Team:Aix-Marseille/Modeling

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     <h1 class="project-title">S.E.colization : Green light, GO!</h1>
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     <h1 class="project-title">Our model</h1>
      
      
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           <span class="project-tag" id="overall"></span>
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           <span class="project-tag" id="intro"></span>
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           <h1>Overall project summary</h1>
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           <h2>Introduction</h2>
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           <p>Our project centers around synchronizing a culture of E.coli cells, so that they all divide synchronously and change color from green to red and back as they go through the cell cycle. More specifically the culture stops dividing full of red cells and then at regular intervals the cells turn green and divide before returning to the red quiescent state.</p>
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           <p>Part modeling was not an easy task. Let me explain. I am a novice in the field of mathematical engineering and that made more than seven years since I was not made of Biology.</p>
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          <p>Our project is based on the feedback cycle of chemiotaxie in <i>Escherichia coli</i>. To develop our model, it was first essential to know the ins and out. To do so, the study of narratives on the general biology were paramount; it was only later that I got interested in the chemiotaxie.</p>
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           <p>This project relies on developing several new and original modules and components which we believe will be generally useful to other teams in future projects. The first component is an inducible Serine production system based on a mutant SerA protein that is insensitive to retro-inhibition by the pathway product (serine) allowing the development of bacteria secreting serine. The second component involves re-engineering the chemotaxis system to drive changes in gene expression rather than changes in flagellar rotation direction. This component is particularly innovative and potentially useful as it can form the basis of several different synthetic signaling system allowing regulation of gene expression by a wide range of different signaling molecules. The third component, or set of components, is a series of switches that change the protein expressed in response to a signal, that is rather than a simple induction of expression as observed with most inducible systems, one protein will be expressed while a second is repressed. Again it is hoped that the bricks that make this system will be applicable in multiple new projects. Each of these components is designed so that if they are introduced together they will produce an oscillator that regularly drives the switch modules between their two states. This oscillator will be coupled to color changes, the initiation of the cell cycle, and serine production (to make the feedback loop). A particularity of the oscillator is that by passing through a secreted substrate and sensor system the oscillations should be culture wide, and all the cells should fall into phase. Furthermore by using the chemotaxis system which has an intrinsically differential sensor (rather than an absolute sensor) it is hoped that the oscillations can be driven over many cell cycles.</p>
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           <p>Subsequently, we made contact with a brilliant modeler of this field from the University of Aix-Marseille: Ms. Elysabeth Remi. Together, we tried to synthesize the system to be modeled and some approximations which we considered natural at first.</p>
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           <p>This project is relatively fundamental but will we hope provide several generally useable and reusable modules for more applied projects where multiple signaling pathways, culture wide oscillators or switches are required. The project involves both experimental constructions, largely derived from previously published work by other authors, resulting in numerous new Biobricks, and also a strong modeling component to understand the function and constraints of the oscillator that we propose to build and the expected effects on bacterial behavior.</p>
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          <span class="project-tag" id="mod_sys"></span>
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          <h2>Model System</h2>
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              <img href="#" class="img-rounded" src="https://static.igem.org/mediawiki/2014/9/9f/Schema_amu_projet.jpg" style="width:100%" id="schema">
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          <p>The scheme is simple. Each cell of Escherichia coli has an amount of <i>CheA</i> in its cytoplasm. This one will phosphorylate <i>CusR</i> which in turn will catalyze the formation of <i>ppGpp</i> (via <i>RelA</i>) and the <i>SerA</i>. The formation of <i>ppGpp</i> will cause failure of cell division. <i>SerA</i> is a protein that will lead to the formation of <i>Serine</i> via <i>SerC</i> and <i>SerB</i>. This intracellular <i>Serine</i> will migrate to the outside of the cell. However, the histidine kinase <i>CheA</i> is sensitive to the gradient of <i>Serine</i> outside, thanks to chemoreceptor. Moreover, since the outer homogeneous media is considered, all cells will receive the same gradient outside <i>Serine</i>. This is the start of cell synchronization. Increasing <i>Serine</i> will create a decrease in the phosphorylation of <i>CheA</i>, involving a decrease <i>CusR</i> phosphorylated. Thus, the rate will decrease <i>ppGpp</i> allow cell division and of all cells at the same time. After their split, the pattern will repeat itself.</p>
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              <small><i>The different cellular pathways involved in the E.coli cells synchronization</i></small>
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          <span class="project-tag" id="simplify"></span>
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          <h2>Simplifying assumptions</h2>
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           <p>In order to simplify our model and lack of experimental data, we overlook some things.</p>
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          <ol>
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            <li>First, we assume that the formation of <i>Serine</i> is done directly by <i>SerA</i>. In reality, training <i>SerC</i> and <i>SerB</i> are much faster than those of <i>SerA</i> and <i>Serine</i>.</li>
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            <li>The concentration of <i>ppGpp</i> being by fluorescence, we do not get that of <i>RelA</i>. We will take into account that the formation of <i>ppGpp</i> by <i>CusR</i> phosphorylated.</li>
