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| | + | #HQ_page #hardwareFrontPage td{ |
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| | + | #HQ_page #hardwareFrontPage img{ |
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| | + | #HQ_page #hardwareFrontPage img:hover{ |
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| | + | #HQ_page .picture1{ |
| | + | width: 320px; |
| | + | height: 155px; |
| | + | background: url("https://static.igem.org/mediawiki/2017/4/45/Valve_hw_home.jpeg") |
| | + | } |
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| | + | #HQ_page .picture1:hover{ |
| | + | background: url("https://static.igem.org/mediawiki/2017/5/53/Pressure_supply_hw_home2.png") |
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| | + | #HQ_page #picture2{ |
| | + | width: 320px; |
| | + | height: 210px; |
| | + | background: url("https://static.igem.org/mediawiki/2017/e/e1/Paper_strip_hw_home.jpeg") |
| | + | } |
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| | + | #HQ_page #picture2:hover{ |
| | + | background: url("https://static.igem.org/mediawiki/2017/2/22/Paper_strip_hw_home3.png") |
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| | + | #HQ_page #picture3{ |
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| | + | background: url("https://static.igem.org/mediawiki/2017/3/39/Heater_hw_home.jpeg") |
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| | + | #HQ_page #picture3:hover{ |
| | + | background: url("https://static.igem.org/mediawiki/2017/5/5d/Heater_cad_hw_home.png") |
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| | + | #HQ_page #picture4{ |
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| | + | background: url("https://static.igem.org/mediawiki/2017/7/7d/Detector_hw_startpage.jpeg"); |
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| | + | #HQ_page #picture4:hover{ |
| | + | background: url("https://static.igem.org/mediawiki/2017/2/2e/Detector_hw_home.png") |
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| | </style> | | </style> |
| | </head></html> | | </head></html> |
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| | <!-- Head End --> | | <!-- Head End --> |
| | <!-- Content Begin --> | | <!-- Content Begin --> |
| − | <img id="TopPicture" width="960" src="https://static.igem.org/mediawiki/2017/b/be/T--Munich--FrontPagePictures_Attributions.jpg">
| |
| | <table width="960" border=0 cellspacing=0 cellpadding=10> | | <table width="960" border=0 cellspacing=0 cellpadding=10> |
| | <tr> | | <tr> |
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| | <td width=160></td> | | <td width=160></td> |
| | </tr> | | </tr> |
| − | <tr><td colspan=6 align=left valign=center> | + | <tr id="hardwareFrontPage"> |
| − | <font size=7 color=#51a7f9><b style="color: #51a7f9">Hardware</b></font> | + | <td colspan=2> |
| − | </td>
| + | <table width=320> |
| − | </tr>
| + | |
| | <tr> | | <tr> |
| − | <td colspan = 6 align="left">
| + | <td> |
| − | <p class="introduction">
| + | <a href="/Team:Munich/Hardware/QuakeValve"><img class="picture1" src="https://static.igem.org/mediawiki/2017/0/08/T--Munich--Overlay.png"></a> |
| − | Our pathogen detection approach relies on Cas13a digesting RNA. A common way of monitoring RNase activityis using commercially available RNaseAlert consisting of a fluorescent RNA beacon. This is impractical for in-fieldapplications because commercial fluorescence detectors are expensive and inconveniently large. We therefore makeour pathogen detection system fit for in-field applications by developing a cheap and handy fluorescence detector. Al-though many previous iGEM teams constructed fluorescence detectors, we could not find any that had a high enoughsensitivity or the ability to measure fluorescence quantitatively. We therefore constructed a detector matching ourrequirements and compared it to others in a cost vs sensitivity diagram.
| + | </td> |
| − | </p>
| + | <td> |
| − | <p class="introduction">
| + | |
| − | Our detector is paper-based and can detect fluorescein concentrations down to 200 nM. The detector is able to automatically
| + | |
| − | measure fluorescence in units of equivalent fluorescein concentrations. It fits in a pipette box and costs less
| + | |
| − | than 15 $. We were able to measure a time trace of Cas13a digesting RNaseAlert with our detector. For comparison
| + | |
| − | we also measured a positive control containing RNase A and a negative control containing only RNaseAlert. The
| + | |
| − | data are displayed in the figure bellow.
