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Noise control and utility: From regulatory network to spatial patterning

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Abstract

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network congurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilitate cell fate decision. Here we review major recent ndings on noise attenuation through regulatory control, the benefit of noise via noise-induced cellular plasticity during developmental patterning and summarize key principles underlying noise control.

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References

  1. Acar M, Mettetal J T, van Oudenaarden A. Stochastic switching as a survival strategy in fluctuating environments. Nat Genet, 2008, 40: 471–475.

    Google Scholar 

  2. Alon U. Network motifs: Theory and experimental approaches. Nat Rev Genetics, 2007, 8: 450–461.

    Google Scholar 

  3. Alon U, Surette M G, Barkai N, et al. Robustness in bacterial chemotaxis. Nature, 1999, 397: 168–171.

    Google Scholar 

  4. An Y Y, Xue G S, Yang S B, et al. Apical constriction is driven by a pulsatile apical myosin network in delaminating Drosophila neuroblasts. Development, 2017, 144: 2153–2164.

    Google Scholar 

  5. Balaskas N, Ribeiro A, Panovska J, et al. Gene regulatory logic for reading the Sonic Hedgehog signaling gradient in the vertebrate neural tube. Cell, 2012, 148: 273–284.

    Google Scholar 

  6. Barkai N, Leibler S. Circadian clocks limited by noise. Nature, 2000, 403: 267–268.

    Google Scholar 

  7. Becskei A, Serrano L. Engineering stability in gene networks by autoregulation. Nature, 2000, 405: 590–593.

    Google Scholar 

  8. Bonner J T, Savage L J. Evidence for the formation of cell aggregates by chemotaxis in the development of the slime mold Dictyostelium discoideum. J Exp Zool, 1947, 106: 1–26.

    Google Scholar 

  9. Brandman O, Ferrell J E Jr, Li R, et al. Interlinked fast and slow positive feedback loops drive reliable cell decisions. Science, 2005, 310: 496–498.

    MathSciNet  MATH  Google Scholar 

  10. Cai A Q, Radtke K, Linville A, et al. Cellular retinoic acid-binding proteins are essential for hindbrain patterning and signal robustness in zebrafish. Development, 2012, 139: 2150–2155.

    Google Scholar 

  11. Cao Y S, Wang H L, Ouyang Q, et al. The free-energy cost of accurate biochemical oscillations. Nat Phys, 2015, 11: 772

    Google Scholar 

  12. Chen M, Wang L, Liu C C, et al. Noise attenuation in the ON and OFF states of biological switches. ACS Synth Biol, 2013, 2: 587–593.

    Google Scholar 

  13. Chen Y, Kim J K, Hirning A J, et al. Emergent genetic oscillations in a synthetic microbial consortium. Science, 2015, 349: 986

    Google Scholar 

  14. Chou C-S, Lo W-C, Gokoffski K K, et al. Spatial dynamics of multistage cell lineages in tissue stratification. Biophys J, 2010, 99: 3145–3154.

    Google Scholar 

  15. Colin R, Rosazza C, Vaknin A, et al. Multiple sources of slow activity fluctuations in a bacterial chemosensory network. eLife, 2017, 6: e26796

  16. Colman-Lerner A, Gordon A, Serra E, et al. Regulated cell-to-cell variation in a cell-fate decision system. Nature, 2005, 437: 699–706.

    Google Scholar 

  17. Du H J, Wang Y Y, Haensel D, et al. Multiscale modeling of layer formation in epidermis. PLoS Comput Biol, 2018, 14: e1006006

    Google Scholar 

  18. Economou A D, Ohazama A, Porntaveetus T, et al. Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate. Nat Genet, 2012, 44: 348

    Google Scholar 

  19. Eldar A, Elowitz M B. Functional roles for noise in genetic circuits. Nature, 2010, 467: 167–173.

    Google Scholar 

  20. Eldar A, Rosin D, Shilo B-Z, et al. Self-enhanced ligand degradation underlies robustness of morphogen gradients. Dev Cell, 2003, 5: 635–646.

    Google Scholar 

  21. Elowitz M B, Leibler S. A synthetic oscillatory network of transcriptional regulators. Nature, 2000, 403: 335–338.

    Google Scholar 

  22. Elowitz M B, Levine A J, Siggia E D, et al. Stochastic gene expression in a single cell. Science, 2002, 297: 1183–1186.

    Google Scholar 

  23. Fei C Y, Cao Y S, Ouyang Q, et al. Design principles for enhancing phase sensitivity and suppressing phase fluctuations simultaneously in biochemical oscillatory systems. Nat Commun, 2018, 9: 1434

    Google Scholar 

  24. Forger D B, Peskin C S. Stochastic simulation of the mammalian circadian clock. Proc Natl Acad Sci USA, 2005, 102: 321–32.