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            <li><i>CheA</i> phosphorylates naturally <i>CheY</i> and not <i>CusR</i>. We have considered the kinetic constants of <i>CheY</i> for <i>CusR</i>.</li>
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            <li>We do not know the constants of <i>CheA</i> deactivation by the gradient of <i>Serine</i>. We've replaced by those of the gradient <i>Aspartate</i> which are easily found in the literature.</li>
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            <li>The threshold of <i>ppGpp</i> for cell division is not known, we took a concentration we know realistic: 1 μM.</li>
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            <li>6. Some kinetics are expected to follow a law of Michaelis-Menten. However, the system is rather slow and concentrations vary only slightly around the concentrations of half-maximal speed. Thus, we assume that they follow linear laws.</li>
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            <li>We didn't have the time to test the model experimentally so we took an arbitrary time scale.</li>
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          <span class="project-tag" id="diff_equa"></span>
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          <h2>Differential equations</h2>
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          <p>Here are the differential equations modeling our system.</p>
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           <span class="project-tag" id="init_val"></span>
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           <h1>Project Details</h1>
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           <h2>Initial values</h2>
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           <p>Some constants have been found experimentally or guessed from existing data.</p>
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            <span class="project-tag" id="serine_part"></span>
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           <div class="project-details">
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            <h2 class="subtitle">Serine, a signal molecule</h2>
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             <img class="img-rounded" src="https://static.igem.org/mediawiki/2014/0/06/AMU_Team-data_values.png" style="width: 40%">
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                <img class="img-rounded" src="https://static.igem.org/mediawiki/2014/1/1a/AMU_Team-serine_part_schema.png">
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              <p>Modified E.coli strains we used for this part of the project were designed and constructed as follows:</p>
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              <ul>
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                <li>The <i>SdaB</i> gene encoding a Serine transporter was deleted,</li>
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                <li>The <i>SdaC</i> gene encoding for a protein able to degrade Serine into 3-PG was deleted.</li>
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                <li>The <i>CheA</i> gene (BBa_K1349006) was fused with a (SH3)<sub>4</sub> module was expressed, and the native CheA gene was deleted. The (SH3)<sub>4</sub> module is to allow a synthetic interaction with the response regulator, see below.</li>
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                <li>A truncated <i>SerA</i> gene (BBa_K1349000) was expressed: the mutated SerA is no longer sensitive to feedback inhibition by serine. Expression of this gene leads to accumulation of high concentrations of serine.</li>
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              </ul>
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              <p>The truncated <i>SerA</i> gene is controlled by CusR promoter which is activated by the accumulation of phosphorylated CusR protein.</p>
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            <span class="project-tag" id="CheA-SH3_part"></span>
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            <h2 class="subtitle">CheA‐SH3, modified chemotaxis signalling</h2>
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              <img class="img-rounded" src="https://static.igem.org/mediawiki/2014/d/d1/AMU_Team-CheA-SH3_part_schema.png">
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            <p>This regulatory circuit is designed as follows. A change in the extracellular Serine concentration is detected by Tsr receptor. The Tsr inhibits the constitutive activity of the CheA (Histidine kinase) and reduces auto-phosphorylation. This natural circuit is modified so that CheA transfers phosphate groups not only to CheB and CheY as usual but also to CusR. Consequently, the CusR transcription factor is less phosphorylated and binds less well to its DNA recognition sequence.</p>
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            <p>When extracellular Serine concentration is stabilized, Tsr is not stimulated anymore and stops inhibiting CheA. As a consequence, CheA becomes activated again and phosphorylates CusR.</p>
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            <p>In order to modify the phosphorylation patern of CheA we have used the synthetic protein interaction modules developped by Whitaker et al. 2012 (PNAS 109: 18090-18095). The CheA (BBa_K1349006) is fused to a (SH3)<sub>4</sub> module (BBa_K1349005) and CusR to a LZa leucine zipper (BBa_K1349007), these two proteins will then interact in the presence of the adaptor module an SH3-pep-LZA protein (Bba_K1349008).</p>
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            <p>The combination of these first two parts defines an culture wide oscilatory control circuit that responds through changing extracellular serine levels.</p>
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             <span class="project-tag" id="ppGpp_part"></span>
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            <h2 class="subtitle">Regulation of intracellular ppGpp concentration; green light, go !</h2>
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                <img class="img-rounded" src="https://static.igem.org/mediawiki/2014/e/e6/AMU_Team-ppG_parGpp_schema.png">
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              <p>To make the oscillator do something we have devised two reporter modules that respond to the level of CusR phosphorylation. The first modulating cellular levels of ppGpp the secondary messanger responsible for the stringent response, and the second leading to green or red cells.</p>
