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- | <td width="750" bgcolor="#414141">
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- | <div class="desc">
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- | <div class="heading">A TOUR OF THE UNIVERSITY OF CALGARY iGEM TEAM</div>
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- | <br>
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- | <center>
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- | <img src="https://static.igem.org/mediawiki/2009/4/41/Calgary_Tour5.png">
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- | </center>
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- | <br>
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- | We've reached modelling, the <b>fifth</b> stop on our tour! We've looked in to two different methods of modelling our system: Differential Equation Based Modelling and Membrane Computing. Here, you can explore the similarities and differences, as well as the functions of each method. As well, you can find the results of our characterization of the signalling pathway. Once you're done, we'll move on to the Second Life component of the project <a href="https://2009.igem.org/Team:Calgary/Second_Life">HERE</a>.
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- | </div>
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- | </td>
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| <td width="750" bgcolor="#414141" valign="top"> | | <td width="750" bgcolor="#414141" valign="top"> |
| <br> | | <br> |
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| + | <div class="heading"> |
| + | INTRODUCTION TO OUR MEMBRANE COMPUTING APPROACH |
| + | </div> |
| + | <div class="desc"> |
| <div class="button"> | | <div class="button"> |
| <img src="http://i1001.photobucket.com/albums/af132/igemcalgary/Mo.gif" align="left"> | | <img src="http://i1001.photobucket.com/albums/af132/igemcalgary/Mo.gif" align="left"> |
| </div> | | </div> |
- | <div class="heading">
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- | DIFFERENTIAL EQUATIONS MODELLING METHODS
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- | </div>
| + | <br> |
- | <div class="desc">
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- | The simbiology interface from Matlab was used to simulate the differential equations model. Chemical Kinetic equations were used to build the model for simulation.
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- | <br><br>
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- | <center> <img src="https://static.igem.org/mediawiki/2009/9/9b/ReactA.JPG"> </center> <br>
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- | <center> Fig : The Reaction of Species A with B to produce C and D </center><br>
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| <br> | | <br> |
- | <center><img src="https://static.igem.org/mediawiki/2009/archive/b/bd/20091019225744%21Rate.JPG">
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- | </center> <br>
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- | <center> Fig : The Chemical Kinetic Rate Equation </center>
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- | <br><br>
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- | k is the kinetic rate constant. The size of k will determine the speed of the reaction. A smaller value of k will produce a slow reaction rate while a larger value of k will produce a fast reaction rate. <br><br>
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- | [A] is the amount of reactant A present. <br><br>
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- | The simulations were run for 50000 seconds . It was considered to be enough time for the system to reach equilibrium after disturbance.<i>
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- | <br><br>
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- | <b>Sundial Solver</b>
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- | The sundial solver (SUNDIALS) was developed so that robust time integrators and non-linear solvers can be easily combined with already existing simulation codes. Minimal information from user is required and this solver allow users to easily supply their own data structures. The Sundials solvers are part of a third-party package developed at Lawrence Livermore National Laboratory. Built-in ordinary differential equation (ODE) solvers (ode45 and ode15s) are also part of the interface.