| + | |
| − | </p>
| + | |
| − | <p class="introduction">
| + | |
| − | The time traces show an enzymatic reaction taking place on filter paper. This proves that our detector is sensitive
| + | |
| − | enough and meets our requirements. However the detector is not limited to our specific application but can be used
| + | |
| − | for the detection of any fluorescence signal in biological or chemical systems. We therefore think that our detector
| + | |
| − | can benefit other iGEM teams and research groups that want to make fluorescence based detection fit for in-field
| + | |
| − | applications.
| + | |
| − | </p>
| + | |
| − | | + | |
| − | </td>
| + | |
| − | </tr>
| + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | | + | |
| − | <tr><td colspan=6 align=center valign=center>
| + | |
| − | <h3>Overall Design</h3>
| + | |
| − | <p>
| + | |
| − | Light from a blue LED is filtered by a blue filter foil and excites fluorophores on a filter paper. The excitation light
| + | |
| − | is blocked by an orange filter foil while the emission light from the fluoroscopes passes through the orange filter foil
| + | |
| − | and illuminates a light dependent resistor (LDR). The LDR changes its resistance corresponding to the intensity
| + | |
| − | of the fluorescence light.Finally an Arduino Nano measures the resistance via a voltage divider and calculates the
| + | |
| − | fluorophore concentration. The two figures bellow show this overall design and the operational detector.</p>
| + | |
| | </td> | | </td> |
| | </tr> | | </tr> |
| | + | </table> |
| | | | |
| − | <tr><td colspan=6 align=center valign=center> | + | <a href="/Team:Munich/Hardware/SampleProcessing"><img id="picture3" src="https://static.igem.org/mediawiki/2017/0/08/T--Munich--Overlay.png"></a> |
| − | <h3>Components</h3></td></tr>
| + | <a href="/Team:Munich/Hardware/Paperstrip"><img id="picture2" src="https://static.igem.org/mediawiki/2017/0/08/T--Munich--Overlay.png"></a> |
| − | <tr><td colspan=6 align=center valign=center> | + | |
| − | <h4>Micro Controller</h4>
| + | |
| − | <p>
| + | |
| − | We used an Arduino Nano for automatized data collection. This micro controller has analog pins that can measure
| + | |
| − | voltages from 0 to 5 V and gives an integer from 0 to 1023 as output. The micro controller is connected via an USB port with a computer or smart-phone where the data can be processed further.</p>
| + | |
| | </td> | | </td> |
| − | </tr>
| + | <td colspan=4> |
| − | | + | < a href="/ Team:Munich/ Hardware/ Detector"><img id=" picture4" src="https://static.igem.org/mediawiki/2017/ 0/ 08/T--Munich-- Overlay.png"></a> |
| − | <tr><td colspan=6 align=center valign=center>
| + | |
| − | <h4>Light dependent resistor (LDR)</h4> | + | |
| − | <p id="equation1">
| + | |
| − | For the detection of fluorescence light we used a light depending resistor (LDR). A LDR decreases its resistance <i>R<sub>LDR</sub></i> with increasing light intensity <i>I</i>. The dependence of the resistance <i>R<sub>LDR</sub></i> on the light intensity <i>I</i> is</p>
| + | |
| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/3/33/T--Munich--Hardware_equation1.png"><span>(1)</span></div>
| + | |
| − | <p>
| + | |
| − | where γ is a parameter depending on the type of resistor being used and can even differ for LDRs with the same type
| + | |
| − | designation.
| + | |
| − | </p>
| + | |
| − | <p>
| + | |
| − | <a href="#equation1">Equation 1</a> is motivated from the equation
| + | |
| − | </p>
| + | |
| − | <div class="equationDiv"><img class=" largeEquation" src="https://static.igem.org/mediawiki/2017/ 4/ 4b/T--Munich-- Hardware_equation2.png"> <span>(2)</ span></div> | + | |
| − | <p>
| + | |
| − | which is given in the data sheet of the LDR. The denominator is the decadic logarithm of the fraction of two light
| + | |
| − | intensities of 100 Lx and 10 Lx. <i>R<sub>10</sub></i> and <i>R<sub>100</sub></i> are the corresponding resistances at these light intensities. The used resistor with the type designation GL5516 NT00183 has a parameter γ of 0.8.
