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Stochastische Genexpression

Genetische Schalter und Multistabilität. Stochastische Genexpression. Vorlesung System-Biophysik 18. Dez. 2007. Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005)

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Stochastische Genexpression

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  1. Genetische Schalter und Multistabilität Stochastische Genexpression Vorlesung System-Biophysik 18. Dez. 2007 Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose utilization network of Escherichia coli, Nature 427, p737

  2. Das Operon-ModellFrancois Jacob und Jaques Monod, 1961 operon • Operon: Genetische Funktionseinheit, die aus regulierten Genen mit verwandter Funktion besteht und enthält: • Promotor: Bindungsstelle für RNA-Polymerase • Operator: kontrolliert Zugang der RNA-Polymerase zu Strukturgen • Strukturgene: Polypeptide codierende Gene • zusätzlich: • Regulatorgen: codiert Repressor Campbell, N.A., Biology

  3. A Transkription-Aktivator and a Transkription-Repressor control the lac-Operon

  4. Genregulation and boolean networks from Weiss, 2000

  5. Boolean expression of the Lac-Operon

  6. Genetische Netze Genregulatorisches Protein translation transcription

  7. Transkription factors show cooperativity (e.g. by dimer-formation) Cooperative binding

  8. Wiederholung

  9. Genregulation and boolean Network from Weiss, 2000

  10. (Nature, Dec 99)

  11. the genetic Toggle Switch (Flip-Flop)

  12. Weiss et al.

  13. the repressilator (genetic oscillator)

  14. Circadian Rhythm – the biological clock [Latein. circa about + dies a day] Genetically controlled oscillation of about 24 hours, adapted to the day-night rythm . A single gen-mutation is responsible for the familial advanced sleep phase syndrome, FASPS. Der 24h Rythm is robust, the phase is coupled to the light/dark cycle.

  15. Die circadiane Uhr at Drosophila Two proteins Per (Period) and Tim (timeless) regulate each other and form a dimere complex. Monomeres of Per in the nucleus supresses expression. The kinase DBT (double time) phosphorylates und degrades Per. The complex fromation Per/Tim supports the entry in the nucleus and stays stable there for 8-10h. This slows down the feedback loop.

  16. Decelerated negative feedback via dclk (dclock) (degradation) and dbt (doubletime) (Transport) Synchronization (Entrainment)due to sunlight dependent TIM degradation rate

  17. A couple of phosporilation steps are part of deceleration mechanism

  18. What is life ? Schrödinger considered 1943 the consequences of the molecular nature of the genetic code in a lecture about „Physics and biology“ 1. How can „biological order“ (life) be explaind by the basic laws of physics? 2. How does life deal with the statistic nature of molecular interactions? „... wenn wir so empfindliche Organismen wären, daß ein einzelnes Atom oder meinet-wegen ein paar Atome einen wahrnehmbaren Eindruck auf unsere Sinnesorgane machen könnten - du lieber Himmel, wie sähe das Leben dann aus!“

  19. The importance of statistical fluctuations in biology Noise can be increased with „positive feedback loops“ with advandtages: • In a fluctuating environment, heterogeneous cell populations have better chances to grow. (e.g. control of lac.operon, immune system, lysis-networks of lambda-phage) • Diversification in isogene phenotypes und celltypes (e.g. stem cell diversification) • Efficiency increase in signal transduction (e.g. chemotaxis regulation oder stochastic resonance (ears)) Noise can be decreased via „negative feedback loops“ • Stabilisation of metabolics / homeostasis

  20. Biochemical noise:fluctuation of protein concentration Noise in the expression: Small numbers of copies of many components e.g. Polymerases, regolatory proteins,  Stochastic effects in gene expression play an important role for variations of protein concentrations of bacteria wit identical genes  Asymetries emerge, which are amplified by feedback loops and influence the development of the cell.

  21. Deterministic model of gene expression from JJ Collins, Nature Reviews 2005

  22. Definitions for noise Variance Distribution noise z: number of data points Noise amplitude decreases with increasing number of particles! Rao, Wolf,Arkin, Nature 2002

  23. finite size effect 0.1µM corresponds to 30 molecules/bacterium : mean value : standard deviation (noise) Decrease of the transcription rate and cell volume with equal factors keeps the protein level constant, but increases noise

  24. „Translational bursting“ beschreibt den Effekt, dass ein Heraufsetzen der translationsrate auch die Fluktuationen verstärkt. Herabsetzen von Transkriptionsrate und Zellvolumen Proteinlevel konstant Fluktuationen erhöht

  25. Slow promotors increase noise low promotor rate Transcriptional bursting High transcription rate

  26. Noise models Set of differntial equations (deterministic): Set of differential-equations (stochastic) Langevin equations: C: concentrations, t: time, v: stoichiometric matrix, r: rates, x(t): white noise Probability density function Simulation for isomerisation : example isomerisation with k1 = k2 = 1s-1 k1 k2 state A state B

  27. Experiment: stochastisc Gen-Expression Distinguish between „intrinsic noise“ (e.g. gene expression) and „extrinsic noise“(e.g. other cell components as RNA polymerase) Idea for an exeriment: Gene for CFP (green fluorescent Protein) und YFP (rot fluorecent Protein) are controlled by the same promotor, hence the mean concentration of CFP and YFP is equal => Expression probability should differ only due to intrinsic noise A: no intrinsic noise => noise is correlated red+green=yellow B: intrinsic noise => noise not correlated, different colors Elowitz, M. et al, Science 2002

  28. Stochastische Genexpressionin einer einzelnen Zelle Elowitz, M. et al, Science 2002 Two distinguishable genes (CFP and YFP)controlled by the same promotor Low induction: (low fluorescence) high noise High induction : (high fluorescene) Low noise

  29. Stochastic gene expression Extrinsic noise: cell to cell variance of expression (noise) Intrinsic noise: inherent stochasticity at identical external conditions

  30. Elowitz et al. 2002

  31. hte „intrinsisc noise“ decreases with increasing protein concentration Elowitz, M. et al, Science 2002

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