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!“

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

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

„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 Simulation for isomerisation : example isomerisation with k1 = k2 = 1s-1 k1 k2 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

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

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

Elowitz et al. 2002

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