Difference between revisions of "Team:Marburg/Model"

Line 1: Line 1:
 
{{Marburg}}
 
{{Marburg}}
 
<html>
 
<html>
 +
<article>
 +
<style>
  
 +
.imageContainer3x3 {
 +
  display: flex;
 +
  flex-wrap: wrap;
 +
  justify-content: space-around;
 +
  align-items: center;
 +
}
 +
.imageContainer3x3 div {
 +
  width: 30%;
 +
  margin-bottom: 2%;
 +
  text-align:center;
 +
}
 +
.imageContainer3x3 div img {
 +
  width: 100%;
 +
}
 +
.imageContainer2x2 {
 +
  display: flex;
 +
  flex-wrap: wrap;
 +
  justify-content: space-around;
 +
  align-items: center;
 +
}
 +
.imageContainer2x2 div {
 +
  width: 50%;
 +
  margin-bottom: 2%;
 +
  text-align:center;
 +
}
 +
.imageContainer2x2 div img {
 +
  width: 100%;
 +
}
  
 +
.center {
 +
    display: block;
 +
    margin-left: auto;
 +
    margin-right: auto;
 +
    width: 50%;
 +
}
  
<div class="clear"></div>
+
.left {
 +
    float: left;
 +
    width: 300px;
 +
    padding: 10px;
 +
}
  
 +
.right {
 +
    float: right;
 +
    width: 300px;
 +
    padding: 10px;
 +
}
  
<div class="column full_size">
+
.figbor {
<h1> Modeling</h1>
+
background-color: aliceblue;
 +
border:thin silver solid;
 +
margin: 0.5em;
 +
padding: 0.5em;
  
<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>
+
text-align: center;
 +
font-style: italic;
 +
font-size: smaller;
 +
}
  
</div>
+
.tab { margin-left: 40px;
<div class="clear"></div>
+
}
  
<div class="column full_size">
+
.imageContainer2x2 {
<h3> Gold Medal Criterion #3</h3>
+
  display: flex;
<p>
+
  flex-wrap: wrap;
Convince the judges that your project's design and/or implementation is based on insight you have gained from modeling. This could be either a new model you develop or the implementation of a model from a previous team. You must thoroughly document your model's contribution to your project on your team's wiki, including assumptions, relevant data, model results, and a clear explanation of your model that anyone can understand.  
+
  justify-content: space-around;
<br><br>
+
  align-items: center;
The model should impact your project design in a meaningful way. Modeling may include, but is not limited to, deterministic, exploratory, molecular dynamic, and stochastic models. Teams may also explore the physical modeling of a single component within a system or utilize mathematical modeling for predicting function of a more complex device.
+
}
</p>
+
.imageContainer2x2 div {
 +
  width: 50%;
 +
  margin-bottom: 2%;
 +
  text-align:center;
 +
}
 +
.imageContainer2x2 div img {
 +
  width: 100%;
 +
}
  
</div>
+
.wrapper {
 +
  text-align: center;
 +
}
  
<div class="column two_thirds_size">
+
.horzcent {
<h3>Best Model Special Prize</h3>
+
  display: inline-block;
 +
}
  
<p>
+
</style>
To compete for the <a href="https://2019.igem.org/Judging/Awards">Best Model prize</a>, please describe your work on this page  and also fill out the description on the <a href="https://2019.igem.org/Judging/Judging_Form">judging form</a>. Please note you can compete for both the Gold Medal criterion #3 and the Best Model prize with this page.
+
<br><br>
+
You must also delete the message box on the top of this page to be eligible for the Best Model Prize.
+
</p>
+
  
</div>
+
<h1> Growth Curves </h1>
 +
<p>
 +
Synthetic Biology was created by introducing engineering principles into the previously existing discipline of biology.
 +
While this came with numerous advantages, one of the most important was the standardization and characterization of parts that larger biological system are built of.
 +
Only with this toolbox of modular, well characterized parts the current achievements in companys like gingko bioworks or the teams of the iGEM competition were made possible and the biobrick standard is a great example.
 +
Not only does this process allow for standardized parts, it also allows to critically question generally agreed on methodologies that otherwise might negatively influence either the reproducibility or performance of experiments.
 +
<br>
 +
However, this standardization is not fully a past achievement but an ongoing process.
 +
We noticed during the research how to optimally grow our cyanobacteria that this process still needs alot of standardization.
 +
This was when we decided that we want to critically question all things currently state of the art and this developed into a project in which we used expertise acquired in chemistry, physics, mathematics and biology in addition to sythetic biology.
 +
For example, in the literature the optical density of a culture is sometimes measured with the absorption at 730 nm (SOURCE) and sometimes at 750 nm (SOURCE).
 +
Since many labs do not have a spectrometer that is able to measure absorption at 750 nm, we decided after valuable input from <a href="https://2019.igem.org/Team:Marburg/Human_Practices">James Golden</a> to measure OD at 730 nm.
 +
<br>
 +
<h2> Light intensity measurements </h2>
 +
One of the first aspects that we found to be unsufficiently or contradictorily documented was the light intensity the cultures need to grow optimally.
 +
Also, the state of the art measururement for light intensity used when describing growth of cyanobacteria is Einstein, which is a non SI unit.
 +
Einstein describes the number of photons that arrive in one second at an area of one square metre, one Einstein being one mole (6.022*10**23) of photons /m<sup>2</sup> *s.
 +
Most of the times when this unit is used in combination with photosyntetic organisms, not all photons are counted but only photosinthetically active photons with a wavelength betwenn 400 and 700 nanometers.
 +
<br>
 +
Since Einstein is not an SI unit, there are no clear definitions how to use it which opens up possibilities for introducing errors.
 +
Due to this for example the definition of photosynthetic photons could be a point that differs between different research groups and is not specifically defined in most publications.
 +
To investigate if there is a better unit to use and if so what and how it should be used, we did an analysis of light units that we describe in the following foray:
  
