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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 or 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 with 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
2
z1
k1jk2nj
Distribution pj
n
k1k2

n
j
noise

12
At 2 At 2
 
  

t



2

N 
A
t



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
 level constant, but increases noise
protein
„Translational bursting“
describes the effect that an increase of the translation rate
also increases the fluctuations.
Lower transcription rate and
cell volume:
Protein level is constant,
but the fluctuations are increased.
(noise from mRNA level determines
the protein concentration noise)
Slow promotors increase noise
low promotor rate
Transcriptional bursting
+ High translation 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“
(gene expression) and „extrinsic
noise“(variations of other cell
components such as RNA polymerase)
Idea for an experiment:
Gene for CFP (green fluorescent protein)
und YFP (yellow fluorescent protein,
shown in red) 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 with identical external conditions

2
2
2





tot int ext
Elowitz et al. 2002
The „intrinsisc noise“ decreases with
increasing protein concentration
(due to decreased promotor noise)
2
2
2
tot



int
ext
Elowitz, M. et al, Science 2002