Operon

Stochastische Genexpression
Genetische Schalter und Multistabilität
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
Das Operon-Modell
Francois 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
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
Genregulatorisches Protein
translation
transcription
Transkription factors show cooperativity
(e.g. by dimer-formation)
 CIO
CID  O
 CID
CIM  CIM 
CI 


 CI 
2
KD
M
D


Cooperative binding
CIM 
CIO




2
O
 total K  K D  CIM 
2
Wiederholung
Genregulation and boolean Network
from Weiss, 2000
(Nature, Dec 99)
the genetic Toggle Switch (Flip-Flop)
Weiss et al.
the repressilator (genetic oscillator)
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.
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.
Decelerated negative feedback via
dclk (dclock) (degradation) and
dbt (doubletime) (Transport)
Synchronization (Entrainment)
due to sunlight dependent TIM degradation rate
A couple of phosporilation steps are part of deceleration
mechanism
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 meinetwegen ein paar Atome einen wahrnehmbaren Eindruck auf unsere Sinnesorgane machen
könnten - du lieber Himmel, wie sähe das Leben dann aus!“
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
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.
Deterministic model of gene expression
from JJ Collins, Nature Reviews 2005
Definitions for noise
Variance
2 
A2  A
Distribution p j  

2
z 1

n
j
k1j k2n j
 k k n
 1 2
 A t 2  A t

   
t  

2
N 
A
t



noise

2 12




z: number of data points

Noise amplitude decreases with increasing
number of particles!
Rao, Wolf,Arkin, Nature 2002
finite size effect
0.1µM corresponds to 30 molecules/bacterium
x : mean value
 x : standard deviation



x
x
(noise)
 1 N

Decrease
of the transcription rate and cell
volume with equal factors keeps the
protein
 level constant, but increases noise
„Translational bursting“
beschreibt den Effekt, dass ein Heraufsetzen der translationsrate auch die
Fluktuationen verstärkt.
Herabsetzen
von Transkriptionsrate und
Zellvolumen
Proteinlevel konstant
Fluktuationen erhöht
Slow promotors increase noise
low promotor rate
Transcriptional bursting
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
state A
state B
Simulation for isomerisation :
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
Stochastische Genexpression
in 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
Stochastic gene expression

Extrinsic noise:
cell to cell variance of expression
x
x
(noise)
Intrinsic noise:
inherent stochasticity at identical external conditions

2
2
2
tot
 int
 ext
Elowitz et al. 2002
hte „intrinsisc noise“ decreases with
increasing protein concentration
2
2
2
tot
 int
 ext
Elowitz, M. et al, Science 2002