    Google Scholar 

  25. Fritsche-Guenther R, Witzel F, Sieber A, et al. Strong negative feedback from Erk to Raf confers robustness to MAPK signalling. Molecular Syst Biol, 2011, 7: 489–489.

    Google Scholar 

  26. Ge H, Qian H, Xie X S. Stochastic phenotype transition of a single cell in an intermediate region of gene state switching. Phys Rev Lett, 2015, 114: 078101

    Google Scholar 

  27. Ghim C-M, Almaas E. Genetic noise control via protein oligomerization. BMC Syst Biol, 2008, 2: 94

    Google Scholar 

  28. Gillespie D T. Exact stochastic simulation of coupled chemical reactions. J Phys Chem, 1977, 81: 2340–2361.

    Google Scholar 

  29. Gord A, Holmes W R, Dai X, et al. Computational modelling of epidermal stratification highlights the importance of asymmetric cell division for predictable and robust layer formation. J R Soc Interface, 2014, 11: 20140631

    Google Scholar 

  30. Hansen M M K, Wen W Y, Ingerman E, et al. A post-transcriptional feedback mechanism for noise suppression and fate stabilization. Cell, 2018, 173: 1609–1621.

    Google Scholar 

  31. Hasty J, Pradines J, Dolnik M, et al. Noise-based switches and amplifiers for gene expression. Proc Natl Acad Sci USA, 2000, 97: 2075–2080.

    Google Scholar 

  32. Holmes W R, de Mochel N S R, Wang Q X, et al. Gene expression noise enhances robust organization of the early mammalian blastocyst. PLoS Comput Biol, 2017, 13: e1005320

    Google Scholar 

  33. Hooshangi S, Thiberge S, Weiss R. Ultrasensitivity and noise propagation in a synthetic transcriptional cascade. Proc Natl Acad Sci USA, 2005, 102: 3581–3586.

    Google Scholar 

  34. Hornung G, Barkai N. Noise propagation and signaling sensitivity in biological networks: A role for positive feedback. PLoS Comput Biol, 2008, 4: e8

    MathSciNet  Google Scholar 

  35. Houchmandzadeh B, Wieschaus E, Leibler S. Establishment of developmental precision and proportions in the early Drosophila embryo. Nature, 2002, 415: 798–802.

    Google Scholar 

  36. Ji N, Middelkoop T C, Mentink R A, et al. Feedback control of gene expression variability in the Caenorhabditis elegans Wnt pathway. Cell, 2013, 155: 869–880.

    Google Scholar 

  37. Kondo S, Miura T. Reaction-diffusion model as a framework for understanding biological pattern formation. Science, 2010, 329: 1616–1620.

    MathSciNet  MATH  Google Scholar 

  38. Kussell E, Leibler S. Phenotypic diversity, population growth, and information in fluctuating environments. Science, 2005, 309: 2075–207.

    Google Scholar 

  39. Lander A D. Pattern, growth, and control. Cell, 2011, 144: 955–969.

    Google Scholar 

  40. Lei J Z, Lo W-C, Nie Q. Mathematical models of morphogen dynamics and growth control. Ann Math Sci Appl, 2016, 1: 427–47.

    MathSciNet  MATH  Google Scholar 

  41. Li A, Figueroa S, Jiang T-X, et al. Diverse feather shape evolution enabled by coupling anisotropic signalling modules with self-organizing branching programme. Nat Commun, 2017, 8: 14139

    Google Scholar 

  42. Li C H, Zhang L, Nie Q. Landscape reveals critical network structures for sharpening gene expression boundaries. BMC Syst Biol, 2018, 12: 67

    Google Scholar 

  43. Lim W A, Lee C M, Tang C. Design principles of regulatory networks: searching for the molecular algorithms of the cell. Mol Cell, 2013, 49: 202–212.

    Google Scholar 

  44. Liu P J, Yuan Z J, Huang L F, et al. Roles of factorial noise in inducing bimodal gene expression. Phys Rev E, 2015, 91: 062706

  45. Ma W, Trusina A, El-Samad H, et al. Defining network topologies that can achieve biochemical adaptation. Cell, 2009, 138: 760–77.

    Google Scholar 

  46. McCullagh E, Seshan A, El-Samad H, et al. Coordinate control of gene expression noise and interchromosomal interactions in a MAP kinase pathway. Nat Cell Biol, 2010, 12: 954–962.

    Google Scholar 

  47. Meinecke L, Sharma P P, Du H J, et al. Modeling craniofacial development reveals spatiotemporal constraints on robust patterning of the mandibular arch. PLoS Comput Biol, 2018, 14: e1006569

    Google Scholar 

  48. Mihalcescu I, Hsing W, Leibler S. Resilient circadian oscillator revealed in individual cyanobacteria. Nature, 2004, 430: 81–85.

