Difference between revisions of "Team:Freiburg/B subtilis"

Latest revision as of 03:15, 20 October 2016

Bacillus subtilis

Our Model Organism

The human colon is home to a lot of tiny microorganisms. To be precise, our whole body contains 10 times more bacteria cells than endogenous cells¹. In most cases, these bacteria are not harmful to the human body. Although, some organisms can cause infectious diseases, nearly 100% of our survey participants knew that this doesn’t mean bacteria are generally harmful.

The digestive system is host to several million of bacteria which are essential for digestion, proper absorbance of nutrients and the synthesis of vitamin K and B². The entire microbiota in the gut is a complex ecosystem that is not well understood yet³. Dis-balances in the composition of the intestinal flora can cause a variety of diseases. We confronted different gastrologists with this topic and they confirmed that the flora is “essential” and “ really important since a disturbed intestinal flora would cause many diseases”. But what exactly is disturbing this intestinal flora? Studies have shown that changes in diets,operations and health condition will perturbate the microbiota and may lead to irritative bowel diseases, chronic inflammation, infectious diseases with harmful bacteria or malabsorption⁴. Due to individual lifestyle and genetic dispositions, everyone has a distinct bacterial flora in his/her gastrointestinal tract. To support and rebuilt the intestinal flora, people often grab for probiotics. Asking the Ulcerative Colitis patients that filled out our survey, whether or not they have consumed probiotics before, almost half of the participant answered with yes. This result lets us assume that the concerns about taking our product too will not be insuperable.

Probiotics are nonpathogenic, living bacteria with health benefits for humans when consumed in a frequent manner⁵.
They play an important role in immunological, digestive and respiratory functions and even the number and type of probiotic in foods and drinks are increasing at the moment.⁶
Typical microorganism used as probiotics today are Lactobacillus, E.coli, Enterococcus and Bacillus subtilis⁷.
For example: the probiotic Biosporin contains Bacillus subtilis and inhibits the growth of Helicobacter pylori, a bacterium which is known to cause gastrointestinal diseases.⁸
In this year's iGEM project we, team Freiburg, decided to work with the model organism Bacillus subtilis because of its innocuousness, robustness and ability to build spores. We wanted to use this spores as a carrier for two tools in combination as our new form of targeted drug delivery system.
In our survey we have also asked people, if they think spores are generally harmful to the human body. In comparison to the same question about bacteria, the results are different. Nearly 18.8% answered with “Yes, spores are generally harmful”.

Bacillus subtilis has a rod shaped appearance and belongs to the family of the gram-positive bacteria. Apart from being widely present in nature, it is also already a part of the microbial gut flora ⁹ and so a perfect candidate for being our probiotic. The US Food and Drug Administration (FDA) classifies Bacillus subtilis as a GRAS (Generally Regarded As Safe) organism ¹⁰. That means it is generally recognized as safe and can be used in S1 laboratories without problems. Bacillus subtilis colonies have an irregular, large size with undulate margin. They have a white and dull colour and a dry texture.

Figure 1: Colonies of Bacillus subtilis

Bacillus subtilis growth follows the typical 4 phases of bacterial growth (Figure 2). The start up phase is called lag phase which comprises the time the bacteria need to adapt to the new environment ¹¹. With reaching the next phase, the exponential growth phase, the bacteria are dividing at their maximum division rate. Bacillus subtilis has a doubling time of 30 minutes under ideal conditions. This can be calculated with the slope of the exponential growth. In our experiment, the doubling time of the wild type is 28 minutes.

Figure 2: Growth curve of the Bacillus subtilis WT strain.

Figure 3: Exponential growth phase of Bacillus subtilis.

When all the substrate is consumed, the stationary stage begins where there is no more additional growth mensurable and the culture is at its highest density. Now the death-phase follows, where the bacterial culture starts to autolyse. Bacillus subtilis is able to form endospore under distress, which is one of the most efficient adaptations to a lack of nutrients.

Figure 4: The process of sporulation.

