Team:XMU-China/Project ConicCurve

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<h3><a href="https://2014.igem.org/Team:XMU-China/Project_ConicCurve">Conic Curve</a></h3>
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     <span style="font-family: Times New Roman;">C</span><span style="font-family: Times New Roman;">onic Curve</span>
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    <span style="font-family: Arial; font-size: 29px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 29px; font-weight: 700;">ONIC CURVE</span>
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     <span style="font-family: Times New Roman; font-size: 18px;">--Form patterns by chemotaxis</span>
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    &nbsp;
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     <span style="font-family: Arial; font-size: 21px; font-weight: 700;">--Form patterns by chemotaxis</span>
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    <span style="font-family: Arial; font-size: 21px; font-weight: 700;">Overview</span>
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     <span style="font-family: Arial; font-size: 16px;">By which means would you like</span><span style="font-family: Arial; font-size: 16px;"> to make a mathematical pattern</span><span style="font-family: Arial; font-size: 16px;">? Draw with compass and ruler, or type a function in a drawing software? Well, </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">E. </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">coli</span><span style="font-family: Arial; font-size: 16px;"> can help us to </span><span style="font-family: Arial; font-size: 16px;">achieve our goals. </span><span style="font-family: Arial; font-size: 16px;">We make the first attempt </span><span style="font-family: Arial; font-size: 16px;">to</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">introduce</span><span style="font-family: Arial; font-size: 16px;"> pseudotaxis to form patterns in shape of conic section (such as ellipse and hyperbola). Firstly, let’s </span><span style="font-family: Arial; font-size: 16px;">recall the </span><span style="font-family: Arial; font-size: 16px;">precise mathematical definition on ellipse, hyperbola and parabola.</span>
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     <span style="font-family: Times New Roman; font-size: 21px;">Overview</span>
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     <span style="font-family: Arial; font-size: 21px; font-weight: 700;">Mathematical definition </span>
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    <span style="font-family: Times New Roman; font-size: 14px;">What means would you like to use to get a mathematical pattern? Draw one with compass and ruler, or type a function in a drawing software? Well, </span><span style="font-family: Times New Roman; font-size: 14px; font-style: italic;">E.coli</span><span style="font-family: Times New Roman; font-size: 14px;"> can help us to </span><span style="font-family: Times New Roman; font-size: 14px;">achieve our goals. </span><span style="font-family: Times New Roman; font-size: 14px;">We make the first attempt </span><span style="font-family: Times New Roman; font-size: 14px;">to</span><span style="font-family: Times New Roman; font-size: 14px;"> </span><span style="font-family: Times New Roman; font-size: 14px;">introduce</span><span style="font-family: Times New Roman; font-size: 14px;"> pseudotaxis to form patterns in shape of conic section (such as ellipse and hyperbola).</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-size: 14px;">Firstly, let’s </span><span style="font-family: Times New Roman; font-size: 14px;">recall the </span><span style="font-family: Times New Roman; font-size: 14px;">precise mathematical definition on ellipse, hyperbola and parabola.</span>
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     <span style="font-family: Times New Roman; font-weight: 400;">M</span><span style="font-family: Times New Roman;">athematical definition </span>
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     <span style="font-family: Arial; font-size: 16px;">I</span><span style="font-family: Arial; font-size: 16px;">n mathematics, </span><span style="font-family: Arial; font-size: 16px;">ellipse </span><span style="font-family: Arial; font-size: 16px;">is a curve on a plane surrounding two focal points</span><span style="font-family: Arial; font-size: 16px;"> such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">(</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure 1</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Arial; font-size: 16px;">).</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; valign: sup;">[1]</span><span style="font-family: Arial; font-size: 16px;"> And hyperbola is a curve which point’s absolute value of the difference of the distance to the two focal points is a constant</span><span style="font-family: Arial; font-size: 16px;"> (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure 1B</span><span style="font-family: Arial; font-size: 16px;">).</span>
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    <span style="font-family: Times New Roman;">I</span><span style="font-family: Times New Roman;">n mathematics, ellipse is a curve on a plane surrounding two focal points</span><span style="font-family: Times New Roman;"> such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">(</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 1</span><span style="font-family: Times New Roman; font-weight: 700;">A</span><span style="font-family: Times New Roman;">).</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; valign: sup;">[1]</span><span style="font-family: Times New Roman;"> And hyperbola is a curve which point’s absolute value of the difference of the distance to the two focal points is a constant</span><span style="font-family: Times New Roman;"> (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 1B</span><span style="font-family: Times New Roman;">).</span>
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                     <span style="font-family: Times New Roman;">B</span>
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                     <span style="font-family: Times New Roman; font-size: 16px;">B</span>
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                     <img width="230" height="251" style="font-family: Times New Roman;" src="http://convert.wenku.baidu.com/rtcs/image?md5sum=8a1d45a689810e868d560563846c1868.docx&l=webapp&ipr={&quot;t&quot;:&quot;img&quot;,&quot;w&quot;:&quot;230.67&quot;,&quot;h&quot;:&quot;251.05&quot;,&quot;dataType&quot;:&quot;png&quot;,&quot;c&quot;:&quot;word\/media\/image2.png&quot;}"/>
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                     <img width="230" height="251" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/7/7f/Xmu_Project_Conic_Curve_figure01B.png"/>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure 1A</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-weight: 700;"> </span><span style="font-family: Times New Roman;">Schematic of ellipse. Point F</span><span style="font-family: Times New Roman; valign: sub;">1</span><span style="font-family: Times New Roman;">, F</span><span style="font-family: Times New Roman; valign: sub;">2</span><span style="font-family: Times New Roman;"> are the two focal points and Point A is on the ellipse curve. The sum of the distance AF</span><span style="font-family: Times New Roman; valign: sub;">1</span><span style="font-family: Times New Roman;"> and AF</span><span style="font-family: Times New Roman; valign: sub;">2</span><span style="font-family: Times New Roman;"> is equal to the constant k: AF</span><span style="font-family: Times New Roman; valign: sub;">1</span><span style="font-family: Times New Roman;">+AF</span><span style="font-family: Times New Roman; valign: sub;">2</span><span style="font-family: Times New Roman;">=k.</span><span style="font-family: Times New Roman; font-weight: 700;"> 1B</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Schematic of hyperbola. Point F</span><span style="font-family: Times New Roman; valign: sub;">1</span><span style="font-family: Times New Roman;">, F</span><span style="font-family: Times New Roman; valign: sub;">2</span><span style="font-family: Times New Roman;"> are the two focal points and Point A is on one of the </span><span style="font-family: Times New Roman;">hyperbola branches. The absolute value of the difference of the distance AF</span><span style="font-family: Times New Roman; valign: sub;">1</span><span style="font-family: Times New Roman;">, AF</span><span style="font-family: Times New Roman; valign: sub;">2</span><span style="font-family: Times New Roman;"> is equal to the constant k: |AF</span><span style="font-family: Times New Roman; valign: sub;">1</span><span style="font-family: Times New Roman;">-AF</span><span style="font-family: Times New Roman; valign: sub;">2</span><span style="font-family: Times New Roman;">|=k.</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure 1A</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;"> </span><span style="font-family: Times New Roman; font-size: 16px;">Schematic of ellipse. Point F</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">1</span><span style="font-family: Times New Roman; font-size: 16px;">, F</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">2</span><span style="font-family: Times New Roman; font-size: 16px;"> are the two focal points and Point A is </span><span style="font-family: Times New Roman; font-size: 16px;">on the ellipse curve. The sum of the distance AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">1</span><span style="font-family: Times New Roman; font-size: 16px;"> and AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">2</span><span style="font-family: Times New Roman; font-size: 16px;"> is equal to the constant k: AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">1</span><span style="font-family: Times New Roman; font-size: 16px;">+AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">2</span><span style="font-family: Times New Roman; font-size: 16px;">=k.</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;"> 1B</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Schematic of hyperbola. Point F</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">1</span><span style="font-family: Times New Roman; font-size: 16px;">, F</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">2</span><span style="font-family: Times New Roman; font-size: 16px;"> are the two focal points and Point A is on one of the hyperbola branches. The absolute value of the difference of the distance AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">1</span><span style="font-family: Times New Roman; font-size: 16px;">, AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">2</span><span style="font-family: Times New Roman; font-size: 16px;"> is equal to the constant k: |AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">1</span><span style="font-family: Times New Roman; font-size: 16px;">-AF</span><span style="font-family: Times New Roman; font-size: 16px; valign: sub;">2</span><span style="font-family: Times New Roman; font-size: 16px;">|=k.</span>
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     <span style="font-family: Times New Roman;">Hyperbola could also be defined as </span><span style="font-family: Times New Roman;">a conic consisting of those points whose distances to some point, called a focus, and some line, called a directrix, are in a fixed ratio (&gt;1)</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">, called the eccentricity</span><span style="font-family: Times New Roman;"> (</span><span style="font-family: Times New Roman; font-weight: 700;">e</span><span style="font-family: Times New Roman;">)</span><span style="font-family: Times New Roman;">. (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 2</span><span style="font-family: Times New Roman; font-weight: 700;">A</span><span style="font-family: Times New Roman;">)</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">Parabola is a conic whose eccentricity is equal to 1</span><span style="font-family: Times New Roman;"> (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 2</span><span style="font-family: Times New Roman; font-weight: 700;">B</span><span style="font-family: Times New Roman;">).</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; valign: sup;">[</span><span style="font-family: Times New Roman; valign: sup;">2</span><span style="font-family: Times New Roman; valign: sup;">]</span>
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     <span style="font-family: Arial; font-size: 16px;">Hyperbola could also be defined as </span><span style="font-family: Arial; font-size: 16px;">a conic consisting of those points whose distances to a focus, and a directrix, are in a fixed ratio (&gt;1)</span><span style="font-family: Arial; font-size: 16px;">,</span><span style="font-family: Arial; font-size: 16px;"> called the eccentricity</span><span style="font-family: Arial; font-size: 16px;"> (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">e</span><span style="font-family: Arial; font-size: 16px;">)</span><span style="font-family: Arial; font-size: 16px;">. (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure 2</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Arial; font-size: 16px;">)</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">Parabola is a conic whose eccentricity is equal to 1</span><span style="font-family: Arial; font-size: 16px;"> (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure 2</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Arial; font-size: 16px;">).</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; valign: sup;">[</span><span style="font-family: Arial; font-size: 16px; valign: sup;">2</span><span style="font-family: Arial; font-size: 16px; valign: sup;">]</span>
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                     <span style="font-family: Times New Roman; font-weight: 700;">A</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A</span>
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                     <img width="256" height="313" style="font-family: Times New Roman;" src="http://convert.wenku.baidu.com/rtcs/image?md5sum=8a1d45a689810e868d560563846c1868.docx&l=webapp&ipr={&quot;t&quot;:&quot;img&quot;,&quot;w&quot;:&quot;256.48&quot;,&quot;h&quot;:&quot;313.07&quot;,&quot;dataType&quot;:&quot;png&quot;,&quot;c&quot;:&quot;word\/media\/image3.png&quot;}"/>
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                     <img width="256" height="313" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/3/31/Xmu_Project_Conic_Curve_figure02A.png"/>
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                     <img width="219" height="311" style="font-family: Times New Roman;" src="http://convert.wenku.baidu.com/rtcs/image?md5sum=8a1d45a689810e868d560563846c1868.docx&l=webapp&ipr={&quot;t&quot;:&quot;img&quot;,&quot;w&quot;:&quot;219.25&quot;,&quot;h&quot;:&quot;311.21&quot;,&quot;dataType&quot;:&quot;png&quot;,&quot;c&quot;:&quot;word\/media\/image4.png&quot;}"/>
