Genregulation

Literature

- Alberts/Lehninger- Kim Sneppen & G. Zocchi: Physics in Molecular Biology- E. Klipp et al. : Systems Biology in Practice

Systems biophysics 2010/05/11

Physics of transcription control and expression analysis

From genetic approach to sytemic approach

genregulation

mRNA regulation

DNA mutations / evolution

protein functions

spatiotemporal structure formationMorphogenesis

signal transduction=> Topics of systems biophysics

Biological Pattern formation and Morphogenesis11.05.2010

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E S k1 ES k2 E P

k 1 Enzymatic Reactions

Michaelis-Menton-KineticsInhibation, Regulation

Reaction-Diffusion-Model of Morphogenesis

Biochemical Network

E.coli as model system

E.coli has a single DNA molecule which is 4.6 106 basepairs long. It encodes 4226 proteins and a couple of RNA molecules. The information content of the genome is is bigger than the structural information of the encoded Proteins-> regulatory mechanisms are encoded

Genregulation allows adaption to changing environmental conditions, and regulation of metabolism

Content of this lecture:

Basics: Monod Model, Lac Operon

Statistical Physics of DNA-binding Proteins

Modelling of genregulatory Networks

(ODE & Boolian Networks)

Dynamics of Protein-DNA binding

DNA looping

Analysis of gene expression data

Synthetic Networks

Operon-Modell

operon

Operon: Genetic subunit, that consists of regulated genes with similar functionality.It includes- Promotor: Binding site for RNA polymerase - Operator: controls access of the RNA-Polymerase structural gene - Structural genes: Polypeptide encoding genes

Francois Jacob und Jaques Monod, 1961

The Trp Operator as a switch:• Within the promotor lies a short DNA region as binding site for a

repressor. A bound repressor prevents the Polymerase from binding.

The OUTSIDE of proteins can be recognized by proteins

Distinct basepairs can be recognized by their marginsDNA binding motivs

Small channel

Large channel

Binding of Tryptophane to the Tryptophane-Repressorproteine changes the conformation of the repressor, Repressor can bind to the repressor binding site

Identification of promotor sequences

Transcription-Activation proteins switch on genes

Gen-Regulation with Feedback:lac-Operon

LacI

IPTG, TMG

Campbell, N.A., Biology

A cis-regulatory element or cis-element is a region of DNA or RNA that regulates the expression of genes located on that same strand. This term is constructed from the Latin word cis, which means "on the same side as". These cis-regulatory elements are often binding sites of one or more trans-acting factors.

IPTG (Isopropyl β-D-1-thiogalactopyranoside)This compound is used as a molecular mimic of allolactose, a lactose metabolite that triggers transcription of the lac operon. Unlike allolactose, the sulfur (S) atom creates a chemical bond which is non-hydrolyzable by the cell, preventing the cell from "eating up" or degrading the inductant. IPTG induces activity of beta-galactosidase, an enzyme that promotes lactose utilization, by binding and inhibiting the lac repressor. In cloning experiments, the lacZ gene is replaced with the gene of interest and IPTG is then used to induce gene expression.

Non-metabolizable inducer are used to induce gene expression

Variation of Protein-Concentration with IPTG

Northern Blot: measurement of the messenger RNA (mRNA) concentration

External and internal Inductor-concentration is equal in equilibriumThe mRNA concentration increases linear with the concentration of inductor, saturation over 60%

The operon enables a variation of Protein concentration. What is missing to make a switch?

60

40

20

0

[mR

NA

]

0.100.00[IPTG Induktor]Long, C et al, J.Bacteriol. 2001

Transkription und Translation in E.coliTypical times and rates

1 Molecule / cell = 1nMComplete mass2.5 106 Da

TRANSKRIPTIONrate 1/s - 1/18sTranskriptionsrate: 30bps-90bps

TRANSLATION10.000-15.000 RibosomesTranslation rate 6-22 codons/s(40 Proteine/mRNA)

The arabinose system1

Uptake

Reporter

Regulator

Break down

pBAD24 2

~55 copies/cell

[1] R. Schleif. Trends in Genetics, 16(12):559–565, 2000[2] L. M. Guzman, D. Belin, M. J. Carson, and J. Beckwith. J.Bacteriol., 177(14):4121–4130, 1995[3] D. A. Siegele and J. C. Hu. Proc. Natl. Acad. Sci. USA, 94(15):8168–8172, 1997

automated data aquisition

define ROIs

measure total intensity

DICtn

N

DICt0

Fluorescencet0

t1

tn

background correction

calibration and conversion into molecular units

Time-lapse Fluorescence Microscopy and Quantitative Image Processing

Judith.Megerle@physik.lmu.de

8x105

6

4

2

0

To

tal F

luo

resc

en

ce [

a.u

.]

806040200

Time [min]

0.2% arabinose

Single cell expression kinetics

30min 40min 60min50min 70min

5min 15min 35min 45min25min

Saturating induction

Subsaturating induction

Image series correspond to blue curves

Fluorescence measurement• Cell outlines are determined using bright field images• The signal is integrated within the outline in each fluorescence image

8x105

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Time [min]

0.01% arabinose

Gene expression model

Deterministic rate model with time delay d

8x105

6

4

2

0

Z(

) [a

.u.]

