Skip to main content
Top

2016 | OriginalPaper | Chapter

6. The Tryptophan Operon

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

Published in: Simple Mathematical Models of Gene Regulatory Dynamics

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Tryptophan is one of the 20 amino acids out of which all proteins are made. Arguably, tryptophan is the most expensive amino acid to synthesize, biochemically speaking. Perhaps, for this reason, humans and many other mammals do not have the enzymes necessary to catalyze tryptophan synthesis and instead they find this amino acid in their diet.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

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!

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!

Literature
go back to reference Abadon ST (2006) The murky origin of Snow White and her T-even dwarfs. Genetics 155:481–486 Abadon ST (2006) The murky origin of Snow White and her T-even dwarfs. Genetics 155:481–486
go back to reference Abramson J, Iwata S, Kaback HR (2004) Lactose permease as a paradigm for membrane transport proteins (review). Mol Membr Biol 21:227–236PubMedCrossRef Abramson J, Iwata S, Kaback HR (2004) Lactose permease as a paradigm for membrane transport proteins (review). Mol Membr Biol 21:227–236PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference Aurell E, Brown S, Johanson J, Sneppen K (2002) Stability puzzles in phage λ. Phys Rev E 65:051914CrossRef Aurell E, Brown S, Johanson J, Sneppen K (2002) Stability puzzles in phage λ. Phys Rev E 65:051914CrossRef
go back to reference Babloyantz A, Sanglier M (1972) Chemical instabilities of “all-or-none” type in beta - galactosidase induction and active transport. FEBS Lett 23:364–366PubMedCrossRef Babloyantz A, Sanglier M (1972) Chemical instabilities of “all-or-none” type in beta - galactosidase induction and active transport. FEBS Lett 23:364–366PubMedCrossRef
go back to reference 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 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
go back to reference Berg OG (1978) A model for the statistical fluctuations of protein numbers in a microbial population. J Theor Biol 71(4):587–603PubMedCrossRef Berg OG (1978) A model for the statistical fluctuations of protein numbers in a microbial population. J Theor Biol 71(4):587–603PubMedCrossRef
go back to reference Blake W, Kaern M, Cantor C, Collins J (2003) Noise in eukaryotic gene expression. Nature 422:633–637PubMedCrossRef Blake W, Kaern M, Cantor C, Collins J (2003) Noise in eukaryotic gene expression. Nature 422:633–637PubMedCrossRef
go back to reference Bliss RD, Painter PR, Marr AG (1982) Role of feedback inhibition in stabilizing the classical operon. J Theor Biol 97:177–193PubMedCrossRef Bliss RD, Painter PR, Marr AG (1982) Role of feedback inhibition in stabilizing the classical operon. J Theor Biol 97:177–193PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Cai L, Friedman N, Xie X (2006) Stochastic protein expression in individual cells at the single molecule level. Nature 440:358–362PubMedCrossRef Cai L, Friedman N, Xie X (2006) Stochastic protein expression in individual cells at the single molecule level. Nature 440:358–362PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference Elowitz M, Levine A, Siggia E, Swain P (2002) Stochastic gene expression in a single cell. Science 297:1183–1186PubMedCrossRef Elowitz M, Levine A, Siggia E, Swain P (2002) Stochastic gene expression in a single cell. Science 297:1183–1186PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Ferrell JE (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol 14(2):140–148PubMedCrossRef Ferrell JE (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol 14(2):140–148PubMedCrossRef
go back to reference 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 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
go back to reference Gardner T, Cantor C, Collins J (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403:339–342PubMedCrossRef Gardner T, Cantor C, Collins J (2000) Construction of a genetic toggle switch in Escherichia coli. Nature 403:339–342PubMedCrossRef
go back to reference 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 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
go back to reference 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 (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22(4):403–434CrossRef
go back to reference Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361CrossRef Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361CrossRef
go back to reference Gillespie DT (1992) A rigorous derivation of the chemical master equation. Physica A 188(1–3):404–425CrossRef Gillespie DT (1992) A rigorous derivation of the chemical master equation. Physica A 188(1–3):404–425CrossRef
go back to reference Gillespie DT (2000) The chemical Langevin equation. J Chem Phys 113(1):297–306CrossRef Gillespie DT (2000) The chemical Langevin equation. J Chem Phys 113(1):297–306CrossRef
go back to reference Giona M, Adrover A (2002) Modified model for the regulation of the tryptophan operon in Escherichia coli. Biotechnol Bioeng 80:297–304PubMedCrossRef Giona M, Adrover A (2002) Modified model for the regulation of the tryptophan operon in Escherichia coli. Biotechnol Bioeng 80:297–304PubMedCrossRef
