Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Generic Deterministic Models of Prokaryotic Gene Regulation Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

4. Noise Effects in Gene Regulation: Intrinsic Versus Extrinsic

verfasst von : Michael C. Mackey, Moisés Santillán, Marta Tyran-Kamińska, Eduardo S. Zeron

Erschienen in: Simple Mathematical Models of Gene Regulatory Dynamics

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

From a modeling perspective there have been a number of studies attempting to understand the effects of noise on gene regulatory dynamics. The now classical Kepler and Elston (Biophy J 81:3116–3136, 2001) really laid much of the ground work for subsequent studies by its treatment of a variety of noise sources and their effect on dynamics. Mackey et al. (J Theor Biol 274:84–96, 2011) examined the effects of either bursting or Gaussian noise on both inducible and repressible operon models, and Waldherr et al. (BMC Syst Biol 4:108, 2010) looked at the role of Gaussian noise in an inducible switch model for ovarian follicular growth.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Master Equation Modeling Approaches
Nächstes Kapitel The Lactose Operon
Fußnoten
1
Blake et al. (2003), Cai et al. (2006), Chubb et al. (2006), Golding et al. (2005), Raj et al. (2006), Sigal et al. (2006), Suter et al. (2011), Yu et al. (2006).
 
2
Kepler and Elston (2001), Friedman et al. (2006), Morelli and Julicher (2007), Bobrowski et al. (2007), Shahrezaei and Swain (2008a), Iyer-Biswas et al. (2009), Mugler et al. (2009), Ribeiro et al. (2009), Elgart et al. (2010), Lei (2010), Rajala et al. (2010), Tang (2010), Bett et al. (2011), Jia and Kulkarni (2011), Cottrell et al. (2012), Feng et al. (2012), Ferguson et al. (2012), Kuwahara and Schwartz (2012), Singh and Bokes (2012), Earnest et al. (2013), Robinson (2013), Tian (2013).
 
Literatur
Abadon ST (2006) The murky origin of Snow White and her T-even dwarfs. Genetics 155:481–486
Abramson J, Iwata S, Kaback HR (2004) Lactose permease as a paradigm for membrane transport proteins (review). Mol Membr Biol 21:227–236PubMedCrossRef
Anderson DF, Kurtz TG (2011) Continuous time Markov chain models for chemical reaction networks. In: Design and analysis of biomolecular circuits. Springer, Berlin, pp 3–42CrossRef
Angeli D, Ferrell JE, Sontag ED (2004) Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc Natl Acad Sci USA 101(7):1822–1827PubMedPubMedCentralCrossRef
Arkin A, Ross J, McAdams HH (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected Escherichia coli cells. Genetics 149:1633–1648PubMedPubMedCentral
Artyomov MN, Das J, Kardar M, Chakraborty AK (2007) Purely stochastic binary decisions in cell signaling models without underlying deterministic bistabilities. Proc Natl Acad Sci USA 104(48):18958–18963PubMedPubMedCentralCrossRef
Aurell E, Brown S, Johanson J, Sneppen K (2002) Stability puzzles in phage λ. Phys Rev E 65:051914CrossRef
Babloyantz A, Sanglier M (1972) Chemical instabilities of “all-or-none” type in beta - galactosidase induction and active transport. FEBS Lett 23:364–366PubMedCrossRef
Beckwith J (1987) The lactose operon. In: Neidhart F, Ingraham J, Low K, Magasanik B, Umbarger H (eds) Escherichia coli and Salmonella thyphymurium: cellular and molecular biology, vol 2. American Society for Microbiology, Washington, DC, pp 1439–1443
Berg OG (1978) A model for the statistical fluctuations of protein numbers in a microbial population. J Theor Biol 71(4):587–603PubMedCrossRef
Bishop LM, Qian H (2010) Stochastic bistability and bifurcation in a mesoscopic signaling system with autocatalytic kinase. Biophys J 98(1):1–11PubMedPubMedCentralCrossRef
