Team:HIT-Harbin/Modeling

For our perspectives, there are some significant issues and stuffs we can never neglect for the modeling of synthetic biology.

A.Whether the relative reactions will be influenced by the metabolism of the adopted cells(i.e. E.coli, yeast)?

B.Whether the established modeling can characterize related features of corresponding projects. For instance, for the project “sensor”, whether the model can accurately deal with every biochemistry step and then precisely output two essential scales of the “sensor”, namely sensitivity range and response time?

C.Is the model valid, whose equations stand in the special reaction environment(minimal space for reactions, the quantized number of molecules)?

D.Is it necessary to consider the effect of noise? If so, then does the divece possess noise immunity and robustness?

E.Can the established model be simulated by current computing devices?

Considering all the elements above, the models are given in two sections. For different issues, related models are discussed step by step. The integration of three models is expected so as to reflect the reality of the reaction given by relative devices, and instruct our design and experiments.

SectionⅠ: Software Simulation for Core Circuit

Modular, mass-action-kinetics-based model of the dioxin sensor circuits

Differently from the work by Ajo-Franklin et al. [1], we did not use a simplified model based on Hill functions but we tried to give a more detailed description of the interactions that take place in our circuits by using mass-action as kinetics. As a novelty, with respect to the model in [1], our model consider

1. cell compartments (nucleus and cytoplasm);

2. mRNA synthesis by RNA polymerase;

3. mRNA splicing, maturation, and transport from the nucleus to the cytoplasm;

4. mRNA translation via ribosomes;

5. activator protein transport from the cytoplasm to the nucleus;

6. the interaction of dioxin with its receptor on the synthetic activator we constructed;

7. the presence of multiple operators along the promoter sequence and their interaction with the activator.

In order to construct our model, we used the software Parts & Pools [2-4]. This software generates models for circuit components such as Standard Biological Parts and Pools of molecules (proteins, mRNA, chemicals, etc.). Complex Parts such as our regulated promoters needs many species and reactions to be described properly. Parts & Pools provides such a detailed Part representation via a “rule-based modeling” approach. Parts & Pools generates, indeed, a set of rules and passes to the software BioNetGen [5] that returns a complete list of species and reaction inside the Part. Parts & Pools converts this information into an MDL (Model Definition Language) [6] file. In this format, Parts and Pools are independent modules that can be wired up together into a circuit. We designed our circuits with the software ProMoT [7]. Finally, we exported out circuit, from the MDL to the SBML format [8] and simulated them with COPASI [9].

Now we namely the hereditary information carrier as transcription factors, small RNAs and chemicals. They regulate circuits by binding DNA,RNA or change the spatial conformation, such as riboswitches and ribozymes. So that here is a pool in the cell for storage the free molecules of signal carriers as bio-batteries to the circuit activity. Also, in a gene circuit design, transcription factor and small RNA pools connect transcription units, whereas chemical pools are interfaces between the whole circuit and the extra-cellular environment (see Figure 1).What’s more, the nucleus has a spliceosome pool, and the cytoplasm contains as many mRNA pools as there are coding regions in the circuit. All of the pools have connections. We can utilize the connections and the parameter value of each factors. To get the parts we want from pools and simulate the different conditions molecules matched. Finally we get the whole complex and accurate model.

2.Steps of the modeling based on Mass-action kinetics

Here we should use 4 kinds of softwares, called BioNetGen/Parts&Pools/SBML and Copasi.

First of all, imagine you have a two-operator-containing promoter. Both the operator can be taken or be free.You also get a repressor in the pools. The corresponding model based on full mass-action kinetics contains 5 species and 4 reversible reactions(see Figure 2). A abstract picture of the system is given by:

1) the types of molecules present in the system and the states they exhibit;

2) the species present at the beginning of the computation (seed species: an unbound repressor and a promoters whose operators are free;

3) rules that describe the interactions between the species.

You can also get the rules will the software Parts&Pools.This information is passed as an input to programs such as BioNetGen that compute all the system's species and reactions returning a complete full mass-action kinetics model.

3.Now you can’t handle these reactions into equations buy your hands,so you can use Parts&Pools again to change your file into “.mdl” with a detail model description.

4.So new, here is want you are good at. You can open the file by ProMoT to simulate your project.

