In this part of modeling work, we mainly center on constructing some crucial circuits in our regulating network, including the light responding upstreams and downstream movement control mechanisms, as well as some middle wares.

The aim of these construction work is to know about the how the messaging delivering system work as a whole, how does the different signals effect each other in the final output level.

Introduction

We've constructed several modeling skeleton in Matlab Simbiology Package, they are:

1. DgrA/DgrB Circuit in regulating the flagellum movement
2. HfiA/HfsJ Circuit in regulating the genesis of composing substances holdfast.
3. The DNA Inverse Circuit which may change the direction in which promoter works.
4. Light Sensors including Blue, Red and Green.

Network

DNA Inverse Enzyme

Introduction

In this model, our aim is to verify that according to use of a recombinase, we can control the relative expressing level of two different kind of Protein.

This is a small picture illustrating its basic condition:

Equations

$ \frac{d(repressor)}{dt} = \frac{K_{repressor} - Vm_{rep} \cdot DNA^n_{rep}}{Kp_{rep}+DNA^n_{rep}} - K_{bind}\cdot lac\cdot repressor$

$ \frac{d(DNA)}{dt} = -\frac{Vm_{rep}\cdot DNA^n_{rep}}{Kp_{rep}+DNA^n_{rep}}$

$ \frac{d([repressor-DNA])}{dt} = \frac{Vm_{rep}\cdot DNA^n_{rep}}{Kp_{rep}+DNA^n_{rep}}$

$ \frac{d([lac-repressor])}{dt} = K_{bind}\cdot lac\cdot repressor$

$ \frac{d(recombinase)}{dt} = K_{recom}\cdot DNA$

$ \frac{d(PromoterDir1)}{dt} = -\frac{Vm_{cata}\cdot PromoterDir1}{Km_{cata}+PromoterDir1}$

$ \frac{d(PromoterDir2)}{dt} = \frac{Vm_{cata}\cdot PromoterDir1}{Km_{cata}+PromoterDir1}$

$ \frac{d(Protein1)}{dt} = K_{forward}\cdot PromoterDir1$

$ \frac{d(Protein2)}{dt} = K_{backward}\cdot PromoterDir2$

Results

DgrA/DgrB Circuit

Equations

$\frac{d([cdiGMP-DgrA])}{dt} = \frac{(Ka \cdot [cdiGMP] \cdot DgrA - Kf \cdot [cdiGMP-DgrA] \cdot FliL - [Kd_{cdiGMP-DgrA}] \cdot [cdiGMP-DgrA])}{cell}$

$\frac{d([cdiGMP-DgrB])}{dt} = \frac{(Kb \cdot [cdiGMP] \cdot DgrB - [Kd_{cdiGMP-DgrB}] \cdot [cdiGMP-DgrB])}{cell}$

$\frac{d(FliL)}{dt} = \frac{(-Kf \cdot [cdiGMP-DgrA] \cdot FliL + Kg_{FliL})}{cell}$

$\frac{d([cdiGMP-DgrA-FliL])}{dt} = \frac{(Kf \cdot [cdiGMP-DgrA] \cdot FliL)}{cell}$

Results

HfiA/HfsJ Circuit

The binding affinity and cellular concentrations of HfiA and HfsJ are tuned such that this regulatory system is responsive to small changes rather than robust to large changes. This prediction is consistent with a highly responsive and sensitive regulatory system.

So the block is clear. Upstream promoter Expression Rate $\rightarrow$ HfiA $\rightarrow$ HfsJ $\rightarrow$ Catalyzing Rate

Equations

$\frac{d(P_{HfiA})}{dt} = -\frac{Vm_{HfiA} \cdot X^n_{HfiA}/(Kp_{HfiA}+X^n_{HfiA})}{cell}$

$\frac{d([X-P_{HfiA}])}{dt} = \frac{Vm_{HfiA} \cdot X^n_{HfiA}/(Kp_{HfiA}+X^n_{HfiA}) - Kd_{c1 }cdot [X-P_{HfiA}]}{cell}$

$\frac{d(mRNA_{HfiA})}{dt} = \frac{Ktc_{HfiA} \cdot P_{HfiA} - Kd_{mRNA_{HfiA}} \cdot mRNA_{HfiA} }{cell}$

$\frac{d(HfiA)}{dt} = \frac{Ktl_{HfiA} \cdot mRNA_{HfiA} - Kd_{HfiA} \cdot HfiA - Kc \cdot HfiA \cdot HfsJ}{cell}$

$\frac{d(P_{HfsJ})}{dt} = \frac{-Vm_{HfsJ} \cdot P_{HfsJ}^n{_{HfsJ}}/(Kp_{HfsJ}+P_{HfsJ}^{n_{HfsJ}})}{cell}$

$\frac{d([CtrA-P_{HfsJ}])}{dt} = \frac{Vm_{HfsJ} \cdot P_{HfsJ}^n{_{HfsJ}}/(Kp_{HfsJ}+P_{HfsJ}^{n_{HfsJ}}) - Kd_{c2 }cdot [CtrA-P_{HfsJ}]}{cell}$

$\frac{d(mRNA_{HfsJ})}{dt} = \frac{Ktc_{HfsJ} \cdot [CtrA-P_{HfsJ}] - Kd_{mRNA_{HfsJ}} \cdot mRNA_{HfsJ}}{cell}$

$\frac{d(HfsJ)}{dt} = \frac{Ktl_{HfsJ} \cdot mRNA_{HfsJ} - Kd_{HfsJ} \cdot HfsJ - Kc \cdot HfiA \cdot HfsJ - Kf \cdot HfsJ \cdot Sub-Kr \cdot EzCom + Kcat \cdot EzCom}{cell}$

$\frac{d([HfiA-HfsJ])}{dt} = \frac{Kc \cdot HfiA \cdot HfsJ}{cell}$

$\frac{d(Sub)}{dt} = \frac{-Kf \cdot HfsJ \cdot Sub-Kr \cdot EzCom}{cell}$

$\frac{d(Pro)}{dt} = \frac{Kcat \cdot EzCom}{cell}$

$\frac{d(EzCom)}{dt} = \frac{Kf \cdot HfsJ \cdot Sub-Kr \cdot EzCom - Kcat \cdot EzCom}{cell}$

Results

Others

Link to our project files