Blake W, Kaern M, Cantor C, Collins J (2003) Noise in eukaryotic gene expression. Nature 422:633–637PubMedCrossRef
Bliss RD, Painter PR, Marr AG (1982) Role of feedback inhibition in stabilizing the classical operon. J Theor Biol 97:177–193PubMedCrossRef
Bobrowski A, Lipniacki T, Pichór K, Rudnicki R (2007) Asymptotic behavior of distributions of mRNA and protein levels in a model of stochastic gene expression. J Math Anal Appl 333(2):753–769CrossRef
Bokes P, King JR, Wood AT, Loose M (2013) Transcriptional bursting diversifies the behaviour of a toggle switch: hybrid simulation of stochastic gene expression. Bull Math Biol 75(2):351–371PubMedCrossRef
Cai L, Friedman N, Xie X (2006) Stochastic protein expression in individual cells at the single molecule level. Nature 440:358–362PubMedCrossRef
Cao Y, Lu HM, Liang J (2010) Probability landscape of heritable and robust epigenetic state of lysogeny in phage lambda. Proc Natl Acad Sci USA 107(43):18445–18450PubMedPubMedCentralCrossRef
Caravagna G, Mauri G, d’Onofrio A (2013) The interplay of intrinsic and extrinsic bounded noises in biomolecular networks. PLoS ONE 8(2):e51174PubMedPubMedCentralCrossRef
Cohn M, Horibata K (1959) Analysis of the differentiation and of the heterogeneity within a population of Escherichia coli undergoing induced beta-galactosidase synthesis. J Bacteriol 78:613–623PubMedPubMedCentral
Díaz-Hernández O, Santillán M (2010) Bistable behavior of the lac operon in E. coli when induced with a mixture of lactose and TMG. Front Physiol 1:22
Earnest T, Roberts E, Assaf M, Dahmen K, Luthey-Schulten Z (2013) DNA looping increases the range of bistability in a stochastic model of the lac genetic switch. Phys Biol 10(2):026002PubMedCrossRef
Elgart V, Jia T, Kulkarni R (2010) Applications of Little’s law to stochastic models of gene expression. Phys Rev E 87(2 Pt 1):021901CrossRef
Elowitz M, Levine A, Siggia E, Swain P (2002) Stochastic gene expression in a single cell. Science 297:1183–1186PubMedCrossRef
Feng H, Hensel Z, Xiao J, Wang J (2012) Analytical calculation of protein production distributions in models of clustered protein expression. Phys Rev E 85(3 Pt 1):155–160
Ferguson M, Le Coq D, Jules M, Aymerich S, Radulescu O, Declerck N, Royer C (2012) Reconciling molecular regulatory mechanisms with noise patterns of bacterial metabolic promoters in induced and repressed states. Proc Natl Acad Sci USA 109(1):155–160PubMedCrossRef
Ferrell JE (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol 14(2):140–148PubMedCrossRef
Friedman N, Cai L, Xie X (2006) Linking stochastic dynamics to population distribution: an analytical framework of gene expression. Phys Rev Lett 97:168302–1/4PubMedCrossRef
Gardner T, Cantor C, Collins J (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403:339–342PubMedCrossRef
Gedeon T, Mischaikow K, Patterson K, Traldi E (2008) Binding cooperativity in phage λ is not sufficient to produce an effective switch. Biophy J 94(9):3384–3392CrossRef
Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22(4):403–434CrossRef
Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361CrossRef
Gillespie DT (1992) A rigorous derivation of the chemical master equation. Physica A 188(1–3):404–425CrossRef
Gillespie DT (2000) The chemical Langevin equation. J Chem Phys 113(1):297–306CrossRef
Giona M, Adrover A (2002) Modified model for the regulation of the tryptophan operon in Escherichia coli. Biotechnol Bioeng 80:297–304PubMedCrossRef
Golding I, Paulsson J, Zawilski S, Cox E (2005) Real-time kinetics of gene activity in individual bacteria. Cell 123:1025–1036PubMedCrossRef
Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore
