C. Pesce,et al.  Regulated cell-to-cell variation in a cell-fate decision system , 2005, Nature.

[38]  D. Volfson,et al.  Origins of extrinsic variability in eukaryotic gene expression , 2006, Nature.

[39]  M. L. Simpson,et al.  Frequency domain analysis of noise in autoregulated gene circuits , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[40]  P. Cullen,et al.  The frequencies of calcium oscillations are optimized for efficient calcium-mediated activation of Ras and the ERK/MAPK cascade. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[41]  O. Pourquié.  The Segmentation Clock: Converting Embryonic Time into Spatial Pattern , 2003, Science.

[42]  T. Elston,et al.  Stochasticity in gene expression: from theories to phenotypes , 2005, Nature Reviews Genetics.

[43]  D. Ish-Horowicz,et al.  Periodic Lunatic fringe expression is controlled during segmentation by a cyclic transcriptional enhancer responsive to notch signaling. , 2002, Developmental cell.

[44]  S. Lowen.  The Biophysical Journal , 1960, Nature.

[45]  Keli Xu,et al.  Calcium oscillations increase the efficiency and specificity of gene expression , 1998, Nature.

[46]  A. van Oudenaarden,et al.  Noise Propagation in Gene Networks , 2005, Science.

[47]  Martin Howard,et al.  Cellular organization by self-organization , 2005, The Journal of cell biology.

[48]  D. Murray,et al.  A genomewide oscillation in transcription gates DNA replication and cell cycle. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[49]  Nigel A. Brown,et al.  Waves of mouse Lunatic fringe expression, in four-hour cycles at two-hour intervals, precede somite boundary formation , 1998, Current Biology.

[50]  Kurt Wiesenfeld,et al.  Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs , 1995, Nature.

[51]  D. Koshland,et al.  Non-genetic individuality: chance in the single cell , 1976, Nature.

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

[53]  Pablo A. Iglesias,et al.  Optimal Noise Filtering in the Chemotactic Response of Escherichia coli , 2006, PLoS Comput. Biol..

[54]  D. Botstein,et al.  Singular value decomposition for genome-wide expression data processing and modeling. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[55]  C. Wilke,et al.  Why highly expressed proteins evolve slowly. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[56]  T. Mak,et al.  Disruption of the mouse RBP-J kappa gene results in early embryonic death. , 1995, Development.

[57]  Jan Walleczek,et al.  Self-Organized Biological Dynamics and Nonlinear Control , 2006 .

[58]  Jan Vijg,et al.  Increased cell-to-cell variation in gene expression in ageing mouse heart , 2006, Nature.

[59]  J. Hasty,et al.  Synthetic gene network for entraining and amplifying cellular oscillations. , 2002, Physical review letters.

[60]  Uri Alon,et al.  Response delays and the structure of transcription networks. , 2003, Journal of molecular biology.

[61]  M. Berridge,et al.  Calcium signalling: dynamics, homeostasis and remodelling , 2003, Nature reviews. Molecular cell biology.

[62]  W. Bialek,et al.  Physical limits to biochemical signaling. , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[63]  Taichiro Tomida,et al.  NFAT functions as a working memory of Ca2+ signals in decoding Ca2+ oscillation , 2003, The EMBO journal.

[64]  J. Ross,et al.  Signal Processing by Simple Chemical Systems , 2002 .

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

[66]  D. Murray,et al.  Genome wide oscillations in expression – Wavelet analysis of time series data from yeast expression arrays uncovers the dynamic architecture of phenotype , 2004, Molecular Biology Reports.

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

[68]  M. L. Simpson,et al.  Gene network shaping of inherent noise spectra , 2006, Nature.

[69]  R. Schimke,et al.  On the Roles of Synthesis and Degradation in Regulation of Enzyme Levels in Mammalian Tissues , 1969 .

[70]  Mads Kærn,et al.  Noise in eukaryotic gene expression , 2003, Nature.

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