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              <p>In the first reporter module the phosphorylated CusR transcription factor binds to the CusR promoter (BBa_K1349003) and activates RelA (BBa_K1349001) expression. <i>RelA</i> is an enzyme that synthesises ppGpp increasing the intracellular concentration. It is known that ppGpp blocks the initiation of S phase in the bacterial cell cycle, leading to the arrest of cell division. At the same time, phosphorylated CusR attaches to the CusR-Box (BBa_K1349002) between a promoter and the <i>Mesh1</i> gene (BBa_K1349004), inhibiting synthesis of the Mesh1 enzyme. Mesh1 is an enzyme from Drosophila melanogaster that hydrolyses ppGpp. Thus in the presence of phosphorylated CusR this module ensures the presence of RelA and the absence of Mesh1 resulting in the accumulation of ppGpp. In the absence of phosphorylated CusR, the regulator is unable to bind to either the promoter or the binding site upstream of the Mesh1 gene. Consequently RelA is not synthsised, but the Mesh1 protein can be synthesised resulting in the hydrolysis of ppGpp. This reporter module constitutes a two way switch synthesising either RelA, in the presence of phosphorylated CusR, or Mesh1, in the presence of unphosphorylated CusR.</p>
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              <p>The second reported module follows the same logic but RelA is replaced with RFP and Mesh1 with GFP. Thus changing levels of CusR phosphorylation can drive red/green color changes.</p>
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            <span class="project-tag" id="refs"></span>
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            <h2 class="subtitle">References</h2>
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              <p>Pertinent articles related to our project:</p>
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              <h3 class="text-info">Top Papers</h2>
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              <ul>
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                <li>Gudipaty SA1, Larsen AS, Rensing C, McEvoy MM. Regulation of Cu(I)/Ag(I) efflux genes in Escherichia coli by the sensor kinase CusS. FEMS Microbiol Lett. 2012 May;330(1):30-7. </li>
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                <li>Rudd KE, Bochner BR, Cashel M, Roth JR. Mutations in the spoT gene of Salmonella typhimurium: effects on his operon expression. J Bacteriol. ;163(2):534-42, 1985.</li>
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                <li>Whitaker WR1, Davis SA, Arkin AP, Dueber JE. Engineering robust control of two-component system phosphotransfer using modular scaffolds. Proc Natl Acad Sci U S A. 2012 Oct 30;109(44):18090-5. </li>
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                <li>Ferullo DJ, Cooper DL, Moore HR, Lovett ST. Cell cycle synchronization of Escherichia coli using the stringent response, with fluorescence labeling assays for DNA content and replication. Methods. 2009 May;48(1):8-13.</li>
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                <li>Peters-Wendisch P1, Stolz M, Etterich H, Kennerknecht N, Sahm H, Eggeling L. Metabolic engineering of Corynebacterium glutamicum for L-serine production. Appl Environ Microbiol. 2005 Nov;71(11):7139-44.</li>
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              <h3 class="text-info">Related Papers</h2>
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              <ul>
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                <li>Wahl A, My L, Dumoulin R, Sturgis JN, Bouveret E.Antagonistic regulation of dgkA and plsB genes of phospholipid synthesis by multiple stress responses in <i>Escherichia coli. Mol Microbiol.</i> 80(5):1260-75, 2011.</li>
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                <li>Collins CH. Cell-cell communication special issue. ACS Synth Biol. 2014 Apr 18;3(4):1978.</li>
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                <li>Hsiao V, de Los Santos EL, Whitaker WR, Dueber JE, Murray RM. Design and Implementation of a Biomolecular Concentration Tracker. ACS Synth Biol. 2014 May 15.</li>
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                <li>Park JH, Oh JE, Lee KH, Kim JY, Lee SY. Rational design of Escherichia coli for L-isoleucine production. ACS Synth Biol. 2012 Nov 16;1(11):532-40. </li>
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                <li>Tan MH1, Kozdon JB, Shen X, Shapiro L, McAdams HH. An essential transcription factor, SciP, enhances robustness of Caulobacter cell cycle regulation. Proc Natl Acad Sci U S A. 2010 Nov 2;107(44):18985-90.</li>
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                <li>Park H, Saha SK, Inouye M. Two-domain reconstitution of a functional protein histidine kinase. Proc Natl Acad Sci U S A. 1998 Jun 9;95(12):6728-32.</li>
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                <li>Porter SL, Wadhams GH, Armitage JP. Signal processing in complex chemotaxis pathways.Nat Rev Microbiol. 2011 Mar;9(3):153-65.</li>
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                <li>Olson EJ, Hartsough LA, Landry BP, Shroff R, Tabor JJ. Characterizing bacterial gene circuit dynamics with optically programmed gene expression signals. Nat Methods. 2014 Apr;11(4):449-55.</li>
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                <li>Skerker JM1, Perchuk BS, Siryaporn A, Lubin EA, Ashenberg O, Goulian M, Laub MT. Rewiring the specificity of two-component signal transduction systems. Cell. 2008 Jun 13;133(6):1043-54.</li>
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                <li>Skerker JM1, Prasol MS, Perchuk BS, Biondi EG, Laub MT. Two-component signal transduction pathways regulating growth and cell cycle progression in a bacterium: a system-level analysis. PLoS Biol. 2005 Oct;3(10):e334.</li>
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                <li>Gonzalez D, Collier J. Effects of (p)ppGpp on the progression of the cell cycle of Caulobacter crescentus. J Bacteriol. 2014 Jul;196(14):2514-25.</li>
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                <li>Thanbichler M. Synchronization of chromosome dynamics and cell division in bacteria. Cold Spring Harb Perspect Biol. 2010 Jan;2(1):a000331.</li>
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                <li>Wang X, Vallurupalli P, Vu A, Lee K, Sun S, Bai WJ, Wu C, Zhou H, Shea JE, Kay LE, Dahlquist FW. The linker between the dimerization and catalytic domains of the CheA histidine kinase propagates changes in structure and dynamics that are important for enzymatic activity. Biochemistry. 2014 Feb 11;53(5):855-61.</li>
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                <li>Eggeling L, Sahm H. New ubiquitous translocators: amino acid export by Corynebacterium glutamicum and Escherichia coli. Arch Microbiol. 2003 Sep;180(3):155-60.</li>
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                <li>Laub MT, Goulian M. Specificity in two-component signal transduction pathways. Annu Rev Genet. 2007;41:121-45.</li>
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                <li>Alon U, Camarena L, Surette MG, Aguera y Arcas B, Liu Y, Leibler S, Stock JB. Response regulator output in bacterial chemotaxis. EMBO J. 1998 Aug 3;17(15):4238-48.</li>
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                <li>Chang YC, Armitage JP, Papachristodoulou A, Wadhams GH. A single phosphatase can convert a robust step response into a graded, tunable or adaptive response. Microbiology. 2013 Jul;159(Pt 7):1276-85.</li>