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- | <br><br>
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- | When sundials solver is selected, the program selects one of teh two sundials solvers that suits your model: CVODE or IDA. CVODE is used for systems of ODEs (stiff or nonstiff) and this type of solver is usually used for a model that has no algebraic rules. IDA is a differential-algebraic equation (DAE) solver and it is usually used when there is one more algebraic rules. Since our model incorporates an event (the addition of autoinducer-II (AI-2)), this type of solver was used in our model. More information can be found here: https://computation.llnl.gov/casc/sundials/description/description.html <i>
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| + | <html> |
| + | <center> |
| + | <img src="https://static.igem.org/mediawiki/2009/0/0b/Calgary_MCLogo.png" width="600" height="500"> |
| + | <br> |
| + | <a href="http://www.wolfram.com"><u>Copyright: "Spikey" is the logo of Wolfram Research Inc.</u></a> |
| + | </center> |
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- | </div>
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| <br> | | <br> |
- | <div class="heading">The Reactions</div>
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- | <div class="desc">
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- | The system was represented by the following reactions. The reactions with double headed arrows have two rate constants(forward/ reverse rate constant). All reactions were assumed to be elementary reactions. </div>
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| <br> | | <br> |
- | <center><img src ="https://static.igem.org/mediawiki/2009/5/5f/Reactions1.tif"></center> | + | <div class="heading"> |
| + | <center> |
| + | A Model of the Quorum Sensing System in Genetically Engineered E.Coli Using Membrane Computing |
| + | </center> |
| <br> | | <br> |
- | <div class="heading">Parameter Rationale</div>
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- | <div class="desc">
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| </div> | | </div> |
- | <center><b>Table: Initial Values of the Species in the System</b> </center> | + | <div class="heading">Abstract:</div> |
| + | Quorum sensing is the way bacteria communicate with each other; they release signaling molecules to their environment and other bacteria receive and recognize the signals. Many species of bacteria use the information obtained to coordinate their gene expression in response to the size of their population, which is known as Quorum Sensing. In this article, we present a novel model of a synthetic Autoinducer-2 signaling system in genetically engineered Escherichia coli (E.coli) bacteria using the recently proposed Membrane Computing (MC) framework. Membrane computing is a branch of natural computing that is inspired by biological membranes structures and functions and is used for modeling features of cells in biological systems. |
| + | <br><br> |
| + | This model allows us to observe the behavior of each individual cell as well as the emergent properties of the whole population. It also enables us to manipulate factors involved in the simulation to understand their effects in individual as well as colony behaviors. |
| + | <br><br> |
| + | Having defined our model in terms of compartments and interactions rules, any biological system that can be explained in terms of compartments and their corresponding rules can be sim- ulated with this platform. In other words, we have developed a biological language for modelling biological systems using MC framework. |
| <br> | | <br> |
- | <table width="700" border="1" bgcolor="#414141" align = "center">
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- | <tr>
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- | <td>Species</td>
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- | <td> Initial Value </td>
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- | <td>Rationale</td>
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- | </tr>
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- | <tr>
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- | <td>AI-2</td>
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- | <td>0</td>
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- | <td><align = "left">Initially the amount of AI-2 is constant at 0. After an equilibruim is established variable amounts of AI-2 are added at different simulations. <br><br> </td>
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- | </tr>
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- | <tr>
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- | <td>LuxPQ</td>
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- | <td>10</td>
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- | <td>The amount of LuxPQ varies depending on the simulation run.<br><br> </td>
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- | </tr>
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- | <tr>
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- | <td>AI-2:LuxPQ</td>
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- | <td>0</td>
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- | <td>This value is kept at time = 0 because the initial concentration of AI-2 is 0. <br><br></td>
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- | </tr>
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- | <tr>
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- | <td>LuxU:p</td>
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- | <td>2</td>
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- | <td>----</td>
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- | </tr>
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- | <tr>
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- | <td>LuxU</td>
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- | <td>1000</td>
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- | <td>There is a lot of this species present in the cell in nature. To signify plenty a value of 1000 is assigned.<br><br></td>
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- | </tr>
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- | <tr>
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- | <td>LuxO:p</td>
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- | <td>2</td>
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- | <td>Equal amounts of LuxO:p and LuxU:p was considered in the model because LuxU:p phosphorylates LuxO . The phosphorylation reaction is considered to be a fast reaction therefore there are equal amounts of the two proteins present.<br><br></td>
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- | </tr>
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- | <tr>
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- | <td>LuxO</td>
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- | <td>1000</td>
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- | <td>There are equal amounts of LuxO and LuxU present since they are encoded within the same operon in the cell.<br><br></td>
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- | </tr>
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- | <tr>
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- | <td>p</td>
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- | <td>10.0658</td>
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- | <td>We assume that there is enough p is the environment that it doesn’t become a limiting factor. For that reason we assign p as a constant value in simbiology. (It doesn’t really matter that the initial amount is presented as a comparatively small number in this case. ) <br><br></td>
