Edda Klipp, Humboldt-Universität zu Berlin Modeling of Gene expression. : Gene mRNA Proteins Cell processes Central Dogma of Molecular Biology Transcription

Edda Klipp, Humboldt-Universität zu Berlin

Modeling of Gene expression.

:

Gene

mRNA

Proteins

Cell processes

Central Dogma of Molecular Biology

Transcription factors


Modeling of Gene Expression

Modeling of Expression of one/few genes- Binding of transcription factors/RNAPolymerasen,... to DNA- Effect of inhibitors/activators- Production of mRNA, proteins- Feedback or regulation by products or external regulators

Discovery of genetic networks- Cause of gene expression patterns or -profils- Modeling of the dynamics of artifical networks- Reverse Engineering- Search for Motifs and Clustern Basis: Data

Basis: Processes and interactions


Direction of Investigation

known to be predicted

Structure FunctionProtein interactions Expression of genesTF bindiung Regulation

Impact of perturbationsDynamic behavior,

Bifurcations,... : :

Function StructureExpression pattern Mutual influence of genesTime courses of Regulation network concentrations, activities,…. : :


Concept of state

The state of a system is a snapshot of the system at a given time that contains enough information to predict the behaviour of the system for all future times. The state of the system is described by the set of variables that must kept track of in a model.

Different models of gene regulation have different representations of the state:

Boolean model: a state is a list containing for each gene involved, of whether it is expressed („1“) or not expressed („0“)

Each model defines what it means by the state of a system.

Given the current state the model predicts what state/s can occur next.

Differential equation model: a list of concentrations of each chemical entity

Probabilistic model: a current probability distribution and/or a list of actual numbers of molecules of a type


Kinetics – change of state

A Bk

Deterministic, continuous time and state: e.g. ODE modelconcentration of A decreases and concentration of B increases. Concentration change in per time interval dt is given by

Akdt

dB

Probabilistic, discrete time and state : transformation of a molecule of type A into a molecule of type Sorte B. The probability of this event in a time interval dt is given by

aktadttaP ,,1a – number of molecules of type A

Deterministic, discrete time and state : e.g. Boolean network modelPresence (or activity) of B at time t+1 depends on presence (or activity) of A at time t tAftB 1


One Network, Different Models

gene a gene b

gene c gene d

C

A

D

B

AB

+

+

repression

activation

transcription

translation

gene

protein

A

a b

c d

Directed graphs

V = {a,b,c,d}

E = {(a,c,+),(b,c,+), (c,b,-),(c,d,-),(d,b,+)}

a b

c d

Boolean network

a(t+1) = a(t)

b(t+1) = (not c(t)) and d(t)

c(t+1) = a(t) and b(t)

d(t+1) = not c(t)

a b

c d

Bayesian network

p(xa)

p(xb)

p(xc|xa,xb),

p(xd|xc),


Directed Graphs

a b

c d

Directed graphs

V = {a,b,c,d}

E = {(a,c,+),(b,c,+), (c,b,-),(c,d,-),(d,b,+)}

A directed graph G is a tuple , with V - Set of verticesE – Set of edges

Vertices are related to Genes (or other components of the system) and edges correspond to their regulatory interactions.

An edge is a tuple of vertices. It is directed, if i and j can be associated with head and tail of the edge.

Label of edges and vertices can be enlarged to store information about genes or interactions.

Then in general, an edge is a tuple

properties: e.g: j activates i (+) or j inhibits i (-), properties e.g. List of regulators and their effects on a specific egde

EV ,

proteinc homodimeri as inhibitionactivation ,,,,, lkji

propertiesji ,,

ji ,

Usually not suited for presenting dynamics


Bayesian Network

Representation of network as directed acyclic graph

Nodes -- Genes

Edges E -- regulatory interactions.

Variables , belonging to nodes i = for regulation relevant properties,

e.g. Gene expression leves or amount of active protein.

A conditional probability distribution is defined for every ,

with parent variables belonging to direct regulators of i.