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                     <img width="219" height="311" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/e/ea/Xmu_Project_Conic_Curve_figure02B.png"/>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure 2A</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> one branch of hyperbola can be defined by directrix and eccentricity. Point A is a spot on the curve, point F is the focus. AB is the distance between A and directrix. The eccentricity e equal to TF/AB, and e&gt;1. </span><span style="font-family: Times New Roman; font-weight: 700;">2B</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Schematic of Parabola. Point A is a spot on the curve, point F is the focus. AB is the distance between A and directrix. The eccentricity e equals to AF/AB, and e=1.</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure 2A</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">O</span><span style="font-family: Times New Roman; font-size: 16px;">ne branch of hyperbola can be defined by directrix and eccentricity. Point A is a spot on the curve, point F is the focus. AB is the distance between A and directrix. The eccentricity e equal to TF/AB, and e&gt;1. </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">2B</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Schematic of Parabola. Point A is a spot on the curve, point F is the focus. AB is the distance between A and directrix. The eccentricity e equals to AF/AB, and e=1.</span>
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     <span style="font-family: Times New Roman;">Hypothes</span><span style="font-family: Times New Roman;">es:</span>
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     <span style="font-family: Arial; font-size: 21px; font-weight: 700;">Hypothes</span><span style="font-family: Arial; font-size: 21px; font-weight: 700;">es</span>
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    <span style="font-family: Times New Roman;">T</span><span style="font-family: Times New Roman;">he </span><span style="font-family: Times New Roman;">focal points, the constant</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-style: italic;">k</span><span style="font-family: Times New Roman;"> and the </span><span style="font-family: Times New Roman;">eccentricity ratio </span><span style="font-family: Times New Roman; font-style: italic;">e</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">are the key of conic</span><span style="font-family: Times New Roman;"> section</span><span style="font-family: Times New Roman;">. </span><span style="font-family: Times New Roman;">Therefore</span><span style="font-family: Times New Roman;">, </span><span style="font-family: Times New Roman;">we can</span><span style="font-family: Times New Roman;"> easily</span><span style="font-family: Times New Roman;"> get </span><span style="font-family: Times New Roman;">any eclipse by presetting reasonable focal points with the acceptable constant, as well as parabola or hyperbola by a fixed ratio</span><span style="font-family: Times New Roman;">.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">Based on th</span><span style="font-family: Times New Roman;">ese</span><span style="font-family: Times New Roman;">,</span><span style="font-family: Times New Roman;"> we </span><span style="font-family: Times New Roman;">need to combine those mathematical concept with our pattern formation system.</span>
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    <span style="font-size: 14px;">1.</span><span style="font-size: 14px;"> </span><span style="font-family: Times New Roman;">If we spot stimulus on semi-solid plate, </span><span style="font-family: Times New Roman;">it</span><span style="font-family: Times New Roman;"> will spread from the spotting center </span><span style="font-family: Times New Roman;">out to the periphery. </span><span style="font-family: Times New Roman;">In the spreading process, </span><span style="font-family: Times New Roman;">t</span><span style="font-family: Times New Roman;">he concentration is negat</span><span style="font-family: Times New Roman;">ive correlation to the distance from center.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">If we draw a line with stimulus</span><span style="font-family: Times New Roman;">, a concentration gradient with square shape will be formed. </span><span style="font-family: Times New Roman;">And </span><span style="font-family: Times New Roman;">the </span><span style="font-family: Times New Roman;">both </span><span style="font-family: Times New Roman;">concentration gradient will maintain for a long period.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">Generally, </span><span style="font-family: Times New Roman;">the stimulus spots are </span><span style="font-family: Times New Roman;">defined as focuses while those lines are defined as directrixes.</span>
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    <span style="font-family: Arial; font-size: 16px;">Focal points, </span><span style="font-family: Arial; font-size: 16px;">constant</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">k</span><span style="font-family: Arial; font-size: 16px;"> and the </span><span style="font-family: Arial; font-size: 16px;">eccentricity ratio </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">e</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">are </span><span style="font-family: Arial; font-size: 16px;">key</span><span style="font-family: Arial; font-size: 16px;"> factors</span><span style="font-family: Arial; font-size: 16px;"> of conic</span><span style="font-family: Arial; font-size: 16px;"> section</span><span style="font-family: Arial; font-size: 16px;">. </span><span style="font-family: Arial; font-size: 16px;">Therefore</span><span style="font-family: Arial; font-size: 16px;">, </span><span style="font-family: Arial; font-size: 16px;">we can</span><span style="font-family: Arial; font-size: 16px;"> easily</span><span style="font-family: Arial; font-size: 16px;"> get </span><span style="font-family: Arial; font-size: 16px;">any eclipse by presetting reasonable focal points with </span><span style="font-family: Arial; font-size: 16px;">an</span><span style="font-family: Arial; font-size: 16px;"> acceptable constant, as well as parabola or hyperbola by a fixed ratio</span><span style="font-family: Arial; font-size: 16px;">.</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">Based on th</span><span style="font-family: Arial; font-size: 16px;">ese</span><span style="font-family: Arial; font-size: 16px;">,</span><span style="font-family: Arial; font-size: 16px;"> we </span><span style="font-family: Arial; font-size: 16px;">need to combine th</span><span style="font-family: Arial; font-size: 16px;">e</span><span style="font-family: Arial; font-size: 16px;">se mathematical concept</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> with our pattern formation system.</span>
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     <span style="font-size: 14px;">2.</span><span style="font-size: 14px;"> </span><span style="font-family: Times New Roman;">There is a threshold </span><span style="font-family: Times New Roman;">ratio</span><span style="font-family: Times New Roman;"> of </span><span style="font-family: Times New Roman;">the</span><span style="font-family: Times New Roman;"> concentration</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;"> of</span><span style="font-family: Times New Roman;"> inducer and repressor.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; valign: sup;">[3]</span><span style="font-family: Times New Roman;"> This means that more repressor will cause more repression</span><span style="font-family: Times New Roman;">,</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">hence more inducer is needed</span><span style="font-family: Times New Roman;"> to relieve the repression, and vice versa.</span><span style="font-family: Times New Roman;"> As the concentration of inducer and repressor are direct</span><span style="font-family: Times New Roman;">ly connected to</span><span style="font-family: Times New Roman;"> the concentration of</span><span style="font-family: Times New Roman;"> stimulus sources, thus </span><span style="font-family: Times New Roman;">we can tell the constant </span><span style="font-family: Times New Roman; font-style: italic;">k</span><span style="font-family: Times New Roman;"> and eccentricity </span><span style="font-family: Times New Roman; font-style: italic;">e</span><span style="font-family: Times New Roman;"> by combining the relationship between distance and concentration.</span>
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     <span style="font-family: Arial; font-size: 16px;">If we spot stimulus on semi-solid plate, </span><span style="font-family: Arial; font-size: 16px;">it</span><span style="font-family: Arial; font-size: 16px;"> will spread from the spotting center </span><span style="font-family: Arial; font-size: 16px;">out to the periphery. </span><span style="font-family: Arial; font-size: 16px;">In the spreading process, </span><span style="font-family: Arial; font-size: 16px;">t</span><span style="font-family: Arial; font-size: 16px;">he concentration is negat</span><span style="font-family: Arial; font-size: 16px;">ive correlat</span><span style="font-family: Arial; font-size: 16px;">ed</span><span style="font-family: Arial; font-size: 16px;"> to the distance from center.</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">If we draw a line with stimulus</span><span style="font-family: Arial; font-size: 16px;">, a concentration gradient with square shape will form. </span><span style="font-family: Arial; font-size: 16px;">And </span><span style="font-family: Arial; font-size: 16px;">both </span><span style="font-family: Arial; font-size: 16px;">of the </span><span style="font-family: Arial; font-size: 16px;">concentration gradient</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> will maintain for a long period.</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">Generally, </span><span style="font-family: Arial; font-size: 16px;">the stimulus spots are </span><span style="font-family: Arial; font-size: 16px;">defined as focuses while those lines are defined as directrixes.</span>
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    <span style="font-family: Times New Roman;">C</span><span style="font-family: Times New Roman;">ircuit</span><span style="font-family: Times New Roman;"> design</span>
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    <span style="font-family: Arial; font-size: 16px;">There is a threshold </span><span style="font-family: Arial; font-size: 16px;">ratio</span><span style="font-family: Arial; font-size: 16px;"> of </span><span style="font-family: Arial; font-size: 16px;">the</span><span style="font-family: Arial; font-size: 16px;"> concentration</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> of</span><span style="font-family: Arial; font-size: 16px;"> inducer and repressor.</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; valign: sup;">[3]</span><span style="font-family: Arial; font-size: 16px;"> This means that more repressor will cause more repression</span><span style="font-family: Arial; font-size: 16px;">,</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">hence more inducer is needed</span><span style="font-family: Arial; font-size: 16px;"> to relieve the repression, and vice versa.</span><span style="font-family: Arial; font-size: 16px;"> As the concentration of inducer and repressor are direct</span><span style="font-family: Arial; font-size: 16px;">ly connected to</span><span style="font-family: Arial; font-size: 16px;"> the concentration of</span><span style="font-family: Arial; font-size: 16px;"> stimulus sources, </span><span style="font-family: Arial; font-size: 16px;">we can tell the constant </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">k</span><span style="font-family: Arial; font-size: 16px;"> and eccentricity </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">e</span><span style="font-family: Arial; font-size: 16px;"> by combining the relationship between distance and concentration.</span>
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    <span style="font-family: Times New Roman;">Our </span><span style="font-family: Times New Roman;">circuit</span><span style="font-family: Times New Roman;"> consists of two parts, of which one is named </span><span style="font-family: Times New Roman; font-weight: 700;">C</span><span style="font-family: Times New Roman;"> (constraint), the other is named </span><span style="font-family: Times New Roman; font-weight: 700;">M</span><span style="font-family: Times New Roman;"> (motile). (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 3</span><span style="font-family: Times New Roman;">):</span>
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     <span style="font-size: 14px;">1.</span><span style="font-size: 14px;"> </span><span style="font-family: Times New Roman;">We build our </span><span style="font-family: Times New Roman;">circuit</span><span style="font-family: Times New Roman;"> in </span><span style="font-family: Times New Roman; font-style: italic;">E.coli</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">which</span><span style="font-family: Times New Roman;"> lacks gene </span><span style="font-family: Times New Roman; font-style: italic;">lacI</span><span style="font-family: Times New Roman;"> and </span><span style="font-family: Times New Roman; font-style: italic;">CheZ </span><span style="font-family: Times New Roman;">(</span><span style="font-family: Times New Roman,宋体;">Δ</span><span style="font-family: Times New Roman;">lacI, </span><span style="font-family: Times New Roman,宋体;">Δ</span><span style="font-family: Times New Roman;">CheZ). </span><span style="font-family: Times New Roman;">In</span><span style="font-family: Times New Roman;"> the absence of </span><span style="font-family: Times New Roman; font-style: italic;">CheZ</span><span style="font-family: Times New Roman;">,</span><span style="font-family: Times New Roman; font-style: italic;"> CL-1</span><span style="font-family: Times New Roman;"> adopts non-motile </span><span style="font-family: Times New Roman;">phenotype</span><span style="font-family: Times New Roman;">.</span>
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     <span style="font-family: Arial; font-size: 21px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 21px; font-weight: 700;">ircuit</span><span style="font-family: Arial; font-size: 21px; font-weight: 700;"> design</span>
