Team:ZJU-China/Modeling

1. The Whole Genetic Pathways

ODE equations:

Before recombination:

Formular.1

After combination, if combination succeeds.

Formular.2

Formular.3

After putting in Ara

Formular.4

Formulary:

Take GFP for example

Name	description
mgfp	The number of GFP mRNA
pgfp	The number of GFP protein
Npla	The number of plasmid
αgfp	The maximal transcription rate of GFP
α0gfp	The leak of the promoter
αmgfp	The degradation rate of mRNA
βmgfp	The translate rate of mRNA
βpgfp	The degradation rate of GFP protein

2. Recombination

description:

In this part, what we want to do is to find out the probability of the recombination of gene of interest through simple molecular dynamics simulation. Although this simulation is quite simple, it

certainly can tell us something right in some aspects within a certain accuracy.

The most important things for simulation are initial conditions and boundary conditions. Next, I will describe the initial conditions and boundary conditions in detail.

Initial conditions:

What is initial condition? Simply, initial condition is the condition when your simulation starts. More simply, initial condition is that you know every molecular coordinate as well as velocity if needs.

Boundary conditions:

What is boundary condition? E coli has a boundary, when the molecule runs out of its boundary, we should adjust it back in the E coli. In this simulation, periodic boundary condition is used.

Some basic biology facts and simulation parameter choice:

figure.1 E.coli cell

1. As shown above, the shape of E coli is similar to a cylinder. So in our simulation, we regard E coli as a cylinder whose radius is 0.5 micrometer, height is 2 micrometer.
2. 2.By looking up some online information, we find the average velocity of protein in cells is about 10 , we estimate the average velocity of gene of interest fragment is the same order of magnitude of the protein for their mass is the same order of magnitude.
3. 3.E coli replicate its chromosome in 40 minutes, the proceed rate of replication fork is about 10^5 bp/min. A fragment about 1kb needs 0.6s.

results

We have simulate this for three times.The results are showed above,Which is consistent with our wet lab result.Although our simulation is quite simple,the result is good.

3. Bistable Switch

ODE equtions：

Formular.5

Formular.6

Formulary:

Name	description
[ ]	[ ] stands for the concentration
kc	Inversion rate constant
kdi	dissociation equilibrium constant of int dimer-recombination site complex
ki	dissociation equilibrium constant of int-int dimer
kdix	dissociation equilibrium constant of int-xis dimer complex on a recombination site
αset	The transcription rate of input set
αreset	The transcription rate of input reset
αI	The maximal transcription rate of int
αX	The maximal transcription rate of xis
γI	The degradation rate of int
γX	The degradation rate of xis
kd	The dissociation equilibrium constant

figure.2The response to set input

Reference

[1]Santos, C. N. S. & Yoshikuni, Y. Engineering complex biological systems in bacteria through recombinase-assisted genome engineering. Nature Protocols 9, 1320-1336, doi:10.1038/nprot.2014.084 (2014).

[2]Tyo, K.E., Ajikumar, P.K. & Stephanopoulos, G. Stabilized gene duplication enables long-term selection-free heterologous pathway expression. Nat. Biotechnol. 27, 760–765 (2009).

[3]Bentley, W.E. & Quiroga, O.E. Investigation of subpopulation heterogeneity and plasmid stability in recombinant Escherichia colivia a simple segregated model. Biotechnol. Bioeng. 42, 222–234 (1993).

[4]Paulsson, J. & Ehrenberg, M. Noise in a minimal regulatory network: plasmid copy number control. Q. Rev. Biophys. 34, 1–59 (2001).