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                <li>Ganesh I, Ravikumar S, Lee SH, Park SJ, Hong SH. Engineered fumarate sensing Escherichia coli based on novel chimeric two-component system. J Biotechnol. 2013 Dec;168(4):560-6.</li>
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                <li>Jonas K. To divide or not to divide: control of the bacterial cell cycle by environmental cues. Curr Opin Microbiol. 2014 Apr;18:54-60.</li>
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           <span class="project-tag" id="protocols"></span>
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           <span class="project-tag" id="resolv_sys"></span>
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           <h1>Protocols</h1>
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           <h2>Resolution of the system</h2>
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          <p>Thanks to our sponsor, MathWorks, and his gift of licenses, we made our computing and simulation in Matlab.</p>
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          <p>Then, we implemented a Runge-Kutta 4 to solve our system. We made our program so that latency between each phase of the cycle. This aspect allows, among other things, to account for the time between the formation of a protein and its interaction with the rest of the cell; for example, the time required for the <i>Serine</i> out after its formation.</p>
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          <p>Now, let's see the result of our work.</p>
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             <span class="project-tag" id="strains_used"></span>
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             <span class="project-tag" id="case1"></span>
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             <h2 class="subtitle">Strains used in the project</h2>
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             <h3 class="subtitle">1.  First Case</h3>
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                <li>Escherichia coli W3110 was used for chassis construction.</li>
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            <img class="img-rounded" src="https://static.igem.org/mediawiki/2014/5/57/AMU_Team-values_case1.png" style="width: 70%">
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                <li>Escherichia coli DH5alpha and TG1 strains were used for regular cloning.</li>
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            <div class="media notes-media">
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            <span class="project-tag" id="strains_storage"></span>
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              <img class="media-object img-rounded pull-right" src="https://static.igem.org/mediawiki/2014/6/6e/AMU_Team-modeling-case1.png" style="width:800px; margin-bottom: 10px;">
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            <h2 class="subtitle">Strain storage</h2>
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              <p>For long-term conservation, 750 μL of an exponentially grown strain were mixed with 250 μL of glycerol 80%, and at -80°c in a cryotube. </p>
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            <p>We can see that our system is oscillating. It is indeed the expected result since after cell division, the system must be reset (with the exception of the outer Serine). But the system needs time to qualibrer (here, from beginning to the first cell division).</p>
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             <span class="project-tag" id="cult_med"></span>
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             <span class="project-tag" id="case2"></span>
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             <h2 class="subtitle">Culture medium</h2>
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             <h3 class="subtitle">2.  Second Case</h3>
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             <ul>
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             <p>We will now see some pathological cases. First, we will observe if all our parameters are multiplied by 5 and here is the result.</p>
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              <li>
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            <div class="media notes-media">
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                <p>Regular bacterial growth was performed in LB medium or LB-agar plates (DIFCO) supplemented with the appropriated antibiotics if necessary: ampicillin 100 μM, kanamycin 50 μM, chloramphenicol 30 μM. When required, IPTG (Isopropyl β-D-1-thiogalactopyranoside ) was added to the final concentration of 500 μM to induce gene expression from Plac promoters.</p>
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               <img class="media-object img-rounded pull-right" src="https://static.igem.org/mediawiki/2014/9/97/AMU_Team-modeling-case2.png" style="width:800px; margin-bottom: 10px;">
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                <p>Growth was conducted at 37°C for regular experiments, and at 30°C when carrying temperature sensitive plasmids.</p>
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             <p><i>CheA</i> concentration reaches zero once. However, its derivative is not zero, the system can still go. Then the next cycle, its derivative is also canceled and the system stabilizes.</p>
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              <li>
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                <p>The SMG medium used to characterize the BBa_K1349001 part was prepared based on the work of (Rudd <i>et al</i>.,1985).</p>
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                <p><u>SMG plate composition:</u></p>
+
-
                <table class="table table-hover table-bordered notes-table">
+
-
                  <tbody>
+
-
                    <tr>
+
-
                      <td>M9 salts</td> <td>1X</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>MgSO4</td> <td>1mM</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>CaCl<sub>2</sub></td> <td>0.1mM</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>VitB1</td> <td>0.5µg/ml</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>Glucose</td> <td>0.2%</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>Serine</td> <td>1mM</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>Methionine</td> <td>1mM</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>Glycine</td> <td>1mM</td>
+
-
                    </tr>
+
-
                    <tr>
+
-
                      <td>Bactoagar</td> <td>15g/L</td>
+
-
                    </tr>
+
-
                  </tbody>
+
-
                </table>
+
-
              </li>
+
-
             </ul>
+
-
             <p><u>References:</u><p>
+
-
            <p>Rudd KE, Bochner BR, Cashel M, Roth JR. Mutations in the spoT gene of Salmonella typhimurium: effects on his operon expression. J Bacteriol. ;163(2):534-42, 1985.</p>
+
           </div>
           </div>
 +
         