| + | |
| − | </p>
| + | |
| − | <p>
| + | |
| − | The response of a LDR depends on the wavelength λ of the incoming light. The data sheet provides information on
| + | |
| − | the relative response normalized to the maximal response. The relative response is maximum for a wavelength of 540
| + | |
| − | nm and is therefore appropriate for detection of green fluorophores.
| + | |
| − | </p>
| + | |
| | </td> | | </td> |
| | </tr> | | </tr> |
| | | | |
| − | <tr><td colspan=6 align=center valign=center> | + | <tr> |
| − | <h4>Circuit for resistance measurements</h4> | + | <td colspan=6> |
| − | <p>
| + | <div class="captionPicture"> |
| − | A voltage divider as shown in the figure bellow is the simplest way to measure resistance.
| + | |
| − | </p>
| + | |
| | <p> | | <p> |
| − | Applying Kirchhoff’s laws we get
| + | Complete overview of all modular hardware parts in our pathogen detection system. Shown are counterclockwise and starting in in the upper left corner: The Quake valve that controls fluid flow, our sample processing device, the paper strip where a reaction mix is stored and the readout reaction takes place and finally our low-cost fluorescence detector "Lightbringer" that performs the readout measurement. Images are clickable and linked to the corresponding wiki subsection. |
| − | </p>
| + | |
| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/b/b1/T--Munich--Hardware_equation3.png"><span>(3)</span></div>
| + | |
| − | <p>
| + | |
| − | and
| + | |
| − | </p>
| + | |
| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/9/99/T--Munich--Hardware_equation4.png"><span>(4)</span></div>
| + | |
| − | <p id="equation5">
| + | |
| − | <i>R<sub>LDR</sub></i> and <i>U<sub>LDR</sub></i> are the resistance and voltage drop at the LDR. <i>R<sub>ref</sub></i> and <i>U<sub>ref</sub></i> are the resistance and voltage drop at a reference resistor. <i>U<sub>0</sub></i> is the supply voltage which we choose to be 5V. This gives
| + | |
| − | </p>
| + | |
| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/c/c7/T--Munich--Hardware_equation5.png"><span>(5)</span></div>
| + | |
| − | <p>
| + | |
| − | an equation to calculate <i>R<sub>LDR</sub></i> from <i>U<sub>LDR</sub></i>, which can be measured with the micro controller.
| + | |
| − | </p>
| + | |
| − | <p>
| + | |
| − | We need to find an equation to choose an optimal resistor <i>R<sub>ref</sub></i> . We want a maximum change of <i>U<sub>LDR</sub></i> for a certain detection range of <i>R<sub>LDR</sub></i>. Therefore <a href="#equation5">equation 5</a> is solved for <i>U<sub>LDR</sub></i> giving
| + | |
| − | </p>
| + | |
| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/3/3f/T--Munich--Hardware_equation6.png"><span>(6)</span></div>
| + | |
| − | <p>
| + | |
| − | The change ∆<i>U<sub>LDR</sub></i> of <i>U<sub>LDR</sub></i> between a maximum value <i>R<sub>max</sub></i> and a minimum value <i>R<sub>min</sub></i> of <i>R<sub>LDR</sub></i> is
| + | |
| − | </p>
| + | |
| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/9/9b/T--Munich--Hardware_equation7.png"><span>(7)</span></div>
| + | |
| − | <p id="equation8">
| + | |
| − | which has a maximum for
| + | |
| − | </p>
| + | |
| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/c/c0/T--Munich--Hardware_equation8.png"><span>(8)</span></div>
| + | |
| − | <p>
| + | |
| − | We expect an <i>R<sub>max</sub></i> of approximately 2 MΩ and an <i>R<sub>min</sub></i> of approximately 1 MΩ. By using <a href="#equation8">equation 8</a> as a guideline we choose <i>R<sub>ref</sub></i> to be 1.5 MΩ.