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     <span style="font-size: 14px;">2.</span><span style="font-size: 14px;"> </span><span style="font-family: Times New Roman;">Without any exogenous stimulus, </span><span style="font-family: Times New Roman; font-style: italic;">E.coli</span><span style="font-family: Times New Roman;"> will produce background amount of AraC to repress pBAD in limi</span><span style="font-family: Times New Roman;">t degree. </span><span style="font-family: Times New Roman;">That means e</span><span style="font-family: Times New Roman;">ven </span><span style="font-family: Times New Roman;">no</span><span style="font-family: Times New Roman;"> L-arabinose involves</span><span style="font-family: Times New Roman;"> in, promoter pBAD has </span><span style="font-family: Times New Roman;">leakage </span><span style="font-family: Times New Roman;">expression, so that part </span><span style="font-family: Times New Roman; font-weight: 700;">C </span><span style="font-family: Times New Roman;">will produces </span><span style="font-family: Times New Roman;">repressor</span><span style="font-family: Times New Roman;"> LacI which can bind to the operon of promoter pLac and thus repress its transcription. Because L-arabinose could induce pBAD, within certain concentration range, </span><span style="font-family: Times New Roman;">the more L-arabinose involves</span><span style="font-family: Times New Roman;"> in</span><span style="font-family: Times New Roman;">, the</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">more repressor LacI </span><span style="font-family: Times New Roman;">part </span><span style="font-family: Times New Roman; font-weight: 700;">C</span><span style="font-family: Times New Roman;"> could produce </span><span style="font-family: Times New Roman;">resulting the inhibition to chemotaxis</span><span style="font-family: Times New Roman;">. Because of its ability to constrain chemotaxis, this part is named </span><span style="font-family: Times New Roman; font-weight: 700;">C</span><span style="font-family: Times New Roman;">.</span>
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     <span style="font-family: Arial; font-size: 16px;">Our </span><span style="font-family: Arial; font-size: 16px;">circuit</span><span style="font-family: Arial; font-size: 16px;"> consists of two parts, of which one is named </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 16px;"> (constraint), the other is named </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">M</span><span style="font-family: Arial; font-size: 16px;"> (motile). (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure 3</span><span style="font-family: Arial; font-size: 16px;">):</span>
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    <span style="font-size: 14px;">3.</span><span style="font-size: 14px;"> </span><span style="font-family: Times New Roman;">When IPTG involve</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;"> in, it can relieve the repression from</span><span style="font-family: Times New Roman;"> repressor</span><span style="font-family: Times New Roman;"> LacI, therefore protein CheZ is produced to make our engineering bacteria (</span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;">) regain motile ability. Within certain L-</span><span style="font-family: Times New Roman;">a</span><span style="font-family: Times New Roman;">rabinose concentration range which means certain constraint condition, </span><span style="font-family: Times New Roman;">the </span><span style="font-family: Times New Roman;">more IPTG involved in</span><span style="font-family: Times New Roman;">,</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">the </span><span style="font-family: Times New Roman;">more </span><span style="font-family: Times New Roman;">C</span><span style="font-family: Times New Roman;">heZ is produced leading to stronger motile ability. Because of its ability to make </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> motile, this part is named </span><span style="font-family: Times New Roman; font-weight: 700;">M</span><span style="font-family: Times New Roman;">.</span>
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    <span style="font-family: Arial; font-size: 16px;">We </span><span style="font-family: Arial; font-size: 16px;">transform</span><span style="font-family: Arial; font-size: 16px;"> our </span><span style="font-family: Arial; font-size: 16px;">circuit</span><span style="font-family: Arial; font-size: 16px;"> in</span><span style="font-family: Arial; font-size: 16px;">to</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">E.</span><span style="font-family: Arial; font-size: 16px; font-style: italic;"> </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">coli</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">which</span><span style="font-family: Arial; font-size: 16px;"> lacks gene </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">lacI</span><span style="font-family: Arial; font-size: 16px;"> and </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">c</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">heZ </span><span style="font-family: Arial; font-size: 16px;">(</span><span style="font-family: Arial,宋体; font-size: 16px; font-style: italic;">Δ</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">lacI</span><span style="font-family: Arial; font-size: 16px;">, </span><span style="font-family: Arial,宋体; font-size: 16px; font-style: italic;">Δ</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">c</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">heZ</span><span style="font-family: Arial; font-size: 16px;">). </span><span style="font-family: Arial; font-size: 16px;">In</span><span style="font-family: Arial; font-size: 16px;"> the absence of </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">c</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">heZ</span><span style="font-family: Arial; font-size: 16px;">,</span><span style="font-family: Arial; font-size: 16px; font-style: italic;"> </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> adopts non-motile </span><span style="font-family: Arial; font-size: 16px;">phenotype</span><span style="font-family: Arial; font-size: 16px;">.</span>
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    <span style="font-family: Arial; font-size: 16px;">Without any exogenous stimulus, </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">E.</span><span style="font-family: Arial; font-size: 16px; font-style: italic;"> </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">coli</span><span style="font-family: Arial; font-size: 16px;"> will produce background amount of AraC to repress pBAD </span><span style="font-family: Arial; font-size: 16px;">at</span><span style="font-family: Arial; font-size: 16px;"> limi</span><span style="font-family: Arial; font-size: 16px;">t degree. </span><span style="font-family: Arial; font-size: 16px;">That means e</span><span style="font-family: Arial; font-size: 16px;">ven </span><span style="font-family: Arial; font-size: 16px;">no</span><span style="font-family: Arial; font-size: 16px;"> L-arabinose involve</span><span style="font-family: Arial; font-size: 16px;">d </span><span style="font-family: Arial; font-size: 16px;">in, promoter pBAD has </span><span style="font-family: Arial; font-size: 16px;">leakage </span><span style="font-family: Arial; font-size: 16px;">expression, so that part </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">C </span><span style="font-family: Arial; font-size: 16px;">will produce</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">repressor</span><span style="font-family: Arial; font-size: 16px;"> LacI which can bind to the operon of promoter pLac and thus repress its transcription. Because L-arabinose could induce pBAD, within certain concentration range, </span><span style="font-family: Arial; font-size: 16px;">the more L-arabinose involve</span><span style="font-family: Arial; font-size: 16px;">d</span><span style="font-family: Arial; font-size: 16px;"> in</span><span style="font-family: Arial; font-size: 16px;">, the</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">more repressor LacI </span><span style="font-family: Arial; font-size: 16px;">part </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 16px;"> could produce </span><span style="font-family: Arial; font-size: 16px;">resulting the inhibition to chemotaxis</span><span style="font-family: Arial; font-size: 16px;">. Because of its ability to constrain chemotaxis, this part is named </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 16px;">.</span>
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    <span style="font-family: Arial; font-size: 16px;">When IPTG involve</span><span style="font-family: Arial; font-size: 16px;">d</span><span style="font-family: Arial; font-size: 16px;"> in, it can relieve the repression from</span><span style="font-family: Arial; font-size: 16px;"> repressor</span><span style="font-family: Arial; font-size: 16px;"> LacI, therefore protein CheZ is produced to make our engineering bacteria (</span><span style="font-family: Arial; font-size: 16px;">CL-1)</span><span style="font-family: Arial; font-size: 16px;"> regain motile ability. Within certain L-</span><span style="font-family: Arial; font-size: 16px;">a</span><span style="font-family: Arial; font-size: 16px;">rabinose concentration range which means certain constraint condition, </span><span style="font-family: Arial; font-size: 16px;">the more IPTG involved in, the </span><span style="font-family: Arial; font-size: 16px;">more </span><span style="font-family: Arial; font-size: 16px;">C</span><span style="font-family: Arial; font-size: 16px;">heZ is produced leading to stronger motile ability. Because of its ability to make </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> motile, this part is named </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">M</span><span style="font-family: Arial; font-size: 16px;">.</span>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure 3.</span><span style="font-family: Times New Roman; font-weight: 700;"> </span><span style="font-family: Times New Roman;">Part</span><span style="font-family: Times New Roman; font-weight: 700;"> C </span><span style="font-family: Times New Roman;">produces LacI to repress the expression of part </span><span style="font-family: Times New Roman; font-weight: 700;">M</span><span style="font-family: Times New Roman;">. Part </span><span style="font-family: Times New Roman; font-weight: 700;">M</span><span style="font-family: Times New Roman;"> could produce CheZ to make </span><span style="font-family: Times New Roman; font-style: italic;">CL-1 </span><span style="font-family: Times New Roman;">regain motile ability.</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure 3.</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;"> </span><span style="font-family: Times New Roman; font-size: 16px;">Part</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;"> C </span><span style="font-family: Times New Roman; font-size: 16px;">produces LacI to repress the expression of part </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">M</span><span style="font-family: Times New Roman; font-size: 16px;">. Part </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">M</span><span style="font-family: Times New Roman; font-size: 16px;"> could produce CheZ to make </span><span style="font-family: Times New Roman; font-size: 16px;">CL-1</span><span style="font-family: Times New Roman; font-size: 16px; font-style: italic;"> </span><span style="font-family: Times New Roman; font-size: 16px;">regain motile ability.</span>
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     <span style="font-family: Times New Roman; font-weight: 700; styleName: Default Paragraph Font;">Characterization of circuit</span>
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     <span style="font-family: Arial; font-size: 16px; font-weight: 700; styleName: Default Paragraph Font;">Characterization of circuit</span>
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    <span style="font-family: Times New Roman;">We sequenced </span><span style="font-family: Times New Roman;">the </span><span style="font-family: Times New Roman;">circuit </span><span style="font-family: Times New Roman;">above </span><span style="font-family: Times New Roman;">and characterized it in </span><span style="font-family: Times New Roman; font-style: italic;">E.coli CL-1</span><span style="font-family: Times New Roman;">. As </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> lacks </span><span style="font-family: Times New Roman; font-style: italic;">LacI</span><span style="font-family: Times New Roman; font-style: italic;"> </span><span style="font-family: Times New Roman;">gene</span><span style="font-family: Times New Roman;">, promoter </span><span style="font-family: Times New Roman;">p</span><span style="font-family: Times New Roman;">Lac won’t be repressed by background</span><span style="font-family: Times New Roman;"> repressor</span><span style="font-family: Times New Roman;"> LacI. </span>
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<p style="font-family: Arial; font-size: 16px; font-weight: 700; styleName: Default Paragraph Font;">
     &nbsp;
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<p style="font-family: Arial; font-size: 16px;">
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     <span style="font-family: Times New Roman;">We apply gradient test to find out which influence would be made on </span><span style="font-family: Times New Roman;">reprogrammed </span><span style="font-family: Times New Roman;">chemotaxis under the following parameters: the concentration of chloramphenicol, IPTG and L-arabinose.</span>
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     <span style="font-family: Arial; font-size: 16px;">We sequenced </span><span style="font-family: Arial; font-size: 16px;">the </span><span style="font-family: Arial; font-size: 16px;">circuit </span><span style="font-family: Arial; font-size: 16px;">above </span><span style="font-family: Arial; font-size: 16px;">and characterized it in </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">E. </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">coli </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;">. As </span><span style="font-family: Arial; font-size: 16px;">CL-1 </span><span style="font-family: Arial; font-size: 16px;">lacks </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">l</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">acI</span><span style="font-family: Arial; font-size: 16px; font-style: italic;"> </span><span style="font-family: Arial; font-size: 16px;">gene</span><span style="font-family: Arial; font-size: 16px;">, promoter </span><span style="font-family: Arial; font-size: 16px;">p</span><span style="font-family: Arial; font-size: 16px;">Lac won’t be repressed by background</span><span style="font-family: Arial; font-size: 16px;"> repressor</span><span style="font-family: Arial; font-size: 16px;"> LacI. </span>
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     <span style="color: rgb(40, 40, 40); font-size: 13px;">1.</span><span style="color: rgb(40, 40, 40); font-size: 13px;"> </span><span style="font-family: Times New Roman; font-size: 14px; font-weight: 700;">Characterization of backbone effect:</span>
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     <span style="font-family: Arial; font-size: 16px;">We apply gradient test to find out which influence would be made on </span><span style="font-family: Arial; font-size: 16px;">reprogrammed </span><span style="font-family: Arial; font-size: 16px;">chemotaxis under the following parameters: the concentration of chloramphenicol, IPTG and L-arabinose.</span>
</p>
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<p style="font-family: Arial; font-size: 16px;">