           <div class="project-subsection">
           <div class="project-subsection">
-
             <span class="project-tag" id="plasmid_extract"></span>
+
             <span class="project-tag" id="case3"></span>
-
             <h2 class="subtitle">Plasmid extraction</h2>
+
             <h3 class="subtitle">3.  Third Case</h3>
-
               <p>Performed with the Macherey-Nagel Kit, following the manufacturer instructions.</p>
+
            <p>Michaelis-Menten constants is divided by 20.</p>
 +
            <div class="media notes-media">
 +
               <img class="media-object img-rounded pull-right" src="https://static.igem.org/mediawiki/2014/2/21/AMU_Team-modeling-case3.png" style="width:800px; margin-bottom: 10px;">
 +
            </div>
 +
            <p>We can even observe more. These constants act as timer. Here, they are very small and the system does not boot even. In next case, we observed that if it is big, the system is perfectly calibrated. This is very understandable. If they are too small, the Michaelis-Menten equations react as constants. Then, some parts of the system will no longer interact with others. For example, the concentration of <i>CheA</i> no longer influences that of <i>CusR</i>.</p>
           </div>
           </div>
 +
         
           <div class="project-subsection">
           <div class="project-subsection">
-
             <span class="project-tag" id="pcr_cleanup"></span>
+
             <span class="project-tag" id="case4"></span>
-
             <h2 class="subtitle">PCR clean-up</h2>
+
             <h3 class="subtitle">4.  Fourth Case</h3>
-
               <p>Performed with the Promega Kit, following the manufacturer instructions.</p>
+
            <div class="media notes-media">
 +
               <img class="media-object img-rounded pull-right" src="https://static.igem.org/mediawiki/2014/2/23/AMU_Team-modeling-case4.png" style="width:800px; margin-bottom: 10px;">
 +
            </div>
 +
            <p>In this case, we took Michaelis-Menten constant and multiplied by only two parameters. It is observed however that the system is still oscillating and the system is not far from the initial case.
 +
So we do have a range of data sets allowing us to stick a little better with reality. This range can also enable us to overcome the errors due to our assumptions that may be too simplistic.</p>
           </div>
           </div>
-
          <div class="project-subsection">
 
