1. 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!“

2. 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

3. 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.

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

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

6. Finite size effect : mean value : standard deviation (noise)
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

7. „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)

8. Slow promotors increase noise
low promotor rate
Transcriptional bursting
+ High translation rate

9. 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

10. 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

11. 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 11

12. Stochastic gene expression
Extrinsic noise:
cell to cell variance of expression
(noise)
Intrinsic noise:
inherent stochasticity with identical external conditions
Intrinsisch:
(Maß für die Abweichung zweier identischer Gene unter gleichen intrazellulären Bedingungen) 12

13. Elowitz et al. 2002

14. The „intrinsisc noise“ decreases with increasing protein concentration (due to decreased promotor noise)
Elowitz, M. et al, Science 2002