go back to reference Golding I, Paulsson J, Zawilski S, Cox E (2005) Real-time kinetics of gene activity in individual bacteria. Cell 123:1025–1036PubMedCrossRef Golding I, Paulsson J, Zawilski S, Cox E (2005) Real-time kinetics of gene activity in individual bacteria. Cell 123:1025–1036PubMedCrossRef
go back to reference Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore
go back to reference Goodwin BC (1963) Temporal organization in cells. Academic, London Goodwin BC (1963) Temporal organization in cells. Academic, London
go back to reference Griffith J (1968a) Mathematics of cellular control processes. I. Negative feedback to one gene. J Theor Biol 20:202–208PubMedCrossRef Griffith J (1968a) Mathematics of cellular control processes. I. Negative feedback to one gene. J Theor Biol 20:202–208PubMedCrossRef
go back to reference Griffith J (1968b) Mathematics of cellular control processes. II. Positive feedback to one gene. J Theor Biol 20:209–216PubMed Griffith J (1968b) Mathematics of cellular control processes. II. Positive feedback to one gene. J Theor Biol 20:209–216PubMed
go back to reference Grigorov L, Polyakova M, Chernavskil D (1967) Model investigation of trigger schemes and the differentiation process (in Russian). Molekulyarnaya Biologiya 1(3):410–418 Grigorov L, Polyakova M, Chernavskil D (1967) Model investigation of trigger schemes and the differentiation process (in Russian). Molekulyarnaya Biologiya 1(3):410–418
go back to reference Groetsch CW, King JT (1988) Matrix methods and applications. Prentice Hall, Englewood Cliffs, NJ Groetsch CW, King JT (1988) Matrix methods and applications. Prentice Hall, Englewood Cliffs, NJ
go back to reference Haken H (1983) Synergetics: an introduction, 3rd edn. Springer series in synergetics, vol 1. Springer, Berlin Haken H (1983) Synergetics: an introduction, 3rd edn. Springer series in synergetics, vol 1. Springer, Berlin
go back to reference Hasty J, Isaacs F, Dolnik M, McMillen D, Collins JJ (2001) Designer gene networks: towards fundamental cellular control. Chaos 11(1):207–220PubMedCrossRef Hasty J, Isaacs F, Dolnik M, McMillen D, Collins JJ (2001) Designer gene networks: towards fundamental cellular control. Chaos 11(1):207–220PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Higham DJ (2008) Modeling and simulating chemical reactions. SIAM Rev 50(2):347–368CrossRef Higham DJ (2008) Modeling and simulating chemical reactions. SIAM Rev 50(2):347–368CrossRef
go back to reference Iyer-Biswas S, Hayot F, Jayaprakash C (2009) Stochasticity of gene products from transcriptional pulsing. Phys Rev E 79(3 Pt 1):031911CrossRef Iyer-Biswas S, Hayot F, Jayaprakash C (2009) Stochasticity of gene products from transcriptional pulsing. Phys Rev E 79(3 Pt 1):031911CrossRef
go back to reference Jacob F, Monod J (1961) Genetic regulatory mechanisms in the synthesis of proteins. J Mol Biol 3:318–356PubMedCrossRef Jacob F, Monod J (1961) Genetic regulatory mechanisms in the synthesis of proteins. J Mol Biol 3:318–356PubMedCrossRef
go back to reference 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 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
go back to reference Jia T, Kulkarni R (2011) Intrinsic noise in stochastic models of gene expression with molecular memory and bursting. Phys Rev Lett 106(5):058102PubMedCrossRef Jia T, Kulkarni R (2011) Intrinsic noise in stochastic models of gene expression with molecular memory and bursting. Phys Rev Lett 106(5):058102PubMedCrossRef
go back to reference Kaern M, Elston T, Blake W, Collins J (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6:451–464PubMedCrossRef Kaern M, Elston T, Blake W, Collins J (2005) Stochasticity in gene expression: from theories to phenotypes. Nat Rev Genet 6:451–464PubMedCrossRef
go back to reference Kepler T, Elston T (2001) Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations. Biophy J 81:3116–3136CrossRef Kepler T, Elston T (2001) Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations. Biophy J 81:3116–3136CrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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] 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]
go back to reference 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 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
go back to reference Lipniacki T, Paszek P, Marciniak-Czochra A, Brasier A, Kimmel M (2006) Transcriptional stochasticity in gene expression. J Theor Biol 238(2):348–367PubMedCrossRef Lipniacki T, Paszek P, Marciniak-Czochra A, Brasier A, Kimmel M (2006) Transcriptional stochasticity in gene expression. J Theor Biol 238(2):348–367PubMedCrossRef
go back to reference 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 (2008) Dynamics and density evolution in piecewise deterministic growth processes. Ann Polon Math 94:111–129CrossRef
go back to reference 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 (2016) The limiting dynamics of a bistable molecular switch with and without noise. J Math Biol 73:367–395PubMedCrossRef
go back to reference 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 (2011) Molecular distributions in gene regulatory dynamics. J Theor Biol 274:84–96PubMedCrossRef
go back to reference 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, 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
go back to reference 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 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
go back to reference 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 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