 +
<h3>Foray to light units</h3>
  
<div class="column third_size">
+
 
<div class="highlight decoration_A_full">
+
<figure style="float:left; height: 400px; width: 400px;" class="left">
<h3> Inspiration </h3>
+
<img style="float:left" src="https://upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Luminosity.svg/1280px-Luminosity.svg.png" alt="HTML IST SCHEI?E" class="left">
<p>
+
<figcaption style="float: left;"><b>Figure 2:</b> Luminosity function.<a href="https://en.wikipedia.org/wiki/Luminosity_function" >(Luminosity function)</abbr></a></figcaption>
Here are a few examples from previous teams:
+
</figure>
</p>
+
 
<ul>
+
 
<li><a href="https://2018.igem.org/Team:GreatBay_China/Model">2018 GreatBay China</a></li>
+
As previously mentioned, Einstein descibres the number of photosinthetically available photons (400-700nm) per square metre per second and is not the SI unit for light intenstiy (luminous flux).
<li><a href="https://2018.igem.org/Team:Leiden/Model">2018 Leiden</a></li>
+
The SI unit is lumen, which is described as candela multiplied with the steradian.
<li><a href="https://2016.igem.org/Team:Manchester/Model">2016 Manchester</a></li>
+
Candela is the unit for luminous intensity and steradian is the threedimensional equivalent to a twodimensional angle [Figure 1].
<li><a href="https://2016.igem.org/Team:TU_Delft/Model">2016 TU Delft</li>
+
 
<li><a href="https://2014.igem.org/Team:ETH_Zurich/modeling/overview">2014 ETH Zurich</a></li>
+
 
<li><a href="https://2014.igem.org/Team:Waterloo/Math_Book">2014 Waterloo</a></li>
+
<figure style="float:center; height: 400px; width: 400px;" class="right">
</ul>
+
<img style="float:center" src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Steradian.svg/1024px-Steradian.svg.png" alt="HTML IST SCHEI?E" class="center">
</div>
+
<figcaption style="float: right;"><b>Figure 1:</b> Visual representation of Steradian.<a href="https://en.wikipedia.org/wiki/Steradian" >(Steradian)</abbr></a></figcaption>
 +
</figure>
 +
 
 +
Candela and therefore also lumen are not only describing the intensities of different wavelenghts and adding those up, but they are weighing them using the so called lumiosity function [Figure 2].
 +
This function weighs each wavelength depending on how well it is recognized by the human eye and this has huge applications in professional photography.
 +
While this is something that is very useful when working in photography where the recognition of the human eye is important, for photosynthetic purposes this is  not useful since photons of various wavelengths can be utilized in a similar way.
 +
<br>
 +
The unit Einstein, while not being an SI unit, seems to be the preferable unit for photosynthetic purposes by now, but as previously discussed it is not accurately defined.
 +
Einstein can also be expressed with only SI units as mol of photons of wavelengths between 400 and 700 nm per square meter per second. 
 +
In this form, there are no insecurities about the definition and while being more voluminous to write out, we strongly believe it is much preferable.
 +
We are still using einstein as laboratory chargon to communicate more efficiently on a daily basis, however when it comes to scientific publications the SI unit version should be used at all times to circumvent communication errors.
 +
<br>
 +
<h2> Practical light measurements</h2>
 +
In addition to the problems using a non SI unit introduces, the process of of measurement itself is not standardized.
 +
The light intensity could either be measured at the lamp or at the cultures, it can be measured with the cultures inside of the incubator, which yields lower light intensities due to their absorbance, or without the cultures at the place they shall be at once growing.
 +
<br>
 +
There are two significantly different devices to measure light intensity, one with a planar sensor and one with a spherical one.
 +
Since the planar sensor has less area and also only measured light from one side it yields lower light intensities than the spherical one.
 +
Depending on the setup and how the planar sensor is used, it can also yield light intensities that are far too high (if pointed at the lamp) or too low (if pointed at e.g. the wall).
 +
The spherical measurement device gives both more reproducable and more accurate light intensities.
 +
There are empirical conversion tables to convert values measured with the planar sensor to values of the spherical measurement and vice versa, but they should be used with great caution.
 +
Again after the valuable input of <a href="https://2019.igem.org/Team:Marburg/Human_Practices">James Golden</a> we decided to use the spherical sensor to measure the light intensity at any given position.
 +
<br>  
 +
<h2>Light model</h2>
 +
Even with the spherical light sensor there are still some difficulties to overcome, for example where to place the cultures for a specific light intensity and that the light intensity has to be measured everytime before a growth curve.
 +
To solve both of these problems we decided to build a <a href="https://2019.igem.org/Team:Marburg/Model">Light Model</a> that models the light distribution in our incubator.
 +
With the help of this model we could enter the exact light intensity we wanted to grow the cultures at and multiple possible places were this light intesity was possible to achieve were given.
 +
The source code and the complete documentation how we designed and executed this model can be found on our <a href="https://2019.igem.org/Team:Marburg/Model">Modelling page</a>.
 +
 
