Team:HZAU-China/Modeling
Mixed-Reality CellBidirectional coupling between real and virtual bio-oscillators
Overview
Our project aims to create a new kind of life form, mixed-reality cells, which are half-real and half-virtual. What should be mentioned is that mixed reality states occur only when a virtual and a real system are sufficiently similar.(Alfred Hübler, 2013). As two genetic oscillators built-in E.coli are alternative, we also simulate two e-oscillators in computer as virtual part corresponding to the genetic oscillators.
To reach the mixed-reality state, the approach is separated into three stages,the former two of which will be mentioned in modeling part. The first stage is virtual-virtual coupling. We use two e-oscillators of identical characteristics to simulate the mixed-reality process. They would transfer parameters and interact with each other to a coupled or synchronized state. Secondly, LED lamp is adopted to replace the fluorescence of real cell as the physical real part. It will connect with e-oscillator to compose a mixed-reality state of physical. On the other hand, it will show that our interface hardware could work as expected. At last, we wish to achieve our goal, mixed-reality state. The genetic oscillator in E.coli will interact with e-oscillator in a computer through our interface hardware and gradually they would be strongly coupled.
E-oscillators
Two genetic oscillators, dual-feedback oscillator and quorum-sensing oscillator, are built in our wetlab, so we first analyze the important biological processes and construct ODE sets to simulate these two oscillators separately. However, due to the time interval between the expression of regulating protein and their binding to promoters, we improve our models more precise by DDEs. Once the better genetic oscillator is selected through experiments, we will adopt the corresponding one as the virtual part.
Quorum-sensing oscillator
ODEs
As for quorum-sensing oscillator, luxI proteins could generate AHL from some substrates consisting of acyl-ACPs and Sadenosylmethionine (SAM). We assume that the amount of substrates is sufficient.
AHL(Acyl homoserine lactones) is a kind of auto-inducer, which could combine with luxR protein and activate the promoter. In addition, the lactonic ring of the AHL will be hydrolyzed once in presence of AiiA protein.
For transcription activation, we use Hill function to describe the rate of production.
is the maximal transcription rate. When the promoter is bound by the transcription factor, gene will be transcribed at the maximal transcription rate. So the Hill function is
In addition, many genes have a non-zero minimal expression level, namely basal expression level. It can be described by adding a term 
.
The translation and degradation processes are governed by the following set of reactions:
Y refers to luxI and AiiA.
is the translation rate. The degradation of mRNA is a much swifter process compared to protein, so we use parameter
representing the degradation rate. LuxI and AiiA protein added with LVA-tag can be degraded by the same enzymatic reaction, so they can be modeled to follow Michaelis-Menten enzyme kinetics. Different values of
and
represent different preferential binding dynamics of LuxI and AiiA to degrading enzyme.
According to the above processes，we can describe the genetic circuit by the following equations:
refers to mRNA while
is protein. The internal and external AHL are described by AHL and Ae. LuxR is constitutively produced at a constant level and the protein is degraded at at a proportion
, since it is not tagged for fast degradation.
DDEs
Due to the time interval between expression of regulating protein and transcriptional activation by the luxR and AHL complex which depends on the past concentration of internal AHL, we decide to use DDEs model. Transcription, translation, and maturation rate of proteins are combined into a single time-delay parameter
. We modeled based on the paper “Rapid and tunable post-translational coupling of genetic circuits”.
The simulation is carried out using custom written software in MATLAB. We get the simulation result of oscillator, as shown in Figure 1.
Figure 1. Simulation result of quorum-sensing oscillator.
Dual-feedback oscillator
ODEs
In the genetic circuit of Dual-feedback oscillator, the three promoters are the same hybrid promoter composed of an activation site and a repression site. They can be activated by the araC protein in the presence of arabinose and repressed by the LacI protein in the absence of IPTG. The mechanism of dual-feedback makes oscillatory behaviour stable and adjustable.
There are four states of promoter: original promoter without inducer, bound with araC dimers (
), bound with lacI tetramers (
), bound with araC and lacI tetramers together.
stands for the proportion of the four states of promoters.
when reached the quasi steady state, we can get
Because of
, we get
We assume that araC dimers and lacI tetramers combine with promoter separately without interference. So it means that
AraC dimers and lacI tetramers are generated through their monomeric versions.
When reached the quasi steady state, we can get
We define that
，
，and plug them into D~D3, then we have
In addition, from the consequence of Jesse Stricker(2008), we know that the binding rates of the activator dimer and repressor tetramer to the operator sites are dependent upon the concentrations of arabinose and IPTG.
are the maximum and minimum affinities of AraC dimers to the binding sites, [ara] is the concentration of arabinose (in % w/v), [IPTG] is the IPTG concentration (in mM),
,
,
,
.
are the maximum and minimum affinities of LacI tetramers to the binding site,
,
.
We put the relationships between
and
into the above equations.
The transcription, translation and degradation processes are listed by the following reactions:
Based on the above analysis,We could construct a set of ODEs to describe the dual-feedback oscillator:
stand for the number of plasmid copies. The degradation rate of protein
,
，
,X is the total number of tags in the system.