-
            <span class="project-tag" id="comp_cells"></span>
 
-
            <h2 class="subtitle">Competent cells</h2>
 
-
              <p>Cells were grown in LB medium as a starter O/N. The day after, the culture was back diluted in 100 mL of LB to reach an OD600=0.05.</p>
 
-
              <p>When the culture reached and OD600 of 0.4 to 0.6, cells were centrifuged at 5000 rpm during 10 min. The cell pellet was carefully re-suspended in 1/2V of CaCl2 50 mM at 4°C. After an incubation of 10 min on ice, the cells were pelleted by centrifugation. The pellet was re-suspended in 1/20V of CaCl2 50 mM, Glycerol 15%. Aliquots of competent cells were stored at -80°C.</p>
 
-
          </div>
 
-
          <div class="project-subsection">
 
-
            <span class="project-tag" id="transfo"></span>
 
-
            <h2 class="subtitle">Transformation</h2>
 
-
              <p>Performed following the protocol published on the iGEM website : <a href="http://parts.igem.org/Help:Protocols/Transformation" target="_blank">here</a></p>
 
-
          </div>
 
-
          <div class="project-subsection">
 
-
            <span class="project-tag" id="lambdaRed_mut"></span>
 
-
            <h2 class="subtitle">Lambda Red mutant construction</h2>
 
-
            <p>This protocol was adapted from the initial protocol published by Datsenko and Wanner (2000).</p>
 
-
            <p><u>Reference:</u><br>
 
-
            Datsenko KA1, Wanner BL. One-step inactivation of chromosomal genes in Escherichia coli K-12 using PCR products. Proc Natl Acad Sci U S A. 2000 6;97(12):6640-5.</p>
 
-
            <ul>
 
-
              <li>
 
-
                <p>Day 1:</p>
 
-
                <ul>
 
-
                  <li>Transform W3110 competent cells with the pKOBEG plasmid (cmR). Grow at 30°C o/n</li>
 
-
                  <li>PCR-amplify the FRT-kan-FRT cassette from the pKD4 plasmid (AmpR) using the set of primers targeting the gene to be deleted. Check the PCR product on an agarose gel. Then digest the pKD4 matrix plasmid with 1uL DpnI enzyme, and incubate at 37°C during 2 hrs. Clean-up the PCR product with the promega kit.</li>
 
-
                </ul>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 2:</p>
 
-
                <p>
 
-
                  <p>From one isolated W3110 pKOBEG clone, grow the cells at 30°C. When the culture reach an OD of 2.2, add arabinose to a final concentration of 0.05% and incubate 2 hrs at 30°C or until OD600=1. Switch the temperature to 42°C to get rid off the pKOBEG plasmid. Centrifuge the culture at 4°C and prepare a stock of electrocompetent cells.</p>
 
-
                  <p>Electroporate 10 ul of purified PCR product into 50 ul of electrocompetent cells. Grow the transformed cells on LB+kan 50uM plates, and incubate at 37°C o/n.</p>
 
-
                </p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 3:</p>
 
-
                <p>Restreak 25 clones on LB+Kan plates and Lb+Cm plates, incubate at 37°C O/N.</p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 4:</p>
 
-
                <p>Select 8 clones resistant to Kan but sensitive to Cm. Check the correct replacement of the targeted gene by the FRT-Kan-FRT cassette with primers exterior to the gene.</p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 5:</p>
 
-
                <p>Cultivate and freeze 2 independent clones.</p>
 
-
              </li>
 
-
              <p>To flip the FRT-KAN-FRT cassette</p>
 
-
              <li>
 
-
                <p>Day 6:</p>
 
-
                <p>
 
-
                  <p>Prepare a stock of electrocompetent W3110 mutant.</p>
 
-
                  <p>Electroporate the pCP20 plasmid (CmR, ApR) encoding the flipase and spread the cells on LB+Ap+Cm. Incubate at 30°C O/N</p>
 
-
                </p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 7:</p>
 
-
                <p>To prepare a culture starter, inoculate 1 clone in LB at 30°c O/N</p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 8:</p>
 
-
                <p>Back-dilute the culture 100x in LB without antibiotics. Grow at 30°c until you reach an OD600=0.3. Switch the temperature to 37°C until OD600= 0.8. Back-dilute the culture 100x in LB for 5 hrs. Spread 10 ul of the culture in LB plate without antibiotics to get isolated colonies.</p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 9:</p>
 
-
                <p>Select 20 isolated clones and re-patch on LB, LB+Kan, LB+AP+CM.</p>
 
-
              </li>
 
-
              <li>
 
-
                <p>Day 10:</p>
 
-
                <p>Select 8 clones sensitive to Kan, Ap and Cm. Check by colony-PCR that the FRT-KAN-FRT cassette was truly deleted.</p>
 
-
              </li>
 
-
            </ul>
 
-
          </div>
 
-
          <div class="project-subsection">
 
-
            <span class="project-tag" id="slic"></span>
 
-
            <h2 class="subtitle">SLIC cloning</h2>
 
-
            <p>One-step sequence- and ligation-independent cloning (SLIC) was performed following the protocol published as supplemental data in the original manuscript of Jeong and collaborators. This protocol can be found <a href="http://aem.asm.org/content/early/2012/05/13/AEM.00844-12" target="_blank">here</a></p>
 
-
            <p><u>References</u><br>
 
-
            Jeong JY1, Yim HS, Ryu JY, Lee HS, Lee JH, Seen DS, Kang SG. One-step sequence- and ligation-independent cloning as a rapid and versatile cloning method for functional genomics studies. <i>Appl Environ Microbiol.</i> 2012 ; 78(15):5440-3.
 
