Model 3:
Fatty acid transport velocity modeling under condition of fadL membrane protein:
The model is based on the idea of Michaelis-Menten kinetic theory . We consider the channel proteins as a kind of enzyme and assume the reaction time of fatty acid passing through the channel to be zero. The mathematical model is showed as follow :
The figure below illustrates overview of the genetic circuit. Crucial elements and their relations are cited in the figure.
We can give a further explanation to the zero rate of change of the with time that the concentration of FadL channel protein remains the same at each instance moment. Accordingly, the model is rational in its biological meanings.
What we really focus on is the changing rate of the fatty acid “inside” the cell membrane. Because it is the actual effective input of the genetic system we designed.
3. Parameter
D.Boolean Network
Our Boolean network is illustrated by figure 5.6 and 7
Fig 5 Graph of Boolean network
A: Fatty acid out A(t+1) = A(t)=1
B: Fatty acid in B(t+1) = D(t) and A(t) = D(t)
C: Acyl-CoA C(t+1) = B(t) and E(t)
D: fadL D(t+1) = not F(t)
E: fadD E(t+1) = not F(t) = D(t+1)
F: fadR F(t+1) = not C(t)
G: PKEK G(t+1) = not F(t)
Fig 6 code number of Boolean network nodes and its Boolean function
Following table T1 illustrates all combination of initial conditions of each node.
Table 1 All combination of initial conditions of each node
Note that A(Fatty acid out) should always be 1, because of an overabundance of the quantity of fatty acid outside the membrane. Besides, the G(PKEK) should be 0 initially because there should not have any product in initial stage. We have simulated all 2^5=32 combination of initial conditions,which represent the functional dynamics of the circuit, and we will map the dynamics characteristics to the experiment result after wet lab team finish the experiment.The mapping may have some insight about the simulated system,such as the oscillation,periodicity, and the relative dominant factor in the system.Following figure 6 shows a example of dynamics of Boolean network. From top to down,that is,from initial condition to final state,the states change through time as discrete step showing the oscillation and periodicity of the system.
A B C D E F G
initial condition 1 0 1 1 0 0 0
1 1 0 1 1 0 1
1 1 1 1 1 1 1
1 1 1 0 0 0 0
1 0 0 1 1 0 1
1 1 0 1 1 1 1
1 1 1 0 0 1 0
1 0 0 0 0 0 0
1 0 0 1 1 1 1
1 1 0 0 0 1 0
1 0 0 0 0 1 0
final state 1 0 0 0 0 1 0
Fig 7 a example of dynamics of Boolean network
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