| + | |
| − | </p>
| + | |
| − | </td>
| + | |
| − | </tr>
| + | |
| | | | |
| − | <tr><td colspan=6 align=center valign=center>
| |
| − | <h4>Light Emitting Diode (LED)</h4>
| |
| − | <p>
| |
| − | To detect green fluorophores we choose a blue LED with peak emission at 470 nm. For optimum performance we
| |
| − | choose the brightest LED we could find. The LED used has a luminous intensity of 12 cd, a maximum current of 20
| |
| − | mA and a forward voltage of 3.2 V.
| |
| | </p> | | </p> |
| − | </td> | + | </div></td> |
| | </tr> | | </tr> |
| | | | |
| − | <tr><td colspan=6 align=center valign=center> | + | <tr><td colspan=6 align=left valign=center> |
| − | <h4>NPN Transistor</h4> | + | <font size=7 color=#51a7f9><b style="color: #51a7f9">Hardware</b></font> |
| − | <p> | + | |
| − | To provide a stable illumination, it is crucial to supply the LED with a constant voltage. We therefore control it via
| + | |
| − | a NPN transistor with type designation BC635. Its base-emitter-on voltage is 2 V.
| + | |
| − | </p> | + | |
| | </td> | | </td> |
| | </tr> | | </tr> |
| | + | <tr> |
| | + | <td colspan = 6 align=center valign=center> |
| | + | <p class="introduction"> |
| | + | |
| | + | The liberation of diagnostic tests from expensive lab infrastructure requires innovative ways of sample processing and measuring. We therefore developed a set of portable hardware tools with the goal of providing an automated sample-to-answer solution. The heart of our system is <a class="myLink" href="https://2017.igem.org/Team:Munich/Hardware/Detector">‘Lightbringer’</a>, our fluorescence detector, which is capable of measuring kinetics of biological or chemical reactions on <a class="myLink" href= "https://2017.igem.org/Team:Munich/Hardware/Paperstrip" >paper.</a> Built from 3D–printed parts and standard electronic components, it can be assembled for less than 15$, while offering a sensitivity competitive to commercial fluorescence readers. Additionally, tackling the challenge of sample pre-processing in field, we developed a portable <a class="myLink" href="https://2017.igem.org/Team:Munich/Hardware/SampleProcessing"> fluidic system</a>, featuring a temperature control unit for lysis and isothermal PCR. Conceiving a platform independent of lab infrastructure, we demonstrate the feasibility of <a class="myLink" href="https://2017.igem.org/Team:Munich/Hardware/QuakeValve"> controlling fluid flow</a> with bike tires and air balloons. All hardware components are designed and documented with the aim of enabling the community to reproduce and extend our set of tools. |
| | + | </p> |
| | | | |
| − | <tr><td colspan=6 align=center valign=center> | + | <div class="captionPicture"> |
| − | <h4>Control Circuit for the LED</h4> | + | <img width=960 src="https://static.igem.org/mediawiki/2017/2/26/Schema_final_lowres.png"> |
| − | <p>
| + | |
| − | The digital output pin is connected to the base of the transistor via a voltage divider, consisting of the resistor <i>R<sub>1</sub></i> with a resistance of 1 kΩ and the resistor <i>R<sub>2</sub></i> with a resistance of 9.1 kΩ. When the output pin is set to 5 V a voltage of 4.5 V is present at the base of the transistor. This is above the base-emitter-on voltage and the LED is turned on.
| + | |
| − | The resistor <i>R<sub>3</sub></i> with resistance 39 Ω was chosen empirically to limit the LEDs working current and to power it at
| + | |
| − | maximum brightness. The control circuit is illustrated in the image bellow.