The sporulation begins with an asymmetrical cell division into the mother cell and the smaller prespore. The smaller prespore is now engulfed by the mother cell and the mother cell starts assembling the multiple layers of the spore. The cortex, a modified form of cell wall, is synthesized to give the spore their typical oval shape. At the same time the crust is formed, the spore coat begins to be deposit on the outside surface of the spore. The last part of the sporulation is called maturation, during this period the characteristics resistance, dormancy and germinability of the spores get established and the mother cell is lysed in order to release the endospore¹². This spore is now highly resistant to heat, enzymatic attacks. UV-light and pressure and can re-enter its life cycle under the right conditions.
Furthermore, it is a big advantage for our approach of working with surface fusion proteins, that the mother cell is able to synthesize the wanted proteins by itself and also assembles the proteins to the spore crust by itself. So the process of bringing a protein through a membrane is not needed. Through this, the cumbersome process of fusing proteins to the surface of artificial beads is obsolete. Since the outermost layer of the spore - the crust - is mostly build up of the proteins CotZ and CgeA ¹³, we use those to set up the fusion proteins. By fusing highly specific binding tools and enzymes to the crust proteins we found a new method of targeted drug delivery to reduce side effects occuring under systemic drug dispersal.

When we started to work with this versatile model organism, we noticed that in our surrounding no one is working with Bacillus subtilis. That’s why we had to reach wider and are glad to got help from Julia Bartels, a former member of the iGEM Team Munich 2012. To ease the work for future iGEM Teams we started a Bacillus subtilis Manual together with iGEM Bonn 2016.

Here are 12 AMAZING Facts about Bacillus subtilis we hope you enjoy:

1. Bacillus subtilis is one of the few bacterial strains which can build endospores.

2. B. subtilis lives all over the world, mostly in soil.

3. Its spores were sent to outer space for one and a half years and were still able to germinate back on earth.

4. B. subtilis creates strong foot odor.

5. If you’d grow a single B. subtilis cell for 100 generations you’d receive 10³⁰ cells after around a day and would need 10¹⁸ liters of media. (luckily they starve with a density of circa one billion cells per milliliter, so don’t panic)

6. B. subtilis is used for synthesis of antibiotics. ( such as Subtilin)

7. The core of its endospores is very dry and resistant to moisture.

8. B. subtilis is an ingredient of washing powder. (can produce proteases & amylases)

9. B. subtilis is used as a natural herbicide due to its ability to produce lethal substances.

10. B. subtilis is widely used as a probiotic. (supports your health especially the digestive system)

11. Once a group was able to resume some spores they found in a 250 million years old salt crystal and were able to “revive” them. (not B. subtilis spores though)

12. Spores are truly amazing

Modeling

Growth and sporulation:

Modeling the growth and sporulation of Bacillus subtilis was a rather easy task.
The growth of bacteria proceeds in four phases. Firstly, the lag-phase describes the time it takes for the bacteria to reach their maximal division rate, depending on the age of the culture and the conditions of the new culture.
Secondly, in the log-phase the bacteria are dividing at their maximal division rate. When the substrate is consumed the stationary-phase begins. This is when the bacterial population reaches its highest density, but stops growing. Toxic products start to develop and have a negative influence on the culture. Lastly, the culture enters the dying-phase, which is defined by the start of autolysis. The molecular mechanism initiating the autolysis is not fully discovered yet¹⁴.

Our model describes the first three stages of bacterial growth. We assume that the growth follows the rules of logistical growth, so it can be described by the following equation¹⁵.

Figure 5: Equation for logistic growth
{dx/dt=change of the total amount of Bacillus subtilis in the time of the interval, k= growth rate of the culture, x[t]= total amount of Bacillus subtilis, G= defines the growth limit of the culture}

Figure 6: Simulation of the logistic growth
{k1=0.148, G=1.988, x[0] = 0.0028, time in five minutes intervals}

The sporulation is one of the most important parts of our project. That's why we used a model that allows us to calculate the amount of spores that come out of one sporulation process.

As mentioned before, we assume that the bacterial culture follows the rules of logarithmic growth during this sporulation.

A certain percentage of our growing culture turns into spores. We assume that spores cannot germinate in the medium. The following formula describes this process.

Figure 7: Equation for B. subtilis vegetative cells
{dx/dt=change of the total amount of Bacillus subtilis in the time of the interval, k=growth rate of the culture, x[t]=total amount of Bacillus subtilis, G=defines the growth limit of the culture}

Figure 8: Equation for B. subtilis spores
{dy/dt=change of the total amount of Bacillus subtilis spores in the time of the interval , k2=sporulation rate, x[t]=total amount of Bacillus subtilis, G=defines the limit of spores per culture}

Figure 9:Simulation of the sporulation process
{k2=0.145, G=1.988,k1=0.148, x[0] = 0.001, y[0] = 0.00000001, time in minutes}
Here you can see the simulation of the sporulation process. The blue line graph represents the total amount of spores the yellow one the total amount of vegetative cells.

