Team:USTC Software/demoMain

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(New page: Using C-N Model we can model systems with great complexity ==The simplest example with only E.coli cell== ===introduction=== As the simplest example, a model of a flask with only E.coli ...)
 
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__NOTOC__
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Using C-N Model we can model systems with great complexity
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<html>
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==The simplest example with only E.coli cell==
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<a href="#BBa_F2620">1. Part: BBa_F2620</a><br/>
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<a href="#ToggleSwitch">2. Toggle Switch</a><br/>
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<a href="#ModelingDetails">2.1. Modeling Details of Toggle Switch</a><br/>
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<a href="#Repressilator">3. Repressilator</a><br/>
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<a href="#RepressilatorDetails">3.1. Modeling Details of Repressilator</a><br/>
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</html>
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===introduction===
 
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As the simplest example, a model of a flask with only E.coli cells inside will be shown. Only one reaction will be considered: the replication of E.coli. However, it is not trivial. '''MoDeL''' enables users to add such an auto-catalytic replication reaction easily and conveniently. The minimal database used for this model could be download here.
 
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===database construction===
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==Part: BBa_F2620==
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We only provide key points regarded with construction of this minimal database. To add the auto-catalytic reaction in the Reaction container, a species with only part E.coli is required. It has the simplest '''Chain-Node''' model format: only one chain with one part and no trees. The auto-catalytic reaction has one modifier and one product and they are both referred to E.coli defined in Species container. Since they are compartment-type species (species representing a compartment), attribute '''itself''' of '''compartmentLabel''' node in modifiers and products definitions should be set the same with label of the compartment they represent in the compartments definition. It ensures that the product and the modifier are the same, avoiding wrong mismatch of the product which is different with the modifier. Since number of E.coli cells will reach a stable level in a long time course, we use <math>k_{g}(1-C_{E.coli}/C_{max})C_{E.coli}V_{Flask}</math> as the reaction rate, where <math>k_{g}</math> is the growth rate of E.coli, <math>V_{Flask}</math>  represents the size of E.coli, and <math>C_{E.coli}</math> and <math>
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C_{max}</math> are concentration of E.coli and its max concentration in the flask, respectively. The negative sign in the rate equation indicates self-repression of E.coli cells.
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===modelling and simulation===
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<html><a name="BBa_F2620">BBa_F2620</a></html>
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[[Image:Ustcs Graph1.png|400px|thumb|Replication of E.coli cell]]
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Model written in '''SBML''' format is shown below. The dynamic curve of E.coli replication is plotted by time course simulation. Exactly speaking, dynamic behaviors of biological system are meaningless after 4000s because of termination of reproduction of E.coli. However, the curve is in qualitative agreement with that from experiments in the first and second stage of reproduction of E.coli.
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==Basic example with pLac-LacI repression system==
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<font size="+1">Part:BBa_F2620</font> had been fully characterized with data in partsregistry [http://partsregistry.org/Part:BBa_F2620 BBa_F2620] page. It is a composite biobrick with three individual biobricks: pTetR (R0040), LuxR(C0062) and lux pR. Without AHL, transcriptional level of lux pR is extremal low because of lack of activator, LuxR-AHL dimer. If we add AHL into the system within a very short time, expression of mature GFP is expected to increase significantly. To measure behaviors of the system consisting of BBa_F2620 using our software tool, we construct a system using plasmid pSB3C5 and Part:BBa_F2620 as well as a reporter gene:
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===introduction===
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[[Image:USTCs_luxr_gfp_assembly.PNG|700px|center]]
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'''MoDeL''' provides poweful supports for description of interactions between two species. No interactions exist in the previous example. In this example, we will construct a plasmid backbone with promoter, rbs, coding sequence and terminator inserted in and transform it into E.coli. LacI repressor are produced after two steps of transcription and translation. It binds with itself to form a dimer and then a tetramer, which could bind with promoter LacI on the plasmid to repress the process of transcription. Besides, replication of E.coli cells, degradation of proteins and mRNAs, as well as dilution due to replication of cells, are also considered.
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===database construction===
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where we use two consecutive terminators to indicate a complete termination. Time course simulation was performed to generate transfer function of stable GFP concentrations versus AHL concentration. It is of high consistence with experiment done by [http://partsregistry.org/Part:BBa_F2620:Transfer_Function Haseloff Lab, MIT]:
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Actually, it is a complex molecular process and takes many steps to complete a transcription reaction. It includes binding and initiation, elongation, and termination. So does translation reactions. The first version of '''MoDeL''' '''<font color='red'>DOES NOT</font>''' support transcription and translation reaction templates and they will be handled by our core program of '''iGame''' and thus no need to write in the database.
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All binding reactions in the database demo are modeled using law of mass action. They are dimerization of two LacI repressors and that of two LacI dimers. LacI tetramers will bind with promoter LacI in the plasmid and thus repressing the expression of plasmid DNAs. However, '''MoDeL''' enables any mathematical model form for species-species interactions and is not constrained within only law of mass action. Users could change the reactants, modifiers, products, as well as kinetic laws arbituarily and validate their models via output of dynamic curves.
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[[Image:USTCs Transfer function.png|700px|center]]
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Species reaction templates are worth mentioning to show features of our new language '''MoDeL'''. It is never a easy problem to calculate degradation rates of proteins since different parts in a fused protein may have different degradation rates and the overall rate is still unknown. What's more, a protein in '''MoDeL''' may have different protein chains and it is more complex to determine the overall rate. In the demo database, we assume all proteins with no parts in bound state have a uniform degradation rate. Proteins with more than one chains are considered stable and non-degradable. This idea could be applied easily by writing reaction templates in '''MoDeL''' format. The reactant is a general species template with only one substituent-type part ('''ANYUB''') of type '''ForwardProtein''' (no reverse reactions happened here). It is similar for degradation of mRNA molecules. Only mRNAs with single chain degrades at the same rate.  