 +
<h2>Early Growth Curves</h2>
 +
<b>HERE THE EARLY GROWTH CURVES AND FACTORIAL PARAMETERS SHALL BE DISCUSSED [TORBEN/BIOLOGIST[</b>
 +
<b>WE ALSO HAVE TO FIT IN A PARAGRAPH ABOUT THE wavelength we measure with</b>
 +
With the measurement question for light solved (for us) we started to do growth curves.
 +
Many of the publications that we used as templates for our growth curves used specialized cultivation systems that were not at our disposal.
 +
With our chosen system (of erlenmeyer flasks in our incubator) there were many adjustable parameters that we stumbled upon once we wanted to do growth curves.
 +
Many of these parameters were categorial variables, but there are also some that are numerical values.
 +
We decided to do comparative growth curves for these parameters to determine which combination of parameters allows for the best possible doubling time.
 +
<h4>Flask Geometry</h4>
 +
<h4>Fill Volume</h4>
 +
<h4>Lid Types</h4>
 +
<h4></h4>
 +
<h4></h4>
 +
<h4></h4>
 +
<h4></h4>
 +
<h4></h4>
 +
 
 +
 
 +
<h2>Growth Curves Development</h2>
 +
<b>HERE THE DEVELOPMENT OF THE CURRENT METHODOLOGY FOR THE GROWTH CURVES IS EXPLAINED [BIOLOGIST]</b>
 +
 
 +
<h2>Growth Curves Model</h2>
 +
 
 +
<h3>Variables responsible for growth</h3>
 +
 
 +
As previously described, for categorial differences one can easily do growth curves with all levels of these categories (i.e. the different lids).
 +
With this it is possible to determine, at least for the chosen parameters, which level of these categories allows for the fastest growth.
 +
In reality, all parameters that play into the growth conditions of the cultures are interlinked and change when other parameters are changed.
 +
However, for some parameters the assumption that they do not change upon changing other parameters is probably a fair approximation while drastically reducing the complexity of the investigated problem.
 +
Some categorial variables (lid type, number of schikanen in the flask) are probably mostly uncorrelated with other heavily correlated parameters (light intensity, rpm, CO<sub>2</sub>, temperature) while there are others (total flask volume, filled flask volume, medium) that are more or less correlated with these parameters.
 +
While we think that the assumption of no correlation is a fair approximation for the previously mentioned categorial variables, for the fill volume of the flask we do not think it is a good approximation.
 +
This variable that as a further approximation we chose to look at as categorical has a big influence on the amount of oxygen and carbon dioxide in the flask.
 +
However, since there were already alot of variables we had to take a look at and it is heavily correlated with the CO<sub>2</sub> percentage that we are also investigating later, we chose to fix this parameter.
 +
This would introduce a (small) error into our model, but it would reduce the complexity and the parameters of oxygen and carbondioxide in our flask can be adjusted with the concentration of carbondioxide in the incubator.
 +
For numerical parameters (light intesity, rpm, CO<sub>2</sub> %, temperature, filled flask volume) it would also be possible to measure certain values for each variable and use the one that fits best, but there is also the possibility to model the combined effect of these parameters on the doubling time.
 +
We did the no correlation assumption of for the previously described categorial variables (lid types, flask geometry, fill volume) and developed based on biological criteria a measurement workflow for other parameters (i.e. how many precultures are used).
 +
For four other numerical parameters (temperature, carbondioxide concentration, light intensity and shaker speed) we do think that they are heavily interlinked and decided to investigate them in conjunction with each other.
 +
We used the previously established growth curve protocol and collected datapoints varying these four parameters.
 +
Due to problems with the incubator and the time constraints going with it we were not able to collect as many datapoints as we would like.
 +
 
 +
<h3>Importance of a mathematical model for growth curve prediction</h3>
 +
 
 +
The data collected is displayed in the following table:
 +
 
 +
<table>
 +
  <thead>
 +
    <tr style="text-align: right;">
 +
      <th></th>
 +
      <th>doubling_time [min] </th>
 +
      <th>light_intensity [&#181;mol Photons / m<sup>2</sup> * s 400-700 nm] </th>
 +
      <th>shaking speed [rpm] </th>
 +
      <th>CO<sub>2</sub> [%]</th>
 +
      <th>temp [&#8451;] </th>
 +
    </tr>
 +
  </thead>
 +
  <tbody>
 +
    <tr>
 +
      <th>0</th>
 +
      <td>89.145</td>
 +
      <td>1500</td>
 +
      <td>130</td>
 +
      <td>5</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>1</th>
 +
      <td>100.014</td>
 +
      <td>1000</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>2</th>
 +
      <td>99.171</td>
 +
      <td>1500</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>3</th>
 +
      <td>96.956</td>
 +
      <td>1800</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>4</th>
 +
      <td>118.375</td>
 +
      <td>1800</td>
 +
      <td>130</td>
 +
      <td>5</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>5</th>
 +
      <td>113.305</td>
 +
      <td>1000</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>38</td>
 +
    </tr>
 +
    <tr>
 +
      <th>6</th>
 +
      <td>117.254</td>
 +
      <td>1500</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>38</td>
 +
    </tr>
 +
    <tr>
 +
      <th>7</th>
 +
      <td>122.141</td>
 +
      <td>1800</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>38</td>
 +
    </tr>
 +
    <tr>
 +
      <th>8</th>
 +
      <td>77.047</td>
 +
      <td>1000</td>
 +
      <td>220</td>
 +
      <td>3</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>9</th>
 +
      <td>81.442</td>
 +
      <td>1500</td>
 +
      <td>220</td>
 +
      <td>3</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>10</th>
 +
      <td>104.293</td>
 +
      <td>1000</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>43</td>
 +
    </tr>
 +
    <tr>
 +
      <th>11</th>
 +
      <td>96.914</td>
 +
      <td>1500</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>43</td>
 +
    </tr>
 +
    <tr>
 +
      <th>12</th>
 +
      <td>97.678</td>
 +
      <td>1800</td>
 +
      <td>220</td>
 +
      <td>5</td>
 +
      <td>43</td>
 +
    </tr>
 +
    <tr>
 +
      <th>13</th>
 +
      <td>102.040</td>
 +
      <td>1800</td>
 +
      <td>220</td>
 +
      <td>7</td>
 +
      <td>41</td>
 +
    </tr>
 +
    <tr>
 +
      <th>14</th>
 +
      <td>110.560</td>
 +
      <td>1500</td>
 +
      <td>220</td>
 +
      <td>7</td>
 +
      <td>41</td>
 +
    </tr>
 +
  </tbody>
 +
</table>
 +
 