Protein expression modeling:

Modeling the protein expression was another task for us due describe generation of our Nanocillus. Having a promotor whose activity is induced during sporulation, we need to choose an mRNA transcription equation that reflects this. Combining this with an equation that simulates the conversion from mRNA into protein terminates our model. This model represents the protein expression under the assumption that the concentration of the activator protein never changes¹⁶.

In more complex models that we did not use, the expression of coat proteins is a highly conserved pathway of feedback loops¹⁷.

The following equations describe the change of the total amount of coat protein mRNA and the change of the total amount of protein in a certain time interval.

Figure 10: Transcription and translation of coat proteins.

Figure 11: Equation for mRNA transkriptionsrate

Figure 12: Equation fot protein-translation-rate
{dmRNA/dt=change of the total amount of coat protein mRNA in a certain time interval, v=DNA concentration per cell ,k11=leaky expression ,k21=expression constant, a=activator concentration ,n=Hill coefficient ,k31=activation constant, k41=mRNA degradation rate ,mRNA[t]=total amount of coat protein mRNA, dP/dt=change of the total amount of protein in a certain time interval, P[t]=total amount of coat protein, k12=expression constant, k22=protein degradation rate}

Figure 13: Increase of coat protein mRNA (blue line graph) and Protein (yellow line graph).

{k11= 0.1, k21= 2, k31= 1.5, k41= 0.1, k12= 2, k22= 0.1, v= 1, n= 2, a= 2, mRNA[0] = 0, P[0] = 0, time in hours, concentration in mM }

1. Guarner, F. , Malagelada, J. , Gut flora in health and disease , 6 Feburary 2003, p. 512
2. De Vrese, M. , Schrezenmeir, J. , Probiotics, Prebiotics, and Synbiotics, 07 May 2008, Volume 111 of the series Advances in Biochemical Engineering/Biotechnology pp 1-66
3. Benson, A.K. , Individuality in gut microbiota composition is a complex polygenic trait shaped by multiple environmental and host genetic factors, 10 June 2010 18933–18938, doi: 10.1073/pnas.1007028107
4. Hayes, P. , Irritable Bowel Syndrome: The Role of Food in Pathogenesis and Management, 2014 Mar; 10(3): 164–174.
5. Guarner, F., Rerdigon, G., Should yoghurt cultures be considered probiotic?, 17 Januaey 2005, British Journal of Nutrition (2005), 93, 783–786
6. Health and Nutritional Properties of Probiotics in Food including Powder Milk with Live LacticAcid Bacteria - Food and Agriculture Organization of the United Nations, 4 october 2001
7. Ouwehand, A. C. , Salminen, S. , Probiotics: an overview of beneficial effects, August 2002, Volume 82, Issue 1, pp 279–289
8. Duc, Le H., Characterization of Bacillus Probiotics Available for Human Use, 20 December 2003, APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Apr. 2004, p. 2161–2171
9. Qin, J. , Li, R. , A human gut microbial gene catalogue established by metagenomic sequencing, Nature 464, 59-65 (4 March 2010)
10. de Boer Sietske, A. & Diderichsen, B. Appl Microbiol Biotechnol (1991) 36: 1. doi:10.1007/BF00164689
11. Buchanan, R.L , Whiting , R.C, When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves , doi:10.1006/fmic.1997.0125
12. Errington, J. , Bacillus subtilis Sporulation: Regulation of Gene Expression and Control of Morphogenesis , MICROBIOLOGICAL REVIEWS, Mar. 1993, p. 1-33
13. Driks, A., Bacillus subtilis Spore Coat , Microbiol. Mol. Biol. Rev. March 1999 vol. 63 no. 1 1-201 March 1999
14. Zwietering, M. H., et al. "Modeling of the bacterial growth curve." Applied and environmental microbiology 56.6 (1990): 1875-1881.
15. Gompertz, B., On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies, 18.10.2016 Philosophical Transactions of the Royal Society of London, Vol. 115 (1825), pp. 513- 583
16. CHEN, T., MODELING GENE EXPRESSION WITH DIFFERENTIAL EQUATIONS, Published in 1999 Pacic Symposium of Biocomputing
17. Errington, J. E. F. F. E. R. Y. "Bacillus subtilis sporulation: regulation of gene expression and control of morphogenesis.", Microbiological reviews 57.1 (1993): 1-33.

