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        <div class = "title">Modeling.</div>
        <p>Rule-based modeling for our estrogen sensor.</p>
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<div class = "title">Purpose</div><br>
  <div class = "description"> Our original goal was to be able to design a fluorimeter solely using the materials available in the Arduino Ultimate Starter Kit. This package came with an Arduino Uno along with several helpful components such as LEDs, buzzers, relays, and a Light Dependent Resistor (LDR). The LDR is a resistor that has resistance inversely proportional to light: it has tiny resistance (100s of ohms) when a lot of light strikes it and very large resistance (10,000s of ohms) when in complete darkness. It soon became apparent, however, that the LDR would not be sufficient for our purposes: the device was not sensitive in low light, the signal was small, and the response time was very slow. Here is a graph of one of our trials where we simply turned the lights off and slowly changed the screen brightness of a computer in the room: 

<br><image src="https://static.igem.org/mediawiki/2015/5/5d/LDR_unimproved.JPG" style="width:600px;"><br>

As the graph shows, there was no discernible change between each level of brightness (just a general upward trend), there is an incredible amount of noise making a stable reading impossible, and the response time was in the order of tens of seconds.
We decided to tackle these problems individually.
<div class = "title">Improvements</div><br>
First, we tried to smooth out the signal. For those who are not in the field of electrical engineering, this required the use of either an inductor or a capacitor. We decided use capacitors since they were more readily available. A capacitor is a device made up of two parallel metal plates that are not touching each other so that, when a voltage is applied to these plates, an electrical field is created in between them! This field stores energy proportional to its capacitance, so it will store energy when voltage is applied over it and it will give off a voltage when there is no voltage across it. To simplify this thought, a capacitor can almost be thought of as a really small rechargeable battery. Thus, when we place a capacitor in parallel with our LDR, if the signal is high it will store energy and if the signal is low it will raise give off energy! Assuming we are using only a small capacitor, this signal will look smoother with the possible trade off of a small time delay capacitor discharges.

<br><image src="https://static.igem.org/mediawiki/2015/2/2a/LDR_improved_6ft.JPG" style="width:600px;"><br>

And here we have a much smoother signal! However, the signal is still much too small and is very slow to respond.
To tackle both of these problems together, we ordered some new parts: a simple photodiode ($2) and two operational amplifiers (op amps, also roughly $2).
<div class = "title">New Circuit</div><br>
Photodiodes are essentially small solar panels and op amps are a complex weave of transistors and capacitors that serve to amplify signals.
This lead to the design of our complete circuit:

<br><image src="https://static.igem.org/mediawiki/2015/a/a5/Circuit.JPG" style="width:600px;"><br>

Two capacitors were used, one to smooth the signal and one to stabilize the voltage source (the Arduino). Our device measures voltage at the V nodes shown in the graph (also done by the Arduino) and the resistors connected to the negative pin of the op amp determine the amplificiation of the signal.

The trade off between capacitors of different sizes is always a matter of speed versus smoothness. We tried three different capacitors and found the one that worked best to be the second:

<br><image src="https://static.igem.org/mediawiki/2015/a/a5/474.JPG" style="width:600px;">
<image src="https://static.igem.org/mediawiki/2015/5/59/102.JPG" style="width:600px;">
<image src="https://static.igem.org/mediawiki/2015/7/74/104.JPG" style="width:600px;"><br>

Compare that with the original photodiode circuit unmodified here!

<br><image src="https://static.igem.org/mediawiki/2015/6/61/Control_no_cap.JPG" style="width:600px;"><br>

As you can see, things are much better now.<br>
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<div class = "title">Results</div><br>
Reattempting our original experiment, we closed the doors and turned off the lights to see how well our new circuit could detect us changing a laptop's backlit display from the six feet away facing away from the circuit:

<br><image src="https://static.igem.org/mediawiki/2015/f/fb/Responsetime.JPG" style="width:600px;"><br>

And it worked! It can clearly be seen when the light changes and the response time is around two seconds per change. Our circuit was finally ready to test on cells!
We further diminished noise by soldering our components to a PCB board (the shorter the wires, the less the noise), surrounding our circuit board with aluminum (known as a Faraday Cage, this technique prevents outside signals like radio waves from entering), and we added a Bluetooth chip to our circuit so that there was no light in the room at all.
For this experiment, we used our Gaussia luciferase and tested it fully saturated to see if we could see anything at that dark. While the biologists added the Coelenterazine in the dark room, the engineers stood outside with laptops to see the results:

<br><image src="https://static.igem.org/mediawiki/2015/0/0e/Booyeah.JPG" style="width:600px;"><br>

It was a success! The point of reaction can clearly be seen, the signal was smooth and fast, and the signal was big (meaning it should work on even diluted solutions). Our luminometer works.

Of course, because things can always be improved, we have now been in the process of further amplifying the signal and diminishing noise. We have done this in several ways:
<br>*3D printed a casing for the reaction to take place to further diminish background light
<br>*Bought more enhanced, larger signal photodiodes (approximately $17)
<br>*Changed the resistors so that our op amp gain increased from 4 to 11.

<br><image src="https://static.igem.org/mediawiki/2015/1/13/Fullpicture.JPG" style="width:600px;"><br>

<div class = "title"> Photodiode Characterization </div><br>
  <div class = "description">
Due to the fact that the output from a photodiode can only be read in terms of units of current (amperes) or units of voltage (volts), we needed to use a standardized device in order to characterize a few selected photodiodes, so that we could convert voltage readings to corresponding power readings, and those corresponding power readings to lumens.
<br><br>
The device we used to characterize the photodiodes was the Field Max II energy meter. The energy meter detects light and converts the detected light reading to wattage. We characterized three separate photodiodes: PDB-C139, APD15-8-150-TO5, and ASM71 PIN 5DP/SB. Using an iPhone we shinned different brightness levels of light on both the photodiode and the energy meter. Thus we could compare the output of the photodiode to the output of the energy meter for the same level of brightness. This allowed us to build a transfer function which mapped the readings from our device to the Field Max II energy meter.
<br><br>
Ultimately we chose to use the PDB-C139 photodiode due to its effectiveness and incredibly low cost (~$2). This enables us to detect light intensities as low as a couple hundred lumens and keep our device affordable.
  </description>
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<div class = "title">Future Directions</div><br>
  <div class = "description">
Future directions will also include extending our implementation to a fluorimeter. This simply requires printing a second half to the casing where we will attach an LED to excite the test tube specimens followed by a lens to only allow the wavelengths we want to measure to pass through. </div>
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<h2> Modeling</h2>


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<h4>Note</h4>
<p>In order to be considered for the <a href="https://2015.igem.org/Judging/Awards#SpecialPrizes">Best Model award</a>, you must fill out this page.</p>
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<p>Mathematical models and computer simulations provide a great way to describe the function and operation of BioBrick Parts and Devices. Synthetic Biology is an engineering discipline, and part of engineering is simulation and modeling to determine the behavior of your design before you build it. Designing and simulating can be iterated many times in a computer before moving to the lab. This award is for teams who build a model of their system and use it to inform system design or simulate expected behavior in conjunction with experiments in the wetlab.</p>

<p>
Here are a few examples from previous teams:
</p>
<ul>
<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">ETH Zurich 2014</a></li>
<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">Waterloo 2014</a></li>
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