 +
With this data alone we can highlight the importance to measure these parameters in conjunction with each other.
 +
In Figure X there are the doubling times with three different light intensities displayed with either 38°C or 41°C as temperature.
 +
While the doubling times for the lower temperature are smaller, also the trend for the light intensity is reverted.
 +
For the high temperature the higher the intensity the lower the doubling time while for the low temperature the contrary is the case.
 +
This shows that these parameters are not independent of each other and should also be investigated not on their own but in conjunction with each other.
 +
 
 +
<figure style="width: 70%;" class="center" class="wrapper">
 +
    <div class="imageContainer2x2">
 +
      <div><a><img src="https://static.igem.org/mediawiki/2019/3/3a/T--Marburg--model_comparison_lowtemp.png"></div></a>
 +
      <div><a><img src="https://static.igem.org/mediawiki/2019/4/40/T--Marburg--model_comparison_normtemp.png"></div></a>
 +
</div>
 +
  <figcaption class="horzcent"><b>Figure X:</b> Comparison of different light intensities at 38 and 41 ° Celsius</figcaption>
 +
</figure>
 +
 
 +
To investigate these parameters in conjunction with each other we decided to build a model that predicts the doubling time based on the investigated parameters.
 +
 
 +
 
 +
<h3>Boundary behaviour</h3>
 +
 
 +
Something that is not part of our data are the boundaries that naturally exist for growth curves of cyanobacteria.
 +
These are partially given be the machines we are using (e.g. the maximal strength of the lamps, the maximum rpm of our shaker) and partially given by the constitution of the cyanobacteria  (e.g. the maximal/minimal temperature they can grow at).
 +
With our knowledge acquired while handling this cyanobacteria, we decided on the following cutoffs:
 +
 
 +
 
 +
<table>
 +
  <tr>
 +
    <th class="tg-0lax">Parameter</th>
 +
    <th class="tg-0lax">Value</th>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">min light [&#181;mol Photons / m<sup>2</sup> * s 400-700 nm] </td>
 +
    <td class="tg-0lax">100</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">max light [&#181;mol Photons / m<sup>2</sup> * s 400-700 nm] </td>
 +
    <td class="tg-0lax">3000</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">min rpm</td>
 +
    <td class="tg-0lax">30</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">max rpm</td>
 +
    <td class="tg-0lax">260/300</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">min temperature</td>
 +
    <td class="tg-0lax">30 [&#8451;] </td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">max temperature</td>
 +
    <td class="tg-0lax">50 [&#8451;] </td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">min CO<sub>2</sub></td>
 +
    <td class="tg-0lax">1</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0lax">max CO<sub>2</sub></td>
 +
    <td class="tg-0lax">10/20</td>
 +
  </tr>
 +
</table>
 +
 
 +
For light and temperature and the lower boundaries of CO<sub>2</sub> and rpm we used cutoffs at which we are convinced that no proper growth is possible.
 +
For the upper boundaries of CO<sub>2</sub> (10) and rpm (260) we used the highgest values that are possible due to the hardware used.
 +
For these two boundaries we also tried to increase the values further to not punish the maximal possible values too much but still incentivize our model to not use the values near the booundaries.
 +
We added one datapoint for each of these boundaries and used the most common values found in our model for the rest of the values.
 +
As example, the datapoint added for the low light and low rpm values are shown in the following table:
 +
 
 +
 
 +
<table>
 +
  <tr>
 +
    <th class="tg-0pky"></th>
 +
    <th class="tg-0pky">doubling time [min] </th>
 +
    <th class="tg-0lax">light intensity [&#181;mol Photons / m<sup>2</sup> * s 400-700 nm] </th>
 +
    <th class="tg-0lax">shaking speed [rpm]</th>
 +
    <th class="tg-0lax">CO<sub>2</sub> [%]</th>
 +
    <th class="tg-0lax">temperature [&#8451;] </th>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0pky">min light</td>
 +
    <td class="tg-0pky">1000</td>
 +
    <td class="tg-0lax">100</td>
 +
    <td class="tg-0lax">220</td>
 +
    <td class="tg-0lax">5</td>
 +
    <td class="tg-0lax">41</td>
 +
  </tr>
 +
  <tr>
 +
    <td class="tg-0pky">min rpm</td>
 +
    <td class="tg-0pky">1000</td>
 +
    <td class="tg-0lax">1500</td>
 +
    <td class="tg-0lax">30</td>
 +
    <td class="tg-0lax">5</td>
 +
    <td class="tg-0lax">41</td>
 +
  </tr>
 +
</table>
 +
 
 +
We added a very high doubling time insted of a doubling time of 0 to ensure that our model has the correct behaviour in edge cases.
 +
For example, that the model predict an increased doubling time the hotter the temperature gets insted of predicting very low doubling times for those edge cases because we fed it a doubling time of 0.
 +
When we entered this data into our model, the performance was drastically reduced.
 +
We even experimented with different doubling times that we entered for this sub dataset, but for all cases tried the performance of the model was still worse than without adding this dataset in the first place.
 +
Again, due to the small amount of data that we have in the original dataset, if we add these 8 datapoints they have a huge effect on the model even outside of the boundary cases.
 +
Due to this decrease in performance we decided to not use this dataset, but we are still convinced that with enough data this would increase the accuracy of the model, especially in boundary cases.
 +
 
