Noise processing by networks

Cell behaviour is determined by complex molecular regulatory networks. Signalling networks are particularly important since they are responsible for the robust transmission of noisy environmental information to the cell's nucleus. However, although important signalling pathways have been well studied, and the manner of noise propagation through regulatory networks has been discussed, the relationship between network architecture and the cell's ability to process environmental noise is not well understood. To approach this problem in this thesis we derive a mathematical formula relating a network's structure to its noise processing ability. We noticed that noise processing is highly affected by the networks complexity, and in particular by the number and length of the weighted paths from the noisy input(s) to the output. In order to explore the utility of this mathematical expression, we apply it to the regulatory network for pluripotency in mouse embryonic stem (ES) cells and assess the effects of network topology on the propagation of noise through this system. We conclude by using the underlying theory to explain the interaction patterns in the ES cell's transcriptional circuit.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  J. Thomson,et al.  Basic FGF and suppression of BMP signaling sustain undifferentiated proliferation of human ES cells , 2005, Nature Methods.

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

[4]  Naama Barkai,et al.  Noise Propagation and Signaling Sensitivity in Biological Networks: A Role for Positive Feedback , 2007, PLoS Comput. Biol..

[5]  U. Alon An introduction to systems biology : design principles of biological circuits , 2019 .

[6]  Dahai Liu,et al.  Molecular basis of embryonic stem cell self-renewal: from signaling pathways to pluripotency network , 2015, Cellular and Molecular Life Sciences.

[7]  ROBERT M. MAY,et al.  Will a Large Complex System be Stable? , 1972, Nature.

[8]  J. Nichols,et al.  BMP Induction of Id Proteins Suppresses Differentiation and Sustains Embryonic Stem Cell Self-Renewal in Collaboration with STAT3 , 2003, Cell.

[9]  Gasper Tkacik,et al.  Cell biology: Networks, regulation, pathways , 2007, 0712.4385.

[10]  Patrick S. Stumpf,et al.  Single Cell Pluripotency Regulatory Networks , 2016, bioRxiv.

[11]  Erwin Frey,et al.  Brownian motion: a paradigm of soft matter and biological physics , 2005, Annalen der Physik.

[12]  C. Gardiner Stochastic Methods: A Handbook for the Natural and Social Sciences , 2009 .

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

[14]  T. Suda,et al.  Single-cell origin of mouse hemopoietic colonies expressing multiple lineages in variable combinations. , 1983, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Ron Weiss,et al.  The effect of negative feedback on noise propagation in transcriptional gene networks. , 2006, Chaos.

[16]  R. Nusse,et al.  An integral program for tissue renewal and regeneration: Wnt signaling and stem cell control , 2014, Science.

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

[18]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[19]  Patrick S. Stumpf,et al.  Nanog-dependent feedback loops regulate murine embryonic stem cell heterogeneity , 2012, Nature Cell Biology.

[20]  R. Iyengar,et al.  Modeling cell signaling networks. , 2004, Biology of the cell.

[21]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[22]  S. Arold,et al.  Noise in cellular signaling pathways: causes and effects. , 2012, Trends in biochemical sciences.

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

[24]  M. Kaufman,et al.  Establishment in culture of pluripotential cells from mouse embryos , 1981, Nature.

[25]  E. Ott,et al.  Approximating the largest eigenvalue of network adjacency matrices. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Megan F. Cole,et al.  Core Transcriptional Regulatory Circuitry in Human Embryonic Stem Cells , 2005, Cell.

[27]  L. Freeman Centrality in social networks conceptual clarification , 1978 .

[28]  Alan Edelman,et al.  The Circular Law and the Probability that a Random Matrix Has k Real Eigenvalues , 1993 .

[29]  Nicola Festuccia,et al.  Esrrb Is a Direct Nanog Target Gene that Can Substitute for Nanog Function in Pluripotent Cells , 2012, Cell stem cell.

[30]  Desmond J. Higham,et al.  Modeling and Simulating Chemical Reactions , 2008, SIAM Rev..

