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Introduction System Modeling Lab note Result Reference

4C3leak switch

We modeled our 4C3 leak switch as deterministic ODE system.

Modelling

Assumption

1.We treated DNA as continuous variabl, since there could be hundreds of plasmid in one E.coli (multicopy plasmid). There are 32 kinds of variables that stand for DNA concentration corresponding to their different internal states.

2.We assumed that cre recombinase operate as tetramer, and other recombinase as dimer (but this seems not to be relevant).

3.We assumed that association and dissociation of DNA recombinase to DNA is sufficiently fast so that equilibrate in the timescale of the whole switch.

4.We ignored the reverse reaction of DNA recombinase because we used irreversible sequence (lox66, lox71 etc).

Variable

Basically, "pn" denotes for protein concentration and "rn" denotes for mRNA concentration

p1,p2,p3,p4 : concentration of 4 recombinase protein

r1,r2,r3,r4 : concentration of 4 recombinass mRNA

u1,u2,u3,u4 : concentration of input mRNA

pc,rc : concentration of cre recombinase protein and mRNA

ps,rs : concentration of SP6 polymerase protein and mRNA

Parameters

k0 : mRNA translation rate

k1 : protein degradation rate

k2 : mRNA translation rate

k3 : cre protein degradation rate

l0 : transcription speed per unit concentration of RNA polymearase

l1 : mRNA degradation rate

l2 : cre mRNA degradation rate

K : recombinase binding constant

v : recombinase reaction rate

pT7 : concentration o T7 polymerase

p : terminator leak probability

Equations

Methods

We used our original python program (4 th order explicit Runge-Kutta algorithm) to solve thess equations.

Results

We input signal 1,2,4 and simulated the time evolution of the system.

The time course of DNA concentration

The time course of mRNA concentration. Note that the output of this system is not protein but mRNA.

Discussion

It is confirmed that the system works as expected with a certain combination of parameters.

In addition, we changed many parameters, especially,l0,v(whose values are unclear) and p(leakiness of terminator) , to see whether the device is able to operate within a large part of parameter space.

As a result, the circuit can function correctly within the range of 0.001< p < 0.1, 0.001 < v <1.0, 0.01 < l0 < 1.0 , demonstrating its robustness. This robustness may come from the assumption that DNA recombination is irreversible, which is supported by our design of the system.

conclusion

The correct operation of the switch was confirmed. By changing parameter exponentially, the robustness of the system was shown.

MS2 phage infection

Whole system

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