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     <span style="font-family: Times New Roman;">To begin with, we test for the best chloramphenicol concentration. We test gradient concentration of chloramphenicol at semi-solid medium culture as Table 1 show. We find that the activity of chemotaxis doesn’t have overt linear relationship to chloramphenicol. Interestingly, 50μg/ml of chloramphenicol gives CL-1 the best chemotaxis. So we apply that to our following characterization.</span>
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    &nbsp;
 +
</p>
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<p style="font-family: Arial; font-size: 16px;">
 +
     <span style="font-family: Arial; font-size: 16px; font-weight: 700;">Characterization of </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">backbone effect</span>
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<p style="font-family: Arial; font-size: 16px;">
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    &nbsp;
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</p>
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<p style="font-family: Arial; font-size: 16px;">
 +
    <span style="font-family: Arial; font-size: 16px;">To begin with, we test for the best chloramphenicol concentration. We test gradient concentration of chloramphenicol at semi-solid </span><span style="font-family: Arial; font-size: 16px;">culture medium</span><span style="font-family: Arial; font-size: 16px;"> as Table 1 show. We find that the activity of chemotaxis doesn’t have overt linear relationship to chloramphenicol. Interestingly, 50μg/ml of chloramphenicol gives </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> the best chemotaxis. So we apply that to our following characterization.</span>
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                 <p style="font-family: Times New Roman; font-size: 16px;">
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                     <span style="font-family: Times New Roman; font-weight: 700;">Table 1</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">Scatter plot of chemotactic</span><span style="font-family: Times New Roman;"> diameter under </span><span style="font-family: Times New Roman;">gradient</span><span style="font-family: Times New Roman;"> concentration</span><span style="font-family: Times New Roman;"> of</span><span style="font-family: Times New Roman;"> Cm (chloramphenicol).</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure 4</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">. </span><span style="font-family: Times New Roman; font-size: 16px;">Scatter plot of chemotactic</span><span style="font-family: Times New Roman; font-size: 16px;"> diameter under </span><span style="font-family: Times New Roman; font-size: 16px;">gradient</span><span style="font-family: Times New Roman; font-size: 16px;"> concentration</span><span style="font-family: Times New Roman; font-size: 16px;"> of</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">chloramphenicol</span><span style="font-family: Times New Roman; font-size: 16px;"> (cm)</span><span style="font-family: Times New Roman; font-size: 16px;">.</span>
                 </p>
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<p style="font-family: Arial; font-size: 16px;">
     &nbsp;
     &nbsp;
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     <span style="color: rgb(40, 40, 40); font-size: 13px;">2.</span><span style="color: rgb(40, 40, 40); font-size: 13px;"> </span><span style=" color: rgb(40, 40, 40); font-family: Times New Roman; font-size: 14px; font-weight: 700;">Characterization of IPTG effect</span>
+
     <span style="color: “blue”; font-family: Arial; font-size: 16px; font-weight: 700;">Characterization of IPTG effect</span>
</p>
</p>
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<p style="font-family: Times New Roman;">
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<p style="font-family: Arial; font-size: 16px;">
-
     <span style="font-family: Times New Roman;">As promoter pBAD leads to a certain level of expression</span><span style="font-family: Times New Roman;"> leakage</span><span style="font-family: Times New Roman;"> of LacI, </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> has the worst chemotaxis</span><span style="font-family: Times New Roman;"> without any stimulus</span><span style="font-family: Times New Roman;">. We added IPTG at gradient concentration and got the result</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;"> (</span><span style="font-family: Times New Roman; font-weight: 700;">Table 2</span><span style="font-family: Times New Roman;">).</span><span style="font-family: Times New Roman;"> We fi</span><span style="font-family: Times New Roman;">nd that </span><span style="font-family: Times New Roman;">the activity of chemotaxis </span><span style="font-family: Times New Roman;">keeps increasing when the concentration of IPTG increase</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;"> from 0</span><span style="font-family: Times New Roman;"> to</span><span style="font-family: Times New Roman;"> 0.02μM and gets the best performance with the </span><span style="font-family: Times New Roman;">IPTG </span><span style="font-family: Times New Roman;">range from </span><span style="font-family: Times New Roman;">0.02 to 0.02</span><span style="font-family: Times New Roman;">5μM. We apply 0.0</span><span style="font-family: Times New Roman;">2</span><span style="font-family: Times New Roman;">5μM IPTG for our following characterization.</span>
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    &nbsp;
 +
</p>
 +
<p style="font-family: Arial; font-size: 16px;">
 +
     <span style="font-family: Arial; font-size: 16px;">As promoter pBAD leads to a certain level of expression</span><span style="font-family: Arial; font-size: 16px;"> leakage</span><span style="font-family: Arial; font-size: 16px;"> of LacI, </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> has the worst chemotaxis</span><span style="font-family: Arial; font-size: 16px;"> without any stimulus</span><span style="font-family: Arial; font-size: 16px;">. We added IPTG at gradient concentration and got the result</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure 5</span><span style="font-family: Arial; font-size: 16px;">).</span><span style="font-family: Arial; font-size: 16px;"> We fi</span><span style="font-family: Arial; font-size: 16px;">nd that </span><span style="font-family: Arial; font-size: 16px;">the activity of chemotaxis </span><span style="font-family: Arial; font-size: 16px;">keeps increasing when the concentration of IPTG increase</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> from 0</span><span style="font-family: Arial; font-size: 16px;"> to</span><span style="font-family: Arial; font-size: 16px;"> 0.02μM and gets the best performance with the </span><span style="font-family: Arial; font-size: 16px;">IPTG </span><span style="font-family: Arial; font-size: 16px;">range from </span><span style="font-family: Arial; font-size: 16px;">0.02 to 0.02</span><span style="font-family: Arial; font-size: 16px;">5μM. We apply 0.0</span><span style="font-family: Arial; font-size: 16px;">2</span><span style="font-family: Arial; font-size: 16px;">5μM IPTG for our following characterization.</span>
</p>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Table 2</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Curve of chemotactic</span><span style="font-family: Times New Roman;"> diameter over time under gradient concentration of IPTG. </span>
+
                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure 5</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">. </span><span style="font-family: Times New Roman; font-size: 16px;">Curve of chemotactic</span><span style="font-family: Times New Roman; font-size: 16px;"> diameter over time under gradient concentration of IPTG. </span>
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     &nbsp;
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-
    <span style="color: rgb(40, 40, 40); font-size: 13px;">3.</span><span style="color: rgb(40, 40, 40); font-size: 13px;"> </span><span style=" color: rgb(40, 40, 40); font-family: Times New Roman; font-size: 14px; font-weight: 700;">Characterization of L-arabinose effect</span>
+
    <span style="font-family: Arial,Arial Unicode MS; font-size: 16px; font-weight: 700;">Characterization of</span><span style="font-family: Arial,Arial Unicode MS; font-size: 16px; font-weight: 700;"> the</span><span style="font-family: Arial,Arial Unicode MS; font-size: 16px; font-weight: 700;"> IPTG</span><span style="font-family: Arial,Arial Unicode MS; font-size: 16px; font-weight: 700;"> tendency</span>
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-
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<p style="font-family: Arial,Arial Unicode MS; font-size: 16px;">
-
    <span style="font-family: Times New Roman;">As more L-arabinose added in, the expression from promoter pBAD will be stronger which leads to more LacI produced resulting in </span><span style="font-family: Times New Roman;">the inhibition to chemotaxis. As our expectation, </span><span style="font-family: Times New Roman;">the activity of chemotaxis</span><span style="font-family: Times New Roman;"> keeps going down </span><span style="font-family: Times New Roman;">as</span><span style="font-family: Times New Roman;"> the concentration of L-arabinose </span><span style="font-family: Times New Roman;">increases</span><span style="font-family: Times New Roman;"> (</span><span style="font-family: Times New Roman; font-weight: 700;">Table 3</span><span style="font-family: Times New Roman;">). We find that 0.2% of L-arabinose has the best inhibitory effect on chemotaxis with 0.025μM of IPTG added in.</span>
+
    &nbsp;
</p>
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-
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<p style="font-family: Arial; font-size: 16px;">
 +
    <span style="font-family: Arial; font-size: 16px;">In order to further characterize the IPTG effect, we spotted IPTG and bacteria as the figure show (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">6</span><span style="font-family: Arial; font-size: 16px;">). As the concentration of IPTG keeps on decreasing as it spreads out. We spotted IPTG with its concentration a little higher than the optimum. We observed that reprogrammed bacteria swim to IPTG source which seemed that the bacteria were attracted by IPTG.</span>
 +
</p>
 +
<p style="text-align: justify;">
 +
    <span style="font-family: 宋体; font-size: 16px;"> &nbsp; &nbsp;</span><span style="font-family: 宋体; font-size: 16px;"> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;</span>
 +
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 +
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                <p style="text-align: justify;">
 +
                    <span style="font-size: 14px;">A</span>
 +
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 +
                <p style="font-family: Times New Roman; font-size: 18px;">
 +
                    <img width="225" height="215" src="https://static.igem.org/mediawiki/2014/2/23/Xmu_Project_Conic_Curve_fig6A.png"/>
 +
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 +
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 +
                <p style="font-family: 宋体; font-size: 16px;">
 +
                    <span style="font-family: 宋体; font-size: 16px;">B</span>
 +
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 +
                <p style="font-family: 宋体; font-size: 16px;">
 +
                    <img width="368" height="209" style="font-family: 宋体; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/1/1d/Xmu_Project_Conic_Curve_fig6B.png"/>
 +
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 +
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 +
                <p style="font-family: Times New Roman; font-size: 18px;">
 +
                    <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">6</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A.</span><span style="font-family: Times New Roman; font-size: 16px;"> Schematic of spo</span><span style="font-family: Times New Roman; font-size: 16px;">t</span><span style="font-family: Times New Roman; font-size: 16px;">ting IPTG and bacteria on semi-solid </span><span style="font-family: Times New Roman; font-size: 16px;">culture medium</span><span style="font-family: Times New Roman; font-size: 16px;">. </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">6</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B.</span><span style="font-family: Times New Roman; font-size: 16px;"> Actual experiment result is shown.</span>
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 +
            </td>
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            <td style="border: currentColor; border-image: none; width: 383px;"></td>
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        </tr>
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 +
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 +
<p style="font-family: Arial; font-size: 16px;">
 +
    &nbsp;
 +
</p>
 +
<p style="font-family: Arial; font-size: 16px;">
 +
    <span style=" color: rgb(40, 40, 40); font-family: Arial; font-size: 16px; font-weight: 700;">Characterization of L-arabinose effect</span>
 +
</p>
 +
<p style="font-family: Arial; font-size: 16px;">
 +
    &nbsp;
 +
</p>
 +
<p style="font-family: Arial; font-size: 16px;">
 +
    <span style="font-family: Arial; font-size: 16px;">As more L-arabinose added in, the expression </span><span style="font-family: Arial; font-size: 16px;">of</span><span style="font-family: Arial; font-size: 16px;"> promoter pBAD </span><span style="font-family: Arial; font-size: 16px;">gets</span><span style="font-family: Arial; font-size: 16px;"> stronger</span><span style="font-family: Arial; font-size: 16px;">,</span><span style="font-family: Arial; font-size: 16px;"> which leads to more LacI produced</span><span style="font-family: Arial; font-size: 16px;">,</span><span style="font-family: Arial; font-size: 16px;"> resulting in </span><span style="font-family: Arial; font-size: 16px;">the inhibition to chemotaxis. As our expectation, </span><span style="font-family: Arial; font-size: 16px;">the activity of chemotaxis</span><span style="font-family: Arial; font-size: 16px;"> keeps going down </span><span style="font-family: Arial; font-size: 16px;">as</span><span style="font-family: Arial; font-size: 16px;"> the concentration of L-arabinose </span><span style="font-family: Arial; font-size: 16px;">increases</span><span style="font-family: Arial; font-size: 16px;"> (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">7</span><span style="font-family: Arial; font-size: 16px;">). We find that 0.2% of L-arabinose has the best inhibitory effect on chemotaxis with 0.025μM of IPTG added in.</span>
 +
</p>
 +
<p style="font-family: Arial; font-size: 16px;">
     &nbsp;
     &nbsp;
</p>
</p>
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                     <img width="533" height="366" src="http://convert.wenku.baidu.com/rtcs/image?md5sum=8a1d45a689810e868d560563846c1868.docx&l=webapp&ipr={&quot;t&quot;:&quot;img&quot;,&quot;w&quot;:&quot;533.00&quot;,&quot;h&quot;:&quot;366.00&quot;,&quot;dataType&quot;:&quot;png&quot;,&quot;c&quot;:&quot;word\/media\/image8.png&quot;}"/>
