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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:
- DgrA/DgrB Circuit in regulating the flagellum movement
- HfiA/HfsJ Circuit in regulating the genesis of composing substances holdfast.
- The DNA Inverse Circuit which may change the direction in which promoter works.
- Light Sensors including Blue, Red and Green.
Networks
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
$$ \frac{d(repressor)}{dt} = K_{repressor} - Vm_{rep}\cdot DNA^n_{rep}/(Kp_{rep}+DNA^n_{rep}) - K_{bind}\cdot lac\cdot repressor$$ $$ \frac{d(DNA)}{dt} = -Vm_{rep}\cdot DNA^n_{rep}/(Kp_{rep}+DNA^n_{rep})$$ $$ \frac{d([repressor-DNA])}{dt} = Vm_{rep}\cdot DNA^n_{rep}/(Kp_{rep}+DNA^n_{rep})$$ $$ \frac{d([lac-repressor])}{dt} = K_{bind}\cdot lac\cdot repressor$$ $$ \frac{d(recombinase)}{dt} = K_{recom}\cdot DNA$$ $$ \frac{d(PromoterDir1)}{dt} = -Vm_{cata}\cdot PromoterDir1/(Km_{cata}+PromoterDir1)$$ $$ \frac{d(PromoterDir2)}{dt} = Vm_{cata}\cdot PromoterDir1/(Km_{cata}+PromoterDir1)$$ $$ \frac{d(Protein1)}{dt} = K_{forward}\cdot PromoterDir1$$ $$ \frac{d(Protein2)}{dt} = K_{backward}\cdot PromoterDir2$$
Results
DgrA/DgrB Circuit
Introduction
The concentration of c-di-GMP is varying, and for our experiment we will promote its expression to inhibit rotation of flagella. It will bind to DgrA and DgrB. The resulting complex will have two routes to go: one is the [c-di-GMP&DgrA] complex which will inhibit FliL, a protein bound to the membrane playing a key role in rotation of flagella. And the other route is that the DgrB will directly affect the rotation of the flagella.
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
Introduction
Ref: A Cell Cycle and Nutritional Checkpoint Controlling Bacterial Surface Adhesion
In this paper, author describes a novel regulatory mechanism by which the C.c. bacterium integrates cell cycle and nutritional signals to control development of an adhesive envelop structure known as holdfast.
They discovered a novel inhibitor of holdfast development. HfiA, that is regulated downstream of lovK-lovR. They also discovered a bio-synthesis related gene named HfsJ. And the suppressing mutations in HfsJ attenuate the HfsJ-HfiA interaction.
These results support a model in which HfiA inhibits holdfast development via direct interaction with an enzyme required for holdfast biosynthesis
In conclusion, author says: We demonstrate that the predicted glycosyltransferase, HfsJ, is a required component of the holdfast development machinery and that residues at the C-terminus of HsfJ mediate a direct interaction with HfiA, leading to a post-translational inhibition of HfsJ.
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