Directed Graph G and conditional probability distribution together

Yield the joint probability distribution, which defines the Bayesian network.

The joint probability distribution can be decomposed to

EVG ,

Vi

ix

ii xLxp ix ixL

xp

i

ii xLxpp x

a b

c d

Bayesian network

p(xa)

p(xb)

p(xc|xa,xb), p(xd|xc),


Bayes‘sche Netze

zy;ixi

ix

Gerichteter Graph: Abhängigkeit von Wahrscheinlichkeiten:Genexpressionslevel eines „Kindknotens“ ist abhängig von Expressionslevel der „Eltern“

Daher auch: bedingte Unabhängigkeiten:

Die bedeuten, dass unabhängig von Variablen y ist, wenn Variablen z gegeben sind.

Zwei Graphen oder Bayes‘sche Netzwerke sind äquivalent, wenn sie den gleichen Satz vonUnabhängigkeiten bestimmen.

Äquivalente Graphen sind durch Beobachtung der Variablen x nicht unterscheidbar.

Für das Beispielnetz sind die bedingten Unabhängigkeiten

Die gemeinsame Wahrscheinlichkeitsverteilung ist

ba xxi ;

cbad xxxxi ,;

cdbacbadcba xxpxxxpxpxpxxxxp ,,,,

a b

c dp(xa)

p(xb)

p(xc|xa,xb),

p(xd|xc),


Boolean Models

(George Boole, 1815-1864)Each gene can assume one of two states:

expressed („1“) or not expressed („0“)

Background: Not enough information for more detailed descriptionIncreasing complexity and computational effort for more specific models

(discrete, deterministic)

Replacement of continuousfunctions (e.g. Hill function)by step function


Boolean Models

Boolean network is characterized by- the number of nodes („genes“): N- the number of inputs per node (regulatory interactions): k

The dynamics are described by rules:

„if input value/s at time t is/are...., then output value at t+1 is....“

Boolean network have always a finite number of possible states and,therefore, a finite number of state transitions.

B C

Linear chain

Ring

A B C D

A B

C D

A

B

A


Boolean Models

gene a gene b

gene c gene d

C

A

D

B

AB

+

+

repression

activation

transcription

translation

gene

protein

a b

c d

Boolean network

a(t+1) = a(t)

b(t+1) = (not c(t)) and d(t)

c(t+1) = a(t) and b(t)

d(t+1) = not c(t)

0000 00010001 01010010 00000011 00000100 00010101 01010110 00000111 0000

Steady state: 0101

1000 10011001 11011010 10001011 10001100 10111101 11111110 10101111 1010

Cycle: 1000 1001 1101 1111 1010 1000


Beschreibung mit Differentialgleichungen

aft

aa

d

d

dcbft

bb ,,

d

d

cbaft

cc ,,

d

d

dcft

dd ,

d

d

akvaf aaa

bkcKdK

dVdcbf bn

Icn

b

nb

bcd

d

,,

ckbaK

baVcbaf cn

c

nc

cab

ab

,,

dkcK

Vdcf dn

Ic

dd

c

,

0 20 40 60 80 100

0

0.5

1

1.5

2

2.5

Time

Co

nce

ntr

atio

n

a

d

b

c

Nur für mRNA:

gene a gene b

gene c gene d

C

A

D

B

AB

+

+

repression

activation

transcription

translation

gene

protein

A


Network motifs

R. Milo, …, U. Alon, Network Motifs: Simple Building Blocks of Complex Networks, Science, 2002

Schematic view of network motif detection. Network motifs are patterns that recur much more frequently (A) in the real network than (B) in an ensemble of randomized networks. Eachnode in the randomized networks has the same number of incoming and outgoing edges as doesthe corresponding node in the real network. Red dashed lines indicate edges that participate in the feedforward loop motif, which occurs five times in the real network.