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where GFP concentration is directly proportional to its synthetic rate. In our simulation, we add AHL of concentration ranging from 1E-10 to 1E-5 M (increasing by order of magnitude) to the reactor within one minute. Details of modeling are described [[here]].  
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For reactions of dilution due to reproduction of cells, quantities of species decrease in a similar way to degradation. The rate of dilution is also similar to the reproduction rate of E.coli:
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We also plot time and dose response measurements of GFP stable concentration following addition of AHL. We choose the same AHL concentrations as done in testing the transfer function and plot their dynamic curves of GFP:
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<math>k_{g}(1-C_{E.coli}/C_{max})C_{species}V_{Flask}</math>
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[[Image:USTC_s_dose_response.PNG|700px|center]]
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----
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<font size="+1">A similar work</font> to measure system response of luxr-plux to inducer AHL was done by [http://2009.igem.org/Team:USTC USTC 2009 iGEM team]. Besides measurement of dose response of GFP stable concentrations following addition of AHL, they construct four constitutive promoters, [http://partsregistry.org/wiki/index.php/Part:BBa_K176026 BBa_K176026], [http://partsregistry.org/wiki/index.php/Part:BBa_K176126 BBa_K176126], [http://partsregistry.org/wiki/index.php/Part:BBa_K176128 BBa_K176128], [http://partsregistry.org/wiki/index.php/Part:BBa_K176130 BBa_K176130], and quantitatively measured their effects to the response curves. The construction is modified by replacing pTet with the four promoters and pSB3C5 with high copy plasmid pSB1A3 (copy number: 200). Since there are no tetR protein existed in the system, we keep lux pR unchanged (it is equivalent to use pLux/Tet hybrid promoter).
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where we only replace the second <math>C_{E.coli}</math> with concentration of species in dilution. To apply this idea, we only need to construct a species with only one substituent-type part (''ANY'') of no specific type and it will be matched to all species. Among them, only species bound in compartment E.coli will be diluted.
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The results is shown for each (we plot GFP concentration versus time and compare it with experiment measument):
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Replication of plasmid DNAs is not as easy as reproduction of living cells in two aspects: first, plasmid backbone with the same replication origin could be found in many species in the system because the original transformed plasmid backbone may bind with other compounds or proteins to form complex; second, the replication of original transformed plasmid DNA molecule tends to be repressed by all species including the same replication origin. However, E.coli cells do not have any effects on the reproduction of other E.coli cells. '''MoDeL''' language perfectly support this idea by separating the template reaction into replications and repressions. The first part describes the exponential amplification of plasmids with reaction rate <math>k_{g}C_{plasmid}V_{E.coli}</math>, where <math>k_{g}</math> is the replication rate of a certain plasmid, <math>C_{plasmid}</math> is the concentration of this plasmid, and <math>V_{E.coli}</math> is the volume of E.coli cell. The product may be different from the reactant. It is possible because the reactant may be a complex, such as complex of LacI tetramer and plasmid with promoter LacI (we call it pLacI:LacI4 below). Only the products of the replication reaction will be repressed with a certain rate.
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*Part:BBa_K176026 (Promoter Strength: 0.55 1/s)
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In this example, pLacI:LacI4 would not be repressed since it is not among the products of its replication. Via '''MoDeL''' language, we design a template reaction with no reactants, two modifiers and one product. The two modifiers are template species containing a certain plasmid backbone (say pSB1A3), and binding state is allowed for both. The product is also a template species containing pSB1A3, however, it has only one chain and no binding is permitted. Hence, modifiers have '''Chain-Node''' structure ''ANY''--pSB1A3--''ANY'', while product has its structure ''ANYUB''--pSB1A3--''ANYUB''. The ''listOfTransferTable'' makes parts transfer from part ''ANY'' of either modifier to its corresponding part ''ANYUB'' of the product. The reaction rate is <math>-k_{g}C_{mod1}C_{mod2}/C_{max}</math>, where <math>k_{g}</math> is the same as that defined in the replication reaction, <math>C_{max}</math> is the max concentration of plasmids containing pSB1A3 as backbone, and <math>C_{mod1}</math>, <math>C_{mod2}</math> are concentrations of modifier1 and modifier2, respectively. The negative sign in the rate law indicates a repressed effect to the replication of the product.
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[[Image:USTCs Comp K176026.PNG|700px|center]]
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*Part:BBa_K176126 (promoter strength: 0.0192 1/s)
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[[Image:USTCs Comp K176126.PNG|700px|center]]
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*Part:BBa_K176128 (promoter strength: 0.0016 1/s)
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[[Image:Comp 176128.PNG|700px|center]]
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*Part:BBa_K176130 (promoter strength: 6.4E-5 1/s)
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[[Image:Comp 176130.PNG|700px|center]]
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==Toggle Switch==
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<html><a name="ToggleSwitch">Toggle Switch</a></html>
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The toggle switch is composed of two repressors and two promoters, each of which is inhibited by the repressor transcribed by the other promoter. We choose pLacI and pTetR as the two promoters, and the repressors are TetR and LacI, respectively. Theoretically, if ratio of LacI to TetR is greater than 1, strong binding of LacI to pLacI repress transcription initiation from pLacI and therefore quantities of TetR will decrease, which in turn relieves its repression to pTet leading to increase of quantities of LacI itself. In this situation, concentration of LacI is far greater than that of tetR, whose expression is repressed at an extream low level and the system enters into its 'LacI' state. Similar analysis will do for TetR and the system will enter into 'TetR' state if its quantity dominates. To show transition between the two states, IPTG is added in 1s after the system enters into 'LacI' state completely. The assembling of parts are construcuted as follows:
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[[Image:USTCs Toggle assembly.PNG|900px|thumb|center|Parts assembling: the top assembling is the construction used in our software and the bottom one is the toggle switch design in [http://www.nature.com/nature/journal/v403/n6767/full/403339a0.html Construction of a genetic toggle switch in Escherichia coli]. ]]
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where we use two consecutive terminators to indicate a complete termination. Time course simulation was performed to generate the state transition:
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[[Image:USTCs State conversion1.png|500px|thumb|center|State of system has changed to 'TetR' state from 'LacI' state after adding inducer IPTG at 40000s.]]
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The legend used in the figure is not clear. 13:DNA;(lacI153)4, 11:DNA;(tetR154)2, and 14:DNA;(lacI153)4;(tetR154)2 means binding products of initial plasmid with lacI tetramer at site pLacI gene, with tetR dimer at site pTet gene, and with lacI tetramer and tetR dimer both, respectively. At the beginning, initial plasmids are all bound with lacI tetramer and the system is in its 'LacI' state. After adding inducer IPTG at 40000s, concentration of tetR dimer increases and plasmids bound with lacI tetramer start to bind with tetR dimer and form complex of plasmids, lacI tetramer, and tetR dimer. At about 70000s, all plasmids bound with lacI tetramer are further bound with tetR dimer. At about 85000s, due to repression of expression of lacI, plasmids bound with LacI tetramer and tetR dimer both start to unbind to form plasmids bound with tetR dimer only and the system steps into its 'TetR' state gradually. Details of modeling is available [http://2010.igem.org/Modeling_page_toggle_here#Modeling_Details_of_Toggle_Switch here].