    Google Scholar 

  49. Munsky B, Neuert G, van Oudenaarden A. Using gene expression noise to understand gene regulation. Science, 2012, 336: 183–187.

    MathSciNet  MATH  Google Scholar 

  50. Newman T J. Modeling multicellular systems using subcellular elements. Math Biosci Eng, 2005, 2: 613–624.

    MathSciNet  MATH  Google Scholar 

  51. Oates A C, Morelli L G, Ares S. Patterning embryos with oscillations: Structure, function and dynamics of the vertebrate segmentation clock. Development, 2012, 625–63.

    Google Scholar 

  52. Ouyang Y, Andersson C R, Kondo T, et al. Resonating circadian clocks enhance fitness in cyanobacteria. Proc Natl Acad Sci USA, 1998, 95: 8660–8664.

    Google Scholar 

  53. Ovadia J, Nie Q. Stem cell niche structure as an inherent cause of undulating epithelial morphologies. Biophys J, 2013, 104: 237–246.

    Google Scholar 

  54. Panovska-Griffiths J, Page K M, Briscoe J. A gene regulatory motif that generates oscillatory or multiway switch Nie Q et al. Sci China Math 15 outputs. J R Soc Interface, 2013, 10: 0120826

  55. Paulsson J. Summing up the noise in gene networks. Nature, 2004, 427: 415–418.

    Google Scholar 

  56. Pedraza J M, van Oudenaarden A. Noise propagation in gene networks. Science, 2005, 307: 1965–1969.

    Google Scholar 

  57. Perez-Carrasco R, Guerrero P, Briscoe J, et al. Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches. PLoS Comput Biol, 2016, 12: e1005154

    Google Scholar 

  58. Potvin-Trottier L, Lord N D, Vinnicombe G, et al. Synchronous long-term oscillations in a synthetic gene circuit. Nature, 2016, 538: 514

    Google Scholar 

  59. Qiao L, Zhao W, Tang C, et al. Network topologies that can achieve dual function of adaptation and noise attenuation. Cell Syst, 2019, 9: 271–285.e7

    Google Scholar 

  60. Qiu Y C, Chen W T, Nie Q. Stochastic dynamics of cell lineage in tissue homeostasis. Discrete Cont Dyn-B, 2019, 24: 3971–3994.

    MathSciNet  MATH  Google Scholar 

  61. Rackauckas C, Schilling T, Nie Q. Mean-independent noise control of cell fates via intermediate states. iScience, 2018, 3: 11–2.

    Google Scholar 

  62. Raser J M, O’Shea E K. Control of stochasticity in eukaryotic gene expression. Science, 2004, 304: 1811–1814.

    Google Scholar 

  63. Raspopovic J, Marcon L, Russo L, et al. Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science, 2014, 345: 566–570.

    Google Scholar 

  64. Rogers K W, Schier A F. Morphogen gradients: From generation to interpretation. Annu Rev Cell Dev Biol, 2011, 27: 377–407.

    Google Scholar 

  65. Sartori P, Tu Y. Noise filtering strategies in adaptive biochemical signaling networks: Application to E. coli chemotaxis. J Stat Phys, 2011, 142: 1206–1217.

    MATH  Google Scholar 

  66. Sartori P, Tu Y. Free energy cost of reducing noise while maintaining a high sensitivity. Phys Rev Lett, 2015, 115: 118102_

    Google Scholar 

  67. Schilling T F, Nie Q, Lander A D. Dynamics and precision in retinoic acid morphogen gradients. Curr Opin Genet Dev, 2012, 22: 562–569.

    Google Scholar 

  68. Shankar P, Nishikawa M, Shibata T. Adaptive responses limited by intrinsic noise. PLoS ONE, 2015, 10: e0136095

    Google Scholar 

  69. Shi B H, Guo X L, Wang Y, et al. Feedback from lateral organs controls shoot apical meristem growth by modulating auxin transport. Dev Cell, 2018, 44: 204–216..e6

    Google Scholar 

  70. Shi J F, Zhao J, Li T J, et al. Detecting direct associations in a network by information theoretic approaches. Sci China Math, 2019, 62: 823–838.

    MathSciNet  MATH  Google Scholar 

  71. Smolen P, Baxter D A, Byrne J H. Modeling transcriptional control in gene networks methods, recent results, and future directions. Bull Math Biol, 2000, 62: 247–292.

    MATH  Google Scholar 

  72. Sosnik J, Zheng L K, Rackauckas C V, et al. Noise modulation in retinoic acid signaling sharpens segmental boundaries of gene expression in the embryonic zebrafish hindbrain. eLife, 2016, 5: e14034

  73. Stelling J, Gilles E D. Doyle F J. Robustness properties of circadian clock architectures. Proc Natl Acad Sci USA, 2004, 101: 13210–13215.

