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

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 : k1 :

unit value meaning k0 1/s 0.1 mRNA translation speed k2 1/s 0.05 mRNA translation speed for external mRNA k1 1/s 0.0002 protein degradation constant k3 1/s 0.02 cre protein degradation constant l1 1/s 0.003 mRNA degradation constant l2 1/s 0.01 cre mRNA degradation rate l0 1/(s*uM) 0.05 translation speed per unit concentration o polymerase K uM^2 0.0001 binding constants of DNA recombinases pT7 uM 0.6 concentration of T7 promoter p unitless 0.01 terminator leak probability v 1/s 0.01 recombinase turnover rate

Equations

Methods

We used original python program (Runge-Kutta) to solve this equation.

Results

MS2 phage infection

Whole system

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