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- | </tr>
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- | <tr>
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- | <td>sigma54</td>
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- | <td>0.14183</td>
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- | <td>This amount is kept at a constant value to ensure that this value does not become a limiting factor.<br><br></td>
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- | </tr>
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- | <tr>
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- | <td>sigma54:LuxO:p:Pqrr4</td>
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- | <td>0.63</td>
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- | <td> There is only 1 copy of Pqrr4 present in each cell . since in the reaction equations Pqrr4 is shared between 2 other equations we decided to break the concentration of Pqrr4 between 3 species: sigma54:LuxO:p:Pqrr4 , Pqrr4 , sigma54:Pqrr4 . The initial values of the three species add up to one. The fractions of the Pqrr4 combination species are weighted differently . Since the Pqrr4 promotor stays on most of the time we decided the sigma54:LuxO:p:Pqrr4 complex should recieve the most weight. Pqrr4 is assumed to stay unbound from any complex for the least amount of time therefore Pqrr4 initial amount is the smallest. <br><br></td>
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- | </tr>
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- | <tr>
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- | <td>Sigma54:Pqrr4</td>
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- | <td>0.345</td>
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- |
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- | </tr>
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- | <tr>
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- | <td>Pqrr4</td>
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- | <td>0.025</td>
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- |
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- | </tr>
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- | <tr>
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- | <td>GFP</td>
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- | <td> 0</td>
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- | <td> The model assumes that initially we have no GFP present . The simulation is allowed to run till the protein reaches equilibrium . The AI-2 is added after equilibrium conditions and a drop in GFP levels is observed.<br><br></td>
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- | </tr>
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- | <tr>
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- | <td>mRNA</td>
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- | <td>0</td>
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- | <td>The justification for the initial value of mRNA is the same as GFP<br><br></td>
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- | </tr>
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- | </table>
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| <br> | | <br> |
- | <center><b> Table: The Kinetic Rate Constant Values</b> </center>
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| <br> | | <br> |
- | <table width="200" border="1" bgcolor="#414141" align = "center"> | + | <div class="heading">Why Model?</div> |
- | <tr>
| + | During the past two decades, biology and computer science have been converging; many biologists use mathematical and computational models as powerful tools to gain a deeper understanding of biological systems [7]. Given that molecular biology experiments in vitro are very expensive and time consuming, building models of biological processes as a preliminary step helps to circumvent some of the drawbacks of performing hypothesis-testing in the wet lab. This is why we feel that computational modeling is important and useful. Particularly with the extent of synthetic biology, many of the biological systems that are being researched could not be found in nature because they are genetically engineered, so their behaviors are unknown and need to be characterized. For instance, in this project, a synthetic autoinducer-2 (AI-2) signaling system constructed in E.coli is taken from its natural counterpart in Vibrio harveyi, bypassing its small regulatory RNA networks. This engineered biological system shows new behaviors that are not observed in nature and need to be studied and characterized. Based on the reasons given above, using models could provide a faster and cheaper shortcut for biologists to gain a better under- standing of the newly engineered system. However, it should be stressed that models, regardless of their accuracy, could not be used as a replacement for vitro experiments; however, they could be used as a preliminary step for characterizing the system and as a shortcut for biologists to gain a better understanding of the newly engineered system. |
- | <td>Rate Constants</td>
| + | <br><br> |
- | <td>Constant Value</td>
| + | Emphasizing compartmentalization as a cornerstone feature of cells, membrane computing (MC) is a powerful approach for studying reactions in biological systems. The most important feature of this approach that we would like to emphasize is that it could create a common modeling language that is mathematical and precise and could be understood by biologists. MC allows the user not only to focus on interactions at the level of an individual cell, but also to observe the emergent properties of entire cell populations. The MC approach seems to be ideal for the construction of a quorum-sensing model since compartmentalization of the signal and the cascade proteins are critical features of this process. |
- | <td>Rationale</td>
| + | |
- | </tr>
| + | |
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- | <tr>
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- | <td> kPhosU</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kPhosO</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kTranscription</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- |
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- | <tr>
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- | <td>kTranslation</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kProtDegrad</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td> kAI2bind </td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kAI2unbind</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kPQphosphatase</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kNSPU</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kNSPO</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kPqrr4Sig54unbind</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kPqrr4Sig54bind</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kOPqrr4Unbind</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kOPqrr4bind</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | <tr>
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- | <td>kRNAdegrad</td>
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- | <td> </td>
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- | <td> </td>
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- | </tr>
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- | </table>
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| + | </div> |
| <br> | | <br> |
| </td> | | </td> |