[31]  H. Lehrach,et al.  A Human Protein-Protein Interaction Network: A Resource for Annotating the Proteome , 2005, Cell.

[32]  Jeffrey L. Wrana,et al.  Signal integration in TGF-β, WNT, and Hippo pathways , 2013, F1000prime reports.

[33]  K. Cadigan,et al.  Celebrating 30 Years of Wnt Signaling , 2012, Science Signaling.

[34]  Holm Zaehres,et al.  LIF/STAT3 Signaling Fails to Maintain Self‐Renewal of Human Embryonic Stem Cells , 2004, Stem cells.

[35]  Yusuke Nakamura,et al.  DKK1, a negative regulator of Wnt signaling, is a target of the β-catenin/TCF pathway , 2004, Oncogene.

[36]  Avi Ma’ayan,et al.  Systems biology of stem cell fate and cellular reprogramming , 2009, Nature Reviews Molecular Cell Biology.

[37]  Tao Wang,et al.  Esrrb Activates Oct4 Transcription and Sustains Self-renewal and Pluripotency in Embryonic Stem Cells* , 2008, Journal of Biological Chemistry.

[38]  Henry Yang,et al.  Mechanisms controlling embryonic stem cell self-renewal and differentiation. , 2006, Critical reviews in eukaryotic gene expression.

[39]  A. Barabasi,et al.  Network biology: understanding the cell's functional organization , 2004, Nature Reviews Genetics.

[40]  Gábor Szabó,et al.  Structure of complex networks , 2005 .

[41]  R. Stewart,et al.  Induced Pluripotent Stem Cell Lines Derived from Human Somatic Cells , 2007, Science.

[42]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[43]  A. Blais,et al.  Constructing transcriptional regulatory networks. , 2005, Genes & development.

[44]  David F Anderson,et al.  Propagation of Fluctuations in Biochemical Systems, I: Linear SSC Networks , 2007, Bulletin of mathematical biology.

[45]  Reinhard Schneider,et al.  Using graph theory to analyze biological networks , 2011, BioData Mining.

[46]  Katherine C. Chen,et al.  Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. , 2003, Current opinion in cell biology.

[47]  Desmond J. Higham,et al.  Network Properties Revealed through Matrix Functions , 2010, SIAM Rev..

[48]  George P Chrousos,et al.  Dynamic aberrant NF-κB spurs tumorigenesis: a new model encompassing the microenvironment. , 2015, Cytokine & growth factor reviews.

[49]  S. Yamanaka,et al.  Induction of Pluripotent Stem Cells from Mouse Embryonic and Adult Fibroblast Cultures by Defined Factors , 2006, Cell.

[50]  K. Zygalakis,et al.  Fast stochastic simulation of biochemical reaction systems by alternative formulations of the chemical Langevin equation. , 2010, The Journal of chemical physics.

[51]  M. Katsuki,et al.  STAT3 activation is sufficient to maintain an undifferentiated state of mouse embryonic stem cells , 1999, The EMBO journal.

[52]  A. Wagner Robustness against mutations in genetic networks of yeast , 2000, Nature Genetics.

[53]  Konrad Basler,et al.  The many faces and functions of β‐catenin , 2012, The EMBO journal.

[54]  B. Merrill Wnt pathway regulation of embryonic stem cell self-renewal. , 2012, Cold Spring Harbor perspectives in biology.

[55]  S. Schreiber,et al.  Signaling Network Model of Chromatin , 2002, Cell.

[56]  Si Tang,et al.  Stability criteria for complex ecosystems , 2011, Nature.

[57]  J. Miyazaki,et al.  Quantitative expression of Oct-3/4 defines differentiation, dedifferentiation or self-renewal of ES cells , 2000, Nature Genetics.

[58]  Haluk Resat,et al.  Rapid and sustained nuclear–cytoplasmic ERK oscillations induced by epidermal growth factor , 2009, Molecular systems biology.

[59]  Aidong Zhang,et al.  Protein Interaction Networks: Computational Analysis , 2009 .

[60]  D. Gillespie A rigorous derivation of the chemical master equation , 1992 .

