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 or 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 with 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

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 determinesthe protein concentration noise)

„Translational bursting“

Slow promotors increase noise

Transcriptional bursting

low promotor rate

+ 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

Simulation for isomerisation :

state A state B

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

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 with identical external conditions

Extrinsic noise: cell to cell variance of expression

Stochastic gene expression

Elowitz et al. 2002

The „intrinsisc noise“ decreases with increasing protein concentration

(due to decreased promotor noise)

Elowitz, M. et al, Science 2002

22int

2exttot