-
          </div>
 
-
          <div class="project-subsection">
 
-
            <span class="project-tag" id="3A_cloning"></span>
 
-
            <h2 class="subtitle">3A cloning</h2>
 
-
            <p>Performed following the protocol published on the iGEM website : <a href="http://parts.igem.org/Assembly:3A_Assembly" target="_blank">here</a></p>
 
-
          </div>
 
-
        </div>
 
-
       
 
-
        <div class="project-section">
 
-
          <span class="project-tag" id="results"></span>
 
-
          <h1>Results and Parts validation</h1>
 
-
            <div class="project-subsection">
 
-
            <span class="project-tag" id="res1_RelA"></span>
 
-
            <h2 class="subtitle">Result 1: validation of the RelA part: BBa_K1349001</h2>
 
-
            <p>The relA gene encodes a ppGpp synthetase. In bacteria, ppGpp (guanosine 3'-diphosphate 5-' diphosphate) acts as a signaling molecule that regulates a variety of cellular metabolisms in response to changes in the nutritional state of the cells.</p>
 
-
            <p>This part was designed to allow the rapid synthesis of the alarmone ppGpp, responsible for the stringent response in E. coli. In the context of our project ppGpp is accumulation used to stop initiation of cell division.</p>
 
-
            <p>
 
-
              <p><u>How we tested the BBa_K1349001 part:</u></p>
 
-
              <p>Expression of the BBa_K1349001 part is expected to cause accumulation of ppGpp and so reduce growth rate of a wild-type cell. At the opposite, expression of this part in a MG1655∆relA mutant unable to make ppGpp is expected to complement the mutant. </p>
 
-
              <p>As seen on the figure below, our part is functional as it is able to fully complement the MG1655∆relA mutant.
 
-
See lab-book for details on the experimental procedure.</p>
 
-
              <div class="project-details">
 
-
                <img class="img-rounded" src="https://static.igem.org/mediawiki/2014/6/63/AMU_Team-RelA_part.png">
 
-
                <p><i>Attribution of the figure: Dr. Emmanuelle Bouveret.</i></p>
 
-
              </div>
 
-
            </p>
 
-
          </div>
 
-
        </div>
 
-
       
 
-
        <div class="project-section">
 
-
          <span class="project-tag" id="conclusions"></span>
 
-
          <h1>Conclusions</h1>
 
-
            <br><br><br>...<br><br><br>
 
         </div>
         </div>
-
       </div>
+
       </div> <!-- /Content -->
-
 
+
     
 +
     
       <!-- Table of Contents -->
       <!-- Table of Contents -->
       <!-- ***************** -->
       <!-- ***************** -->
Line 381: Line 199:
           <ul class="nav">
           <ul class="nav">
             <li class="active">
             <li class="active">
-
               <a data-scroll href="#overall">Overall project summary</a>
+
               <a data-scroll href="#intro">Introduction</a>
             </li>
             </li>
             <li>
             <li>
-
               <a data-scroll href="#details">Project Details</a>
+
               <a data-scroll href="#mod_sys">Model system</a>
-
              <ul class="nav">
+
-
                <li><a data-scroll href="#serine_part">Serine, a signal molecule</a></li>
+
-
                <li><a data-scroll href="#CheA-SH3_part">CheA‐SH3, modifier chemotaxis signalling</a></li>
+
-
                <li><a data-scroll href="#ppGpp_part">Regulation of intracellular ppGpp concentration</a></li>
+
-
                <li><a data-scroll href="#refs">References</a></li>
+
-
              </ul>
+
             </li>
             </li>
             <li>
             <li>
-
               <a data-scroll href="#protocols">Protocols</a>
+
               <a data-scroll href="#simplify">Simplifying assumptions</a>
             </li>
             </li>
             <li>
             <li>
-
               <a data-scroll href="#results">Results and Parts validation</a>
+
               <a data-scroll href="#diff_equa">Differential equations</a>
             </li>
             </li>
             <li>
             <li>
-
               <a data-scroll href="#conclusions">Conclusions</a>
+
               <a data-scroll href="#init_val">Initial values</a>
 +
            </li>
 +
            <li>
 +
              <a data-scroll href="#resolv_sys">Resolution of the system</a>
 +
              <ul class="nav">
 +
                <li><a data-scroll href="#case1">First case</a></li>
 +
                <li><a data-scroll href="#case2">Second case</a></li>
 +
                <li><a data-scroll href="#case3">Third case</a></li>
 +
                <li><a data-scroll href="#case4">Fourth case</a></li>
 +
              </ul>
             </li>
             </li>
           </ul>
           </ul>

Latest revision as of 11:28, 17 October 2014

Our model

Introduction

Part modeling was not an easy task. Let me explain. I am a novice in the field of mathematical engineering and that made more than seven years since I was not made of Biology.

