Post on 27-Mar-2015
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
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
A Transkription-Aktivator and a Transkription-Repressor control the lac-Operon
Genregulation and boolean networks
from Weiss, 2000
Boolean expression of the Lac-Operon
Genetische Netze
transcriptiontranscription
translationtranslation
Genregulatorisches ProteinGenregulatorisches Protein
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
Wiederholung
Genregulation and boolean Network
from Weiss, 2000
(Nature, Dec 99)
the genetic Toggle Switch (Flip-Flop)
Weiss et al.
the repressilator (genetic oscillator)
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
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.
Decelerated negative feedback via dclk (dclock) (degradation) anddbt (doubletime) (Transport)Synchronization (Entrainment) due to sunlight dependent TIM degradation rate
A couple of phosporilation steps are part of deceleration mechanism
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“
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“
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:
Deterministic model of gene expression
from JJ Collins, Nature Reviews 2005
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
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
beschreibt den Effekt, dass ein Heraufsetzen der translationsrate auch dieFluktuationen verstärkt.
Herabsetzenvon Transkriptionsrate undZellvolumen
Proteinlevel konstantFluktuationen erhöht
„Translational bursting“
Slow promotors increase noise
Transcriptional bursting
low promotor rate
High transcription rate
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
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
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
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
Elowitz et al. 2002
hte „intrinsisc noise“ decreases with increasing protein concentration
Elowitz, M. et al, Science 2002
22int
2exttot