| + | |
| − | </p>
| + | |
| − | </td>
| + | |
| − | </tr>
| + | |
| − | | + | |
| − | <tr><td colspan=6 align=center valign=center>
| + | |
| − | <h4>Light Filter Foils</h4>
| + | |
| − | <p>
| + | |
| − | For filtering the emission and excitation light we used filter foils from LEE filters. The producer provides transmission
| + | |
| − | spectra for every filter foil. For the excitation filter we choose the filter color "TOKYO BLUE" and for the emission
| + | |
| − | filter we choose the filter color "RUST". We used our UV-Vis spectrometer to measure the spectra of different combinations
| + | |
| − | of filter foils. As shown in the figure bellow, a combination of one orange and two blue filter foils blocks
| + | |
| − | nearly all light up to 700 nm. This combination is therefore ideal for blocking the excitation light of the blue LED
| + | |
| − | from reaching the LDR.
| + | |
| − | </p>
| + | |
| − | </td>
| + | |
| − | </tr>
| + | |
| − | | + | |
| − | <tr><td colspan=6 align=center valign=center>
| + | |
| − | <h4>Filter Paper</h4>
| + | |
| − | <p>
| + | |
| − | We choose glass fiber filter paper from Whatman Laboratory Products with type designation "934-AH" to detect
| + | |
| − | fluorescence on. In contrast, cellulose or nitrocellulose filter paper is auto fluorescent and causes a high background
| + | |
| − | signal.
| + | |
| − | </p>
| + | |
| − | </td>
| + | |
| − | </tr>
| + | |
| − | | + | |
| − | <tr><td colspan=6 align=center valign=center>
| + | |
| − | <h4>3D Printed Parts</h4>
| + | |
| − | <p>
| + | |
| − | We intended to put the LED,the fluorescence sample and the LDR in direct proximity, to ensures a maximum use
| + | |
| − | of excitation light and emission light. We therefore chose a sandwich-like design for our sample holder that can be
| + | |
| − | placed into a slot where the detection system snaps in keeps the sample in position.
| + | |
| − | </p>
| + | |
| | <p> | | <p> |
| − | In detail, two blue filter foils are stacked and glued with tape in front of two excitation windows of the upper half of
| |
| − | the sandwich. One orange filter foil is glued to the lower half of the sandwich. The two detection windows enable us
| |
| − | to measure a blank sample and an actual sample with the exact same set-up. We avoid using scotch tape to cover
| |
| − | the detection windows because tape is usually auto fluorescent and causes a high background signal. A piece of filter
| |
| − | paper is placed between the two halves of the sandwich. The upper and lower part of this sandwich are pressed
| |
| − | together with magnets to hold the filter paper in position and ensure an user-friendly exchange of filter papers. A
| |
| − | explosion drawing of the sample holder is shown in the figure bellow.
| |
| | </p> | | </p> |
| − | <p>
| + | </div> |
| − | The sandwich can now be inserted into the slot of the detection device. The LED and the LDR are mounted onto
| + | |
| − | beams at opposite sites of the detection device. The sandwich snaps in when the LED and the LDR are at the right
| + | |
| − | position under the excitation and over detection window. Four magnets apply an additional force to the beams and
| + | |
| − | press the LED and the LDR close together. This design ensures that the distance between filter paper, LED and
| + | |
| − | LDR is only limited by the thickness of the filter foils.
| + | |
| − | </p> | + | |
| − | </td>
| + | |
| − | </tr>
| + | |
| | | | |
| − | <tr class="lastRow"><td colspan=6 align=center valign=center>
| |
| − | <h4>List of materials and cost calculation</h4>
| |
| − | <table class="myTable" width=60%>
| |
| − | <th class="leftAligned">Used item</th>
| |
| − | <th class="rightAligned">Cost in EUR</th>
| |
| − | <tr>
| |
| − | <td class="leftAligned">Geekcreit ATmega328P Arduino compatible Nano</td>
| |
| − | <td class="rightAligned">2.51</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">USB cable</td>
| |
| − | <td class="rightAligned">1.50</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">LDR</td>
| |
| − | <td class="rightAligned">0.15</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">Blue LED</td>
| |
| − | <td class="rightAligned">0.10</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">2 NPN Transistors</td>
| |
| − | <td class="rightAligned">0.12</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">Green LED</td>
| |
| − | <td class="rightAligned">0.10</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">Hole raster board</td>
| |
| − | <td class="rightAligned">0.42</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">8 resistors</td>
| |
| − | <td class="rightAligned">0.48</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">Filter foils</td>
| |
| − | <td class="rightAligned">0.10</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">10 Magnets</td>
| |
| − | <td class="rightAligned">4.80</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">ca. 100 g PLA</td>
| |
| − | <td class="rightAligned">3.00</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">4 M3 screws</td>
| |
| − | <td class="rightAligned">0.04</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">4 M3 nutts</td>
| |
| − | <td class="rightAligned">0.04</td>
| |
| − | </tr>
| |
| − | <tr>
| |
| − | <td class="leftAligned">Total cost</td>
| |
| − | <td class="rightAligned">13.36</td>
| |
| − | </tr>
| |
| − | </table>
| |
| − | <p>
| |
| − | We kept an eye on using only low cost and easy available items for the construction of our detector.