 +
 
 +
<h3>Modelling approach</h3>
 +
Due to the small amount of data we were able to collect we decided to use a polynomial regression model instead of a more data demanding approach like k nearest neighbors, support vector machines or neural networks.
 +
Even with this approach, the amount of data we have at our disposal is not enough to deliver a model that we would describe as accurate within and especially not outside of our training data.
 +
Nevertheless, we think a model like this is the best way forward if we want to properly predict the doubling time and with more data a very accurate model can be built.
 +
We used a common approach to polynomial regression models in that we performed a linear regression on nonlinear functions of the data.
 +
This means that we use the previously established variables (temp, rpm, light intensity, CO<sub>2</sub>) and construct the polynomial features of this dataset.
 +
For two variables x1 and x2 and a polynomial with the degree 2 this would mean we have the following values as data : [1, x1, x2, x1*x2, x1*x1, x2*x2].
 +
This is possible due to the fact that a linear model is not limited to a linear function but to linear parameters for the variables it builds on.
 +
The code used to build this model is shown here :
 +
 
 +
<div class="wrap-collabsible">
 +
  <input id="model_code_poly" class="toggle" type="checkbox">
 +
  <label for="model_code_poly" class="lbl-toggle">Code </label>
 +
  <div class="collapsible-content">
 +
    <div class="content-inner">
 +
      <p>
 +
        Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse pulvinar rutrum libero eu tincidunt.
 +
        Maecenas id maximus risus, ac varius leo. Proin vulputate nulla ut sapien tincidunt varius.
 +
        Donec venenatis lacinia imperdiet. Cras nulla est, varius id ornare hendrerit, viverra nec lorem.
 +
        Fusce ac fermentum purus, vitae mattis ipsum. Vestibulum faucibus elit vitae vehicula tincidunt.
 +
        Maecenas placerat, lorem id vulputate egestas, lectus dui faucibus urna, sed mollis nulla nulla nec ipsum.
 +
        Nulla commodo viverra aliquam.
 +
      </p>
 +
    </div>
 +
  </div>
 
</div>
 
</div>
 +
 +
 +
Again due to the lack of data normal ways of benchmarking the model like train test splits and crossvalidation are not rationally possible.
 +
If there would be more data we would use LASSO regression, because this would allow us to eliminate variables that are not useful and avoid a high variance mistake.
 +
 +
To showcase how this model using our existing data predicts new data, we decided to predict and measure three new growth curves at unsampled regions within the boundaries of our measurement data.
 +
We decided to not calculate the minima that our model predicts, but data that is inside the range of our existing data to properly estimate how well this suboptimal model is working.
 +
 +
The predictions of different model versions different only in the degree of polynomials used and the measured doubling time is shown in Figure X.
 +
 +
 +
 +
  <figure style="float:center; width: 800px;" class="right">
 +
      <img style="float:center" src="https://static.igem.org/mediawiki/2019/b/b6/T--Marburg--model_comparison_predictions.png" alt="HTML IST SCHEI?E" class="center">
 +
      <figcaption style="float: right;"><b>Figure X:</b> Prediction of the model and measurement of the doubling time of four growth curves. Growth curves have been measured with 3.8 % CO<sub>2</sub>, 40.5 &#8451; and 147 rpm. Light intensity in [&#181;mol Photons / m<sup>2</sup> * s 400-700 nm] is color coded in the graph. X axis shows the complexity of the model (numbers indicate the degree of the polynomial used to fit) or m for measurement. Y axis shows the doubling time.</abbr></a></figcaption>
 +
    </figure>
 +
 +
As we can see in Figure X the prediction quality of the model is poor.
 +
The degree of the polynomial is influencing the performance of the model, but there is no clear trend visible.
 +
The data for the polynomial degree 3 was excluded since the predictions were negative.
 +
The ranking of the different doubling times is the same in all model predictions except for degree 1, with the model predicting the growth curves with the higher light intensities to show a smaller doubling time.
 +
However, not only are the predicted doubling time values significantly different from the measured ones, the measured ones are also ranked in a different order (1388>1850>1541>1750).
 +
In addition to that the spread of values is higher in the predicted doubling times compared to the measured ones.
 +
As expected, the models performance is not good enough to get quantitatively or even qualitatively correct predictions. 
 +
 +
 +
<br>
 +
<h2>Summary and Outlook</h2>
 +
<b>WHAT FACTORS DID WE LOOK AT, WHERE IS FURTHER NEED FOR STANDARDIZATION, HOW CAN A STANDARDIZATION BE ACHIEVED [TORBEN/BIOLOGIST]</b>
 +
<br>
 +
 +
During this investigation into how to grow UTEX2973 in the optimal way we stumbled upon many things that we thought to be insufficiently documented or standardized. 
 +
We investigated how to optimally measure light intensity and thought critically about the state of the art light units.
 +
To make it possible to grow cultures at specific light intensities as well as to make a model of the light intensity in our incubator to help in the everyday life of the wetlab team.
 +
After investigating which wavelength to optimally measure the optical density of our cultures at we started to measure comparative growth curves and developed a reproducable growth curve protocol.
 +
For all parameters that had an effect on the growth curves of UTEX2973 we critically questioned if they could be approximated as independent from other parameters and decided to investigate the temperature, shaking speed, carbon dioxide concentration and light intensity in conjunction with each other.
 +
Since the investigation of four or more different dependent parameters and their effect on the growth is not exhaustively possible for humans we built an easily extendable model that uses polynomial regression to predict the doubling time of various parametercombinations.
 +
However, since measuring a single (or more) doubling time(s) is a very time demanding process, we did not manage to collect a sufficient amount of data to train a model that is able to accurately predict doubling times.
 +
In addition to "just" supplying it with more data, if we have more data more steps can be done to increase the performance of the model.
 +
In addition to a train test split and cross validation to improve the perfomance and decrease the bias of the model towards new data, LASSO regression can be used which would allow to investigate easily how high dimensional the polynome the model is utilizing has to be.
 +
 +
<!--
 +
[<sup>&#181;mol Photons</sup>/<sub>m<sup>2</sup> * s</sub> 400-700 nm]
 +
HERE ARE USEFUL THINGYS
 +
Lichteinheit in html [&#181;mol Photons / m<sup>2</sup> * s 400-700 nm]
 +
CO2 einheit [%]
 +
temperature einheit [&#8451;]
 +
CO2 in correct : CO<sub>2</sub>
 +
-->
 +
 +
 +
 +
</p>
 +
</body>
 +
</article>
  