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===Modeling Details of Toggle Switch===
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<html><a name="ModelingDetails">Modeling Details of Toggle Switch</a></html>
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Key points of this modeling are:
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*LacI protein tends to form LacI dimer, which tends to form LacI tetramer further.
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*Only LacI tetramer binds with pLacI gene and thus repressing expression of its downstream genes.
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*TetR protein only forms dimer.
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*Only tetR dimer binds with pTet gene and thus repressing expression of its downstream genes.
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*One IPTG molecule binds with one LacI tetramer to form complex IPTG:LacI4 and one aTc molecule binds with one tetR dimer to form complex aTc:TetR2.
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An overview of species list is provided:
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[[Image:USTCs Species list.PNG|700px|center| Species list of toggle-switch network.]]
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where each species with its specific identifier has its own meaning:
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*0:E_coli : E.coli cell;
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*1:IPTG: IPTG in flask;
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*2:DNA: initial transformed plasmids;
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*3:IPTG: IPTG in E.coli due to diffusion;
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*4:RNA: mRNA of tetR and GFP;
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*5:RNA: mRNA of LacI;
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*6:tetR154: tetR protein;
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*7:GFP12923: GFP;
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*8:lacI153: LacI protein;
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*9:(tetR154)2: tetR dimer;
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*10:(lacI153)2: LacI dimer;
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*11:DNA;(tetR154)2: complex of tetR dimer binding to pTet gene of plasmid DNA;
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*12:(lacI153)4: LacI tetramer;
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*13:DNA;(lacI153)4: complex of LacI tetramer binding to pLacI gene of plasmid DNA;
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*14:DNA;(lacI153)4;(tetR154)2: complex of plasmid DNA with both pLacI and pTet genes bound with LacI tetramer and tetR dimer, respectively;
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*15:IPTG;(lacI153)4: complex of IPTG binding with LacI tetramer;
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Since there are 65 reactions in total, we only provide a screenshot (<font color="red">we strongly recommend users to run our example to learn more details about automatic modeling</font>):
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[[Image:USTCs Reactionshot.PNG|700px|center| Species list of toggle-switch network.]]
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Moreover, parameters of our modeling network are provided (we spend much efforts on tuning parameters) based on papers and estimates together:
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*Initial time: 0 s
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*Initial volumes:
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**Flask: 0.4 l
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**E_coli: 1.6856e-012 l
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*Initial concentrations:
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**0:E_coli: 1e-020 mol/l
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**1:IPTG: 0 mol/l
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**2:DNA: 2.4e-009 mol/l
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**3:IPTG: 0 mol/l
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**4:RNA: 0 mol/l
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**5:RNA: 0 mol/l
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**6:tetR154: 0 mol/l
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**7:GFP12923: 0 mol/l
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**8:lacI153: 0 mol/l
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**9:(tetR154)2: 0 mol/l
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**10:(lacI153)2: 0 mol/l
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**11:DNA;(tetR154)2: 0 mol/l
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**12:(lacI153)4: 0 mol/l
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**13:DNA;(lacI153)4: 0 mol/l
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**14:DNA;(lacI153)4;(tetR154)2: 0 mol/l
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**15:IPTG;(lacI153)4: 0 mol/l
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*Reaction parameters:
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**reproduction of Ecoli cell
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***growth constant: 0.000192 1/s
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***maximum concentration: 1.66e-012 mol/l
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**diffusion of IPTG molecule
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***diffusion constant: 0.014 1/s
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**transcription
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***transcription rate of pTet/pLacI: 0.5 1/s
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**replication of reverse pSB3C5
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***replication constant: 0.003 1/s
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**repression of reverse pSB3C5 replication
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***max concentration of pSB3C5: 2.847e-008 mol/l
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**translation
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***translation rate: 0.1 1/s
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**degradation of mRNAs
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***degradation of mRNA molecules:  0.0048 1/s
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**degradation of proteins in E.coli_3
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***degradation rate of proteins: 0.0023 1/s
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**Laci-Laci dimerization
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***kon: 1.25e+007 l/(mol*s)
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***koff: 10 1/s
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**binding forward-ptetR:tetR2
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***kon: 1e+008 l/(mol*s)
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***koff: 0.001 1/s
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**tetR-tetR dimerization_2
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***kon:  4e+011 1/(mol*s)
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***koff: 10 1/s
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**LacI2-LacI2 dimerization
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***kon: 1e+014 l/(mol*s)
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***koff: 10 1/s
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**binding reverse-placI:lacI4
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***kon: 4e+011 l/(mol*s)
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***koff:        0.04 1/s
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**IPTG:lacI4 binding
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***kon: 154000 l/(mol*s)
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***koff: 0.2 1/s
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===modelling and simulation===
 