@@ Line 1: / Line 1: @@
-{{Freiburg/Main}}
+{{Freiburg/Styles}} {{Freiburg/Menubar}} {{Freiburg/Away}} {{Freiburg/Main}} {{Freiburg/Top}}
-{{Freiburg/Menubar}}
 <html>
+<div class="column full_size">
+    <div class="color8">
+        <div class="para_center_20">
+            <h5 style="text-align: center"> <i>Bacillus subtilis</i> </h5>
+            <h3 style="text-align: center"> Our Model Organism </h3> </div>
+    </div>
+    <div class="color8">
+        <div class="para_center_20"> <font color="#e7d9d9">
+The human colon is home to a lot of tiny microorganisms. To be precise, our whole body contains 10 times more bacteria cells than endogenous cells<sup>1</sup>.
+In most cases, these bacteria are not harmful to the human body. Although, some organisms can cause infectious diseases, nearly 100% of our survey participants knew that this doesn’t mean bacteria are generally harmful.
+</font> </div>
+    </div>
+    <!--Figure 1-->
+    <div class="color7">
+        <div class="para_center_20">
+            <center> <img style="width:60%" src="https://static.igem.org/mediawiki/2016/1/13/T--Freiburg--BacillusGraph1.png"> </center>
+        </div>
+    </div>
+    <div class="color8">
+        <div class="para_center_20"><font color="#e7d9d9">
+The digestive system is host to several million of bacteria which are essential for digestion, proper absorbance of nutrients and the synthesis of vitamin K and B<sup>2</sup>.
+The entire microbiota in the gut is a complex ecosystem  that is  not well understood yet<sup>3</sup>. Dis-balances in the composition of the intestinal flora can cause a variety of diseases.
+We confronted different gastrologists with this topic and they confirmed that the flora is “essential” and “ really important since a disturbed intestinal flora would cause many diseases”.
-<div class="column full_size" >
+But what exactly is disturbing this intestinal flora?
-<h5> Bacillus subtilis </h5>
+Studies have shown that changes in diets,operations and health condition will perturbate the microbiota and may lead to irritative bowel diseases, chronic inflammation, infectious diseases with harmful bacteria or malabsorption<sup>4</sup>.
-<p> This page will be about our model organism: Bacillus subtilis.
+Due to individual lifestyle and genetic dispositions, everyone has a distinct bacterial flora in his/her gastrointestinal tract.
-It is a gram positiv, rod-shaped bacterium that is able to form spores under distress.
+To support and rebuilt the intestinal flora, people often grab for probiotics.
+Asking the Ulcerative Colitis patients that filled out our survey, whether or not they have consumed probiotics before, almost half of the participant answered with yes. This result lets us assume that the concerns about taking our product too will not be insuperable.
+</font> </div>
+    </div>
+    <!--Figure 2-->
+    <div class="color7">
+        <div class="para_center_20">
+            <center> <img style="width:60%" src="https://static.igem.org/mediawiki/2016/2/25/T--Freiburg--BacillusGraph2.png"> </center>
+        </div>
+    </div>
+    <div class="color8">
+        <div class="para_center_20"> <font color="#e7d9d9">
+Probiotics are nonpathogenic, living bacteria with health benefits for humans when consumed in a frequent manner<sup>5</sup>.<br>
+They play an important role in  immunological, digestive and respiratory functions and even the number and type of probiotic in foods and drinks are increasing at the moment.<sup>6</sup> <br>
- </p>
+Typical microorganism used as probiotics today are <i>Lactobacillus</i>, <i>E.coli</i>, <i>Enterococcus</i> and <i>Bacillus subtilis</i><sup>7</sup>.<br>
+For example: the probiotic Biosporin contains <i>Bacillus subtilis</i> and inhibits the growth of Helicobacter pylori, a bacterium which is known to cause gastrointestinal diseases.<sup>8</sup>
+<br>
+In this year's iGEM project we, team Freiburg, decided to work with the model organism <i>Bacillus subtilis</i> because of its innocuousness, robustness and ability to build spores.
+We wanted to use this spores as a carrier for two tools in combination as our new form of targeted drug delivery system.<br>
+In our survey we have also asked people, if they think spores are generally harmful to the human body. In comparison to the same question about bacteria, the results are different.
+Nearly 18.8% answered with “Yes, spores are generally harmful”.