Goodwin BC (1963) Temporal organization in cells. Academic, London
Goodwin BC (1965) Oscillatory behaviour in enzymatic control process. Adv Enzyme Regul 3:425–438PubMedCrossRef
Griffith J (1968a) Mathematics of cellular control processes. I. Negative feedback to one gene. J Theor Biol 20:202–208PubMedCrossRef
Griffith J (1968b) Mathematics of cellular control processes. II. Positive feedback to one gene. J Theor Biol 20:209–216PubMed
Grigorov L, Polyakova M, Chernavskil D (1967) Model investigation of trigger schemes and the differentiation process (in Russian). Molekulyarnaya Biologiya 1(3):410–418
Groetsch CW, King JT (1988) Matrix methods and applications. Prentice Hall, Englewood Cliffs, NJ
Haken H (1983) Synergetics: an introduction, 3rd edn. Springer series in synergetics, vol 1. Springer, Berlin
Hasty J, Isaacs F, Dolnik M, McMillen D, Collins JJ (2001) Designer gene networks: towards fundamental cellular control. Chaos 11(1):207–220PubMedCrossRef
Heinrich R, Rapoport TA (1980) Mathematical modeling of translation of mRNA in eucaryotes: Steady states, time-dependent processes and application to reticulocytes. J Theor Biol 86:279–313PubMedCrossRef
Hernández-Valdez A, Santillán M (2010) Cyclic expression and cooperative operator interaction in the trp operon of Escherichia coli. J Theor Biol 263:340–352PubMedCrossRef
Higham DJ (2008) Modeling and simulating chemical reactions. SIAM Rev 50(2):347–368CrossRef
Iyer-Biswas S, Hayot F, Jayaprakash C (2009) Stochasticity of gene products from transcriptional pulsing. Phys Rev E 79(3 Pt 1):031911CrossRef
Jacob F, Monod J (1961) Genetic regulatory mechanisms in the synthesis of proteins. J Mol Biol 3:318–356PubMedCrossRef
Jacob F, Perrin D, Sanchez C, Monod J (1960) Operon: a group of genes with the expression coordinated by an operator. C R Hebd Seances Acad Sci 250:1727–1729PubMed
Jia T, Kulkarni R (2011) Intrinsic noise in stochastic models of gene expression with molecular memory and bursting. Phys Rev Lett 106(5):058102PubMedCrossRef
Kaern M, Elston T, Blake W, Collins J (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6:451–464PubMedCrossRef
Kepler T, Elston T (2001) Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations. Biophy J 81:3116–3136CrossRef
Kuhlman T, Zhang Z, Saier MH, Hwa T (2007) Combinatorial transcriptional control of the lactose operon of Escherichia coli. Proc Natl Acad Sci USA 104:6043–6048PubMedPubMedCentralCrossRef
Kuwahara H, Schwartz R (2012) Stochastic steady state gain in a gene expression process with mRNA degradation control. J R Soc Interface 9(72):1589–1598PubMedPubMedCentralCrossRef
Lei J (2010) Stochasticity in single gene expression with both intrinsic noise and fluctuation in kinetic parameters. J Theor Biol 256(4):485–492 [Erratum appears in J Theor Biol 2010 Jan 21; 262(2):381]
Lendenmann U, Snozzi M, Egli T (1996) Kinetics of the simultaneous utilization of sugar mixtures by Escherichia coli in continuous culture. Appl Environ Microbiol 62:1493–1499PubMedPubMedCentral
Lipniacki T, Paszek P, Marciniak-Czochra A, Brasier A, Kimmel M (2006) Transcriptional stochasticity in gene expression. J Theor Biol 238(2):348–367PubMedCrossRef
Mackey MC, Tyran-Kamińska M (2008) Dynamics and density evolution in piecewise deterministic growth processes. Ann Polon Math 94:111–129CrossRef
Mackey MC, Tyran-Kamińska M (2016) The limiting dynamics of a bistable molecular switch with and without noise. J Math Biol 73:367–395PubMedCrossRef
Mackey MC, Tyran-Kamińska M, Yvinec R (2011) Molecular distributions in gene regulatory dynamics. J Theor Biol 274:84–96PubMedCrossRef
