Introduction

We propose post-integration conditions, rationally simplify the complex situation, and split the whole process into a series of chemical reactions. Assuming that intervals between two reactions obey exponential distribution, we use the Gillespie algorithm [1] to calculate the changes in various substances in the system with reference to the Dynamics of the Brusselator [2]. The ideas and methods of this model have strong promotion prospects and adaptability. Our model demonstrates the necessity of using the recombinase(rec) system，the improvement effect of the system after adding the pathways expressing RDF-inhibitor and rec-inhibitor in turn, and the robustness of the model .The experimental team verified some assumptions and results of the model and selected materials according to the parameters of the model.

What kind of modeling is being done and what information it will provide?
Model Interpretation
We use the Gillespie algorithm to calculate the changes in various substances in the system

What assumptions were made and why?
Assumptions One of our assumptions is that the length of the interval between consecutive reactions obeys an exponential distribution so that we can use the Gillespie algorithm [1] to calculate the changes in various substances in the system.

What kind of data was used to build/assess the model Parameters
(a) Expression rate of each gene (production rate of related proteins, consumption rate of each protein.
(b) The computing coefficient of each reaction’s rate.

How the model results affected the project design and development?
Our model shows the improvement effect of the system after adding the pathways expressing RDF-inhibitor and rec-inhibitor in turn, so as to provide guidance to the experimental team. Guide for Experiment

1. How impressive is the modeling?
做了一个概念验证，并在指导实验方向和通路设计等方面发挥了极为关键的作用

2. Did the model help the team understand a part, device, or system?
Of course we did Guide for Experiment

3. Did the team use measurements of a part, device, or system to develop the model?
实验分布验证了同路的可行性，以及大致确定了参数量纲

4. Does the modeling approach provide a good example for others?
The ideas and methods of this model have strong promotion prospects and adaptability. The codes are showed on our wiki , you can copy and run in you Matlab convenient.

Symbol System

Symbol	Meaning
Grec	Gene of recombinase
rec	Recombinase [3]
GsynNotch-TEV	SynNotch-TEV gene
synNotch	Active synNotch [4] on endomembrane system. In our model synNotch is synNotch-TEV
GTetR	Gene of operon TetO’s repressor proteins [5]
TetR	TetO operon’s repressor proteins
tetO	Operon which can be repressed by TetR
TetOR	Binary complex of operon TetO and repressor proteins TetR
TEV	synNotch’s intracellular domain which is falling off by shearing, an enzyme can divide TetOR binary complex while separate TetR and degrade it [6].
RDF	Reverse recombination factor, which can inverse DNA sequence between sites and make it back to the morphology not affected by rec [7].
Ts	Target signal
Gx	Gene of a protein x
\emptyset	Degraded material
U	Unconsidered substance

Assumptions

Tips: Click the button named Aim.

1. Normal protein expression is a reaction which satisfies the post-integration conditions. All reactions which satisfy post-integration conditions can be viewed as one single chemical reaction. part1 . Aim>>To simplify calculation.Model Interpretation

2. Different reactions in cells occur independently. Aim>>To determine when the next reaction occurs and which reaction occurs.

3. The length of the interval between consecutive reactions obeys an exponential distribution. Aim>>To determine when the next reaction occurs and which reaction occurs.

4. The degradation of protein can be viewed as linear degradation. Aim>>To simplified calculation，this model is also compatible with other methods of calculating degradation for example Michaelis-Menten equation.

5. The repressor effect of the protein can be described by the Hill equation. Aim>>To calculate the expression of rec.

Parameters

c21=5;	% TetR Gene expression
c22=0.001;	% TetR degradation
c23=200;	% generate dipolymer
c24=0.003;	% TEV causes decomposition of dipolymer
c25=0.000005;	% self decomposition of dipolymer
NTetO=5;	% Hill coefficient
Swichpoint=2000;	% parameter to the hill equation
c31=8;	% rec's Maximum gene expression rate
c32=12;	% RDF-inhibitor's Maximum gene expression rate
c33=0.01;	% rec degradation
c34=0.01;	% rec-RDF-inhibitor degradation
c35=2;	% rec-inhibitor Gene expression（No rec-inhibitor can be set to 0）
c36=0.1;	% rec-inhibitor in combination with rec
c37=200;	% The noise reduction reaction of rec
c41=0.0000006;	% rec reverse reaction
c51=7;	% Turn on GENE expression downstream
c52=0.01;	% RDF degradation
c53=200;	% rec-inhibitor in combination with rec
c61=0.0000005;	% rec-RDF reverse reaction

Guide for Experiment

1. By improving the cell culture environment, the noise in signal conversion process could be reduced by more than 10 percent. Model Interpretation part4

2. Our model shows the improvement effect of the system after adding the pathways expressing RDF-inhibitor and rec-inhibitor in turn, so as to provide guidance to the experimental team. Model Interpretation part5.

3. We determined the design parameters to simulate the ideal results and verify the feasibility of the experimental design. Model Interpretation part6.

References

[1] Gillespie, D. T. Exact Stochastic Simulation of couple chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977).

[2] Ault, S. & Holmgreen, E. Dynamics of the Brusselator. Math 715 Proj. (Autumn 2002) 1–17 (2003). doi:10.1103/PhysRevE.61.2361

[3] Stark WM. 2014. The serine recombinase. MicrobiolSpectrum2 (6):MDNA3-0046-2014.

[4] Morsut, L. et al. Engineering Customized Cell Sensing and Response Behaviors Using Synthetic Notch Receptors. Cell 164, 780–791 (2016).

[5] Ramos, J. L. et al. The TetR Family of Transcriptional Repressors The TetR Family of Transcriptional Repressors. Microbiol. Mol. Biol. Rev. 69, 326–356 (2005).

[6] Phan, J. et al. Structural basis for the substrate specificity of tobacco etch virus protease. J. Biol. Chem. 277, 50564–50572 (2002).