Download - Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation
![Page 1: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/1.jpg)
Lecture 3: Models of gene regulation
![Page 2: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/2.jpg)
DNA
Replication
RNA ProteinTranscription Translation
![Page 3: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/3.jpg)
Bacterial growth on sugars
maxmax
Batch reactor:
( ) bacterialgrowth
1substrateconsumption
Substrate metabolised by a Michaelis Menten enzyme:
( ) , enzyme concentrationM
dCS C
dtdS dC
dt Y dt
SS
S K
How does the cell know which enzymes to express?
![Page 4: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/4.jpg)
hours
[conc.]
glucose lactose
Bacterial growth on two substrates:
Two things to notice:
1.Glucose metabolized before lactose
2.Lag between glucose and lactose growth phases
[Monod, Thesis 1942]
![Page 5: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/5.jpg)
• Monod realized this was operating like a genetic “switch”– Genes required for lactose metabolism
turned off in presence of glucose– But turned on in absence of glucose and
presence of lactose
Input/Ouput relation: Lactose
+ -
Glucose+ - -- + -
![Page 6: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/6.jpg)
crp
lacI lacZ lacY lacA
Three main components:
1. Genes: encode protein sequence
2. Promoters: RNAP binding sites
3. Operators: Transcription factor binding sites
lacZ
The lac Operon
![Page 7: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/7.jpg)
The Prokaryotic Promoter
NNNNTTGACANNNNNNNNNNNNNNNNNTATAATNNN
-35 -10
17 bp
• The promoter is a binding site for the protein RNA polymerase, responsible for transcription
![Page 8: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/8.jpg)
DNA
Replication
RNA ProteinTranscription Translation
Transcription factor (protein that repress or activate)Rate usually depends on transcription factor
![Page 9: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/9.jpg)
Gene regulation functions(rate of transcription as a function of factors or regulators)
21
12
2
1
21
(
( )
(
,
)
)n
repression n n
n
n
n
activation n n
nn
n
n
KV R A
K RThe ef
V R R A
fect of two regulators
R
RV R A
K R
K R
K
K R
![Page 10: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/10.jpg)
Dynamics: single regulated gene
deg, 1 2
model of protein conc.:
accumulation=- degradation+ synthesis
( , ,...)pp p
A
dCk C AV R R
dt
![Page 11: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/11.jpg)
Single regulated gene(U= protein conc or expression level)
1
.
Steady state: . ( )( )
Piecewise linear model: ( )
0,Steady state:
/ ,
n
n n
n n
s sn n
s
dU KkU A
dt K R
AK AU U H K R
k K R k
dUkU AH K R
dtR K
UA k R K
![Page 12: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/12.jpg)
Graphical analysis of steady states and stability
sU
, repressor concentrationRR K
U
![Page 13: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/13.jpg)
Mutual inhibition network of transcription factors
11 1 1 1 2
22 2 2 2 1
( )
( )
dRk R AH R
dtdR
k R A H Rdt
R1R2
After eliminating the mRNA variables
![Page 14: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/14.jpg)
Nullclines
1R
2R
2 2/A k
2 1R
2R
1
1 1/A k
1 0dR
dt2 0
dR
dt
![Page 15: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/15.jpg)
Phase plane
2R
2 2/A k
2
1
1 1/A k1R
1 1 2 2 1 23 Steady states: ( / ,0), (0, / ), ( , )A k A k
![Page 16: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/16.jpg)
Domain of bistability
For both genes: maximal expression level should be able to repress the repressor
1 22 1
1 2
, .A A
k k
1 1A k
2 2A k
2
1
HW: Sketch the phase planes for the 4 different regimes in the model
Expression of both
R1 off
![Page 17: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/17.jpg)
![Page 18: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/18.jpg)
Mutual repression circuit
![Page 19: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/19.jpg)
Toggling the switch(transients: IPTG affects R1, temp affects R2)
![Page 20: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/20.jpg)
Parametric dependenceof steady states
(GFP- flourescence protein)
![Page 21: Lecture 3: Models of gene regulation. DNA Replication RNA Protein TranscriptionTranslation](https://reader030.vdocuments.net/reader030/viewer/2022032702/56649cd75503460f9499f71b/html5/thumbnails/21.jpg)
Parametric dependenceof steady statesindividual cells