 
</html>
 
</html>
 
{{Marburg/footer}}
 
{{Marburg/footer}}

Revision as of 14:30, 21 October 2019

Growth Curves

Synthetic Biology was created by introducing engineering principles into the previously existing discipline of biology. While this came with numerous advantages, one of the most important was the standardization and characterization of parts that larger biological system are built of. Only with this toolbox of modular, well characterized parts the current achievements in companys like gingko bioworks or the teams of the iGEM competition were made possible and the biobrick standard is a great example. Not only does this process allow for standardized parts, it also allows to critically question generally agreed on methodologies that otherwise might negatively influence either the reproducibility or performance of experiments.
However, this standardization is not fully a past achievement but an ongoing process. We noticed during the research how to optimally grow our cyanobacteria that this process still needs alot of standardization. This was when we decided that we want to critically question all things currently state of the art and this developed into a project in which we used expertise acquired in chemistry, physics, mathematics and biology in addition to sythetic biology. For example, in the literature the optical density of a culture is sometimes measured with the absorption at 730 nm (SOURCE) and sometimes at 750 nm (SOURCE). Since many labs do not have a spectrometer that is able to measure absorption at 750 nm, we decided after valuable input from James Golden to measure OD at 730 nm.

Light intensity measurements

One of the first aspects that we found to be unsufficiently or contradictorily documented was the light intensity the cultures need to grow optimally. Also, the state of the art measururement for light intensity used when describing growth of cyanobacteria is Einstein, which is a non SI unit. Einstein describes the number of photons that arrive in one second at an area of one square metre, one Einstein being one mole (6.022*10**23) of photons /m2 *s. Most of the times when this unit is used in combination with photosyntetic organisms, not all photons are counted but only photosinthetically active photons with a wavelength betwenn 400 and 700 nanometers.
Since Einstein is not an SI unit, there are no clear definitions how to use it which opens up possibilities for introducing errors. Due to this for example the definition of photosynthetic photons could be a point that differs between different research groups and is not specifically defined in most publications. To investigate if there is a better unit to use and if so what and how it should be used, we did an analysis of light units that we describe in the following foray:

Foray to light units

HTML IST SCHEI?E
Figure 2: Luminosity function.(Luminosity function)
As previously mentioned, Einstein descibres the number of photosinthetically available photons (400-700nm) per square metre per second and is not the SI unit for light intenstiy (luminous flux). The SI unit is lumen, which is described as candela multiplied with the steradian. Candela is the unit for luminous intensity and steradian is the threedimensional equivalent to a twodimensional angle [Figure 1].
HTML IST SCHEI?E
Figure 1: Visual representation of Steradian.(Steradian)
Candela and therefore also lumen are not only describing the intensities of different wavelenghts and adding those up, but they are weighing them using the so called lumiosity function [Figure 2]. This function weighs each wavelength depending on how well it is recognized by the human eye and this has huge applications in professional photography. While this is something that is very useful when working in photography where the recognition of the human eye is important, for photosynthetic purposes this is not useful since photons of various wavelengths can be utilized in a similar way.
The unit Einstein, while not being an SI unit, seems to be the preferable unit for photosynthetic purposes by now, but as previously discussed it is not accurately defined. Einstein can also be expressed with only SI units as mol of photons of wavelengths between 400 and 700 nm per square meter per second. In this form, there are no insecurities about the definition and while being more voluminous to write out, we strongly believe it is much preferable. We are still using einstein as laboratory chargon to communicate more efficiently on a daily basis, however when it comes to scientific publications the SI unit version should be used at all times to circumvent communication errors.

Practical light measurements

In addition to the problems using a non SI unit introduces, the process of of measurement itself is not standardized. The light intensity could either be measured at the lamp or at the cultures, it can be measured with the cultures inside of the incubator, which yields lower light intensities due to their absorbance, or without the cultures at the place they shall be at once growing.
There are two significantly different devices to measure light intensity, one with a planar sensor and one with a spherical one. Since the planar sensor has less area and also only measured light from one side it yields lower light intensities than the spherical one. Depending on the setup and how the planar sensor is used, it can also yield light intensities that are far too high (if pointed at the lamp) or too low (if pointed at e.g. the wall). The spherical measurement device gives both more reproducable and more accurate light intensities. There are empirical conversion tables to convert values measured with the planar sensor to values of the spherical measurement and vice versa, but they should be used with great caution. Again after the valuable input of James Golden we decided to use the spherical sensor to measure the light intensity at any given position.

Light model

Even with the spherical light sensor there are still some difficulties to overcome, for example where to place the cultures for a specific light intensity and that the light intensity has to be measured everytime before a growth curve. To solve both of these problems we decided to build a Light Model that models the light distribution in our incubator. With the help of this model we could enter the exact light intensity we wanted to grow the cultures at and multiple possible places were this light intesity was possible to achieve were given. The source code and the complete documentation how we designed and executed this model can be found on our Modelling page.