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{| cellpadding="10" cellspacing="0"
 
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|-
 
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|Only one copy of plasmid is transformed into E.coli cell at initial time. To give a reasonable dynamic curve of species in the biological system, parameters are obtained from experiments if they are available. Besides E.coli, there are 6 species:  DNA with pLacI and LacI (DNA0), LacI mRNA (with RBS), LacI protein, LacI dimer, LacI tetramer, and complex of LacI tetramer and DNA0 (DNA1). Concentrations of LacI mRNA, protein, dimer and tetramer versus time are plotted in Figure 4. Since dissociation constant (Kd) of LacI-LacI monomer interaction (77nM) is mush larger than that of LacI dimer-dimer interaction (0.1pM), steady-state concentrations of LacI mRNA and protein are in different scales with that of LacI dimer and tetramer. Due to very large Kd of LacI dimer-dimer interaction, LacI protein would finally exist in form of tetramer in the system (concentration of LacI dimer is several orders of magnitude lower than the scale of the left Y axis and thus be ignored).
 
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|[[Image:Ustcs plac lacI 1.png|400px|thumb|Figure 4: Dynamic curves of LacI mRNA, protein, dimer and tetramer]]
 
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|-
 
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|Figure 5 shows dynamic behaviors of plasmids in our model. Since only one copy of plasmid DNA0 was transformed, its quantity increases at the very beginning and decrease soon because all DNA0 will bind with LacI tetramer and no free plasmid exists. The process will end in one hour and quantities of both DNA0 and DNA1 enter into a stable level. It is worth mentioning that the stable concentration of DNA1 is about 380 nM, a little lower than its maximum concentration 475 nM. It is owing to reproduction of E.coli cells. After quantities of E.coli cell go into its stable stage, its concentration will continue to increase until the maximum setup value.
 
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|rowspan="2"|[[Image:Ustcs plac lacI 2.png|400px|thumb|Figure 5: Dynamic curves of DNA0 and DNA1]]
 
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|-
 
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|This basic example proves great success for '''iGAME''' to automatically model genetic regulatory systems. It shows real biological process in a qualitative manner and give suggestions for users to adjust their experiment plans.
 
