Sudoku

Introduction System Modeling Lab note Result Reference

4C3leak switch

We modeled our 4C3 leak switch as ODE system.

Modelling

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

Besides, 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 corresponding to their different internal states.

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

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

Methods

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

Results

Discussion

conclusion

MS2 phage infection

Whole system

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