![Page 1: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/1.jpg)
Stochastische Genexpression
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
Vorlesung System-Biophysik 18. Dez. 2007
Genetische Schalter und Multistabilität
![Page 2: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/2.jpg)
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 Genezusätzlich:Regulatorgen: codiert Repressor Campbell, N.A., Biology
![Page 3: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/3.jpg)
A Transkription-Aktivator and a Transkription-Repressor control the lac-Operon
![Page 4: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/4.jpg)
Genregulation and boolean networks
from Weiss, 2000
![Page 5: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/5.jpg)
Boolean expression of the Lac-Operon
![Page 6: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/6.jpg)
Genetische Netze
transcriptiontranscription
translationtranslation
Genregulatorisches ProteinGenregulatorisches Protein
![Page 7: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/7.jpg)
Transkription factors show cooperativity (e.g. by dimer-formation)
CI D O CIO
KD CI M 2
CI D
CIO Ototal
CI M 2
K KD CI M 2
Cooperative binding
CI M CI M
CI D
![Page 8: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/8.jpg)
Wiederholung
![Page 9: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/9.jpg)
Genregulation and boolean Network
from Weiss, 2000
![Page 10: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/10.jpg)
(Nature, Dec 99)
![Page 11: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/11.jpg)
the genetic Toggle Switch (Flip-Flop)
![Page 12: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/12.jpg)
![Page 13: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/13.jpg)
Weiss et al.
![Page 14: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/14.jpg)
the repressilator (genetic oscillator)
![Page 15: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/15.jpg)
Genetically controlled oscillation of about 24 hours, adapted to the day-night rythm.
Der 24h Rythm is robust, the phase is coupled to the light/dark cycle.
A single gen-mutation is responsible for the familial advanced sleep phase syndrome, FASPS.
[Latein. circa about + dies a day]
Circadian Rhythm – the biological clock
![Page 16: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/16.jpg)
Die circadiane Uhr at Drosophila
The complex fromation Per/Tim supports the entry in the nucleus and
stays stable there for 8-10h. This slows down the feedback loop.
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.
![Page 17: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/17.jpg)
Decelerated negative feedback via dclk (dclock) (degradation) anddbt (doubletime) (Transport)Synchronization (Entrainment) due to sunlight dependent TIM degradation rate
![Page 18: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/18.jpg)
A couple of phosporilation steps are part of deceleration mechanism
![Page 19: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/19.jpg)
What is life ?
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!“
Schrödinger considered 1943 the consequences of the molecular nature of the genetic code in a lecture about „Physics and biology“
![Page 20: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/20.jpg)
The importance of statistical fluctuations in biology
• 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 increased with „positive feedback loops“ with advandtages:
• Stabilisation of metabolics / homeostasis
Noise can be decreased via „negative feedback loops“
![Page 21: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/21.jpg)
Biochemical noise: fluctuation of protein concentration
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.
Noise in the expression:
![Page 22: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/22.jpg)
Deterministic model of gene expression
from JJ Collins, Nature Reviews 2005
![Page 23: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/23.jpg)
Definitions for noise
2 A2 A
2
z 1
noise
Distribution
Noise amplitude decreases with increasing number of particles!
z: number of data points
Rao, Wolf,Arkin, Nature 2002
Variance
p j jn k1
jk2n j
k1 k2 n
t N
A t 2 A t 2
A t 2
1 2
![Page 24: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/24.jpg)
finite size effect
x
x (noise)
x : mean value
x : standard deviation
1 N
0.1µM corresponds to 30 molecules/bacterium
Decrease of the transcription rate and cell volume with equal factors keeps the protein level constant, but increases noise
![Page 25: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/25.jpg)
beschreibt den Effekt, dass ein Heraufsetzen der translationsrate auch dieFluktuationen verstärkt.
Herabsetzenvon Transkriptionsrate undZellvolumen
Proteinlevel konstantFluktuationen erhöht
„Translational bursting“
![Page 26: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/26.jpg)
Slow promotors increase noise
Transcriptional bursting
low promotor rate
High transcription rate
![Page 27: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/27.jpg)
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
example isomerisation with
k1 = k2 = 1s-1
k1
k2
Simulation for isomerisation :
state A state B
![Page 28: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/28.jpg)
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
![Page 29: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/29.jpg)
Two distinguishable genes (CFP and YFP)controlled by the same promotor
Low induction:(low fluorescence)high noise
High induction :(high fluorescene)Low noise
Elowitz, M. et al, Science 2002
Stochastische Genexpressionin einer einzelnen Zelle
![Page 30: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/30.jpg)
x
x
tot2 int
2 ext2
(noise)
Intrinsic noise: inherent stochasticity at identical external conditions
Extrinsic noise: cell to cell variance of expression
Stochastic gene expression
![Page 31: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/31.jpg)
Elowitz et al. 2002
![Page 32: Stochastische Genexpression Literatur Kaern et al. Nature Reviews Genetics Vol.6 p.451 (2005) Ozbudak, Oudenaarden et al (2004) Multistability in the lactose](https://reader035.vdokument.com/reader035/viewer/2022070305/551483f5550346b0158b5981/html5/thumbnails/32.jpg)
hte „intrinsisc noise“ decreases with increasing protein concentration
Elowitz, M. et al, Science 2002
22int
2exttot