+</font> </div>
+    </div>
+    <!--Figure 3-->
+    <div class="color7">
+        <div class="para_center_20">
+            <center> <img style="width:60%" src="https://static.igem.org/mediawiki/2016/f/f1/T--Freiburg--BacillusGraph3.png"> </center>
+        </div>
+    </div>
+    <div class="color8">
+        <div class="para_center_20"><font color="#e7d9d9">
+<i>Bacillus subtilis</i> has a rod shaped appearance and belongs to the family of the gram-positive bacteria.
+Apart from being widely present in nature, it is also already a part of the microbial gut flora <sup>9</sup> and so a perfect candidate for being our probiotic. The US Food and Drug Administration (FDA) classifies <i>Bacillus subtilis</i> as a GRAS (Generally Regarded As Safe) organism <sup>10</sup>. That means it is generally recognized as safe and can be used in S1 laboratories without problems.
+<i>Bacillus subtilis</i> colonies have an irregular, large size with undulate margin. They have a white and dull colour and a dry texture.
 </div>
+</div>
+<!--Figure 4-->
+<div class="color7">
+<div class="para_center_20">
+<center>
+<font color="#7a7f7a">
+<img style="width:40%" src="https://static.igem.org/mediawiki/2016/3/31/T--Freiburg--Bacillus_Colonies2.jpg"><br>
+<b>Figure 1: Colonies of <i>Bacillus subtilis </i></b>
+</center>
+</div>
+</div>
+<div class="color8">
+<div class="para_center_20">
+<font color="#e7d9d9">
+<i>Bacillus subtilis</i> growth follows the typical 4 phases of bacterial growth (Figure 2). The start up phase is called lag phase which comprises the time the bacteria need to adapt to the new environment <sup>11</sup>. With reaching the next phase, the exponential growth phase, the bacteria are dividing at their maximum division rate. <i>Bacillus subtilis</i> has a doubling time of 30 minutes under ideal conditions. This can be calculated with the slope of the exponential growth. In our experiment, the doubling time of the wild type is 28 minutes.
+</font> </div>
+    </div>
+    <!--Groths Curves-->
+    <div class="color0">
+        <div class="para_center_20">
+            <center> <font color="#7a7f7a">
+<img style="width:40%" src="https://static.igem.org/mediawiki/2016/1/15/T--Freiburg--BacillusGraph5.png"><br>
+ <b>Figure 2: Growth curve of the <i>Bacillus subtilis</i> WT strain.</b>
+<br>
+<img style="width:40%" src="https://static.igem.org/mediawiki/2016/8/82/T--Freiburg--BacillusGraph6.png"><br>
+ <b>Figure 3: Exponential growth phase of <i>Bacillus subtilis</i>.</b>
+</center>
+</div>
+</div>
+<div class="color8">
+<div class="para_center_20">
+<font color="#e7d9d9">
+When all the substrate is consumed, the stationary stage begins where there is no more additional growth mensurable and the culture is at its highest density. Now the death-phase follows, where the bacterial culture starts to autolyse.
+<i>Bacillus subtilis</i> is able to form <a target="_blank" href='https://static.igem.org/mediawiki/2016/7/71/T--Freiburg--SporulationProtocol.pdf' >endospore</a> under distress, which is one of the most efficient adaptations to a lack of nutrients.
+</font> </div>
+    </div>
+    <!--Figure 7-->
+    <div class="color7">
+        <div class="para_center_20">
+            <center> <font color="#7a7f7a">
+<img style="width:80%" src="https://static.igem.org/mediawiki/2016/f/f1/T--Freiburg--Sporulation.png"><br>
+<b>Figure 4: The process of sporulation.</b>
+</center>
+</div>
+</div>
+<div class="color8">
+<div class="para_center_20">
+<font color="#e7d9d9">
+The sporulation begins with an asymmetrical cell division into the mother cell and the smaller prespore. The smaller prespore is now engulfed by the mother cell and the mother cell starts assembling the multiple layers of the spore. The cortex, a modified form of cell wall, is synthesized to give the spore their typical oval shape. At the same time the crust is formed, the spore coat begins to be deposit on the outside surface of the spore. The last part of the sporulation is called maturation, during this period the characteristics resistance, dormancy and germinability of the spores get established and the mother cell is lysed in order to release the endospore<sup>12</sup>. This spore is now highly resistant to heat, enzymatic attacks. UV-light and pressure and can re-enter its life cycle under the right conditions.<br>