Mackey MC, Tyran-Kamińska M, Yvinec R (2013) Dynamic behavior of stochastic gene expression models in the presence of bursting. SIAM J Appl Math 73(5):1830–1852CrossRef
Mackey MC, Santillan M, Tyran-Kamińska M, Zeron ES (2015) The utility of simple mathematical models in understanding gene regulatory dynamics. In Silico Biol 12(1–2):23–53CrossRef
Mier-y-Teran-Romero L, Silber M, Hatzimanikatis V (2010) The origins of time-delay in template biopolymerization processes. PLOS Comp Biol 6:e1000726–1–15
Monod J (1941) Recherches sur la croissance des cultures bactériennes. Ph.D. thesis, Université de Paris, Paris
Monod J, Jacob F (1961) Teleonomic mechanisms in cellular metabolism, growth, and differentiation. Cold Spring Harb Symp Quant Biol 26:389–401PubMedCrossRef
Morelli L, Julicher F (2007) Precision of genetic oscillators and clocks. Phys Rev Lett 98(22):228101PubMedCrossRef
Morelli MJ, Allen RJ, Tanase-Nicola S, ten Wolde PR (2008a) Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch. J Chem Phys 128(4):045105PubMedCrossRef
Morelli MJ, Tanase-Nicola S, Allen RJ, ten Wolde PR (2008b) Reaction coordinates for the flipping of genetic switches. Biophys J 94(9):3413–3423PubMedPubMedCentralCrossRef
Mugler A, Walczak A, Wiggins C (2009) Spectral solutions to stochastic models of gene expression with bursts and regulation. Phys Rev E 80(4 Pt 1):041921CrossRef
Narang A (2007) Effect of DNA looping on the induction kinetics of the lac operon. J Theor Biol 247:695–712PubMedCrossRef
Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York
Ochab-Marcinek A, Tabaka M (2015) Transcriptional leakage versus noise: a simple mechanism of conversion between binary and graded response in autoregulated genes. Phys Rev E Stat Nonlin Soft Matter Phys 91(1):012704PubMedCrossRef
Oehler S, Eismann ER, Krämer H, Müller-Hill B (1990) The three operators of lac operon cooperate in repression. EMBO J 9:973–979PubMedPubMedCentral
Oppenheim I, Schuler K, Weiss G (1969) Stochastic and deterministic formulation of chemical rate equations. J Chem Phys 50:460–466CrossRef
Oppenheim AB, Kobiler O, Stavans J, Court DL, Adhya S (2005) Switches in bacteriophage lambda development. Annu Rev Genet 39(1):409–429PubMedCrossRef
Othmer H (1976) The qualitative dynamics of a class of biochemical control circuits. J Math Biol 3:53–78PubMedCrossRef
Ozbudak E, Thattai M, Lim H, Shraiman B, van Oudenaarden A (2004) Multistability in the lactose utilization network of Escherichia coli. Nature 427:737–740PubMedCrossRef
Penazzio S (2006) The origin of phage virology. Riv Biol 99(1):103–129
Pichór K, Rudnicki R (2000) Continuous Markov semigroups and stability of transport equations. J Math Anal Appl 249:668–685CrossRef
Ptashne M (1986) A genetic switch: gene control and Phage Lambda. Cell Press, Cambridge, MA
Qian H, Shi PZ, Xing J (2009) Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity. Phys Chem Chem Phys 11(24):4861–4870PubMedCrossRef
Raj A, Peskin C, Tranchina D, Vargas D, Tyagi S (2006) Stochastic mRNA synthesis in mammalian cells. PLoS Biol 4:1707–1719CrossRef
Rajala T, Hakkinen A, Healy S, Yli-Harja O, Ribeiro A (2010) Effects of transcriptional pausing on gene expression dynamics. PLoS Comput Biol 6(3):e1000704PubMedPubMedCentralCrossRef
Reinitz J, Vaisnys JR (1990) Theoretical and experimental analysis of the phage lambda genetic switch implies missing levels of co-operativity. J Theor Biol 145:295–318PubMedCrossRef
Reznikoff WS (1992) The lactose operon-controlling elements: a complex paradigm. Mol Microbiol 6:2419–2422PubMedCrossRef
Ribeiro A, Smolander O, Rajala T, Hakkinen A, Yli-Harja O (2009) Delayed stochastic model of transcription at the single nucleotide level. J Comput Biol 16(4):539–553PubMedCrossRef
