Chemotaxis: Another go

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

Tumbling via CheY

CheA-P

RmR

RmR

CheBPCheB

S

CheAPCheA

RmR

CheBPCheB

S

CheAPCheA

Use MM kinetics to describe each of the enzyme reactions

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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’

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are needed to see this picture. [R]Rate of reaction per unit CheBP concentration

[S]0.0001 0.001 0.01 0.1

[Rm] = Methylated Receptor

[CheA-P] ≈ tumbling frequency

[CheB-P]

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.

BioNetSBioNetS

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Easy to use

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

are needed to see this picture.CheZ

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