[61]  Paul Bertone,et al.  Identification of the missing pluripotency mediator downstream of leukaemia inhibitory factor , 2013, The EMBO journal.

[62]  D. Gillespie A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[63]  H. Niwa Wnt: What's Needed To maintain pluripotency? , 2011, Nature Cell Biology.

[64]  M. Elowitz,et al.  Functional roles for noise in genetic circuits , 2010, Nature.

[65]  Ulrik Brandes,et al.  Biological Networks , 2013, Handbook of Graph Drawing and Visualization.

[66]  T. Hwa,et al.  Stochastic fluctuations in metabolic pathways , 2007, Proceedings of the National Academy of Sciences.

[67]  Ulrike von Luxburg,et al.  A tutorial on spectral clustering , 2007, Stat. Comput..

[68]  H. Ng,et al.  The transcriptional and signalling networks of pluripotency , 2011, Nature Cell Biology.

[69]  Donald Metcalf,et al.  Myeloid leukaemia inhibitory factor maintains the developmental potential of embryonic stem cells , 1988, Nature.

[70]  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.

[71]  Graziano Martello,et al.  The nature of embryonic stem cells. , 2014, Annual review of cell and developmental biology.

[72]  John K. Heath,et al.  Inhibition of pluripotential embryonic stem cell differentiation by purified polypeptides , 1988, Nature.

[73]  H. Schöler,et al.  Formation of Pluripotent Stem Cells in the Mammalian Embryo Depends on the POU Transcription Factor Oct4 , 1998, Cell.

[74]  S. Emmott,et al.  Defining an essential transcription factor program for naïve pluripotency , 2014, Science.

[75]  V. Shahrezaei,et al.  The stochastic nature of biochemical networks. , 2008, Current opinion in biotechnology.

[76]  M. Buchanan,et al.  Networks in cell biology , 2010 .

[77]  LUKASZ SZPRUCH,et al.  Comparing Hitting Time Behavior of Markov Jump Processes and Their Diffusion Approximations , 2010, Multiscale Model. Simul..

[78]  E. M. Adler,et al.  2015: Signaling Breakthroughs of the Year , 2016, Science Signaling.

[79]  W. Huisinga,et al.  Solving the chemical master equation for monomolecular reaction systems analytically , 2006, Journal of mathematical biology.

[80]  Ping Li,et al.  Embryonic stem cell self‐renewal pathways converge on the transcription factor Tfcp2l1 , 2013, The EMBO journal.

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

[82]  F. Markowetz,et al.  Systems-level dynamic analyses of fate change in murine embryonic stem cells , 2009, Nature.

[83]  P. Savatier,et al.  Krüppel-like transcription factors and control of pluripotency , 2010, BMC Biology.

[84]  Claude Desplan,et al.  Stochasticity and Cell Fate , 2008, Science.

[85]  M. Gerstein,et al.  Getting connected: analysis and principles of biological networks. , 2007, Genes & development.

[86]  S. L. Wong,et al.  Towards a proteome-scale map of the human protein–protein interaction network , 2005, Nature.

[87]  X. Chen,et al.  The Oct4 and Nanog transcription network regulates pluripotency in mouse embryonic stem cells , 2006, Nature Genetics.

[88]  Daniel T. Gillespie,et al.  The multivariate Langevin and Fokker–Planck equations , 1996 .

[89]  M. Elowitz,et al.  Frequency-modulated nuclear localization bursts coordinate gene regulation , 2008, Nature.

[90]  C. Bordenave,et al.  The circular law , 2012 .

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

[92]  D. Gillespie Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[93]  D. Gillespie The Chemical Langevin and Fokker−Planck Equations for the Reversible Isomerization Reaction† , 2002 .

[94]  J. Thomson,et al.  Pluripotent stem cell lines. , 2008, Genes & development.

[95]  Stuart H. Orkin,et al.  A protein interaction network for pluripotency of embryonic stem cells , 2006, Nature.

[96]  D. Bray Protein molecules as computational elements in living cells , 1995, Nature.

[97]  L. Allen An introduction to stochastic processes with applications to biology , 2003 .