Advantages

The Mass-action kinetics is totally different form the Hill-Gleichung. When you build the model, you have to finger out the details of the reaction such as the numbers of the operator of the promoter.But at the same time, this method allows for the construction of interconnectable genetic modules with high numbers of species and reactions such as promoters, bacterial RBS, and eukaryotic mRNA pools. It is a possible tool might exploit a new, recently developed ProMoT feature: the Process Interaction Model (PIM) concept that gives a compact specification of a rule-based model and has been applied to the modeling of signaling pathways. This could lead to a fully rule-based,modular design of synthetic signaling networks, from the receptor membrane proteins down to the genes regulated in the nucleus.

Also when you build the modeling, the software will given via the whole modules in the yeast pools.It will give you a more accurate result for your project.

We spent a whole day to design and simulate related devices with this software and ProMoT. The models reflect several problems:

a)The influence the metabolism system has on our genetic circuit is quite small. We have built up some models for corresponding reactions by Hill Equation. It turns out that their results are similar to others. So the models given by Law of Mass Action will not deviate too much from the reality.

b)The period of time to achieve homeostasis: 25h with memory system; 38h without memory system;

c)After adding memory system, the time for GFP to be steady become significantly shorter. Meanwhile, after eliminating dioxin, GFP produced by device without memory system will attenuate to 50%. But for those devices with memory system, the attenuation of GFP will be less than 10%.

d)Memory system has a process of positive feedback. Thus, just a trace of leakage of promoters can cause a lot of GFP being transcribed and end up interfering the result. That’s the reason why we add in insulating parts.

Section Ⅱ: Differential Equation Model for Supplementary Circuit

Originally, we intended to keep on utilizing Prof. Mario’s software to model for our supplementary project. However, it is limited by the processing capacity of computers. As is shown in the previous models, our device can neglect the metabolism system of yeast. Hence, we turn to the approach of differential equation.

a)Relevant Parameters

b) Assumptions

1)All the reactions follow the Law of Mass Action

2)Adjacent genes have the same speed of transcription

3)Terminator and LexA have no leakage

4)All of LexA-CYC1 are equivalent

5)All LexA regulatory factors degrade naturally

c) Model Simplification

One significant parameter of “sensor” is the response time. So the negligible biochemical reaction period in traditional systematic biologic model need to be taken into consideration.

1)Is the time of synthesis of mRNA negligible?

2)Is the time of synthesis of GFP/LexA negligible?

3)Can the concentration of dioxin+LexADBD be approximated as the concentration of pure dioxin?

1) The influence from the time of synthesis of mRNA

Suppose the concentration of mRNA is cmr, the synthesis rate is s, and the half life of mRNA is T. Then we have: Solving the differential equation, we can obtain the result:

According to the statistics from bionumbers, mRNA’s half life is around 2mins, while its synthesis time is less than 5s. There’s no harm to assume that mRNA’s synthesis rate is 0.01mol/s. By computing with C program, we can observe that after 9s, the corresponding change of concentration of mRNA is less than 0.1%. Comparing with the synthesis time for protein which is more than 3mins, it is less than 10%. So basically, the concentration of mRNA during the phase of synthesis of protein is fixed and it satisfies: , which is cmr=sT/ln2

2) The influence from the time of synthesis of regulatory factors GFP/LexA

In accordance with the result of search, the half life of GFP/LexA is around one hour, while synthesis takes about 2mins. By using qtiplot, we can see the whole process with C programing. The result shows that, it makes little difference whether considering the reaction process or not.

Hence, basically, the time of synthesis of regulatory factors GFP/LexA can be neglected for related reactions.

d) Construction of Model

cactd=d

d(cactd)/dt=ced*edkcat*cactd/(K+cactd)

czifp=ced=cactg=cgfp=lhill(actd+actg) cmp=zhill(czifp)

e) Results

Concentration of GFP-Time

Concentration of Membrane Protein-Time

Dioxin-Time

Dioxin-GFP Concentrations' relation and linear fitting

f) Conclusion/h4>

1. The realtionship between the dioxin and the GFP concentration is nearly linear, which is perfect for the signal transformation.

2. The quorum sensing speed is quite rapid, which is suitable for the dioxin's enrichment

3. The efficiency of dioxin degrading enzyme does not meet our expectation. But its presence shortens the settling time of the concentration of GFP of sensor to 30000s, which is largely faster than current methods.