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].

1. Main ideas

Synthetic gene circuits are designed as the electronic ones. We used Standard Biological Parts such as promoters, coding regions, and terminators that have a well-defined function in transcription or translation. Together with Parts, we used Pools as stores for different kind of molecules.

Parts and Pools exchange fluxes of molecules like electric components exchange a flux of electrons (current). Biological currents are, for instance, (PoPS: Polymerases Per Second) and (RiPS: Ribosomes Per Second). RNA polymerases, indeed, scan entire DNA transcription units and ribosomes go through all the Parts on the mRNA.

Our synthetic activators are also stored into a Pool. Their flux (Factor Per Second) puts in communication the two transcription units in our circuits. Finally, the dioxin (chemical) Pool is an interface between the circuit and the cell environment. The nucleus has also a Pool for the spliceosome and RNA polymerase, whereas the cytoplasm contains as many mRNA pools as there are coding regions in the circuit, a Pool for the ribosome, and one for the fluorescent protein, the circuit read-out. Each Part (and each Pool) has an independent model (MDL file). After wiring them together, the model of the whole circuit comes from the composition of the models of all its components.

2. Building the model

As mentioned above, we used four different kinds of software: Parts & Pools, BioNetGen, ProMoT, and Copasi.

Every Part has its own input file. A promoter input file requires specifying the promoter structure (operator number) and the kind of regulation transcription regulation, if present. Since every operator can lie in two states (free, or taken by a transcription factor), a promoter with N operators can lie into at least 2^N states (combinatorial explosion). Indeed, the promoters we used in our circuits with simple activation host 4 operators, each bound by the same activator. Overall, these promoters host 36 species and 174 reactions. More complex is the promoter we used in the memory circuit. It has 6 operators: 3 bound by the simple LexA-DR (Dioxin Receptor) activator, and the other 3 by the fusion protein GFP-LexA-DR (we could not model operators shared by the two activators but this design is totally equivalent). The model of this promoter shows, on the whole, 133 species and 958 reactions. Such a complex description can be achieved with a rules-based modeling approach. Parts & Pools converts, therefore, an input file into a list of rules that are sent to BioNetGen. BioNetGen returns a list of species and reactions to Parts & Pools. Parts & Pools adds to this the only information missing to have a model for the promoter as an independent Part: the fluxes of molecules it exchanges with other Parts and Pools in a circuit. This final description (species, reaction, and fluxes of molecules) is written into an MDL file. These files are generated for each circuit components. They are loaded into ProMoT, the software we used for our circuit visual design. ProMoT generates the model for the complete circuits and permits to export it into SBML format for running circuit simulations. We simulated the dynamics of our circuits with COPASI (see the Figure above).

Results

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

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.

f) Reference

[1] Ajo-Franklin C.M. et al.,Rational design of memory in eukaryotic cells. Genes Dev, 2007, 21, 2271-2276

[2] Marchisio M.A., Parts & Pools: a framework for modular design of synthetic gene circuits, Frontiers Bioeng Biotech, 2014, 42, doi: 10.3389/fbioe.2014.00042

[3] Marchisio, M. A. and Stelling, J.Computational design of synthetic gene circuits with composable parts. Bioinformatics (Oxford, England), 2008, 24, 1903-1910

[4] Marchisio, M. A et al, Modular, rule-based modeling for the design of eukaryotic synthetic gene circuits. BMC systems biology, 2013, 7, 42

[5] Blinov, M.L. et al., BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains.Bioinformatics (Oxford, England), 2004, 20, 3289-3291

[6] Ginkel, M. et al. Modular modeling of cellular systems with ProMoT/Diva. Bioinformatics (Oxford, England), 2003, 19, 1169-1176

[7] Mirschel, Set al. PROMOT: modular modeling for systems biology. Bioinformatics (Oxford, England), 2009, 25, 687-689

[8] Hucka, M. et al. The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics (Oxford, England), 2003, 19, 524-531

[9] Hoops, Set al. COPASI--a COmplex PAthway SImulator. Bioinformatics (Oxford, England), 2006, 22, 3067-3074