    Google Scholar 

  74. Stricker J, Cookson S, Bennett M R, et al. A fast, robust and tunable synthetic gene oscillator. Nature, 2008, 456

  75. Swain P S, Elowitz M B, Siggia E D. Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Natl Acad Sci USA, 2002, 99: 12795–12800.

    Google Scholar 

  76. Tay S, Hughey J J, Lee T K, et al. Single-cell NF-sk B dynamics reveal digital activation and analogue information processing. Nature, 2010, 466: 267–271.

    Google Scholar 

  77. Thattai M, van Oudenaarden A. Attenuation of noise in ultrasensitive signaling cascades. Biophysical J, 2002, 82: 2943–2950.

    Google Scholar 

  78. Thattai M, van Oudenaarden A. Stochastic gene expression in fluctuating environments. Genetics, 2004, 167: 523–530.

    Google Scholar 

  79. Towers M, Tickle C. Growing models of vertebrate limb development. Development, 2009, 136: 179–190.

    Google Scholar 

  80. Tsai T Y-C, Choi Y S, Ma W Z, et al. Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science, 2008, 321: 126–129.

    Google Scholar 

  81. Turing A M. The chemical basis of morphogenesis. Bull Math Biol, 1990, 52: 153–197.

    Google Scholar 

  82. Veliz-Cuba A, Hirning A J, Atanas A A, et al. Sources of variability in a synthetic gene oscillator. PLoS Comput Biol, 2015, 11: 1–2.

    Google Scholar 

  83. Vilar J M G, Kueh H Y, Barkai N. Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci USA, 2002, 99: 5988–5992.

    Google Scholar 

  84. Wang L, Xin J, Nie Q. A critical quantity for noise attenuation in feedback systems. PLoS Comput Biol, 2010, 6: e1000764

    MathSciNet  Google Scholar 

  85. Wang Q X, Holmes W R, Sosnik J, et al. Cell sorting and noise-induced cell plasticity coordinate to sharpen boundaries between gene expression domains. PLoS Comput Biol, 2017, 13: e1005307

    Google Scholar 

  86. Wang S-W, Lan Y H, Tang L-H. Energy dissipation in an adaptive molecular circuit. J Stat Mech-Theory E, 2015, 2015: P07025

    MathSciNet  Google Scholar 

  87. Wang W K, Tao K, Wang J, et al. Exploring the inhibitory effect of membrane tension on cell polarization. PLoS Comput Biol, 2017, 13: e1005354

    Google Scholar 

  88. White R J, Nie Q, Lander A D, et al. Complex regulation of cyp26a1 creates a robust retinoic gradient in the zebrfish embryo. PLoS Biol, 2007, 5: e304

    Google Scholar 

  89. Wilkinson D G. Establishing sharp and homogeneous segments in the hindbrain. F1000Research, 2018, doi: 10.12688_/f1000research.15391.1

    Google Scholar 

  90. Wolpert L. Positional information and the spatial pattern of cellular differentiation. J Theor Biol, 1969, 25: 1–47.

    Google Scholar 

  91. Yu P J, Nie Q, Tang C, et al. Nanog induced intermediate state in regulating stem cell differentiation and reprogramming. BMC Syst Biol, 2018, 12: 22

    Google Scholar 

  92. Zhang L, Lander A D, Nie Q. A reaction-diffusion mechanism influences cell lineage progression as a basis for formation, regeneration, and stability of intestinal crypts. BMC Syst Biol, 2012, 6: 93

    Google Scholar 

  93. Zhang L, Radtke K, Zheng L, et al. Noise drives sharpening of gene expression boundaries in the zebrash hindbrain. Mol Syst Biol, 2012, 8: 613

    Google Scholar 

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11861130351 and 11622102). The first author was supported by National Science Foundation of USA (Grant No. DMS1763272) and the Simons Foundation (Grant No. 594598).

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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA

    Qing Nie & Yuchi Qiu

  2. Department of Developmental and Cell Biology, NSF-Simons Center for Multiscale Cell Fate Research, University of California at Irvine, Irvine, CA, 92697, USA

    Qing Nie

  3. Beijing International Center for Mathematical Research, Peking University, Beijing, 100871, China

    Lingxia Qiao & Lei Zhang

  4. Center for Quantitative Biology, Peking University, Beijing, 100871, China

    Lei Zhang & Wei Zhao

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  1. Qing Nie
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  2. Lingxia Qiao
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  3. Yuchi Qiu
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  4. Lei Zhang
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  5. Wei Zhao
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Correspondence to Qing Nie or Lei Zhang.

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Nie, Q., Qiao, L., Qiu, Y. et al. Noise control and utility: From regulatory network to spatial patterning. Sci. China Math. 63, 425–440 (2020). https://doi.org/10.1007/s11425-019-1633-1

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