Network motifs

X Y

X Y

X Y Z

X Y Z

X Y Z

X Y Z

X Y Z

X

Z1 Z2 Z3 Zn

X1 X2 X3 Xm

Z1 Z2 Z3 Zn

Singleinput

HighDensity

Feedforwardloop

Feedback loop

Activation

Inhibition

R. Milo, …, U. Alon, Network Motifs: Simple Building Blocks of Complex Networks, Science, 2002

X

YZ


Transcription

http://www.berkeley.edu/news/features/1999/12/09_nogales.html


Structure of Eukaryotic Promoter

(a)

Figure 6.1

TATA INR DPETFIIA

TBPTFIIF

TFIIB

RNAPII/GTF complex

TF binding sitesDistal promoter module

TF binding sitesProximal promoter module

TATA box Transcriptionstart

Downstream promoterelement

(b) TCCCTGAACGGTCCGAGAACCTTTGCTCCGCA_TTCCTGAGCTGTTCGTAAGGAG

A 00001142020C 02430110410G 00120303113T 53004000011

Aligned TFBSs

TYCSTGARCNG

Positional WeightMatrix

Consensus


Transcription

activeDNARNAPolIIDNA

DNATFDNA

DNATFDNA

x

221

110

mRNANukleotideDNA aktiv

...

NukleotidekDNAmRNAdt

daktiv

n

j

j

mmBm

n

iiBi

aktiv

TFK

TFK

Y

YDNADNAdt

d

1 1

1

0

1

n

ii

n

nn

nBn

B

DNA

DNAY

TFDNA

DNAK

DNADNA

DNAY

TFDNA

DNAK

0

1

10

1

10

11

,

,


Time delay in Transcription

TF-RE

TF-A

P

TF-ATF-AP

P

TF-ATF-AP

tf-a

Delay, translocation of mRNA

Delay, translocation of protein

+

0 5 10 15 20 25 30

1

0.5

0

0.5

1

1.5

kf /min

Lo

g 10T

F-A Region of

multistability

basdD

fRATFkt

KATF

ATFk

dt

ATFd

2

2

Transkriptionsfaktor TF-A aktiviert seine eigene Transkriptionals phosphorylierter Homodimer, der an Enhancer TF-RE bindet.

Modell nach Smolen mit time delay: - schnelles Gleichgewicht von Monomer und Dimer- Sättigungskinetik für Transkription- Abbau von TF mit kd, basale Produktion mit Rbas

t – delay time


Protein Biosynthesis


Model for Elongation of a Peptid chain

Heyd A & Drew DA, Bulletin of Mathematical Biology (2003) 65, 1095–1109

[mRNA] - concentration of messenger RNA,

[mRNA0] - concentration of the mRNA–ribosome complex

[mRNAj ] - concentration of the mRNA–ribosome complex with a nascent peptide chain of length j attached.

reaction rate –kR [R][mRNA] - rate at which the mRNA–ribosome complex is formed

(rate of binding of the mRNA to the ribosome)

reaction rate j [aj ][mRNAj-1] is the elongation rate

(rate constant times the concentrations of the amino acid to be attached,

and the mRNA–ribosome complex with the nascent chain)


Modell for Elongation of a Peptid chain

A—EF-Tu:aa-tRNA complex. A1 - correct complex, and A2 - wrong complex.B—open A-site on ribosome. In this configuration, the ribosome is available to any amino acid.C—initial binding.D—codon recognition.E—GTPase activation and GTP hydrolysis.F—EF-Tu released after EF-Tu conformation change.G—accommodation and peptide transfer.

A ready ribosome [B] initially binds (reversibly) with EF-Tu:aa-tRNA complex [A]. This is followed by codon recognition [D]. After codon recognition, GTPase activation and GTP hydrolysis follow successively [E]. EF-Tu then undergoes a conformation change allowing EF-Tu to be released [F]. At this point proofreading occurs. If the wrong aa-tRNA is present, it is rejected, and the A-site is open again [B]. If the correct aa-tRNA is present, it is accommodated and the peptide bond forms almost immediately [G]. The ribosome then resets back to its open position [B].

k52=0

incorrect aa-tRNA [A2]

correct aa-tRNA [A1]


Elongation model

correct aa-tRNA [A1]


Jacob-Monod-Modell Jacob, F. & Monod, J. (1961) On the Regulation of Gene Activity, Cold Spring Harb. Symp. Quant. Biol., 26, 193-211.