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                     <img width="540" height="396" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/2/23/Xmu_Project_Conic_Curve0_table03.png"/>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Table 3</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Curve of chemotactic</span><span style="font-family: Times New Roman;"> diameter under gradient concentration of L-arabinose.</span>
+
                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">7</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Curve of chemotactic</span><span style="font-family: Times New Roman; font-size: 16px;"> diameter under gradient concentration of L-arabinose.</span>
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<p style="font-family: Arial; font-size: 16px;">
     &nbsp;
     &nbsp;
</p>
</p>
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<p style="font-family: Arial; font-size: 21px;">
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     <span style="font-family: Times New Roman;">Results</span>
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     <span style="font-family: Arial; font-size: 21px; font-weight: 700;">Results</span>
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</p>
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<p style="font-family: Arial; font-size: 21px;">
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     <span style="font-family: Times New Roman;">Eclipse</span>
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    &nbsp;
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</p>
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<p style="font-family: Arial; font-size: 16px;">
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     <span style="font-family: Times New Roman;">If we spot IPTG on the center of the semi-solid culture medium</span><span style="font-family: Times New Roman;">, concentration gradient will be formed as </span><span style="font-family: Times New Roman; font-weight: 700;">Figure</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-weight: 700;">4</span><span style="font-family: Times New Roman; font-weight: 700;">A</span><span style="font-family: Times New Roman;">. </span><span style="font-family: Times New Roman;">Larger circle represents l</span><span style="font-family: Times New Roman;">ower concentration with a lower number labeled.</span>
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     <span style="font-family: Arial; font-size: 16px; font-weight: 700;">Eclipse</span>
 +
</p>
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<p style="font-family: Arial; font-size: 16px;">
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    &nbsp;
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</p>
 +
<p style="font-family: Arial; font-size: 16px;">
 +
     <span style="font-family: Arial; font-size: 16px;">If we spot IPTG on the center of the semi-solid culture medium</span><span style="font-family: Arial; font-size: 16px;">, concentration gradient will be formed as </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">8</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Arial; font-size: 16px;">. </span><span style="font-family: Arial; font-size: 16px;">Larger circle represents l</span><span style="font-family: Arial; font-size: 16px;">ower concentration with a lower number labeled.</span>
</p>
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                     <span style="font-family: Times New Roman; font-weight: 700;">A</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A</span>
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                     <img width="229" height="229" style="font-family: Times New Roman,宋体; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/d/d4/Xmu_project_CircuitsDesign09.png"/>
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                     <img width="258" height="259" style="font-family: Times New Roman,宋体; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/d/d4/Xmu_project_CircuitsDesign09.png"/>
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                     <span style="font-family: Times New Roman; font-weight: 700;">B</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B</span>
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                     <img width="354" height="243" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/1/16/Xmu_project_CircuitsDesign10.png"/>
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                 <p style="font-family: Times New Roman; font-size: 16px;">
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-weight: 700;">4.</span><span style="font-family: Times New Roman;"> Schematic of concentration gradient. </span><span style="font-family: Times New Roman; font-weight: 700;">A</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">single point spreading</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">model</span><span style="font-family: Times New Roman;">. Larger number represents higher concentration while </span><span style="font-family: Times New Roman;">smaller</span><span style="font-family: Times New Roman;"> number represents lower concentration. </span><span style="font-family: Times New Roman; font-weight: 700;">B</span><span style="font-family: Times New Roman;">.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">double points spreading </span><span style="font-family: Times New Roman;">model</span><span style="font-family: Times New Roman;">.</span><span style="font-family: Times New Roman;"> Letter A~J represent</span><span style="font-family: Times New Roman;"> equal concentration points on the ellipse</span><span style="font-family: Times New Roman;"> with two labeled number added up to 6</span><span style="font-family: Times New Roman;">. Red curve represents the ellipse with two foca</span><span style="font-family: Times New Roman;">l points on the IPTG spots.</span>
+
                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">8</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Schematic of concentration gradient. </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">single spot</span><span style="font-family: Times New Roman; font-size: 16px;"> spreading</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">model</span><span style="font-family: Times New Roman; font-size: 16px;">. Larger number represents higher concentration while </span><span style="font-family: Times New Roman; font-size: 16px;">smaller</span><span style="font-family: Times New Roman; font-size: 16px;"> number represents lower concentration. </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Times New Roman; font-size: 16px;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">double spot</span><span style="font-family: Times New Roman; font-size: 16px;">s spreading </span><span style="font-family: Times New Roman; font-size: 16px;">model</span><span style="font-family: Times New Roman; font-size: 16px;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Letter A~J represent</span><span style="font-family: Times New Roman; font-size: 16px;"> equal concentration points on the ellipse</span><span style="font-family: Times New Roman; font-size: 16px;"> with two labeled number added up to 6</span><span style="font-family: Times New Roman; font-size: 16px;">. Red curve represents the ellipse with two foca</span><span style="font-family: Times New Roman; font-size: 16px;">l points on the IPTG spots.</span>
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<p style="font-family: Arial; font-size: 16px;">
     &nbsp;
     &nbsp;
</p>
</p>
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<p style="font-family: Times New Roman;">
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<p style="font-family: Arial; font-size: 16px;">
-
     <span style="font-family: Times New Roman;">If we spot two IPTG simultaneously, two </span><span style="font-family: Times New Roman;">spots’ concentration gradient will interact with each other to form the ellipse</span><span style="font-family: Times New Roman;"> boundary as image</span><span style="font-family: Times New Roman;"> in </span><span style="font-family: Times New Roman; font-weight: 700;">Figure 4</span><span style="font-family: Times New Roman; font-weight: 700;">B</span><span style="font-family: Times New Roman;">. </span>
+
     <span style="font-family: Arial; font-size: 16px;">If we spot two IPTG simultaneously, two </span><span style="font-family: Arial; font-size: 16px;">spots’ concentration gradient will interact with each other to form the ellipse</span><span style="font-family: Arial; font-size: 16px;"> boundary as image</span><span style="font-family: Arial; font-size: 16px;"> in </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">8</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Arial; font-size: 16px;">. </span>
</p>
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+
<p style="font-family: Arial; font-size: 16px;">
     &nbsp;
     &nbsp;
</p>
</p>
-
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<p style="font-family: Arial; font-size: 16px;">
-
     <span style="font-family: Times New Roman;">If we spot </span><span style="font-family: Times New Roman; font-style: italic;">E.coli</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> with </span><span style="font-family: Times New Roman;">circuit</span><span style="font-family: Times New Roman;"> above</span><span style="font-family: Times New Roman;"> transformed in</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">at</span><span style="font-family: Times New Roman;"> the center between two IPTG spots</span><span style="font-family: Times New Roman;"> on semi-solid culture plate</span><span style="font-family: Times New Roman;"> as</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-weight: 700;">Figure 5</span><span style="font-family: Times New Roman;">. </span><span style="font-family: Times New Roman;">The concentration of L-Arabinose added in the </span><span style="font-family: Times New Roman;">culture</span><span style="font-family: Times New Roman;"> medium </span><span style="font-family: Times New Roman;">determine</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">the</span><span style="font-family: Times New Roman;"> degree of constraint </span><span style="font-family: Times New Roman;">from</span><span style="font-family: Times New Roman;"> part </span><span style="font-family: Times New Roman; font-weight: 700;">C</span><span style="font-family: Times New Roman;">.</span><span style="font-family: Times New Roman;"> Each </span><span style="font-family: Times New Roman;">red ellipse curve </span><span style="font-family: Times New Roman;">represents </span><span style="font-family: Times New Roman;">equal </span><span style="font-family: Times New Roman;">IPTG </span><span style="font-family: Times New Roman;">concentration, </span><span style="font-family: Times New Roman;">and there are a series of such ellipses from inside to outside represent IPTG concentrations from highest to lowest. </span><span style="font-family: Times New Roman;">One of the ellipses is the </span><span style="font-family: Times New Roman; font-weight: 700;">critical line</span><span style="font-family: Times New Roman;"> indicating that the</span><span style="font-family: Times New Roman;"> constraint from part </span><span style="font-family: Times New Roman; font-weight: 700;">C</span><span style="font-family: Times New Roman;"> can just be relieved by the certain concentration of IPTG. </span><span style="font-family: Times New Roman;">Initially, as the concentration of IPTG is</span><span style="font-family: Times New Roman;"> e</span><span style="font-family: Times New Roman;">nough to relieve the constraint, </span><span style="font-family: Times New Roman;">bacteria </span><span style="font-family: Times New Roman;">can </span><span style="font-family: Times New Roman;">swim from the center out to periphery</span><span style="font-family: Times New Roman;">. </span><span style="font-family: Times New Roman;">When the bacteria</span><span style="font-family: Times New Roman;"> swim out of</span><span style="font-family: Times New Roman;"> the </span><span style="font-family: Times New Roman; font-weight: 700;">critical line</span><span style="font-family: Times New Roman;">, </span><span style="font-family: Times New Roman;">the concentration of IPTG can’</span><span style="font-family: Times New Roman;">t relieve </span><span style="font-family: Times New Roman;">the constraint, so the </span>
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     <span style="font-family: Arial; font-size: 16px;">If we spot </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">E.</span><span style="font-family: Arial; font-size: 16px; font-style: italic;"> </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">coli</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> with </span><span style="font-family: Arial; font-size: 16px;">circuit</span><span style="font-family: Arial; font-size: 16px;"> above</span><span style="font-family: Arial; font-size: 16px;"> transformed in</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">at</span><span style="font-family: Arial; font-size: 16px;"> the center between two IPTG spots</span><span style="font-family: Arial; font-size: 16px;"> on semi-solid culture plate</span><span style="font-family: Arial; font-size: 16px;"> as</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">9</span><span style="font-family: Arial; font-size: 16px;">. </span><span style="font-family: Arial; font-size: 16px;">The concentration o</span><span style="font-family: Arial; font-size: 16px;">f </span><span style="font-family: Arial; font-size: 16px;">L-Arabinose added in the </span><span style="font-family: Arial; font-size: 16px;">culture</span><span style="font-family: Arial; font-size: 16px;"> medium </span><span style="font-family: Arial; font-size: 16px;">determine</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">the</span><span style="font-family: Arial; font-size: 16px;"> degree of constraint </span><span style="font-family: Arial; font-size: 16px;">from</span><span style="font-family: Arial; font-size: 16px;"> part </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 16px;">.</span><span style="font-family: Arial; font-size: 16px;"> Each </span><span style="font-family: Arial; font-size: 16px;">red ellipse curve </span><span style="font-family: Arial; font-size: 16px;">represents </span><span style="font-family: Arial; font-size: 16px;">equal </span><span style="font-family: Arial; font-size: 16px;">IPTG </span><span style="font-family: Arial; font-size: 16px;">concentration, </span><span style="font-family: Arial; font-size: 16px;">and there are</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">series of such ellipses from inside to outside represent</span><span style="font-family: Arial; font-size: 16px;">ing</span><span style="font-family: Arial; font-size: 16px;"> IPTG concentrations from highest to lowest. </span><span style="font-family: Arial; font-size: 16px;">One of the ellipses is the </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">critical line</span><span style="font-family: Arial; font-size: 16px;"> indicating that the</span><span style="font-family: Arial; font-size: 16px;"> constraint from part </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">C</span><span style="font-family: Arial; font-size: 16px;"> can just be relieved by the certain concentration of IPTG. </span><span style="font-family: Arial; font-size: 16px;">Initially, as the concentration of IPTG is</span><span style="font-family: Arial; font-size: 16px;"> e</span><span style="font-family: Arial; font-size: 16px;">nough to relieve the constraint, </span><span style="font-family: Arial; font-size: 16px;">bacteria </span><span style="font-family: Arial; font-size: 16px;">can </span><span style="font-family: Arial; font-size: 16px;">swim from the center out to periphery</span><span style="font-family: Arial; font-size: 16px;">. </span><span style="font-family: Arial; font-size: 16px;">When the bacteria</span><span style="font-family: Arial; font-size: 16px;"> swim out of</span><span style="font-family: Arial; font-size: 16px;"> the </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">critical line</span><span style="font-family: Arial; font-size: 16px;">, </span><span style="font-family: Arial; font-size: 16px;">the concentration of IPTG can’</span><span style="font-family: Arial; font-size: 16px;">t relieve </span><span style="font-family: Arial; font-size: 16px;">the constraint, so the </span>