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|}
 
==Repressilator==
==Repressilator==
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<html><a name="Repressilator">Repressilator</a></html>
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The repressilator is a synthetic genetic regulatory network designed to exhibit a stable oscillation shown via expression of GFP (green fluorescent protein). The work is reported by Michael B. Elowitz and Stanislas Leibler in their [http://www.nature.com/nature/journal/v403/n6767/full/403335a0.html work] at 2000. They constructed a system of three genes connected in a cyclical negative feedback loop so that gene A represses gene B, which represses gene C, which represses gene A. The implementation of this idea used a low copy plasmid encoding the repressilator, and the higher copy reporter, which were used to transform a culture of Escherichia coli.
The repressilator is a synthetic genetic regulatory network designed to exhibit a stable oscillation shown via expression of GFP (green fluorescent protein). The work is reported by Michael B. Elowitz and Stanislas Leibler in their [http://www.nature.com/nature/journal/v403/n6767/full/403335a0.html work] at 2000. They constructed a system of three genes connected in a cyclical negative feedback loop so that gene A represses gene B, which represses gene C, which represses gene A. The implementation of this idea used a low copy plasmid encoding the repressilator, and the higher copy reporter, which were used to transform a culture of Escherichia coli.
[[Image:USTCs Oscillator assembling.PNG|700px|thumb|center|Parts assembling: the top assembling is the construction used in our software and the bottom one is the toggle switch design in their work.]]
[[Image:USTCs Oscillator assembling.PNG|700px|thumb|center|Parts assembling: the top assembling is the construction used in our software and the bottom one is the toggle switch design in their work.]]
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We construct a model to stimulate the behavior of repressilator, the results are showed as following:
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[[Image:USTCS_repressilator.JPG|600px|thumb|center]]
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The meanings of the legend used in the figure are demonstrated as follows: [14 (lacI153)4] refers to the binding product of four lacI protein molecules, [12 (CIlam154)2] refers to the binding product of two CIlam protein molecules, while [10 (tetR154)2] refers to the binding product of two tetR protein molecules. The system exhibits oscillation behavior after initial time of 86000, the concentration of (lacI)4, (CIlam)2 and (tetR)2 changes periodically as the function of time. To be specific, the concentration of (tetR)2 increase when the concentration of (lacI)4 declines due to the remove of repression. And the concentration reaches the peak level when the concentration of (LacI)4 reaches its lowest level. Then the concentration of (tetR)2 decreases while the concentration of (CIlam)2 begins to arise because the repression from (tetR)2 is gradually relieved. Noted that the concentration peak level of (CIlam)2 and (tetR)2 are nearly more than twice the max concentration of (lacI)4, this may attribute to the difference of binding tendency between (CIlam)2, (tetR)2 and (lacI)4. The internal binding strength of (tetR)2 dimer and (CIlam)2 dimer are stronger than that of (lacI)4 tetramer.
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[[Team:USTC_Software/detail|<font size="5">''more details''</font>]]
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===Modeling Details of Repressilator===
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<html><a name="RepressilatorDetails">Modeling Details of Repressilator</a></html>
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<br/>
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Key points of this modeling are:
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* LacI protein tends to form LacI dimer, which tends to form LacI tetramer further.
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* Only LacI tetramer binds with pLacI gene and thus repressing expression of its downstream genes.
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* TetR protein only forms dimer.
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* Only tetR dimer binds with pTet gene and thus repressing expression of its downstream genes.
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* One IPTG molecule binds with one LacI tetramer to form complex IPTG:LacI4.
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* cIlam protein only forms dimer.
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* Only cIlam dimer binds with pcIlam gene and thus repressing expression of its downstream genes.
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<br/>
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An overview of species list is provided:
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<br/>
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[[Image:USTCS_graph1.JPG|600px|thumb|center]]
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<br/>
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where each species with its specific identifier has its own meaning:
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<br/>
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*0:E_coli: E.Coli cell;
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*1:IPTG: IPTG in flask;
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*2:DNA: initial transformed plasmids;
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*3:IPTG: IPTG in E.Coli due to diffusion;
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*4:RNA: mRNA of tetR;
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*5:RNA: mRNA of lacI;
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*6:RNA: mRNA of cIlam;
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*7:tetR154: tetR protein;
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*8:lacI153: lacI protein;
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*9:cIlam156: lacI protein;
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*10:(tetR154)2: tetR dimer;
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*11:(lacI153)2: lacI dimer;
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*12:(cIlam156)2: cIlam dimer;
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*13:DNA;(tetR154)2: complex of tetR dimer binding to pTet gene of plasmid DNA;
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*14:(lacI153)4; lacI tetramer;
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*15:DNA;(cIlam156)2: complex of cIlam dimer binding to pCI gene of plasmid DNA;
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*16:DNA;(cIlam156)2;(tetR154)2: complex of plasmid of DNA with both pCI and pTet genes bound with cIlam dimer and tetR dimer;
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*17:DNA;(lacI153)4: complex of LacI tetramer binding to pLacI gene plasmid DNA;
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*18:DNA;(lacI153)4;(tetR154)2: complex of plasmid DNA with both pLacI and pTet genes bound with LacI tetramer and tetR dimer, respectively;
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*19:IPTG;(lacI153)4: complex of LacI tetramer binding to pLacI gene of plasmid DNA;
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*20:DNA;(cIlam156)2;(lacI153)4: complex of plasmid DNA with both pCI and placI genes bound with cIlam dimer and lacI tetramer, respectively;
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*21:DNA;(cIlam156)2;(lacI153)4;(tetR154)2: complex of plasmid DNA with both pCI, placI and pTet genes bound with cIlam dimer, lacI tetramer and tetR dimer, respectively;
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Since there are 153 reactions in total, we only provide a screenshot (we strongly recommend users to run our example to learn more details about automatic modeling):
 +
 +
[[Image:USTCS_graph2.JPG|600px|thumb|center]]
 +
Moreover, parameters of our modeling network are provided below:
 +
 +
*Initial time: 0 s
 +
 +
*Initial volumes:
 +
 +
*Chemostat 0.1 l
 +
*E_coli 4.4247e-006 l
 +
 +
*Initial concentrations:
 +
 +
*0:E_coli 1.05e-013 mol/l
 +
*1:IPTG 0.001 mol/l
 +
*2:DNA 2.4e-009 mol/l
 +
*3:IPTG 0 mol/l
 +
*4:RNA 0 mol/l
 +
*5:RNA 0 mol/l
 +
*6:RNA 0 mol/l
 +
*7:tetR154 0 mol/l
 +
*8:lacI153 0 mol/l
 +
*9:cIlam156 0 mol/l
 +
*10:(tetR154)2 0 mol/l
 +
*11:(lacI153)2 0 mol/l
 +
*12:(cIlam156)2 0 mol/l
 +
*13:DNA;(tetR154)2 0 mol/l
 +
*14:(lacI153)4 0 mol/l
 +
*15:DNA;(cIlam156)2 0 mol/l
 +
*16:DNA;(cIlam156)2;(tetR154)2 0 mol/l
 +
*17:DNA;(lacI153)4 0 mol/l
 +
*18:DNA;(lacI153)4;(tetR154)2 0 mol/l
 +
*19:IPTG;(lacI153)4 0 mol/l
 +
*20:DNA;(cIlam156)2;(lacI153)4 0 mol/l
 +
*21:DNA;(cIlam156)2;(lacI153)4;(tetR154)2 0 mol/l
 +
 +
*Initial values of global quantities:
 +
 +
*ts 0
 +
*te 40000
 +
*s 0.001
 +
*t 0
 +
 +
*Reaction parameters:
 +
 +
*reproduction of Ecoli cell
 +
**  kgr 0.000192 1/s
 +
**  maxc 1.66e-012 mol/l
 +
 +
*dilution of species in chemostat
 +
**  k1 0.00017 1/s
 +
 +
*diffusion of IPTG molecule
 +
**  k_diff 0.014 ?
 +
 +
*dilution_2 of species in E.coli
 +
**  kgr 0.000192 1/s
 +
**  maxc 1.66e-012 mol/l
 +
 +
*transcription
 +
**  k_tc 0.5 1/s
 +
 +
*replication of reverse pSB1A3
 +
**  kgr 0.003 1/s
 +
 +
*repression of reverse pSB1A3 replication
 +
**  kgr -0.003 ?
 +
**  maxc 4.746e-007 ?
 +
 +
*translation
 +
**  k_tl 0.1 1/s
 +
 +
*degradation of mRNAs
 +
**  k1 0.0048 1/s
 +
 +
*tetR-tetR dimerization
 +
**  kon 1.79e+011 l/(mol*s)
 +
 +
*degradation of proteins in E.coli
 +
**  k1 0.0023 1/s
 +
 +
*Laci-Laci dimerization
 +
**  kon 1.25e+007 l/(mol*s)
 +
 +
*cI (lambda)-cI (lambda) dimerization
 +
**  kon 1.79e+011 l/(mol*s)
 +
 +
*binding reverse-ptetR:tetR2
 +
**  kon 1e+008 l/(mol*s)
 +
 +
*LacI2-LacI2 dimerization
 +
**  kon 1e+014 l/(mol*s)
 +
 +
*binding reverse-pcI (lambda):cI2 (lambda)
 +
**  kon 1e+009 l/(mol*s)
-
LacI binds to form dimer and LacI dimer will continue to bind to form LacI tetramer, which acts as the repressor of pLacI gene. Meanwhile, TetR and cI only dimerize. Repressors of pTetR and pCI genes are TetR and cI dimers, respectively.
+
*binding reverse-placI:lacI4
-
    