[98]  Lawrence Hunter,et al.  Artificial Intelligence and Molecular Biology , 1992, AI Mag..

[99]  A. Smith,et al.  Self-renewal of pluripotent embryonic stem cells is mediated via activation of STAT3. , 1998, Genes & development.

[100]  P. Maini,et al.  A practical guide to stochastic simulations of reaction-diffusion processes , 2007, 0704.1908.

[101]  Austin G Smith,et al.  FGF stimulation of the Erk1/2 signalling cascade triggers transition of pluripotent embryonic stem cells from self-renewal to lineage commitment , 2007, Development.

[102]  Ingo Roeder,et al.  Nanog Variability and Pluripotency Regulation of Embryonic Stem Cells - Insights from a Mathematical Model Analysis , 2010, PloS one.

[103]  Hitoshi Niwa,et al.  How is pluripotency determined and maintained? , 2007, Development.

[104]  B. Thiers Induction of Pluripotent Stem Cells from Adult Human Fibroblasts by Defined Factors , 2008 .

[105]  J. Ferrell Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. , 2002, Current opinion in cell biology.

[106]  R. Iyengar,et al.  Signaling Networks The Origins of Cellular Multitasking , 2000, Cell.

[107]  H. J. Beaumont,et al.  Experimental evolution of bet hedging , 2009, Nature.

[108]  B. Alberts,et al.  Molecular Biology of the Cell (Fifth Edition) , 2008 .

[109]  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.

[110]  P. Greengard,et al.  Maintenance of pluripotency in human and mouse embryonic stem cells through activation of Wnt signaling by a pharmacological GSK-3-specific inhibitor , 2004, Nature Medicine.

[111]  Signal Transduction Pathways in Development: Hedgehog Proteins and their Receptors , 2001 .

[112]  D. Sherrington Stochastic Processes in Physics and Chemistry , 1983 .

[113]  David F Anderson,et al.  A modified next reaction method for simulating chemical systems with time dependent propensities and delays. , 2007, The Journal of chemical physics.

[114]  E. Yamoah,et al.  Identification of transcription factor-DNA interactions using chromatin immunoprecipitation assays. , 2009, Methods in molecular biology.

[115]  J. Nichols,et al.  Suppression of SHP-2 and ERK signalling promotes self-renewal of mouse embryonic stem cells. , 1999, Developmental biology.

[116]  Ernesto Estrada,et al.  Communicability in complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[117]  R. Ewing,et al.  A Protein Interaction between β-Catenin and Dnmt1 Regulates Wnt Signaling and DNA Methylation in Colorectal Cancer Cells , 2015, Molecular Cancer Research.

[118]  Desmond J. Higham,et al.  An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations , 2001, SIAM Rev..

[119]  Hoon Kim,et al.  Modulation of β-catenin function maintains mouse epiblast stem cell and human embryonic stem cell self-renewal , 2013, Nature Communications.

[120]  E. O’Shea,et al.  Living with noisy genes: how cells function reliably with inherent variability in gene expression. , 2007, Annual review of biophysics and biomolecular structure.

[121]  G. Yvert,et al.  How does evolution tune biological noise? , 2014, Front. Genet..

[122]  J. A. Rodríguez-Velázquez,et al.  Subgraph centrality in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[123]  B. Snel,et al.  Comparative assessment of large-scale data sets of protein–protein interactions , 2002, Nature.

[124]  J. Doob,et al.  The Brownian Movement and Stochastic Equations , 1942 .

[125]  D. Gillespie The chemical Langevin equation , 2000 .

[126]  Marios P. Stavridis,et al.  A discrete period of FGF-induced Erk1/2 signalling is required for vertebrate neural specification , 2007, Development.

[127]  J A Thomson,et al.  Clonally derived human embryonic stem cell lines maintain pluripotency and proliferative potential for prolonged periods of culture. , 2000, Developmental biology.

[128]  B. Doble,et al.  The ground state of embryonic stem cell self-renewal , 2008, Nature.

[129]  Jonathan M Irish,et al.  Single Cell Profiling of Potentiated Phospho-Protein Networks in Cancer Cells , 2004, Cell.