Rozanov DV, D’Ari R, Sineoky SP (1998) RecA-independent pathways of lambdoid prophage induction in Escherichia coli. J Bacteriol 180:6306–6315PubMedPubMedCentral
Ruan S, Wei J (2001) On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion. IMA J Math Appl Med Biol 18:41–52PubMedCrossRef
Salazar-Cavazos E, Santillán M (2013) Optimal performance of the tryptophan operon of E. coli: A stochastic, dynamical, mathematical-modeling approach. Bull Math Biol 76:314–334PubMedCrossRef
Samoilov M, Plyasunov S, Arkin AP (2005) Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proc Natl Acad Sci USA 102(7):2310–2315PubMedPubMedCentralCrossRef
Santillán M (2008) Bistable behavior in a model of the lac operon in Escherichia coli with variable growth rate. Biophys J 94:2065–2081PubMedCrossRef
Santillán M (2008) On the use of the Hill functions in mathematical models of gene regulatory networks. Math Model Nat Phenom 3(2):85–97CrossRef
Santillán M (2014) Chemical kinetics, stochastic processes, and irreversible thermodynamics. Springer, HeidelbergCrossRef
Santillán M, Mackey MC (2001) Dynamic regulation of the tryptophan operon: Modeling study and comparison with experimental data. Proc Natl Acad Sci USA 98:1364–1369PubMedPubMedCentralCrossRef
Santillán M, Mackey MC (2004b) Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon. Biophys J 86:1282–1292PubMedPubMedCentralCrossRef
Santillán M, Mackey MC (2005) Dynamic behaviour of the B12 riboswitch. Phys Biol 2(1):29–35PubMedCrossRef
Santillán M, Mackey MC (2008) Quantitative approaches to the study of bistability in the lac operon of Escherichia coli. J R Soc Interface 5:S29–S39PubMedPubMedCentralCrossRef
Santillán M, Zeron ES (2004) Dynamic influence of feedback enzyme inhibition and transcription attenuation on the tryptophan operon response to nutritional shifts. J Theor Biol 231(2):287–298PubMedCrossRef
Santillán M, Zeron ES (2006) Analytical study of the multiplicity of regulatory mechanisms in the tryptophan operon. Bull Math Biol 68:343–359PubMedCrossRef
Selgrade J (1979) Mathematical analysis of a cellular control process with positive feedback. SIAM J Appl Math 36:219–229CrossRef
Sen AK, Liu WM (1990) Dynamic analysis of genetic control and regulation of amino acid synthesis: the tryptophan operon in Escherichia coli. Biotechnol Bioeng 35:185–194PubMedCrossRef
Serebriiskii IG, Golemis EA (2000) Uses of lacZ to study gene function: Evaluation of β-galactosidase assays employed in the yeast two-hybrid system. Anal Biochem 285:1–15PubMedCrossRef
Shahrezaei V, Swain P (2008b) The stochastic nature of biochemical networks. Curr Opin Biotechnol 19:369–374PubMedCrossRef
Shea MA, Ackers GK (1985) The OR control system of bacteriophage lambda: A physical-chemical model for gene regulation. J Mol Biol 181:211–230PubMedCrossRef
Shenker JQ, Lin MM (2015) Cooperativity leads to temporally-correlated fluctuations in the bacteriophage lambda genetic switch. Front Plant Sci 6:214PubMedPubMedCentralCrossRef
Sigal A, Milo R, Cohen A, Geva-Zatorsky N, Klein Y, Liron Y, Rosenfeld N, Danon T, Perzov N, Alon U (2006) Variability and memory of protein levels in human cells. Nature 444:643–646PubMedCrossRef
Simpson ML, Cox CD, Allen MS, McCollum JM, Dar RD, Karig DK, F CJ (2009) Noise in biological circuits. Wiley Interdiscip Rev Nanomed Nanobiotechnol 1(2):214–225
Smith H (1995) Monotone dynamical systems. Mathematical surveys and monographs, vol 41. American Mathematical Society, Providence, RI
Strasser M, Theis FJ, Marr C (2012) Stability and multiattractor dynamics of a toggle switch based on a two-stage model of stochastic gene expression. Biophys J 102(1):19–29PubMedPubMedCentralCrossRef