Modell of Griffith Griffith, J.S. (1971) Mathematical Neurobiology, Academic Press, London. Keener, J. & Sneyd, J. (1998) Mathematical Physiology, Springer-Verlag, New York.

Nicolis-Prigogine-Modell Nicolis, G. & Prigogine, I. (1977) Self-Organization in Non-Equilibrium Systems, John Wiley & Sons, New York.

Regulation der Genexpression am Beispiel des Lac-Operons


Experimentelle Fakten

Organismus: E.coli

Bildung von Tryptophansynthase ist reguliert durch ein Strukturgen.

In Abwesenheit von Tryptophan wird dieses Enzym synthetisiert.

In Anwesenheit von Tryptophan wird seine Synthese gestoppt.

Repression der Enzymsynthese: spezifisch für Enzyme des Trp-Syntheseweges

Bildung des Enzyms -Galactosidase ist unter Kontrolle eines Strukturgens.

In Abwesenheit eines Galactosides wird kaum -Galactosidase synthetisiert.

Sobald Galactosid da ist, wird die Syntheserate um das 10 000-fache gesteigert.

Induktion der Enzymsynthese, ebenfalls sehr spezifisch


J a c o b a n d M o n o d : A l l g e m e i n e s M o d e l l , A n n a h m e n

1 . D a s p r i m ä r e P r o d u k t s t r u k t u r e l l e r G e n e i s t d i e “ m e s s e n g e r R N A ” . S i e i s t k u r z l e b i g u n db r i n g t d i e I n f o r m a t i o n z u d e n R i b o s o m e n . D i e “ z w e i t e T r a n s k r i p t i o n ” f i n d e t a n d e nR i b o s o m e n s t a t t , d a b e i w e r d e n P o l y p e p t i d e g e f o r m t , d i e m e s s e n g e r R N A z e r s t ö r t , d i eR i b o s o m e n a b e r f ü r d e n n ä c h s t e n T r a n s k r i p t i o n s z y k l u s e r h a l t e n .

2 . D i e m R N A - S y n t h e s e i s t e i n s e q u e n t i e l l e r , o r i e n t i e r t e r P r o z e s s , d e r n u r a n b e s t i m m t e nR e g i o n e n d e r D N A , d e n O p e r a t o r e n , b e g i n n e n k a n n . M a n c h m a l k o n t r o l l i e r t e i n O p e r a t o rd i e T r a n s k r i p t i o n m e h r e r e r a u f e i n a n d e r f o l g e n d e r s t r u k t u r e l l e r G e n e . D i e s e G r u p p e h e i ß td a n n O p e r o n , e i n e “ E i n h e i t p r i m ä r e r T r a n s k r i p t i o n ” .

3 . N e b e n s t r u k t u r e l l e n G e n e n g i b t e s r e g u l a t o r i s c h e G e n e . E i n r e g u l a t o r i s c h e s G e n k o d i e r tf ü r e i n e n R e p r e s s o r . D e r R e p r e s s o r h a t e i n e A f f i n i t ä t z u u n d b i n d e t r e v e r s i b e l a n e i n e ns p e z i f i s c h e n O p e r a t o r . D i e s e K o m b i n a t i o n b l o c k i e r t d i e T r a n s k r i p t i o n s - i n i t i a t i o n d e sg e s a m t e n O p e r o n s u n d v e r h i n d e r t d i e P r o t e i n s y n t h e s e .

