OVERVIEW
Huge scale of our experimental design based firmly on
modelling results, for instance, the optimal proportioning of synthetase, the
modification on repressilator and so on.Modelling instruction pulled through the
whole project for less defect trials and more efficient variable adjustment.
1.Why we did this model?

1) Synthetic genetic circuits work comparatively to a higher degree resemble electric circuits. In especial, repressilator is not only an artificial system which kinetic parameters and stability of the system remain to be determined, but also a dynamic and complicated loop that has those intrinsic regulation on its components themselves. So we need to connect it smoothly with Melatonin sybthesis.

2) Human work and rest time is about 24 hours, which is quite beyond the results shown in the reference. So we ought to elongate its period as long as possible.

3) We have no reason to believe that cells’ repressilator will start to work at the same time. So in a cluster of cells, generally, the time to reach expression peak value is different from each other, and we can easily imagine that the average expression of cells must be a random noise. The only solution to this is to find a way to synchronize their oscillation and make sure they are stable.
2.How was our model constructed?

1) We derived the system step by step with ordinary differential equations. Secondly, we added quorum sensing part to the original equations.

2) We estimated the diffusion time to analyze the behavior of quasisteadystate. With the derivations above, we got the final equations to describe our system.

3) Different situations of delayed system were analyzed by changing the strength of quorum sensing.

4) A numerical simulation of 900 cells was ran to see the expression of Melatonin by linking it with CFP comparing our experimental result.
3.What did the modeling tell us?

Problem(1) is related to our modeling part of Melatonin. It can give us a possible way to make sure the concentration of NAS is stable. Problem(2) is simple. According to the modeling result, we just need to decrease protein lifetime or increase mRNA lifetime. Approximately, we may be able to elongate the period to 1.53 hours. Furthermore, if we can have 4 to 5 times mRNA lifetime, we may hopefully reach 12 hours. As for problem(3), we would have to enhance the strength of quorum sensing. A simple way is just to make those cells feel a crowded environment.
1.Why we did this model?

1） Extra energy consumption of heterologous expression is not conducive to cell growth, which may lead to unpredictable sideeffects. Therefore, we ought to select the best promoter combination so that we could make best use of E.coli’s energy consumption to make sure cells won’t be so ‘tired’.

2） Different promoters come with different rate parameters. Supposing that we measured all kinds of combination, we would be able to see different production rate of Nacetylserotonin. Only in this way, a complex enzyme reaction system can have a costeffective production rate.
2.How was our model constructed?

1) We introduced traditional MichaelisMenten theory.

2) It’s poor when it is applied on a complex enzyme reaction system since the byproduction’s starting concentration is zero instead of several magnitudes larger than the enzyme.

3) We improved the theory by making the reaction fully reversible. The comparison in our modeling showed the difference.

4) We even figured out a possible way to measure the relative rate parameters in each reaction, since our new theory require much more parameters than the traditional theory. At last, a numerical ideal result is shown.
3.What did the modeling tell us?

The modeling part tells us the possible result of the complex enzyme reactions in cellA. Apparently, numerically solving a 12dimension enzyme equations’ result is far better than traditional MichaelisMenten equations. With different promoters, To be honest, some parameters are still hard to measure, but we believe that we would get the result of different kind of promoter combination if we successfully measured those parameters.
1.Why we did this model?

1) Modeling results of repressilator indicated that faster translation is helpful to the period elongation, which is necessary to mimic the process of melatonin production in human.

2) RBS sequence is a main determinant of translation rate, so we decided to design some RBS with higher strength.

3) Random mutation of RBS will generate a huge library, which will increase our workload grandly with numbers of useless mutations.

4) Bioinformatics method can predict the sequence of a synthetic RBS with a target translation initiation rate on a proportional scale, without too many experiments.
2.How was our model constructed?

1) We designed our RBS via the RBS calculator tools (https://salislab.net/software/doForwardRBS).

2) The RBS Calculator is based on the theory that build on previous work that characterized the free energies of key molecular interactions involved in translation initiation and on measurements of the sequencedependent energetic changes that occur during RNA folding and hybridization.
3.What did the modeling tell us?

We designed a set of RBS with different strength of predicted translation rate, and chose three of them, named P1, P2, P3, which were predicted to be 5、10、50 times stronger than B0034 respectively. And then, we did some experiments for characterization.
Name of Parameter  Meaning  Value  Name of Parameter  Meaning  Value 

O_{u}  Concentration of unbound operator  α  dimensionless maximum production rate  216  
O_{b}  Concentration of unbound operator  α_{0}  Dimensionless leakiness  α/1000  
P  Concentration of protein  i_{max}  Total cell number  1 or 20 or 900  
K  Hill constant  κ  dimensionless maximum contribution to CI transcription in the presence of saturating amounts of AI  20  
α_{leak}  leakiness  j_{s}  flux through the membrane  
α_{u}/α_{b}  Promoter fire rate  P_{s}  a number depending on both the membrane and the molecule whose permeation  
μ  Volume growth rate  A  Cell surface area  ~π μm^{2}  
m  Concentration of promoters  V  Cell volume  ~1 μm^{3}  
β  Ratio of protein decay rate and mRNA decay rate  0.05  S_{e}  Extracellular Ai signal concentration  
r_{0}  Stable point  η  Diffusion constant  2.0  
k_{0}  Dimensionless degradation rate constant of S_{i}  1.0  Q  Controlling parameter to represent cell density or strength of quorum sensing  0~1.0 
k_{1}  Dimensionless synthesis rate constant of S_{i}  0.01  n  Hill coefficient  2.0 
τ  Dimensionless delay time of diffusion through membrane  4  C_{E}  Concentration of enzyme  
C_{E0}  Concentration of total enzyme  C_{S}  Concentration of substrate  
C_{p}  Concentration of product  K_{cat}  turnover number  
K_{M}  Michaelis constant  V(part 2)  Reaction velocity  
k_{1},k_{1},k_{2},k_{2}(part 2)  Rate constant  K_{eq}  Chemical equilibrium constant 