+Furthermore, it is a big advantage for our approach of working with surface fusion proteins, that the mother cell is able to synthesize the wanted proteins by itself and also assembles the proteins to the spore crust by itself. So the process of bringing a protein through a membrane is not needed. Through this, the cumbersome process of fusing proteins to the surface of artificial beads is obsolete.
+Since the outermost layer of the spore - the crust - is mostly build up of the proteins CotZ and CgeA <sup>13</sup>, we use those to set up the fusion proteins.
+By fusing highly specific binding tools and enzymes to the crust proteins we found a new method of targeted drug delivery to reduce side effects occuring under systemic drug dispersal.</font> </div>
+    </div>
+<div class="color7">
+<div class="para_center_20">
+<font color="#dcbfbf">
+When we started to work with this versatile model organism, we noticed that in our surrounding no one is working with <i>Bacillus subtilis</i>. That’s why we had to reach wider and are glad to got help from Julia Bartels, a former member of the iGEM Team Munich 2012. To ease the work for future iGEM Teams we started a <a href="https://static.igem.org/mediawiki/2016/8/8c/T--Freiburg--BacillussubtilisManueliGEMFreiburgandBonn2016new3.pdf" target="_blank" style="color:#e8a126"><i>Bacillus subtilis</i> Manual</a> together with iGEM Bonn 2016.<br><br>
+Here are 12 AMAZING Facts about <i>Bacillus subtilis</i> we hope you enjoy:<br><br>
+.   <i>Bacillus subtilis</i> is one of the few bacterial strains which can build endospores.<br><br>
+.   <i>B. subtilis</i> lives all over the world, mostly in soil.<br><br>
+.   Its spores were sent to outer space for one and a half years and were still able to germinate back on earth.<br><br>
+.   <i>B. subtilis</i> creates strong foot odor.<br><br>
+.   If you’d grow a single <i>B. subtilis</i> cell for 100 generations you’d receive 10<sup>30</sup> cells after around a day and would need 10<sup>18</sup> liters of media. (luckily they starve with a density of circa one billion cells per milliliter, so don’t panic)<br><br>
+.   <i>B. subtilis</i> is used for synthesis of antibiotics. ( such as Subtilin)<br><br>
+.   The core of its endospores is very dry and resistant to moisture.<br><br>
+.   <i>B. subtilis</i> is an ingredient of washing powder. (can produce proteases & amylases)<br><br>
+.   <i>B. subtilis</i> is used as a natural herbicide due to its ability to produce lethal substances.<br><br>
+.                 <i>B. subtilis</i> is widely used as a probiotic. (supports your health especially the digestive system)<br><br>
+.                 Once a group was able to resume some spores they found in a 250 million years old salt crystal and were able to “revive” them. (not <i>B. subtilis</i> spores though)<br><br>
+.                 Spores are truly amazing<br><br>
+</font>
+</div>
+</div>
+    <div class="color0">
+        <div class="para_center_20"> <font color="#6e5454">
+<h5> Modeling </h5>
+<h5> Growth and sporulation:</h5>
+Modeling the growth and sporulation of <i>Bacillus subtilis</i> was a rather easy task. <br>
+The growth of bacteria proceeds in four phases. Firstly, the lag-phase describes the time it takes for the bacteria to reach their maximal division rate, depending on the age of the culture and the conditions of the new culture.<br>Secondly, in the log-phase the bacteria are dividing at their maximal division rate. When the substrate is consumed the stationary-phase begins. This is when the bacterial population reaches its highest density, but stops growing. Toxic products start to develop and have a negative influence on the culture. Lastly, the culture enters the dying-phase, which is defined by the start of autolysis. The molecular mechanism initiating the autolysis is not fully discovered yet<sup>14</sup>.<br><br>
+Our model describes the first three stages of bacterial growth. We assume that the growth follows the rules of logistical growth, so it can be described by the following equation<sup>15</sup>.<br><br>
+<center><img class="something" style="width:50%" src="https://static.igem.org/mediawiki/2016/f/f2/T--Freiburg--Modeling22.png"> </center><br>
+<font color="#01afb7"> <b>Figure 5: Equation for logistic growth</b> <br>
+ {dx/dt=change of the total amount of <i>Bacillus subtilis</i> in the time of the interval, k= growth rate of the culture, x[t]= total amount of <i>Bacillus subtilis</i>, G= defines the growth limit of the culture}</font>