Our project is based on the feedback cycle of chemiotaxie in Escherichia coli. To develop our model, it was first essential to know the ins and out. To do so, the study of narratives on the general biology were paramount; it was only later that I got interested in the chemiotaxie.

Subsequently, we made contact with a brilliant modeler of this field from the University of Aix-Marseille: Ms. Elysabeth Remi. Together, we tried to synthesize the system to be modeled and some approximations which we considered natural at first.

Model System

The scheme is simple. Each cell of Escherichia coli has an amount of CheA in its cytoplasm. This one will phosphorylate CusR which in turn will catalyze the formation of ppGpp (via RelA) and the SerA. The formation of ppGpp will cause failure of cell division. SerA is a protein that will lead to the formation of Serine via SerC and SerB. This intracellular Serine will migrate to the outside of the cell. However, the histidine kinase CheA is sensitive to the gradient of Serine outside, thanks to chemoreceptor. Moreover, since the outer homogeneous media is considered, all cells will receive the same gradient outside Serine. This is the start of cell synchronization. Increasing Serine will create a decrease in the phosphorylation of CheA, involving a decrease CusR phosphorylated. Thus, the rate will decrease ppGpp allow cell division and of all cells at the same time. After their split, the pattern will repeat itself.

Simplifying assumptions

In order to simplify our model and lack of experimental data, we overlook some things.

  1. First, we assume that the formation of Serine is done directly by SerA. In reality, training SerC and SerB are much faster than those of SerA and Serine.
  2. The concentration of ppGpp being by fluorescence, we do not get that of RelA. We will take into account that the formation of ppGpp by CusR phosphorylated.
  3. CheA phosphorylates naturally CheY and not CusR. We have considered the kinetic constants of CheY for CusR.
  4. We do not know the constants of CheA deactivation by the gradient of Serine. We've replaced by those of the gradient Aspartate which are easily found in the literature.
  5. The threshold of ppGpp for cell division is not known, we took a concentration we know realistic: 1 μM.
  6. 6. Some kinetics are expected to follow a law of Michaelis-Menten. However, the system is rather slow and concentrations vary only slightly around the concentrations of half-maximal speed. Thus, we assume that they follow linear laws.
  7. We didn't have the time to test the model experimentally so we took an arbitrary time scale.

Differential equations

Here are the differential equations modeling our system.

Initial values

Some constants have been found experimentally or guessed from existing data.

Resolution of the system

Thanks to our sponsor, MathWorks, and his gift of licenses, we made our computing and simulation in Matlab.

Then, we implemented a Runge-Kutta 4 to solve our system. We made our program so that latency between each phase of the cycle. This aspect allows, among other things, to account for the time between the formation of a protein and its interaction with the rest of the cell; for example, the time required for the Serine out after its formation.

Now, let's see the result of our work.

1. First Case

We can see that our system is oscillating. It is indeed the expected result since after cell division, the system must be reset (with the exception of the outer Serine). But the system needs time to qualibrer (here, from beginning to the first cell division).

2. Second Case

We will now see some pathological cases. First, we will observe if all our parameters are multiplied by 5 and here is the result.

CheA concentration reaches zero once. However, its derivative is not zero, the system can still go. Then the next cycle, its derivative is also canceled and the system stabilizes.

3. Third Case

Michaelis-Menten constants is divided by 20.

We can even observe more. These constants act as timer. Here, they are very small and the system does not boot even. In next case, we observed that if it is big, the system is perfectly calibrated. This is very understandable. If they are too small, the Michaelis-Menten equations react as constants. Then, some parts of the system will no longer interact with others. For example, the concentration of CheA no longer influences that of CusR.

4. Fourth Case

In this case, we took Michaelis-Menten constant and multiplied by only two parameters. It is observed however that the system is still oscillating and the system is not far from the initial case. So we do have a range of data sets allowing us to stick a little better with reality. This range can also enable us to overcome the errors due to our assumptions that may be too simplistic.

Contact us

Email : equipe.igem.amu@gmail.com

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Retrieved from "http://2014.igem.org/Team:Aix-Marseille/Modeling"