4 . D e r R e p r e s s o r R k a n n m i t k l e i n e n M o l e k ü l e n ( E f f e k t o r e n , F ) s p e z i f i s c h r e a g i e r e n :

I n i n d u z i e r b a r e n S y s t e m e n k a n n n u r d i e R - F o r m m i t d e m O p e r a t o r a s s o z i i e r e n u n d d i eT r a n s k r i p t i o n b l o c k e n . D e r E f f e k t o r = I n d u c e r i n a k t i v i e r t d e n R e p r e s s o r u n d e r m ö g l i c h td a m i t d i e T r a n s k r i p t i o n .I n r e p r e m i e r b a r e n S y s t e m e n i s t n u r d i e R ’ - F o r m a k t i v ; d i e T r a n s k r i p t i o n e r f o l g t i nA b w e s e n h e i t d e s E f f e k t o r s u n d w i r d i n s e i n e r A n w e s e n h e i t u n t e r d r ü c k t .

R+F R'+F'


RG O SG1 SG2

RF

R'

r n

m1 m2

r n

aa

P1 P2

ribosomes

Operon

Jacob-Monod-Model


lactose + E allolactose + E

lactose + E glucose + galactose + E

Ginactiv + m P Gactiv mmeq

m

Pk

Pp

Genaktivierung

Durchschnittliche Produktion von mRNA MkPk

PkM

dt

dMmm

eq

m

21

0

Konzentrationsänderungen von Permease (E1) und ß-Galactosidase (E2) 111

1 EdMcdt

dE 222

2 EdMcdt

dE

ex

exex

Lack

LacE

dt

dLac

010

ins

in

ex

exin

Lack

LacE

Lack

LacE

dt

dLac

21

010

Pk

PE

Lack

LacE

dt

dP

pins

in

2221

Laktose Aufnahme

Interne Laktose (Aufnahme, Umwandlung zu Allolaktose)

Allolaktose (von Laktose, to Glukose und Galaktose)

RG O SG1 SG2

RF

R'

r n

m1 m2

r n

aa

P1 P2

ribosomes

Operon

Modell von Griffith

Expressionsrate


2

0

2

1

k

M

Pk

P

k

kM

mmeq

m

Vereinfachungen Quasi-steady state für mRNA

Gleiche Enzymkonzentrationen 2121 ddEE ,11

2

11

2

01

1 EdPk

P

k

kc

k

Mc

dt

dEmm

eq

m

Pk

PE

Lack

LacE

dt

dP

pex

ex

12

010

Keine Verzögerung in der Umwandlungvon Laktose in Allolaktose

0dtdLacin

Dimensionlose Variablen 0kLaclac ex pkPp 01 eEe 0tt

ep

pm

d

demm

m

0

p

p

lac

lace

d

dp

11

s

se

d

dlac

1

Gleichungssystem

20

10120 k

kkce

00

00e

kt

0

2

pk

k0 p

eq

k

k

1

00k

Mm 10dt

Modell von Griffith


20 40 60 80 100

0.2

0.4

0.6

0.8

1lactose

allolactose

b- galactosidase

50 100 150 200

0.02

0.04

0.06

0.08

0.1lactose

allolactose

b- galactosidase

1 010.

00100 .m

2m

Lösung der Differentialgleichungen

010 .lac 0100 .e 000 .p

Parameter

Anfangsbedingungen

100 .lac 0100 .e 000 .p

Modell von Griffith


Catabolite Repression

CAP = Catabolite Activator ProteinCRP = cyclic AMP Receptor Protein

positive regulation factor

cAMP

CAP, active CAP, inactive

cAMP

Aktives CAP bindet an die CAP Bindungsregion.

Glukose reguliert die Catabolitrepression durch Senkung der freien cAMP-Konzentration.