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     <span style="font-family: Times New Roman;">bacteria</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">adopt</span><span style="font-family: Times New Roman;"> non-motile phenotype. On the contrary, when the bacteria</span><span style="font-family: Times New Roman;"> are</span><span style="font-family: Times New Roman;"> inside of the critical line, </span><span style="font-family: Times New Roman;">they </span><span style="font-family: Times New Roman;">adopt</span><span style="font-family: Times New Roman;"> motile phenotype.</span><span style="font-family: Times New Roman;"> When the bacteria swim </span><span style="font-family: Times New Roman;">from inside to outside</span><span style="font-family: Times New Roman;">, motile bacteria become</span><span style="font-family: Times New Roman;"> non-motile, so the bacteria will aggregate outside the </span><span style="font-family: Times New Roman; font-weight: 700;">critical line</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">thus </span><span style="font-family: Times New Roman; font-size: 14px; styleName: Default Paragraph Font;">the </span><span style="font-family: Times New Roman; font-size: 14px; styleName: Default Paragraph Font;">b</span><span style="font-family: Times New Roman;">acteria density inside the</span><span style="font-family: Times New Roman; font-weight: 700;"> critical line</span><span style="font-family: Times New Roman;"> will decline.</span><span style="font-family: Times New Roman;"> Thus, an ellipse boundary is formed.</span>
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     <span style="font-family: Arial; font-size: 16px;">bacteria</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">adopt</span><span style="font-family: Arial; font-size: 16px;"> non-motile phenotype. On the contrary, when the bacteria</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">are </span><span style="font-family: Arial; font-size: 16px;">inside of the critical line, </span><span style="font-family: Arial; font-size: 16px;">they </span><span style="font-family: Arial; font-size: 16px;">adopt</span><span style="font-family: Arial; font-size: 16px;"> motile phenotype.</span><span style="font-family: Arial; font-size: 16px;"> When the bacteria swim </span><span style="font-family: Arial; font-size: 16px;">from inside to outside</span><span style="font-family: Arial; font-size: 16px;">, motile bacteria become</span><span style="font-family: Arial; font-size: 16px;"> non-motile, so the bacteria will aggregate outside the </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">critical line</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">thus </span><span style="font-family: Arial; font-size: 16px; styleName: Default Paragraph Font;">the </span><span style="font-family: Arial; font-size: 16px; styleName: Default Paragraph Font;">b</span><span style="font-family: Arial; font-size: 16px;">acteria density inside the</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;"> critical line</span><span style="font-family: Arial; font-size: 16px;"> will decline.</span><span style="font-family: Arial; font-size: 16px;"> Thus, an ellipse boundary is formed.</span>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure 5</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">Schematic of Critical Line model</span><span style="font-family: Times New Roman;"> for ellipse</span><span style="font-family: Times New Roman;">. Critical line represents the IPTG concentration which can just relieve the repression from part </span><span style="font-family: Times New Roman; font-weight: 700;">C</span><span style="font-family: Times New Roman;">. </span><span style="font-family: Times New Roman;">So that </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> is motile inside </span><span style="font-family: Times New Roman;">t</span><span style="font-family: Times New Roman;">he ell</span><span style="font-family: Times New Roman;">ipse while non-motile outside </span><span style="font-family: Times New Roman;">the ellipse.</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">9</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">Schematic of Critical Line model</span><span style="font-family: Times New Roman; font-size: 16px;"> for ellipse</span><span style="font-family: Times New Roman; font-size: 16px;">. Critical line represents the IPTG concentration which just relieve the repression from part </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">C</span><span style="font-family: Times New Roman; font-size: 16px;">. </span><span style="font-family: Times New Roman; font-size: 16px;">So that </span><span style="font-family: Times New Roman; font-size: 16px;">CL-1</span><span style="font-family: Times New Roman; font-size: 16px;"> is motile inside </span><span style="font-family: Times New Roman; font-size: 16px;">t</span><span style="font-family: Times New Roman; font-size: 16px;">he ell</span><span style="font-family: Times New Roman; font-size: 16px;">ipse while non-motile outside </span><span style="font-family: Times New Roman; font-size: 16px;">the ellipse.</span>
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     <span style="font-family: Times New Roman;">Parabola and hyperbola</span>
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     <span style="font-family: Arial; font-size: 16px; font-weight: 700;">Parabola and hyperbola</span>
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     <span style="font-family: Times New Roman;">We got the optimum concentrations of IPTG and L-arabinose as inducer and repressor through preliminary experiments. Because the concentration of stimulus will decrease during spreading, so does their effect, we use IPTG and L-arabinose of which concentrations are a little bit higher than </span><span style="font-family: Times New Roman;">the optimum values for our experiments.</span>
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     <span style="font-family: Arial; font-size: 16px;">We </span><span style="font-family: Arial; font-size: 16px;">got</span><span style="font-family: Arial; font-size: 16px;"> the optimum concentrations of IPTG and L-arabinose as inducer and repressor through preliminary experiments. Because the concentration of stimulus will decrease during spreading, so do their effect, we use IPTG and L-arabinose of which concentrations are a little bit higher than the optimum values for our experiments.</span>
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     <span style="font-family: Times New Roman;">We draw a s</span><span style="font-family: Times New Roman;">t</span><span style="font-family: Times New Roman;">raight line with L-arabinose on the semi-solid culture medium, and a spot with the mixture of IPTG and CL-1 on one side of the line. In the area around the spot, the induction of IPTG is stronger than the repression of L-arabinose, </span><span style="font-family: Times New Roman; font-style: italic;">CheZ</span><span style="font-family: Times New Roman;"> is expressed and the bacteria adopt motile phenotype. However, when they approach the line where the repressor have a greater effect on the motility, they will lost their motile phenotype and stop. </span>
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     <span style="font-family: Arial; font-size: 16px;">We draw a s</span><span style="font-family: Arial; font-size: 16px;">t</span><span style="font-family: Arial; font-size: 16px;">raight line with L-arabinose on the semi-solid culture medium, and a spot with the mixture of IPTG and </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;"> on one side of the line. In the area around the spot, the induction of IPTG is stronger than the repression of L-arabinose, </span><span style="font-family: Arial; font-size: 16px; font-style: italic;">c</span><span style="font-family: Arial; font-size: 16px; font-style: italic;">heZ</span><span style="font-family: Arial; font-size: 16px;"> is expressed and the bacteria adopt motile phenotype. However, when they approach the line where the repressor ha</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> a greater effect on the motility, they will lost their motile phenotype and stop. </span>
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     <span style="font-family: Times New Roman;">According to the hypothesis 2, on the threshold ratio of the concentration of inducer and repressor, their effects are offset and a critical line is formed. Distances of the points on the critical line to the IPTG spot (focus), and the L-arabinose line (directrix) are in a fixed ratio (eccentricity). If the ratio is equal to 1, the critical line is a parabola. If the ratio is larger than 1, it is a branch of a hyperbola.</span><span style="font-family: Times New Roman;"> Then we conducted experiment to </span><span style="font-family: Times New Roman;">verify the mechanism (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 6B</span><span style="font-family: Times New Roman;">). Left boundary of the colony is regarded as the critical line.</span><span style="font-family: Times New Roman;"> We found that cells has the tendency to swim away from L-arabinose line which is an expected performance of the circuit.</span>
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     <span style="font-family: Arial; font-size: 16px;">According to the hypothesis 2, on the threshold ratio of the concentration of inducer and repressor, their effects are offset and a critical line is formed. Distances of the points on the critica</span><span style="font-family: Arial; font-size: 16px;">l line to the IPTG spot (focus)</span><span style="font-family: Arial; font-size: 16px;"> and the L-arabinose line (directrix) are in a fixed ratio (eccentricity). If the ratio equal</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> to 1, the critical line is a parabola. If the ratio is larger than 1, it is a branch of a hyperbola.</span><span style="font-family: Arial; font-size: 16px;"> Then we conducted experiment to </span><span style="font-family: Arial; font-size: 16px;">verify the mechanism (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">10</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Arial; font-size: 16px;">). Left boundary of the colony is regarded as the critical line.</span><span style="font-family: Arial; font-size: 16px;"> We found that cells ha</span><span style="font-family: Arial; font-size: 16px;">ve</span><span style="font-family: Arial; font-size: 16px;"> the tendency to swim away from L-arabinose line which is an expected performance of the </span><span style="font-family: Arial; font-size: 16px;">bacteria</span><span style="font-family: Arial; font-size: 16px;">.</span>
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                     <span style="font-family: Times New Roman; font-weight: 700;">B</span><span style="border: 1px rgb(0, 0, 0); border-image: none;"><span style="background: rgb(0, 0, 0); color: rgb(0, 0, 0); font-family: Times New Roman; font-size: 0px;"> </span></span><img width="493" height="347" style="font-family: Times New Roman; font-weight: 700;" src="http://convert.wenku.baidu.com/rtcs/image?md5sum=8a1d45a689810e868d560563846c1868.docx&l=webapp&ipr={&quot;t&quot;:&quot;img&quot;,&quot;w&quot;:&quot;493.34&quot;,&quot;h&quot;:&quot;347.07&quot;,&quot;dataType&quot;:&quot;png&quot;,&quot;c&quot;:&quot;word\/media\/image13.png&quot;}"/>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B</span></p> <p style="font-family: Times New Roman; font-size: 16px;"><img width="493" height="347" style="font-family: Times New Roman; font-size: 16px; font-weight: 700;" src="https://static.igem.org/mediawiki/parts/6/68/Xmu_Project_Conic_Curve_figure_hyperbola.png"/>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure 6A</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-weight: 700;"> </span><span style="font-family: Times New Roman;">Schematic of Critical Line model for parabola and hyperbola. </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;"> becomes no-motile on the left side of the critical line while motile on the other side. The eccentricity e equals to PF/PB. If e=1, we define the critical line as parabola. If e&gt;1, we define that as one branch of hyperbola.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-weight: 700;">6B</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">Actual experiment result is shown.</span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">10</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;"> </span><span style="font-family: Times New Roman; font-size: 16px;">Schematic of Critical Line model for parabola and hyperbola. </span><span style="font-family: Times New Roman; font-size: 16px;">CL-1</span><span style="font-family: Times New Roman; font-size: 16px;"> becomes no-motile on the left side of the critical line while motile on the other side. The eccentricity e equals to PF/PB. If e=1, we define the critical line as parabola. If e&gt;1, we define that as one branch of hyperbola.</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">10</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> An a</span><span style="font-family: Times New Roman; font-size: 16px;">ctual experiment result is shown.</span>
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     <span style="font-family: Times New Roman;">Other function curves</span><span style="font-family: Times New Roman; font-weight: 400;">--</span><span style="font-size: 14px;"> </span><span style="font-family: Times New Roman;">Quasi-hyperbola</span>
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     <span style="font-family: Arial; font-size: 16px; font-weight: 700;">Other function curves</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">-- </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">q</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">uasi-hyperbola</span>