+
**   kon 4e+011 l/(mol*s)
-
To design a database specially used for this classical system, we model the
+
-
==Synchronized genetic oscillators==
+
*IPTG:lacI4 binding
-
==E. coli Automatic Directed Evolution Machine==
+
**  kon 154000 l/(mol*s)
-
The strength of promoters used in the model, characterized by attribute ''forwardPromoterEfficiency'' could be obtained [[Team:USTC_Software/downloads/ADEM/parameter#Characterization_of_activities_of_promoters|<font size="5">''here''</font>]].
+

Latest revision as of 02:44, 28 October 2010


1. Part: BBa_F2620
2. Toggle Switch
2.1. Modeling Details of Toggle Switch
3. Repressilator
3.1. Modeling Details of Repressilator


Part: BBa_F2620

BBa_F2620

Part:BBa_F2620 had been fully characterized with data in partsregistry BBa_F2620 page. It is a composite biobrick with three individual biobricks: pTetR (R0040), LuxR(C0062) and lux pR. Without AHL, transcriptional level of lux pR is extremal low because of lack of activator, LuxR-AHL dimer. If we add AHL into the system within a very short time, expression of mature GFP is expected to increase significantly. To measure behaviors of the system consisting of BBa_F2620 using our software tool, we construct a system using plasmid pSB3C5 and Part:BBa_F2620 as well as a reporter gene:

USTCs luxr gfp assembly.PNG

where we use two consecutive terminators to indicate a complete termination. Time course simulation was performed to generate transfer function of stable GFP concentrations versus AHL concentration. It is of high consistence with experiment done by Haseloff Lab, MIT:

USTCs Transfer function.png

where GFP concentration is directly proportional to its synthetic rate. In our simulation, we add AHL of concentration ranging from 1E-10 to 1E-5 M (increasing by order of magnitude) to the reactor within one minute. Details of modeling are described here.

We also plot time and dose response measurements of GFP stable concentration following addition of AHL. We choose the same AHL concentrations as done in testing the transfer function and plot their dynamic curves of GFP:

USTC s dose response.PNG

A similar work to measure system response of luxr-plux to inducer AHL was done by USTC 2009 iGEM team. Besides measurement of dose response of GFP stable concentrations following addition of AHL, they construct four constitutive promoters, BBa_K176026, BBa_K176126, BBa_K176128, BBa_K176130, and quantitatively measured their effects to the response curves. The construction is modified by replacing pTet with the four promoters and pSB3C5 with high copy plasmid pSB1A3 (copy number: 200). Since there are no tetR protein existed in the system, we keep lux pR unchanged (it is equivalent to use pLux/Tet hybrid promoter).

The results is shown for each (we plot GFP concentration versus time and compare it with experiment measument):

  • Part:BBa_K176026 (Promoter Strength: 0.55 1/s)
USTCs Comp K176026.PNG
  • Part:BBa_K176126 (promoter strength: 0.0192 1/s)
USTCs Comp K176126.PNG
  • Part:BBa_K176128 (promoter strength: 0.0016 1/s)
Comp 176128.PNG
  • Part:BBa_K176130 (promoter strength: 6.4E-5 1/s)
Comp 176130.PNG


Toggle Switch

Toggle Switch

The toggle switch is composed of two repressors and two promoters, each of which is inhibited by the repressor transcribed by the other promoter. We choose pLacI and pTetR as the two promoters, and the repressors are TetR and LacI, respectively. Theoretically, if ratio of LacI to TetR is greater than 1, strong binding of LacI to pLacI repress transcription initiation from pLacI and therefore quantities of TetR will decrease, which in turn relieves its repression to pTet leading to increase of quantities of LacI itself. In this situation, concentration of LacI is far greater than that of tetR, whose expression is repressed at an extream low level and the system enters into its 'LacI' state. Similar analysis will do for TetR and the system will enter into 'TetR' state if its quantity dominates. To show transition between the two states, IPTG is added in 1s after the system enters into 'LacI' state completely. The assembling of parts are construcuted as follows:

Parts assembling: the top assembling is the construction used in our software and the bottom one is the toggle switch design in Construction of a genetic toggle switch in Escherichia coli.

where we use two consecutive terminators to indicate a complete termination. Time course simulation was performed to generate the state transition:

State of system has changed to 'TetR' state from 'LacI' state after adding inducer IPTG at 40000s.

The legend used in the figure is not clear. 13:DNA;(lacI153)4, 11:DNA;(tetR154)2, and 14:DNA;(lacI153)4;(tetR154)2 means binding products of initial plasmid with lacI tetramer at site pLacI gene, with tetR dimer at site pTet gene, and with lacI tetramer and tetR dimer both, respectively. At the beginning, initial plasmids are all bound with lacI tetramer and the system is in its 'LacI' state. After adding inducer IPTG at 40000s, concentration of tetR dimer increases and plasmids bound with lacI tetramer start to bind with tetR dimer and form complex of plasmids, lacI tetramer, and tetR dimer. At about 70000s, all plasmids bound with lacI tetramer are further bound with tetR dimer. At about 85000s, due to repression of expression of lacI, plasmids bound with LacI tetramer and tetR dimer both start to unbind to form plasmids bound with tetR dimer only and the system steps into its 'TetR' state gradually. Details of modeling is available here.


Modeling Details of Toggle Switch

Modeling Details of Toggle Switch

Key points of this modeling are:

  • LacI protein tends to form LacI dimer, which tends to form LacI tetramer further.
  • Only LacI tetramer binds with pLacI gene and thus repressing expression of its downstream genes.
  • TetR protein only forms dimer.
  • Only tetR dimer binds with pTet gene and thus repressing expression of its downstream genes.
  • One IPTG molecule binds with one LacI tetramer to form complex IPTG:LacI4 and one aTc molecule binds with one tetR dimer to form complex aTc:TetR2.