go back to reference Monod J (1941) Recherches sur la croissance des cultures bactériennes. Ph.D. thesis, Université de Paris, Paris Monod J (1941) Recherches sur la croissance des cultures bactériennes. Ph.D. thesis, Université de Paris, Paris
go back to reference Monod J, Jacob F (1961) Teleonomic mechanisms in cellular metabolism, growth, and differentiation. Cold Spring Harb Symp Quant Biol 26:389–401PubMedCrossRef Monod J, Jacob F (1961) Teleonomic mechanisms in cellular metabolism, growth, and differentiation. Cold Spring Harb Symp Quant Biol 26:389–401PubMedCrossRef
go back to reference Morelli L, Julicher F (2007) Precision of genetic oscillators and clocks. Phys Rev Lett 98(22):228101PubMedCrossRef Morelli L, Julicher F (2007) Precision of genetic oscillators and clocks. Phys Rev Lett 98(22):228101PubMedCrossRef
go back to reference 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, 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
go back to reference 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 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
go back to reference Narang A (2007) Effect of DNA looping on the induction kinetics of the lac operon. J Theor Biol 247:695–712PubMedCrossRef Narang A (2007) Effect of DNA looping on the induction kinetics of the lac operon. J Theor Biol 247:695–712PubMedCrossRef
go back to reference Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York Nicolis G, Prigogine I (1977) Self-organization in nonequilibrium systems. From dissipative structures to order through fluctuations. Wiley, New York
go back to reference 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 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
go back to reference Oehler S, Eismann ER, Krämer H, Müller-Hill B (1990) The three operators of lac operon cooperate in repression. EMBO J 9:973–979PubMedPubMedCentral Oehler S, Eismann ER, Krämer H, Müller-Hill B (1990) The three operators of lac operon cooperate in repression. EMBO J 9:973–979PubMedPubMedCentral
go back to reference Oppenheim I, Schuler K, Weiss G (1969) Stochastic and deterministic formulation of chemical rate equations. J Chem Phys 50:460–466CrossRef Oppenheim I, Schuler K, Weiss G (1969) Stochastic and deterministic formulation of chemical rate equations. J Chem Phys 50:460–466CrossRef
go back to reference Oppenheim AB, Kobiler O, Stavans J, Court DL, Adhya S (2005) Switches in bacteriophage lambda development. Annu Rev Genet 39(1):409–429PubMedCrossRef Oppenheim AB, Kobiler O, Stavans J, Court DL, Adhya S (2005) Switches in bacteriophage lambda development. Annu Rev Genet 39(1):409–429PubMedCrossRef
go back to reference Othmer H (1976) The qualitative dynamics of a class of biochemical control circuits. J Math Biol 3:53–78PubMedCrossRef Othmer H (1976) The qualitative dynamics of a class of biochemical control circuits. J Math Biol 3:53–78PubMedCrossRef
go back to reference 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 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
go back to reference Penazzio S (2006) The origin of phage virology. Riv Biol 99(1):103–129 Penazzio S (2006) The origin of phage virology. Riv Biol 99(1):103–129
go back to reference Pichór K, Rudnicki R (2000) Continuous Markov semigroups and stability of transport equations. J Math Anal Appl 249:668–685CrossRef Pichór K, Rudnicki R (2000) Continuous Markov semigroups and stability of transport equations. J Math Anal Appl 249:668–685CrossRef
go back to reference Ptashne M (1986) A genetic switch: gene control and Phage Lambda. Cell Press, Cambridge, MA Ptashne M (1986) A genetic switch: gene control and Phage Lambda. Cell Press, Cambridge, MA
go back to reference 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 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
go back to reference Raj A, Peskin C, Tranchina D, Vargas D, Tyagi S (2006) Stochastic mRNA synthesis in mammalian cells. PLoS Biol 4:1707–1719CrossRef Raj A, Peskin C, Tranchina D, Vargas D, Tyagi S (2006) Stochastic mRNA synthesis in mammalian cells. PLoS Biol 4:1707–1719CrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Reznikoff WS (1992) The lactose operon-controlling elements: a complex paradigm. Mol Microbiol 6:2419–2422PubMedCrossRef Reznikoff WS (1992) The lactose operon-controlling elements: a complex paradigm. Mol Microbiol 6:2419–2422PubMedCrossRef
go back to reference 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 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
go back to reference Rozanov DV, D’Ari R, Sineoky SP (1998) RecA-independent pathways of lambdoid prophage induction in Escherichia coli. J Bacteriol 180:6306–6315PubMedPubMedCentral Rozanov DV, D’Ari R, Sineoky SP (1998) RecA-independent pathways of lambdoid prophage induction in Escherichia coli. J Bacteriol 180:6306–6315PubMedPubMedCentral
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference 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) Bistable behavior in a model of the lac operon in Escherichia coli with variable growth rate. Biophys J 94:2065–2081PubMedCrossRef
go back to reference 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 (2008) On the use of the Hill functions in mathematical models of gene regulatory networks. Math Model Nat Phenom 3(2):85–97CrossRef