Early Growth Curves

HERE THE EARLY GROWTH CURVES AND FACTORIAL PARAMETERS SHALL BE DISCUSSED [TORBEN/BIOLOGIST[ WE ALSO HAVE TO FIT IN A PARAGRAPH ABOUT THE wavelength we measure with With the measurement question for light solved (for us) we started to do growth curves. Many of the publications that we used as templates for our growth curves used specialized cultivation systems that were not at our disposal. With our chosen system (of erlenmeyer flasks in our incubator) there were many adjustable parameters that we stumbled upon once we wanted to do growth curves. Many of these parameters were categorial variables, but there are also some that are numerical values. We decided to do comparative growth curves for these parameters to determine which combination of parameters allows for the best possible doubling time.

Flask Geometry

Fill Volume

Lid Types

Growth Curves Development

HERE THE DEVELOPMENT OF THE CURRENT METHODOLOGY FOR THE GROWTH CURVES IS EXPLAINED [BIOLOGIST]

Growth Curves Model

Variables responsible for growth

As previously described, for categorial differences one can easily do growth curves with all levels of these categories (i.e. the different lids). With this it is possible to determine, at least for the chosen parameters, which level of these categories allows for the fastest growth. In reality, all parameters that play into the growth conditions of the cultures are interlinked and change when other parameters are changed. However, for some parameters the assumption that they do not change upon changing other parameters is probably a fair approximation while drastically reducing the complexity of the investigated problem. Some categorial variables (lid type, number of schikanen in the flask) are probably mostly uncorrelated with other heavily correlated parameters (light intensity, rpm, CO2, temperature) while there are others (total flask volume, filled flask volume, medium) that are more or less correlated with these parameters. While we think that the assumption of no correlation is a fair approximation for the previously mentioned categorial variables, for the fill volume of the flask we do not think it is a good approximation. This variable that as a further approximation we chose to look at as categorical has a big influence on the amount of oxygen and carbon dioxide in the flask. However, since there were already alot of variables we had to take a look at and it is heavily correlated with the CO2 percentage that we are also investigating later, we chose to fix this parameter. This would introduce a (small) error into our model, but it would reduce the complexity and the parameters of oxygen and carbondioxide in our flask can be adjusted with the concentration of carbondioxide in the incubator. For numerical parameters (light intesity, rpm, CO2 %, temperature, filled flask volume) it would also be possible to measure certain values for each variable and use the one that fits best, but there is also the possibility to model the combined effect of these parameters on the doubling time. We did the no correlation assumption of for the previously described categorial variables (lid types, flask geometry, fill volume) and developed based on biological criteria a measurement workflow for other parameters (i.e. how many precultures are used). For four other numerical parameters (temperature, carbondioxide concentration, light intensity and shaker speed) we do think that they are heavily interlinked and decided to investigate them in conjunction with each other. We used the previously established growth curve protocol and collected datapoints varying these four parameters. Due to problems with the incubator and the time constraints going with it we were not able to collect as many datapoints as we would like.

Importance of a mathematical model for growth curve prediction

The data collected is displayed in the following table:
doubling_time [min] light_intensity [µmol Photons / m2 * s 400-700 nm] shaking speed [rpm] CO2 [%] temp [℃]
0 89.145 1500 130 5 41
1 100.014 1000 220 5 41
2 99.171 1500 220 5 41
3 96.956 1800 220 5 41
4 118.375 1800 130 5 41
5 113.305 1000 220 5 38
6 117.254 1500 220 5 38
7 122.141 1800 220 5 38
8 77.047 1000 220 3 41
9 81.442 1500 220 3 41
10 104.293 1000 220 5 43
11 96.914 1500 220 5 43
12 97.678 1800 220 5 43
13 102.040 1800 220 7 41
14 110.560 1500 220 7 41
With this data alone we can highlight the importance to measure these parameters in conjunction with each other. In Figure X there are the doubling times with three different light intensities displayed with either 38°C or 41°C as temperature. While the doubling times for the lower temperature are smaller, also the trend for the light intensity is reverted. For the high temperature the higher the intensity the lower the doubling time while for the low temperature the contrary is the case. This shows that these parameters are not independent of each other and should also be investigated not on their own but in conjunction with each other.
Figure X: Comparison of different light intensities at 38 and 41 ° Celsius
To investigate these parameters in conjunction with each other we decided to build a model that predicts the doubling time based on the investigated parameters.

Boundary behaviour

Something that is not part of our data are the boundaries that naturally exist for growth curves of cyanobacteria. These are partially given be the machines we are using (e.g. the maximal strength of the lamps, the maximum rpm of our shaker) and partially given by the constitution of the cyanobacteria (e.g. the maximal/minimal temperature they can grow at). With our knowledge acquired while handling this cyanobacteria, we decided on the following cutoffs:
Parameter Value
min light [µmol Photons / m2 * s 400-700 nm] 100
max light [µmol Photons / m2 * s 400-700 nm] 3000
min rpm 30
max rpm 260/300
min temperature 30 [℃]
max temperature 50 [℃]
min CO2 1
max CO2 10/20
For light and temperature and the lower boundaries of CO2 and rpm we used cutoffs at which we are convinced that no proper growth is possible. For the upper boundaries of CO2 (10) and rpm (260) we used the highgest values that are possible due to the hardware used. For these two boundaries we also tried to increase the values further to not punish the maximal possible values too much but still incentivize our model to not use the values near the booundaries. We added one datapoint for each of these boundaries and used the most common values found in our model for the rest of the values. As example, the datapoint added for the low light and low rpm values are shown in the following table:
doubling time [min] light intensity [µmol Photons / m2 * s 400-700 nm] shaking speed [rpm] CO2 [%] temperature [℃]
min light 1000 100 220 5 41
min rpm 1000 1500 30 5 41
We added a very high doubling time insted of a doubling time of 0 to ensure that our model has the correct behaviour in edge cases. For example, that the model predict an increased doubling time the hotter the temperature gets insted of predicting very low doubling times for those edge cases because we fed it a doubling time of 0. When we entered this data into our model, the performance was drastically reduced. We even experimented with different doubling times that we entered for this sub dataset, but for all cases tried the performance of the model was still worse than without adding this dataset in the first place. Again, due to the small amount of data that we have in the original dataset, if we add these 8 datapoints they have a huge effect on the model even outside of the boundary cases. Due to this decrease in performance we decided to not use this dataset, but we are still convinced that with enough data this would increase the accuracy of the model, especially in boundary cases.