An overview of species list is provided:

Species list of toggle-switch network.

where each species with its specific identifier has its own meaning:

  • 0:E_coli : E.coli cell;
  • 1:IPTG: IPTG in flask;
  • 2:DNA: initial transformed plasmids;
  • 3:IPTG: IPTG in E.coli due to diffusion;
  • 4:RNA: mRNA of tetR and GFP;
  • 5:RNA: mRNA of LacI;
  • 6:tetR154: tetR protein;
  • 7:GFP12923: GFP;
  • 8:lacI153: LacI protein;
  • 9:(tetR154)2: tetR dimer;
  • 10:(lacI153)2: LacI dimer;
  • 11:DNA;(tetR154)2: complex of tetR dimer binding to pTet gene of plasmid DNA;
  • 12:(lacI153)4: LacI tetramer;
  • 13:DNA;(lacI153)4: complex of LacI tetramer binding to pLacI gene of plasmid DNA;
  • 14:DNA;(lacI153)4;(tetR154)2: complex of plasmid DNA with both pLacI and pTet genes bound with LacI tetramer and tetR dimer, respectively;
  • 15:IPTG;(lacI153)4: complex of IPTG binding with LacI tetramer;

Since there are 65 reactions in total, we only provide a screenshot (we strongly recommend users to run our example to learn more details about automatic modeling):

Species list of toggle-switch network.

Moreover, parameters of our modeling network are provided (we spend much efforts on tuning parameters) based on papers and estimates together:

  • Initial time: 0 s
  • Initial volumes:
    • Flask: 0.4 l
    • E_coli: 1.6856e-012 l
  • Initial concentrations:
    • 0:E_coli: 1e-020 mol/l
    • 1:IPTG: 0 mol/l
    • 2:DNA: 2.4e-009 mol/l
    • 3:IPTG: 0 mol/l
    • 4:RNA: 0 mol/l
    • 5:RNA: 0 mol/l
    • 6:tetR154: 0 mol/l
    • 7:GFP12923: 0 mol/l
    • 8:lacI153: 0 mol/l
    • 9:(tetR154)2: 0 mol/l
    • 10:(lacI153)2: 0 mol/l
    • 11:DNA;(tetR154)2: 0 mol/l
    • 12:(lacI153)4: 0 mol/l
    • 13:DNA;(lacI153)4: 0 mol/l
    • 14:DNA;(lacI153)4;(tetR154)2: 0 mol/l
    • 15:IPTG;(lacI153)4: 0 mol/l
  • Reaction parameters:
    • reproduction of Ecoli cell
      • growth constant: 0.000192 1/s
      • maximum concentration: 1.66e-012 mol/l
    • diffusion of IPTG molecule
      • diffusion constant: 0.014 1/s
    • transcription
      • transcription rate of pTet/pLacI: 0.5 1/s
    • replication of reverse pSB3C5
      • replication constant: 0.003 1/s
    • repression of reverse pSB3C5 replication
      • max concentration of pSB3C5: 2.847e-008 mol/l
    • translation
      • translation rate: 0.1 1/s
    • degradation of mRNAs
      • degradation of mRNA molecules: 0.0048 1/s
    • degradation of proteins in E.coli_3
      • degradation rate of proteins: 0.0023 1/s
    • Laci-Laci dimerization
      • kon: 1.25e+007 l/(mol*s)
      • koff: 10 1/s
    • binding forward-ptetR:tetR2
      • kon: 1e+008 l/(mol*s)
      • koff: 0.001 1/s
    • tetR-tetR dimerization_2
      • kon: 4e+011 1/(mol*s)
      • koff: 10 1/s
    • LacI2-LacI2 dimerization
      • kon: 1e+014 l/(mol*s)
      • koff: 10 1/s
    • binding reverse-placI:lacI4
      • kon: 4e+011 l/(mol*s)
      • koff: 0.04 1/s
    • IPTG:lacI4 binding
      • kon: 154000 l/(mol*s)
      • koff: 0.2 1/s



Repressilator

Repressilator

The repressilator is a synthetic genetic regulatory network designed to exhibit a stable oscillation shown via expression of GFP (green fluorescent protein). The work is reported by Michael B. Elowitz and Stanislas Leibler in their work at 2000. They constructed a system of three genes connected in a cyclical negative feedback loop so that gene A represses gene B, which represses gene C, which represses gene A. The implementation of this idea used a low copy plasmid encoding the repressilator, and the higher copy reporter, which were used to transform a culture of Escherichia coli.

Parts assembling: the top assembling is the construction used in our software and the bottom one is the toggle switch design in their work.

We construct a model to stimulate the behavior of repressilator, the results are showed as following:

USTCS repressilator.JPG

The meanings of the legend used in the figure are demonstrated as follows: [14 (lacI153)4] refers to the binding product of four lacI protein molecules, [12 (CIlam154)2] refers to the binding product of two CIlam protein molecules, while [10 (tetR154)2] refers to the binding product of two tetR protein molecules. The system exhibits oscillation behavior after initial time of 86000, the concentration of (lacI)4, (CIlam)2 and (tetR)2 changes periodically as the function of time. To be specific, the concentration of (tetR)2 increase when the concentration of (lacI)4 declines due to the remove of repression. And the concentration reaches the peak level when the concentration of (LacI)4 reaches its lowest level. Then the concentration of (tetR)2 decreases while the concentration of (CIlam)2 begins to arise because the repression from (tetR)2 is gradually relieved. Noted that the concentration peak level of (CIlam)2 and (tetR)2 are nearly more than twice the max concentration of (lacI)4, this may attribute to the difference of binding tendency between (CIlam)2, (tetR)2 and (lacI)4. The internal binding strength of (tetR)2 dimer and (CIlam)2 dimer are stronger than that of (lacI)4 tetramer. more details

Modeling Details of Repressilator

Modeling Details of Repressilator


Key points of this modeling are:

  • LacI protein tends to form LacI dimer, which tends to form LacI tetramer further.
  • Only LacI tetramer binds with pLacI gene and thus repressing expression of its downstream genes.
  • TetR protein only forms dimer.
  • Only tetR dimer binds with pTet gene and thus repressing expression of its downstream genes.
  • One IPTG molecule binds with one LacI tetramer to form complex IPTG:LacI4.
  • cIlam protein only forms dimer.
  • Only cIlam dimer binds with pcIlam gene and thus repressing expression of its downstream genes.