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     <span style="font-family: Times New Roman;">After explorations, we </span><span style="font-family: Times New Roman;">tried different</span><span style="font-family: Times New Roman;"> way</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;"> to </span><span style="font-family: Times New Roman;">arrange</span><span style="font-family: Times New Roman;"> bacteria and stimulus </span><span style="font-family: Times New Roman;">on semisolid culture medium. We got some interesting results.</span>
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     <span style="font-family: Arial; font-size: 16px;">After explorations, we </span><span style="font-family: Arial; font-size: 16px;">tried different</span><span style="font-family: Arial; font-size: 16px;"> way</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;"> to </span><span style="font-family: Arial; font-size: 16px;">arrange</span><span style="font-family: Arial; font-size: 16px;"> bacteria and stimulus </span><span style="font-family: Arial; font-size: 16px;">on semisolid culture medium. We got some interesting results.</span>
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     <span style="font-family: Times New Roman;">We draw two spots on the semi-solid culture medium, one with L-arabinose</span><span style="font-family: Times New Roman;"> (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 7A</span><span style="font-family: Times New Roman;">)</span><span style="font-family: Times New Roman;"> and the other with the mixture of IPTG and </span><span style="font-family: Times New Roman; font-style: italic;">CL-1</span><span style="font-family: Times New Roman;">. Similarly, </span><span style="font-family: Times New Roman;">on the threshold ratio of the concentration of inducer and repressor, their effects are offset and a</span><span style="font-family: Times New Roman; font-weight: 700;"> critical line</span><span style="font-family: Times New Roman;"> is formed. Distances of the points on the</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">right </span><span style="font-family: Times New Roman;">side </span><span style="font-family: Times New Roman;">of colony boundary</span><span style="font-family: Times New Roman;"> to the spot A and the spot B are in a </span><span style="font-family: Times New Roman;">very narrow </span><span style="font-family: Times New Roman;">ratio</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman;">(</span><span style="font-family: Times New Roman; font-weight: 700;">Figure 7B</span><span style="font-family: Times New Roman;">)</span><span style="font-family: Times New Roman;">. Actually, as the critical line is quiet similar to hyperbola</span><span style="font-family: Times New Roman;">, we name it</span><span style="font-family: Times New Roman;"> quasi-hyperbola.</span>
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     <span style="font-family: Arial; font-size: 16px;">We draw two spots on the semi-solid culture medium, one with L-arabinose</span><span style="font-family: Arial; font-size: 16px;"> (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">11</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Arial; font-size: 16px;">)</span><span style="font-family: Arial; font-size: 16px;"> and the other with the mixture of IPTG and </span><span style="font-family: Arial; font-size: 16px;">CL-1</span><span style="font-family: Arial; font-size: 16px;">. Similarly, </span><span style="font-family: Arial; font-size: 16px;">on the </span><span style="font-family: Arial; font-size: 16px;">threshold ratio of the concentration of inducer and repressor, their effects are offset and a</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;"> critical line</span><span style="font-family: Arial; font-size: 16px;"> is formed. Distances of the points on the </span><span style="font-family: Arial; font-size: 16px;">right side of colony boundary</span><span style="font-family: Arial; font-size: 16px;"> to the spot A and the spot B are in a </span><span style="font-family: Arial; font-size: 16px;">very narrow </span><span style="font-family: Arial; font-size: 16px;">ratio</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">(</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">8</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Arial; font-size: 16px;">)</span><span style="font-family: Arial; font-size: 16px;">. Actually, as the critical line is quiet similar to hyperbola</span><span style="font-family: Arial; font-size: 16px;">, we name it</span><span style="font-family: Arial; font-size: 16px;"> quasi-hyperbola.</span>
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                     <img width="229" height="229" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/5/53/Xmu_project_CircuitsDesign13.png"/>
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                     <img width="315" height="270" style="font-family: Times New Roman; font-size: 16px;" src="https://static.igem.org/mediawiki/2014/3/3f/Xmu_Project_Conic_Curve_figure07B.png"/>
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                    <span style="font-family: Times New Roman; font-weight: 700;">Figure 7A</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Schematic of</span><span style="font-family: Times New Roman;"> quasi-hyperbola formation on semi-solid medium culture. </span><span style="font-family: Times New Roman; font-weight: 700;">7B</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Actual e</span><span style="font-family: Times New Roman;">xperiment result</span><span style="font-family: Times New Roman;"> is shown.</span>
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                    <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">11</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Schematic of</span><span style="font-family: Times New Roman; font-size: 16px;"> quasi-hyperbola formation on semi-solid </span><span style="font-family: Times New Roman; font-size: 16px;">culture medium</span><span style="font-family: Times New Roman; font-size: 16px;">. </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">10</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> </span><span style="font-family: Times New Roman; font-size: 16px;">An a</span><span style="font-family: Times New Roman; font-size: 16px;">ctual e</span><span style="font-family: Times New Roman; font-size: 16px;">xperiment result</span><span style="font-family: Times New Roman; font-size: 16px;"> is shown.</span>
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     <span style="font-family: Times New Roman;">O</span><span style="font-family: Times New Roman;">ther interesting ways to spot bacteria and stimulus are </span><span style="font-family: Times New Roman;">waiting to be discovered</span><span style="font-family: Times New Roman;">, </span><span style="font-family: Times New Roman;">and t</span><span style="font-family: Times New Roman;">he idea can be extended to other function curves and pattern</span><span style="font-family: Times New Roman;">s</span><span style="font-family: Times New Roman;">.</span>
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     <span style="font-family: Arial; font-size: 16px;">O</span><span style="font-family: Arial; font-size: 16px;">ther interesting ways to spot bacteria and stimulus are </span><span style="font-family: Arial; font-size: 16px;">waiting to be discovered</span><span style="font-family: Arial; font-size: 16px;">, </span><span style="font-family: Arial; font-size: 16px;">and t</span><span style="font-family: Arial; font-size: 16px;">he idea can be extended to other function curves and pattern</span><span style="font-family: Arial; font-size: 16px;">s</span><span style="font-family: Arial; font-size: 16px;">.</span>
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     <span style="font-family: Times New Roman;">We </span><span style="font-family: Times New Roman;">took two kinds of stimulus to construct a square (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-weight: 700;">8</span><span style="font-family: Times New Roman; font-weight: 700;">A</span><span style="font-family: Times New Roman;">). Two opposite sides were paved by one kind of stimulus to form thin paths. Programmed cells were spotted on the center of the square, we got two oval rings after 24 hours culturing (</span><span style="font-family: Times New Roman; font-weight: 700;">Figure </span><span style="font-family: Times New Roman; font-weight: 700;">8</span><span style="font-family: Times New Roman; font-weight: 700;">B</span><span style="font-family: Times New Roman;">). We find that cells rings are stretched by IPTG sides while squeezed by L-arabinose sides.</span>
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     <span style="font-family: Arial; font-size: 16px;">We took two kinds of stimulus to construct a square (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">1</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">2</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Arial; font-size: 16px;">). Two opposite sides were paved by one kind of stimulus to form thin paths. Programmed cells were spotted on the center of the square, we got two oval rings after 24 hours culturing (</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">Figure </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">1</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">2</span><span style="font-family: Arial; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Arial; font-size: 16px;">). We find that cell</span><span style="font-family: Arial; font-size: 16px;"> </span><span style="font-family: Arial; font-size: 16px;">rings are stretched by IPTG sides while squeezed by L-arabinose sides.</span>
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                     <span style="font-family: Times New Roman; font-weight: 700;">Figure 8A</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Spotting cells on semi-solid culture medium with two IPTG lines and two L-arabinose lines.</span><span style="font-family: Times New Roman;"> </span><span style="font-family: Times New Roman; font-weight: 700;">8B</span><span style="font-family: Times New Roman; font-weight: 700;">.</span><span style="font-family: Times New Roman;"> Zoom in to the left picture, two oval rings could be observed on the medium. </span>
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                     <span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">Figure 1</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">2</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">A</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Spotting cells on semi-solid culture medium with two IPTG lines and two L-arabinose lines. </span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">1</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">2</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">B</span><span style="font-family: Times New Roman; font-size: 16px; font-weight: 700;">.</span><span style="font-family: Times New Roman; font-size: 16px;"> Zoom in to the left picture, two oval rings could be observed on the medium. </span>
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     <span style="font-family: Times New Roman; font-size: 18px;">Reference</span><span style="font-family: Times New Roman; font-size: 18px;">s</span>
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     <span style="font-family: Arial; font-size: 16px;">Apart from forming patterns, reprogrammed chemotaxis can help us in a broad field. We offer some examples in </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;"><a href="https://2014.igem.org/Team:XMU-China/Project_Application">APPLICATION</a></span><span style="font-family: Arial; font-size: 16px;">. </span>
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    <span style="font-family: Times New Roman;">1. </span><span style="color: rgb(0, 0, 255); text-decoration: underline; styleName: Default Paragraph Font;">http://en.wikipedia.org/wiki/Ellipse</span>
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    <span style="font-size: 14px;">2. </span><span style="color: rgb(0, 0, 255); text-decoration: underline; styleName: Default Paragraph Font;">http://en.wikipedia.org/wiki/Hyperbola</span>
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     <span style="font-family: Times New Roman;">3.</span><span style="font-family: Times New Roman;"> </span><span style="font-size: 14px;">O’Gorman, R. B., Rosenberg, J. M., Kallai, O. B., Dickerson, R. E., Itakura, K., Riggs, A. D., &amp; Matthews, K. S. (1980). Equilibrium binding of inducer to lac repressor.operator DNA complex. </span><span style="font-size: 14px;">Journal of Biological Chemistry</span><span style="font-size: 14px;">, </span><span style="font-size: 14px;">255</span><span style="font-size: 14px;">, 10107–10114.</span>
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     <span style="font-family: Arial; font-size: 16px;">And we</span><span style="font-family: Arial; font-size: 16px;"> analyzed the process and the results by mathematical model in </span><span style="font-family: Arial; font-size: 16px; font-weight: 700;"><a href="https://2014.igem.org/Team:XMU-China/Project_Modelling">MODELLING</a></span><span style="font-family: Arial; font-size: 16px;">.</span>
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     <span style="color: rgb(0, 0, 255); text-decoration: underline; styleName: Default Paragraph Font;">http://www.jbc.org/content/255/21/10107.abstract</span>
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    <span style="font-family: Arial; font-size: 21px; font-weight: 700;">Reference</span><span style="font-family: Arial; font-size: 21px; font-weight: 700;">s</span>
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    <span style="font-family: Arial; font-size: 16px;">1. </span><span style="color: rgb(0, 0, 255); font-family: Arial; font-size: 16px; text-decoration: underline; styleName: Default Paragraph Font;"><a href="http://en.wikipedia.org/wiki/Ellipse" target="_blank">http://en.wikipedia.org/wiki/Ellipse </a></span>
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    <span style="font-family: Arial; font-size: 16px;">2. </span><span style="color: rgb(0, 0, 255); font-family: Arial; font-size: 16px; text-decoration: underline; styleName: Default Paragraph Font;"><a href="http://en.wikipedia.org/wiki/Hyperbola" target="_blank">http://en.wikipedia.org/wiki/Hyperbola</a></span>
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    <span style="font-family: Arial; font-size: 16px;">3. </span><span style="font-family: Arial; font-size: 16px;">    <a href="http://www.jbc.org/content/255/21/10107.abstract" target="_blank">O’Gorman, R. B., Rosenberg, J. M., Kallai, O. B., Dickerson, R. E., Itakura, K., Riggs, A. D., &amp; Matthews, K. S. (1980). Equilibrium binding of inducer to lac repressor.operator DNA complex. Journal of Biological Chemistry, 255, 10107–10114.</a> </span>
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Latest revision as of 13:22, 23 November 2014