Modelling approach

Due to the small amount of data we were able to collect we decided to use a polynomial regression model instead of a more data demanding approach like k nearest neighbors, support vector machines or neural networks. Even with this approach, the amount of data we have at our disposal is not enough to deliver a model that we would describe as accurate within and especially not outside of our training data. Nevertheless, we think a model like this is the best way forward if we want to properly predict the doubling time and with more data a very accurate model can be built. We used a common approach to polynomial regression models in that we performed a linear regression on nonlinear functions of the data. This means that we use the previously established variables (temp, rpm, light intensity, CO2) and construct the polynomial features of this dataset. For two variables x1 and x2 and a polynomial with the degree 2 this would mean we have the following values as data : [1, x1, x2, x1*x2, x1*x1, x2*x2]. This is possible due to the fact that a linear model is not limited to a linear function but to linear parameters for the variables it builds on. The code used to build this model is shown here :

Lorem ipsum dolor sit amet, consectetur adipiscing elit. Suspendisse pulvinar rutrum libero eu tincidunt. Maecenas id maximus risus, ac varius leo. Proin vulputate nulla ut sapien tincidunt varius. Donec venenatis lacinia imperdiet. Cras nulla est, varius id ornare hendrerit, viverra nec lorem. Fusce ac fermentum purus, vitae mattis ipsum. Vestibulum faucibus elit vitae vehicula tincidunt. Maecenas placerat, lorem id vulputate egestas, lectus dui faucibus urna, sed mollis nulla nulla nec ipsum. Nulla commodo viverra aliquam.

Again due to the lack of data normal ways of benchmarking the model like train test splits and crossvalidation are not rationally possible. If there would be more data we would use LASSO regression, because this would allow us to eliminate variables that are not useful and avoid a high variance mistake. To showcase how this model using our existing data predicts new data, we decided to predict and measure three new growth curves at unsampled regions within the boundaries of our measurement data. We decided to not calculate the minima that our model predicts, but data that is inside the range of our existing data to properly estimate how well this suboptimal model is working. The predictions of different model versions different only in the degree of polynomials used and the measured doubling time is shown in Figure X.
HTML IST SCHEI?E
Figure X: Prediction of the model and measurement of the doubling time of four growth curves. Growth curves have been measured with 3.8 % CO2, 40.5 ℃ and 147 rpm. Light intensity in [µmol Photons / m2 * s 400-700 nm] is color coded in the graph. X axis shows the complexity of the model (numbers indicate the degree of the polynomial used to fit) or m for measurement. Y axis shows the doubling time.
As we can see in Figure X the prediction quality of the model is poor. The degree of the polynomial is influencing the performance of the model, but there is no clear trend visible. The data for the polynomial degree 3 was excluded since the predictions were negative. The ranking of the different doubling times is the same in all model predictions except for degree 1, with the model predicting the growth curves with the higher light intensities to show a smaller doubling time. However, not only are the predicted doubling time values significantly different from the measured ones, the measured ones are also ranked in a different order (1388>1850>1541>1750). In addition to that the spread of values is higher in the predicted doubling times compared to the measured ones. As expected, the models performance is not good enough to get quantitatively or even qualitatively correct predictions.

Summary and Outlook

WHAT FACTORS DID WE LOOK AT, WHERE IS FURTHER NEED FOR STANDARDIZATION, HOW CAN A STANDARDIZATION BE ACHIEVED [TORBEN/BIOLOGIST]
During this investigation into how to grow UTEX2973 in the optimal way we stumbled upon many things that we thought to be insufficiently documented or standardized. We investigated how to optimally measure light intensity and thought critically about the state of the art light units. To make it possible to grow cultures at specific light intensities as well as to make a model of the light intensity in our incubator to help in the everyday life of the wetlab team. After investigating which wavelength to optimally measure the optical density of our cultures at we started to measure comparative growth curves and developed a reproducable growth curve protocol. For all parameters that had an effect on the growth curves of UTEX2973 we critically questioned if they could be approximated as independent from other parameters and decided to investigate the temperature, shaking speed, carbon dioxide concentration and light intensity in conjunction with each other. Since the investigation of four or more different dependent parameters and their effect on the growth is not exhaustively possible for humans we built an easily extendable model that uses polynomial regression to predict the doubling time of various parametercombinations. However, since measuring a single (or more) doubling time(s) is a very time demanding process, we did not manage to collect a sufficient amount of data to train a model that is able to accurately predict doubling times. In addition to "just" supplying it with more data, if we have more data more steps can be done to increase the performance of the model. In addition to a train test split and cross validation to improve the perfomance and decrease the bias of the model towards new data, LASSO regression can be used which would allow to investigate easily how high dimensional the polynome the model is utilizing has to be.