DDEs
In consideration of the delay of transcription, translation and maturation, DDEs may be more capable. Based on the project of HUST-China 2013, we simulate the genetic circuit by DDE sets
Due to the delay, we denote
as the time interval parameters of araC dimers and lacI tetramers. And attaching delay to three parameters:
Then we code in MATLAB, and the simulation result is shown in Figure 2.
Figure 2. Simulation result of dual-feedback oscillator.
Parameters
Parameters play an important role in simulating, which would determine the behaviors of the system. In our modeling part, parameters in quorum-sensing e-oscillator are from parameter part of Original Full Model by Tsinghua-A iGEM 2011 and the paper “Rapid and tunable post-translational coupling of genetic circuits” by Arthur Prindle et al. And parameters used in dual-feedback e-oscillator are based on the paper “A fast, robust and tunable synthetic gene oscillator” and parameter table in HUST-China iGEM 2013. Although these previous work give us some experience, we still adjust some parameters more reasonable in terms of our system and some experimental tests.
Regulation to oscillator--light control system
In order to establish the connection between genetic oscillator in E.coli and e-oscillator in computer, we adopt light as the medium and bond. A light control system is employed in our project as the wetlab mentioned (Figure 3). Therefore, we can change the expression level of the gene behind the ompc promoter through different light intensity.
Figure 3. Light control system.(Tabor J J, et al,2009)
Based on the paper of Jeffrey J. Tabor(2009), we get the transfer function between light intensity and expression rate:
where
is the expression rate, the fit parameter is K=0.0017
,
,
are the maximum and minimum expression level, L is the intensity of light ().
In our project, the expression of lacI behind the ompc promoter will change with the light intensity. So we add it to the DDEs model of dual-feedback oscillator,
and modify the procedure in MATLAB.
Coupling
Virtual-virtual coupling
Based on the experimental result, we select the dual-feedback oscillator to finish the modulating and coupling process. First, we will finish the virtual-virtual coupling. So different initial values of parameters are set to the simulation to form two e-oscillators which are of the same properties.
Then how could they adjust to each other and be strongly coupled or synchronized? We think about the dynamic equilibrium of wolf and rabbit. If the number of wolves increases rapidly, lots of rabbits would be eaten and the number would reduce. Faced with the decrease of prey, the quantity of wolves would also cut down. On the contrary, rabbits would multiply with fewer natural predators. Cycling like these, wolf and rabbit would finally reach the dynamic balance.
According to the above mechanism, we make the two e-oscillators pass the parameters and affect each other. In terms of the transfer function, with the enhancement of the light intensity, the expression of lacI will reduce, which is proportional to the other e-oscillator’s light intensity. It means that the illumination intensity of e-oscillator 2 will decrease and the corresponding lacI will increase. Then lacI will also be inversely linked to the e-oscillator 1. With the circulation and regulation, the two e-oscillator will be coupled or synchronized gradually.
To achieve the process of coupling or synchronization, we write programs in MATLAB and get the simulation result shown in video 1.
video 1. Simulation result of virtual-virtual coupling.
Mixed-reality of physics
In the second stage, LED lamp controlled by single-chip replace the fluorescence released by E.coli. Based on the virtual-virtual coupling, LED will glow following one of the e-oscillators simulated above as the physical real part, while the other e-oscillator will be the virtual part.
Through a camera, intensity of LED will be transfer to computer and affect the e-oscillator. The returned value of e-oscillator will also be passed to the physical real part by single-chip. With the interaction, the two parts will get coupled in the end. The details of connecting device are specified in our Interface Hardware part.
Figure 4. The complete design of physical device.
We program scripts in Python with an embedded code in MATLAB(You can click here to download the codes). And then we put the LED lamp and camera in dark place and run the program. We get the simulation result in Video 2.
video 2. Simulation result of mixed-reality of physics.
Oscillator 1 is the dynamic trajectory of e-oscillator in computer, while Oscillator 2 represents the state of LED. The blue square in the upper right corner is the light intensity image of LED observed by camera(we only read the B values of RGB). As you can see, the brightness of blue changes following the interaction. Besides, the small box in the upper left corner shows the facade of LED lamp, which is manually shot by us in dark environment. From the oscillation images, we can find that the virtual part and the physical real part get synchronized gradually.
So far we have finished the second stage of our project. The next step, we will achieve the third stage, mixed-reality state.
Reference
1.Arthur P, Jangir S, Howard L, et al. Rapid and tunable post-translational coupling of genetic circuits.[J]. Nature, 2014, 508(7496):387-391.
2.Stricker J, Cookson S, Bennett M R, et al. A fast, robust and tunable synthetic gene oscillator[J]. Nature, 2008, 456(7221):516-519.
3.O’Brien E L, Itallie E V, Bennett M R. Modeling synthetic gene oscillators[J]. Mathematical Biosciences, 2012, 236(1):1–15.
4.Tabor J J, Salis H M, Simpson Z B, et al. A synthetic genetic edge detection program.[J]. Cell, 2009, 137(7):1272-1281.
5.Hubler A, Gintautas V. Experimental evidence for mixed reality states[J]. Complexity, 2011, 13(6):7–10.
© 2015 Huazhong Agricultural University iGEM Team. All rights reserved.
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