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CONIC CURVE

 

--Form patterns by chemotaxis

 

Overview

 

By which means would you like to make a mathematical pattern? Draw with compass and ruler, or type a function in a drawing software? Well, E. coli can help us to achieve our goals. We make the first attempt to introduce pseudotaxis to form patterns in shape of conic section (such as ellipse and hyperbola). Firstly, let’s recall the precise mathematical definition on ellipse, hyperbola and parabola.

 

Mathematical definition

 

In mathematics, ellipse is a curve on a plane surrounding two focal points such that a straight line drawn from one of the focal points to any point on the curve and then back to the other focal point has the same length for every point on the curve (Figure 1A). [1] And hyperbola is a curve which point’s absolute value of the difference of the distance to the two focal points is a constant (Figure 1B).

 

A

B

Figure 1A. Schematic of ellipse. Point F1, F2 are the two focal points and Point A is on the ellipse curve. The sum of the distance AF1 and AF2 is equal to the constant k: AF1+AF2=k. 1B. Schematic of hyperbola. Point F1, F2 are the two focal points and Point A is on one of the hyperbola branches. The absolute value of the difference of the distance AF1, AF2 is equal to the constant k: |AF1-AF2|=k.

 

Hyperbola could also be defined as a conic consisting of those points whose distances to a focus, and a directrix, are in a fixed ratio (>1), called the eccentricity (e). (Figure 2A) Parabola is a conic whose eccentricity is equal to 1 (Figure 2B). [2]

 

A

B

Figure 2A. One branch of hyperbola can be defined by directrix and eccentricity. Point A is a spot on the curve, point F is the focus. AB is the distance between A and directrix. The eccentricity e equal to TF/AB, and e>1. 2B. Schematic of Parabola. Point A is a spot on the curve, point F is the focus. AB is the distance between A and directrix. The eccentricity e equals to AF/AB, and e=1.

 

Hypotheses

 

Focal points, constant k and the eccentricity ratio e are key factors of conic section. Therefore, we can easily get any eclipse by presetting reasonable focal points with an acceptable constant, as well as parabola or hyperbola by a fixed ratio. Based on these, we need to combine these mathematical concepts with our pattern formation system.

 

If we spot stimulus on semi-solid plate, it will spread from the spotting center out to the periphery. In the spreading process, the concentration is negative correlated to the distance from center. If we draw a line with stimulus, a concentration gradient with square shape will form. And both of the concentration gradients will maintain for a long period. Generally, the stimulus spots are defined as focuses while those lines are defined as directrixes.

 

There is a threshold ratio of the concentrations of inducer and repressor. [3] This means that more repressor will cause more repression, hence more inducer is needed to relieve the repression, and vice versa. As the concentration of inducer and repressor are directly connected to the concentration of stimulus sources, we can tell the constant k and eccentricity e by combining the relationship between distance and concentration.

 

Circuit design

 

Our circuit consists of two parts, of which one is named C (constraint), the other is named M (motile). (Figure 3):

 

We transform our circuit into E. coli CL-1 which lacks gene lacI and cheZ (ΔlacI, ΔcheZ). In the absence of cheZ, CL-1 adopts non-motile phenotype.

 

Without any exogenous stimulus, E. coli will produce background amount of AraC to repress pBAD at limit degree. That means even no L-arabinose involved in, promoter pBAD has leakage expression, so that part C will produce repressor LacI which can bind to the operon of promoter pLac and thus repress its transcription. Because L-arabinose could induce pBAD, within certain concentration range, the more L-arabinose involved in, the more repressor LacI part C could produce resulting the inhibition to chemotaxis. Because of its ability to constrain chemotaxis, this part is named C.

 

When IPTG involved in, it can relieve the repression from repressor LacI, therefore protein CheZ is produced to make our engineering bacteria (CL-1) regain motile ability. Within certain L-arabinose concentration range which means certain constraint condition, the more IPTG involved in, the more CheZ is produced leading to stronger motile ability. Because of its ability to make CL-1 motile, this part is named M.

 

Figure 3. Part C produces LacI to repress the expression of part M. Part M could produce CheZ to make CL-1 regain motile ability.

 

Characterization of circuit

 

We sequenced the circuit above and characterized it in E. coli CL-1. As CL-1 lacks lacI gene, promoter pLac won’t be repressed by background repressor LacI.

 

We apply gradient test to find out which influence would be made on reprogrammed chemotaxis under the following parameters: the concentration of chloramphenicol, IPTG and L-arabinose.

 

Characterization of backbone effect

 

To begin with, we test for the best chloramphenicol concentration. We test gradient concentration of chloramphenicol at semi-solid culture medium as Table 1 show. We find that the activity of chemotaxis doesn’t have overt linear relationship to chloramphenicol. Interestingly, 50μg/ml of chloramphenicol gives CL-1 the best chemotaxis. So we apply that to our following characterization.

 

Figure 4. Scatter plot of chemotactic diameter under gradient concentration of chloramphenicol (cm).

 

Characterization of IPTG effect

 

As promoter pBAD leads to a certain level of expression leakage of LacI, CL-1 has the worst chemotaxis without any stimulus. We added IPTG at gradient concentration and got the results (Figure 5). We find that the activity of chemotaxis keeps increasing when the concentration of IPTG increases from 0 to 0.02μM and gets the best performance with the IPTG range from 0.02 to 0.025μM. We apply 0.025μM IPTG for our following characterization.

Figure 5. Curve of chemotactic diameter over time under gradient concentration of IPTG.

 

Characterization of the IPTG tendency

 

In order to further characterize the IPTG effect, we spotted IPTG and bacteria as the figure show (Figure 6). As the concentration of IPTG keeps on decreasing as it spreads out. We spotted IPTG with its concentration a little higher than the optimum. We observed that reprogrammed bacteria swim to IPTG source which seemed that the bacteria were attracted by IPTG.

                                       

A

B

Figure 6A. Schematic of spotting IPTG and bacteria on semi-solid culture medium. 6B. Actual experiment result is shown.

 

Characterization of L-arabinose effect

 

As more L-arabinose added in, the expression of promoter pBAD gets stronger, which leads to more LacI produced, resulting in the inhibition to chemotaxis. As our expectation, the activity of chemotaxis keeps going down as the concentration of L-arabinose increases (Figure 7). We find that 0.2% of L-arabinose has the best inhibitory effect on chemotaxis with 0.025μM of IPTG added in.

 

Figure 7. Curve of chemotactic diameter under gradient concentration of L-arabinose.

 

Results

 

Eclipse

 

If we spot IPTG on the center of the semi-solid culture medium, concentration gradient will be formed as Figure 8A. Larger circle represents lower concentration with a lower number labeled.

A

B

Figure 8. Schematic of concentration gradient. A. single spot spreading model. Larger number represents higher concentration while smaller number represents lower concentration. B. double spots spreading model. Letter A~J represent equal concentration points on the ellipse with two labeled number added up to 6. Red curve represents the ellipse with two focal points on the IPTG spots.

 

If we spot two IPTG simultaneously, two spots’ concentration gradient will interact with each other to form the ellipse boundary as image in Figure 8B.

 

If we spot E. coli CL-1 with circuit above transformed in at the center between two IPTG spots on semi-solid culture plate as Figure 9. The concentration of L-Arabinose added in the culture medium determines the degree of constraint from part C. Each red ellipse curve represents equal IPTG concentration, and there are series of such ellipses from inside to outside representing IPTG concentrations from highest to lowest. One of the ellipses is the critical line indicating that the constraint from part C can just be relieved by the certain concentration of IPTG. Initially, as the concentration of IPTG is enough to relieve the constraint, bacteria can swim from the center out to periphery. When the bacteria swim out of the critical line, the concentration of IPTG can’t relieve the constraint, so the

bacteria adopt non-motile phenotype. On the contrary, when the bacteria are inside of the critical line, they adopt motile phenotype. When the bacteria swim from inside to outside, motile bacteria become non-motile, so the bacteria will aggregate outside the critical line thus the bacteria density inside the critical line will decline. Thus, an ellipse boundary is formed.

 

Figure 9. Schematic of Critical Line model for ellipse. Critical line represents the IPTG concentration which just relieve the repression from part C. So that CL-1 is motile inside the ellipse while non-motile outside the ellipse.

 

Parabola and hyperbola

 

We got the optimum concentrations of IPTG and L-arabinose as inducer and repressor through preliminary experiments. Because the concentration of stimulus will decrease during spreading, so do their effect, we use IPTG and L-arabinose of which concentrations are a little bit higher than the optimum values for our experiments.

 

We draw a straight line with L-arabinose on the semi-solid culture medium, and a spot with the mixture of IPTG and CL-1 on one side of the line. In the area around the spot, the induction of IPTG is stronger than the repression of L-arabinose, cheZ is expressed and the bacteria adopt motile phenotype. However, when they approach the line where the repressor has a greater effect on the motility, they will lost their motile phenotype and stop.

 

According to the hypothesis 2, on the threshold ratio of the concentration of inducer and repressor, their effects are offset and a critical line is formed. Distances of the points on the critical line to the IPTG spot (focus) and the L-arabinose line (directrix) are in a fixed ratio (eccentricity). If the ratio equals to 1, the critical line is a parabola. If the ratio is larger than 1, it is a branch of a hyperbola. Then we conducted experiment to verify the mechanism (Figure 10B). Left boundary of the colony is regarded as the critical line. We found that cells have the tendency to swim away from L-arabinose line which is an expected performance of the bacteria.

 

A

B

Figure 10A. Schematic of Critical Line model for parabola and hyperbola. CL-1 becomes no-motile on the left side of the critical line while motile on the other side. The eccentricity e equals to PF/PB. If e=1, we define the critical line as parabola. If e>1, we define that as one branch of hyperbola. 10B. An actual experiment result is shown.

 

Other function curves-- quasi-hyperbola

 

After explorations, we tried different ways to arrange bacteria and stimulus on semisolid culture medium. We got some interesting results.

 

We draw two spots on the semi-solid culture medium, one with L-arabinose (Figure 11A) and the other with the mixture of IPTG and CL-1. Similarly, on the threshold ratio of the concentration of inducer and repressor, their effects are offset and a critical line is formed. Distances of the points on the right side of colony boundary to the spot A and the spot B are in a very narrow ratio (Figure 8B). Actually, as the critical line is quiet similar to hyperbola, we name it quasi-hyperbola.

 

A

B

Figure 11A. Schematic of quasi-hyperbola formation on semi-solid culture medium. 10B. An actual experiment result is shown.

 

Other interesting ways to spot bacteria and stimulus are waiting to be discovered, and the idea can be extended to other function curves and patterns.

 

We took two kinds of stimulus to construct a square (Figure 12A). Two opposite sides were paved by one kind of stimulus to form thin paths. Programmed cells were spotted on the center of the square, we got two oval rings after 24 hours culturing (Figure 12B). We find that cell rings are stretched by IPTG sides while squeezed by L-arabinose sides.

 

A

B

Figure 12A. Spotting cells on semi-solid culture medium with two IPTG lines and two L-arabinose lines. 12B. Zoom in to the left picture, two oval rings could be observed on the medium.

 

Apart from forming patterns, reprogrammed chemotaxis can help us in a broad field. We offer some examples in APPLICATION.

 

And we analyzed the process and the results by mathematical model in MODELLING.

 

References

 

1. http://en.wikipedia.org/wiki/Ellipse

2. http://en.wikipedia.org/wiki/Hyperbola

3. O’Gorman, R. B., Rosenberg, J. M., Kallai, O. B., Dickerson, R. E., Itakura, K., Riggs, A. D., & Matthews, K. S. (1980). Equilibrium binding of inducer to lac repressor.operator DNA complex. Journal of Biological Chemistry, 255, 10107–10114.