| |
| − | </p>
| |
| | </td> | | </td> |
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| − | <tr class="lastRow"><td colspan=6 align=center valign=center>
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| − | <h3>Calibration</h3></td></tr>
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| − | <tr><td colspan=6 align=center valign=center>
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| − | <h4>Derivation of a calibration function</h4>
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| − | <p>
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| − | We want to find an equation that relates fluorophore concentration <i>c</i> and the corresponding resistance <i>R<sub>LDR</sub></i>. The light intensity <i>I</i> at the LDR during a fluorescence measurement is a sum of signal intensity <i>I<sub>s</sub></i> and background intensity <i>I<sub>b</sub></i>:
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| − | </p>
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| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/4/4f/T--Munich--Hardware_equation9.png"><span>(9)</span></div>
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| − | <p>
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| − | We assume that <i>I<sub>b</sub></i> is the intensity for a water sample. Importantly, wet samples give a different background signal than dry ones, suspectedly due to different light scattering on the filter paper. With equation 1 this gives an equation for the resistance <i>R<sub>b</sub></i> of a water sample and for the resistance <i>R<sub>LDR</sub></i> for a fluorescence sample,
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| − | </p>
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| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/8/88/T--Munich--Hardware_equation10.png"><span>(10)</span></div>
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| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/3/3f/T--Munich--Hardware_equation11.png"><span>(11)</span></div>
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| − | <p id="equation12">
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| − | Then, the normalized resistance can be expressed as
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| − | </p>
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| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/c/cc/T--Munich--Hardware_equation12.png"><span>(12)</span></div>
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| − | <p>
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| − | We assume that the intensity Is of fluorescence light depends linearly on the concentration c of fluorophores and the
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| − | light intensity I0 produced by the LED,
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| − | </p>
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| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/7/7e/T--Munich--Hardware_equation13.png"><span>(13)</span></div>
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| − | <p>
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| − | and that the background intensity <i>I<sub>b</sub></i> depends also linearly on <i>I<sub>0</sub></i>,
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| − | </p>
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| − | <div class="equationDiv"><img src="https://static.igem.org/mediawiki/2017/c/c7/T--Munich--Hardware_equation14.png"><span>(14)</span></div>
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| − | <p id="equation15">
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| − | Therefore
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| − | </p>
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| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/7/7b/T--Munich--Hardware_equation15.png"><span>(15)</span></div>
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| − | <p>
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| − | where <i>k</i> is a constant that depends on the transmission spectra of the filter foils, the spectra of the fluorophore, the
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| − | spectra of the LED and light scattering effects of the filter paper,but not on <i>I<sub>0</sub></i>. <i>k</i> can be assumed to be constant for one specific measurement set-up.
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| − | </p>
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| − | <p>
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| − | <a href="#equation15">Equation 15</a> inserted into <a href="#equation12">equation 12</a> gives the final equation relating <i>c</i> to <i>R<sub>LDR</sub></i>
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| − | </p>
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| − | <div class="equationDiv"><img class="largeEquation" src="https://static.igem.org/mediawiki/2017/f/f7/T--Munich--Hardware_equation16.png"><span>(16)</span></div>
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| − | </td>
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| − | </tr>
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