806040200

[min]

Reporter module Uptake module

Induction: t=0min

Curve Fitting

Fixed Parameters

Saturating induction

Subsaturating induction

Fit Parameters

Fit expression function

Time delay

Protein synthesisrate

Literature

Measured

8x105

6

4

2

0

To

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luo

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806040200

Time [min]

0.01% arabinose

8x105

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2

0

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luo

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0.2% arabinose

Ohter example: Quorum Sensing

Squid with floodlamp

Phänomena:Squid (Euprymna scolopes) emmits light due the night Squid isn´t recognized as prey in the moonlight

Explanation:

Light organ of the squid collects luminescent bacteria (Vibrio fischerei)

Question:

Why does V. fischerei emmit light within the lightorgan of the squid, but not in open sea?

Quorum sensing

Bakterien detect their own cell density Density regulates the expression of luminescent genes

K. Nelson, Cell-Cell Signalling in Bacteria

Bacteria increase exponentialOD: optical density

Molekular picture of QS

• Bakteria export oligopeptides (Pheromones)• Oligopeptides accumulate with increasing cell density• Oligopeptide diffuse into cell membrane and regulates the expression of luminescent genes

Searching the binding site

Searching the binding site: timescales

D kT

6R

P(r, t) 1

4tDexp

r2

4Dt

tdiffusion d2

2D

Stokes Einstein equation(z.B. DGFP=3-7µm2/s)

Probability distribution

1µm

Typical timescale for a proteine to find an arbitrary point in an E.coli: tD 0.1s

Diffusion to a target site (binding disc)

J D4r2 dC

dr

dC

dt

1

r2D

d

dr4r2 dC

dr

C(r) J

D4r C()

C() N V

C() 0

J 4DN

V

on V

4DN20s N

Residence times for transcription factors

1

off

1

on

V exp G kT 4D M exp G kT

(from on=20s/N follows, that 1 molecule in 1µm3 occupies half an Operator)

for specific bindings (operon) with 1M-1=1.6nm3 and Gspez=-12.6kcal/mol, =1 follows

off 20s

for unspecific binding sites with Guspez=-10-4 kcal/mol, follows

off 10 4 s

Search of the binding sites on a DNA strand

DayssD

L2000.200

2 1

2

Unspecific binding events of TFs is a problem, since the time to find a binding site is increased. For a infinite staytime, a 1D- random walk over the strand would last:

(L=1.5mm und D1≈D)

Accelerated search: jumps between strands decrease time to find a binding site.

l2

D1

L

l

Ll

D1

Mit L=1.5mm, l=150nm follows

50s

Boolian Networks, or what cells and computers have in common.

(Nature, Dec 99)

Combinatoric gene regulation: Genetic networks

transcriptiontranscription

translationtranslation

Genregulatoric proteineGenregulatoric proteine

A transcription-activator and a transcription-repressor regulate the lac-Operon

Thermodynamicc model of a combinatoric transcription logics

P : bindingprobability

Gerland et al. PNAS, 2005

Gene regulation follows the mechanics of „Boltzmann-machines“

Statistical physics of protein - DNA binding

CI O CIO

K k

k

CI O CIO

CIO Ototal

CI

K CI

Binding-isothermes:

Cooperativity due to dimer binding

CI D O CIO

KD CI M 2

CI D

CIO Ototal

CI M 2

K KD CI M 2

Cooperative binding

CI M CI M

CI D

The statistical weight of the „on“ state

Pon Z(on)

Z

Pon

Poff

Z(on)

Z(off )

c

exp G kT CI K

The free-energy difference is normalized to 1mol/l . The real change in free energy of the binding event depends on the concentration of TF in solution [Cl] :

G* kT ln Z(on) ln Z(off ) G kT ln CI

A model for lac networks

Glukoseconc.constant

GFP: Reportermolekül, Abbildung durchFluoreszenz-Mikroskopie=> je höher das Fluoreszenz-Signal desto mehr LacZ,Y wird exprimiert

Experimental proof for a switch

Start: not induced

After induction exist 2 populations:

green: induced bacteria

white, not induced population

Bistable area (grey)

Arrow marks the start state:

on-off state of bacteria depend on the on-off state in the beginning!

switch with hysteresisOzbudak et al, Nature 2004

modelling of genregulatory networks: example

Modelling in mRNA level

Timetrace of mRNA concentrations

Problem: kinetic binding constants are usually not known and hard to measure

Steady state

Simplification of genregulatory networks

transcriptiontranscription

translationtranslation

Genregulatory proteinGenregulatory protein

Abstraction of genetic networks

Gen X

Gen Y

Gen Z

+

-

Boolean networks(Kauffman 1989)

Boolean networkmodel

• N Genes (nodes)

• with 2N different states

• with possible rules

• K is the number of possible inputs per node

22K

Boolean rules for N=2 und K=2

Back to the example:

We learn: if a=0, then follows0101 stationary

if a=1, then follows oscilatory behaviour1000->1001->1111->1010->1000