An overview of species list is provided:

USTCS graph1.JPG


where each species with its specific identifier has its own meaning:

  • 0:E_coli: E.Coli cell;
  • 1:IPTG: IPTG in flask;
  • 2:DNA: initial transformed plasmids;
  • 3:IPTG: IPTG in E.Coli due to diffusion;
  • 4:RNA: mRNA of tetR;
  • 5:RNA: mRNA of lacI;
  • 6:RNA: mRNA of cIlam;
  • 7:tetR154: tetR protein;
  • 8:lacI153: lacI protein;
  • 9:cIlam156: lacI protein;
  • 10:(tetR154)2: tetR dimer;
  • 11:(lacI153)2: lacI dimer;
  • 12:(cIlam156)2: cIlam dimer;
  • 13:DNA;(tetR154)2: complex of tetR dimer binding to pTet gene of plasmid DNA;
  • 14:(lacI153)4; lacI tetramer;
  • 15:DNA;(cIlam156)2: complex of cIlam dimer binding to pCI gene of plasmid DNA;
  • 16:DNA;(cIlam156)2;(tetR154)2: complex of plasmid of DNA with both pCI and pTet genes bound with cIlam dimer and tetR dimer;
  • 17:DNA;(lacI153)4: complex of LacI tetramer binding to pLacI gene plasmid DNA;
  • 18:DNA;(lacI153)4;(tetR154)2: complex of plasmid DNA with both pLacI and pTet genes bound with LacI tetramer and tetR dimer, respectively;
  • 19:IPTG;(lacI153)4: complex of LacI tetramer binding to pLacI gene of plasmid DNA;
  • 20:DNA;(cIlam156)2;(lacI153)4: complex of plasmid DNA with both pCI and placI genes bound with cIlam dimer and lacI tetramer, respectively;
  • 21:DNA;(cIlam156)2;(lacI153)4;(tetR154)2: complex of plasmid DNA with both pCI, placI and pTet genes bound with cIlam dimer, lacI tetramer and tetR dimer, respectively;

Since there are 153 reactions in total, we only provide a screenshot (we strongly recommend users to run our example to learn more details about automatic modeling):

USTCS graph2.JPG

Moreover, parameters of our modeling network are provided below:

  • Initial time: 0 s
  • Initial volumes:
  • Chemostat 0.1 l
  • E_coli 4.4247e-006 l
  • Initial concentrations:
  • 0:E_coli 1.05e-013 mol/l
  • 1:IPTG 0.001 mol/l
  • 2:DNA 2.4e-009 mol/l
  • 3:IPTG 0 mol/l
  • 4:RNA 0 mol/l
  • 5:RNA 0 mol/l
  • 6:RNA 0 mol/l
  • 7:tetR154 0 mol/l
  • 8:lacI153 0 mol/l
  • 9:cIlam156 0 mol/l
  • 10:(tetR154)2 0 mol/l
  • 11:(lacI153)2 0 mol/l
  • 12:(cIlam156)2 0 mol/l
  • 13:DNA;(tetR154)2 0 mol/l
  • 14:(lacI153)4 0 mol/l
  • 15:DNA;(cIlam156)2 0 mol/l
  • 16:DNA;(cIlam156)2;(tetR154)2 0 mol/l
  • 17:DNA;(lacI153)4 0 mol/l
  • 18:DNA;(lacI153)4;(tetR154)2 0 mol/l
  • 19:IPTG;(lacI153)4 0 mol/l
  • 20:DNA;(cIlam156)2;(lacI153)4 0 mol/l
  • 21:DNA;(cIlam156)2;(lacI153)4;(tetR154)2 0 mol/l
  • Initial values of global quantities:
  • ts 0
  • te 40000
  • s 0.001
  • t 0
  • Reaction parameters:
  • reproduction of Ecoli cell
    • kgr 0.000192 1/s
    • maxc 1.66e-012 mol/l
  • dilution of species in chemostat
    • k1 0.00017 1/s
  • diffusion of IPTG molecule
    • k_diff 0.014 ?
  • dilution_2 of species in E.coli
    • kgr 0.000192 1/s
    • maxc 1.66e-012 mol/l
  • transcription
    • k_tc 0.5 1/s
  • replication of reverse pSB1A3
    • kgr 0.003 1/s
  • repression of reverse pSB1A3 replication
    • kgr -0.003 ?
    • maxc 4.746e-007 ?
  • translation
    • k_tl 0.1 1/s
  • degradation of mRNAs
    • k1 0.0048 1/s
  • tetR-tetR dimerization
    • kon 1.79e+011 l/(mol*s)
  • degradation of proteins in E.coli
    • k1 0.0023 1/s
  • Laci-Laci dimerization
    • kon 1.25e+007 l/(mol*s)
  • cI (lambda)-cI (lambda) dimerization
    • kon 1.79e+011 l/(mol*s)
  • binding reverse-ptetR:tetR2
    • kon 1e+008 l/(mol*s)
  • LacI2-LacI2 dimerization
    • kon 1e+014 l/(mol*s)
  • binding reverse-pcI (lambda):cI2 (lambda)
    • kon 1e+009 l/(mol*s)
  • binding reverse-placI:lacI4
    • kon 4e+011 l/(mol*s)
  • IPTG:lacI4 binding
    • kon 154000 l/(mol*s)