Chemotaxis: Another goChemotaxis: Another go
Chrisantha Fernando
Systems Biology Centre
Birmingham University
Chrisantha Fernando
Systems Biology Centre
Birmingham UniversityQuickTime™ and a
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= Active Tar
= Methyl group
= Inactive Tar
TUMBLE
Now add Chemoattractant
RUN
CheY-P
CheY
CheB-P
CheB
Motor
CheA
RmR
CheBPCheB
S
CheAPCheA
Use MM kinetics to describe each of the enzyme reactions
i.e.QuickTime™ and a
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RmR
CheBPCheB
S
CheAPCheA
€
d[CheBP]
dt=
V2[CheAP][CheB]
K2 +[CheB]−
V2 '[CheBP]
K2 '+[CheBP]
€
d[Rm]
dt= −
V3[CheBP][Rm]
K3 +[Rm]+
V3 '[R]
K3 '+[R]
€
d[CheAP]
dt=
V1[Rm][CheA]
K1 +[CheA]−
V1'[CheAP]
K1'+[CheAP]
€
d[CheAP]
dt=
V1
1+ S[ t ]
KS
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥[Rm][CheA]
K1 +[CheA]−
V1'[CheAP]
K1'+[CheAP]€
Vmax I =Vmax
1+[Inhibitor]
K i
⎡
⎣ ⎢
⎤
⎦ ⎥
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Initial values
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Parameters
Methylation and De-methylation is ‘Saturated’
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture. [R]Rate of reaction per unit CheBP concentration
0.001
0.01 0.1 1.0
[Rm] = Methylated Receptor
The limit of perfect adaptationoccurs when new Rm can no longer be produced
[S]0.0001
0.001 0.01 0.1
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Non-saturated methylation and demethylation
No-perfect adaptation.
The First (wrong) ModelThe First (wrong) Model
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Available at…http://www.pdn.cam.ac.uk/groups/comp-cell/Publications.html
Moving on… Moving on…
We can go through points that were confusing again…
It is important you understand the principles of how to model these systems.. Mass action kinetics MM kinetics Inhibition (competitive and non-competitive) Saturation of enzymes
We can go through points that were confusing again…
It is important you understand the principles of how to model these systems.. Mass action kinetics MM kinetics Inhibition (competitive and non-competitive) Saturation of enzymes
Stochastic ModelingStochastic Modeling
So far we have been doing deterministic modeling. Stochastic models consider individual molecules,
undergoing discrete reaction events. These models diverge when particle numbers are
low. By the end of this course you will be able to
model both using ODEs and stochastic modeling, all the circuits I’ve talked about previously, and more. For now, familiarize yourself with bionetS.
So far we have been doing deterministic modeling. Stochastic models consider individual molecules,
undergoing discrete reaction events. These models diverge when particle numbers are
low. By the end of this course you will be able to
model both using ODEs and stochastic modeling, all the circuits I’ve talked about previously, and more. For now, familiarize yourself with bionetS.
Here is a paper written using the tool…
Here is a paper written using the tool…
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Lets start with some simple chemical networks…
Lets start with some simple chemical networks…
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QuickTime™ and aTIFF (LZW) decompressor
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QuickTime™ and aTIFF (LZW) decompressor
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RCheZQuickTime™ and aTIFF (LZW) decompressor
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R
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Rm
Example of a Saturated Enzyme (CheZ) acting to methylate R