Stratonovich RL (1963) Topics in the theory of random noise. Vol. I: general theory of random processes. Nonlinear transformations of signals and noise. Revised English edition. Translated from the Russian by Richard A. Silverman, Gordon and Breach Science Publishers, New York
Summers WS (2011) In the beginning…Bacteriophage 1(1):50–51
Suter D, Molina N, Gatfield D, Schneider K, Schibler U, Naef F (2011) Mammalian genes are transcribed with widely different bursting kinetics. Science 332(6028):472–474PubMedCrossRef
Tang M (2010) The mean frequency of transcriptional bursting and its variation in single cells. J Math Biol 60(1):27–58PubMedCrossRef
Titular U (1978) A systematic solution procedure for the Fokker-Planck equation of a Brownian particle in the high-friction case. Physica A 91A:321–344CrossRef
Tyson J, Othmer H (1978) The dynamics of feedback control circuits in biochemical pathways. In: Rosen R (ed) Progress in biophysics, vol 5. Academic, New York, pp 1–62
Tyson JJ (1975) On the existence of oscillatory solutions in negative feedback cellular control processes. J Theor Biol 1:311–315
Tyson JJ, Chen KC, Novak B (2003) Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15(2):221–231PubMedCrossRef
van Kampen N (1992) Stochastic processes in physics and chemistry, 2nd edn. Elesvier-North Holland, Amsterdam
Vellela M, Qian H (2009) Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited. J R Soc Interface 6(39):925–940PubMedCrossRef
Wilemski G (1976) On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion. J Stat Phys 14:153–169CrossRef
Wilson CJ, Zhan H, Swint-Kruse L, Matthews KS (2007) The lactose repressor system, paradigms for regulation, allosteric behavior and protein folding. Cell Mol Life Sci 64:3–16PubMedCrossRef
Yanofsky C, Horn V (1994) Role of regulatory features of the trp operon of Escherichia coli in mediating a response to a nutritional shift. J Bacteriol 176:6245–6254PubMedPubMedCentralCrossRef
Yildirim N, Mackey MC (2003) Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data. Biophys J 84:2841–2851PubMedPubMedCentralCrossRef
Yildirim N, Santillán M, Horike D, Mackey MC (2004) Dynamics and bistability in a reduced model of the lac operon. Chaos 14:279–292PubMedCrossRef
Yu J, Xiao J, Ren X, Lao K, Xie X (2006) Probing gene expression in live cells, one protein molecule at a time. Science 311:1600–1603PubMedCrossRef
Yvinec R, Zhuge C, Lei J, Mackey MC (2014) Adiabatic reduction of a model of stochastic gene expression with jump Markov process. J Math Biol 68(5):1051–1070PubMedCrossRef
Zamora-Chimal C, Santillán M, Rodríguez-González J (2012) Influence of the feedback loops in the trp operon of B. subtilis on the system dynamic response and noise amplitude. J Theor Biol 310:119–131PubMedCrossRef
Zeron ES, Santillán M (2010) Distributions for negative-feedback-regulated stochastic gene expression: dimension reduction and numerical solution of the chemical master equation. J Theor Biol 264(2):377–385PubMedCrossRef
Zeron ES, Santillán M (2011) Numerical solution of the chemical master equation uniqueness and stability of the stationary distribution for chemical networks, and mRNA bursting in a gene network with negative feedback regulation. Methods Enzymol 487:147–169PubMedCrossRef
Metadaten
Titel
Noise Effects in Gene Regulation: Intrinsic Versus Extrinsic
verfasst von
Michael C. Mackey
Moisés Santillán
Marta Tyran-Kamińska
Eduardo S. Zeron
Copyright-Jahr
2016
Buch
Simple Mathematical Models of Gene Regulatory Dynamics

Print ISBN: 978-3-319-45317-0

Electronic ISBN: 978-3-319-45318-7

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-45318-7_4