go back to reference Santillán M (2014) Chemical kinetics, stochastic processes, and irreversible thermodynamics. Springer, HeidelbergCrossRef Santillán M (2014) Chemical kinetics, stochastic processes, and irreversible thermodynamics. Springer, HeidelbergCrossRef
go back to reference 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 (2001) Dynamic regulation of the tryptophan operon: Modeling study and comparison with experimental data. Proc Natl Acad Sci USA 98:1364–1369PubMedPubMedCentralCrossRef
go back to reference 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 (2004b) Influence of catabolite repression and inducer exclusion on the bistable behavior of the lac operon. Biophys J 86:1282–1292PubMedPubMedCentralCrossRef
go back to reference 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, Mackey MC (2008) Quantitative approaches to the study of bistability in the lac operon of Escherichia coli. J R Soc Interface 5:S29–S39PubMedPubMedCentralCrossRef
go back to reference 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 (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
go back to reference Santillán M, Zeron ES (2006) Analytical study of the multiplicity of regulatory mechanisms in the tryptophan operon. Bull Math Biol 68:343–359PubMedCrossRef Santillán M, Zeron ES (2006) Analytical study of the multiplicity of regulatory mechanisms in the tryptophan operon. Bull Math Biol 68:343–359PubMedCrossRef
go back to reference Selgrade J (1979) Mathematical analysis of a cellular control process with positive feedback. SIAM J Appl Math 36:219–229CrossRef Selgrade J (1979) Mathematical analysis of a cellular control process with positive feedback. SIAM J Appl Math 36:219–229CrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Shahrezaei V, Swain P (2008b) The stochastic nature of biochemical networks. Curr Opin Biotechnol 19:369–374PubMedCrossRef Shahrezaei V, Swain P (2008b) The stochastic nature of biochemical networks. Curr Opin Biotechnol 19:369–374PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference Smith H (1995) Monotone dynamical systems. Mathematical surveys and monographs, vol 41. American Mathematical Society, Providence, RI Smith H (1995) Monotone dynamical systems. Mathematical surveys and monographs, vol 41. American Mathematical Society, Providence, RI
go back to reference 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 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
go back to reference 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 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
go back to reference Summers WS (2011) In the beginning…Bacteriophage 1(1):50–51 Summers WS (2011) In the beginning…Bacteriophage 1(1):50–51
go back to reference 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 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
go back to reference Tang M (2010) The mean frequency of transcriptional bursting and its variation in single cells. J Math Biol 60(1):27–58PubMedCrossRef Tang M (2010) The mean frequency of transcriptional bursting and its variation in single cells. J Math Biol 60(1):27–58PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference Tyson JJ (1975) On the existence of oscillatory solutions in negative feedback cellular control processes. J Theor Biol 1:311–315 Tyson JJ (1975) On the existence of oscillatory solutions in negative feedback cellular control processes. J Theor Biol 1:311–315
go back to reference 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 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
go back to reference van Kampen N (1992) Stochastic processes in physics and chemistry, 2nd edn. Elesvier-North Holland, Amsterdam van Kampen N (1992) Stochastic processes in physics and chemistry, 2nd edn. Elesvier-North Holland, Amsterdam
go back to reference 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 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
go back to reference Wilemski G (1976) On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion. J Stat Phys 14:153–169CrossRef Wilemski G (1976) On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion. J Stat Phys 14:153–169CrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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, Mackey MC (2003) Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data. Biophys J 84:2841–2851PubMedPubMedCentralCrossRef
go back to reference Yildirim N, Santillán M, Horike D, Mackey MC (2004) Dynamics and bistability in a reduced model of the lac operon. Chaos 14:279–292PubMedCrossRef Yildirim N, Santillán M, Horike D, Mackey MC (2004) Dynamics and bistability in a reduced model of the lac operon. Chaos 14:279–292PubMedCrossRef
go back to reference 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 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
go back to reference 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 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
go back to reference 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 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
go back to reference 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 (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
go back to reference 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 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
Metadata
Title
The Tryptophan Operon
Authors
Michael C. Mackey
Moisés Santillán
Marta Tyran-Kamińska
Eduardo S. Zeron
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-45318-7_6

Premium Partner