1 20 40 60 80-20-40-60-80

operator

CRP binding RNA polymerase binding

coding region for -galactosidase

replication origin

+ glucose+ lactose

+ glucose- lactose

- glucose- lactose

- glucose+ lactose

CRP

CRP

repressor

repressor

RNA polymerase

transcription

Lac-Operon, Gene regulation and CAP protein


Non-induced InducedGenotypes

-gal

acto

-

sida

se

gala

ctos

ide-

perm

ease

gala

ctos

ide-

tran

sace

tyla

se

-gal

acto

-

sida

se

gala

ctos

ide-

perm

ease

gala

ctos

ide-

tran

sace

tyla

se

1. i+,z+,y+ <0.1 <1 <1 100 100 100

2. i-,z+,y+ 120 120 120 120 120 120

3. i+,z-,y+/F i-,z+,y+ 2 2 2 200 250 250

4. i-,z-,y+/F i+,z+,y- 2 2 2 250 120 120

5. i-,z-,y+/F i-,z+,y+ 250 250 250 200 250 250

6. izy /F i-,z+,y+ 200 200 200 200 200 200

Table: Production of -galactosidase, galactoside-transacetylase and galactoside-permease by haploid and heterogenote, regulator-consitutive mutants.i: regulator gene (i+: inducible; i-: constitutive). z and y: structural genes for -galactosidase and galactoside permease, resp. F: sex factor of E. coli K12. izy - deletion

of the Lac region.


r p o z y a

Ri Ra

E MIeIi

F1

G

-

1

2

3

4 4

5

678

9

Lac-Operon, Model of Nicolis and Prigogine

R – RepressorI – InducerE, M – EnzymeG – GlukoseO – Operator


( 1 )

( 2 )

( 3 )

( 4 )

( 5 )

( 6 )

( 7 )

( 8 )

( 9 )

k 1

k -1

R i R a

O cR a +O fk -2

k 2

k 3

k -3

R a + n I I i F 1

k 4 +O f O f +E+M

M+I ek -5

k 5M+I i

F 2Mk 6

k 7E F 3

R a +DR i + n G Gk -8

k 8

G+EI i +Ek 9

DRkGRkFkIRk

OkORkRkRkdt

dR

an

in

ia

cfaaia

GI88133

2211

cfaf

OkORkdt

dO22

EkOkdt

dEf 74

MkOkdt

dMf 64

EIkMIkMIkFknIRkndt

dIiieI

niaI

i I955133

EIkDRknGRkndt

dGiaG

niG

G988

.constOO cf

Mathematical formulation of theNicolis-Prigogine-Model

r p o z y a

Ri Ra

E MIeIi

F1

G

-

1

2

3

4 4

5

678

9


- 1 0 1 2 3 4 5external inducer

0

0.5

1

1.5

2

2.5

3

b-esadisotcalag

All-or-None Transition

Figure 9.2. Dependence of the -galactosidase concentration of external inducer concentration

( eI , lactose concentration). The sigmoidal shape of the curve can be interpreted as All-Or-None

Transition: for low inducer concentrations almost no enzyme is detectable, increasing inducer

concentrations lead to a switch to a -galactosidase concentration of mol21023 . .Parameters:..........

All or None Transitions

analysis of steady state while neglecting

the catabolite repression ( 0988 kkk )

sigmoidal dependence of the enzyme

concentration E on the external inducer eI .

low value 610 , high value 3103 ,

correspond to experimentally determined values

All or None Transition in dependence on the inducer,


T h e d y n a m i c b e h a v i o u r

q u a n t i t i e s k n o w n f r o m e x p e r i m e n t s : aR , 1F , , , 2k , 2k , 3k , 3k , 5k , 5k

s t o c h i o m e t r i c c o e f f i c i e n t s i n s t e p s ( 3 ) a n d ( 9 ) a r e c h o o s e n a s 2 GI nn

p a r a m e t e r s : eI , 1k , 1k , 4k , 6k , 7k , 8k , 8k , 9k

s i m p l i f i c a t i o n s : Dkk 88 81 kk 131 FkRk i

28

2322 GRkIRkOkORkR

dt

dRiiaffaa

a

ffaf

OkORkdt

dO 22

EkOkdt

dEf 74

MkOkdt

dMf 64

EIkMIkMIkFkIRkdt

dIiieia

i95513

23 22

EIkRkGRkdt

dGiai 98

28 22

r p o z y a

Ri Ra

E MIeIi

F1

G

-

1

2

3

4 4

5

678

9


Dynamic behaviour under catabolite repression

Assuming a quasi-steady state for the active repressor aR, the free operator fO , and for the

enzymes E and M, one obtains for the time dependence of the glucose concentration and of theinternal inducer:

2

322

827

2342595

1323

282

3 22ii

iie

i

ii

i

IkkGRkkk

IkkkIkkIkFk

Ik

GRkIk

dt

dI

2

322

827

23429

23

2882

82

2ii

ii

i

ii

IkkGRkkk

IkkkIk

Ik

GRkkGRk

dt

dG

For this equation system the steady state has been analysed for fixed parameters exept of varying

1k .


11

min k

M

F

1

218

min M

k

M

I e

119

min M

k

11

min k s t e a d y s t a t e s

0 . 2 3106 0 . 0 3 9 1 1 0 0 5 0 0 0 0 . 1 S t a b l e F o c u s

0 . 0 9 9 -0 . 0 0 0 2 4 8

S F +U L C ( min110T )S L C ( min300T )

0 . 0 0 0 2 4 7 -1 0 - 5

S F + U L C

0 . 2 3106 0 . 0 0 3 5 1 1 0 0 5 0 0 2 . 0 S F , n o L C

0 . 1 -0 . 0 0 0 2 4 8

U n s t a b l e F +S L C ( min1500T )

0 . 0 0 0 2 4 7 -1 0 - 5

U F + S t a b l e N o d e


0.0000250.000050.000075 0.0001 0.0001250.000150.000175 0.0002k- 1

- 4

- 3

- 2

- 1

0

1

2

goLHI iL

Steady States, Catabolite Repression


0 250 500 750 1000 1250 1500 1750Time

0

5

10

15

20

25

snoitartnecnoC

Time evolution , Catabolite Repression

0 2 4 6 8internal inducer

5

10

15

20

25

esoculg

Phase plane, Catabolite Repression

P a r a m e t e r s :1

1 min2.0 k ,1

1 min008.0 k ,

1152 min104 Mk ,

12 min03.0

k ,21

3 min2.0 Mk ,1

3 min60 k

134 min105 k ,

115 min6.0 Mk ,

115 min006.0

Mk 16

76 min103 kk ,21

8 min03.0 Mk ,118

8 min10 Mk ,

1139 min105 Mk ,

MR i 210 , MF 31 10 ,

M 310002.2


Bakterielle Genexpression mit Reportergen gusA

Quantifizierung der Regulation der Genexpression durch ein externes Signal, O2

Operon cytNOQP von A. brasilense codiert eine Cytochrome cbb3 Oxidase,die bei Wachstum und Atmung eine Rolle spielt.

Die Expression ist abhängig vom Sauerstoffgehalt.

Die Expression von cytN wurde mittels der Fusion von cytN-gusA gemessen.

Modell

kPDPXdt

dP

DSDSXdt

dS

DXXdt

dX

in

X – Biomasse-KonzentrationS – Konzentration der KohlenhydratquelleSin – Konz. der zugefütterten KohlenhydrateP – Konzentration des FusionsproteinsD – Verdünnungsrateµ - spezifische Wachstumsrate – spezifische Kohlenstoffverbrauchsrate – spezifische Expressionsrate des Fusionsproteinsk – Abbaurate des Fusionsproteins


Bakterielle Genexpression mit Reportergen gusA

VorgegebenesSauerstoffprofil

Kohlenstoffquelle,Hier:Malat

Verdünnungsrate

Gus Aktivitätß-Glucuronidase

als Maß fürcytN-Expression

Documents

Edda Klipp, Humboldt-Universität zu Berlin Modeling of Gene expression. : Gene mRNA Proteins Cell processes Central Dogma of Molecular Biology Transcription