+            <br>
+            <br>
+            <center><img class="something" src="https://static.igem.org/mediawiki/2016/6/62/T--Freiburg--Modeling17.png"> </center>
+            <br> <font color="#01afb7"> <b>Figure 6: Simulation of the logistic growth</b><br>
+ {k1=0.148, G=1.988, x[0] = 0.0028, time in five minutes intervals}<br>
+<br><br></font> The sporulation is one of the most important parts of our project. That's why we used a model that allows us to calculate the amount of spores that come out of one sporulation process.
+            <br>
+            <br> As mentioned before, we assume that the bacterial culture follows the rules of logarithmic growth during this sporulation.
+            <br>
+            <br> A certain percentage of our growing culture turns into spores. We assume that spores cannot germinate in the medium. The following formula describes this process.
+            <br>
+            <br>
+            <center><img class="something" style="width:50%" src="https://static.igem.org/mediawiki/2016/4/43/T--Freiburg--Modeling23.png"> </center>
+            <br> <font color="#01afb7"> <b>Figure 7: Equation for <i>B. subtilis</i> vegetative cells</b> <br>
+ {dx/dt=change of the total amount of <i>Bacillus subtilis</i> in the time of the interval, k=growth rate of the culture, x[t]=total amount of <i>Bacillus subtilis</i>, G=defines the growth limit of the culture}</font>
+            <br>
+            <br>
+            <br>
+            <br>
+            <center><img class="something" style="width:50%" src="https://static.igem.org/mediawiki/2016/6/6c/T--Freiburg--Modeling24.png"> </center>
+            <br> <font color="#01afb7"> <b>Figure 8: Equation for <i>B. subtilis</i> spores</b><br>
+ {dy/dt=change of the total amount of <i>Bacillus subtilis</i> spores in the time of the interval , k2=sporulation rate, x[t]=total amount of <i>Bacillus subtilis</i>, G=defines the limit of spores per culture}</font>
+            <br>
+            <br>
+            <center><img class="something" src="https://static.igem.org/mediawiki/2016/b/b5/T--Freiburg--Modeling16.png"> </center>
+            <br> <font color="#01afb7"> <b>Figure 9:Simulation of the sporulation process</b> <br>
+ {k2=0.145, G=1.988,k1=0.148, x[0] = 0.001, y[0] = 0.00000001, time in minutes} <br>
+Here you can see the simulation of the sporulation process. The blue line graph represents the total amount of spores the yellow one the total amount of vegetative cells.</font>
+            <br>
+            <br>
+            <h5>Protein expression modeling:</h5>
+            <br>
+            <br> Modeling the protein expression was another task for us due describe generation of our Nanocillus. Having a promotor whose activity is induced during sporulation, we need to choose an mRNA transcription equation that reflects this. Combining this with an equation that simulates the conversion from mRNA into protein terminates our model. This model represents the protein expression under the assumption that the concentration of the activator protein never changes<sup>16</sup>.
+            <br>
+            <br> In more complex models that we did not use, the expression of coat proteins is a highly conserved pathway of feedback loops<sup>17</sup>.
+            <br>
+            <br> The following equations describe the change of the total amount of coat protein mRNA and the change of the total amount of protein in a certain time interval.
+            <br>
+            <br>
+            <center><img class="something" src="https://static.igem.org/mediawiki/2016/8/8a/T--Freiburg--Modeling21.png"> </center> <font color="#01afb7"> <b>Figure 10: Transcription and translation of coat proteins.</b></font>
+            <br>
+            <br>
+            <center><img class="something" src="https://static.igem.org/mediawiki/2016/e/ea/T--Freiburg--Modeling25.png"> </center> <font color="#01afb7"> <b>Figure 11: Equation for mRNA transkriptionsrate</b> </font>
+            <center><img class="something" style="width:50%" src="https://static.igem.org/mediawiki/2016/0/08/T--Freiburg--Modeling26.png"> </center> <font color="#01afb7"> <b>Figure 12: Equation fot protein-translation-rate </b><br>
+ {dmRNA/dt=change of the total amount of coat protein mRNA in a certain time interval, v=DNA concentration per cell ,k11=leaky expression ,k21=expression constant, a=activator concentration ,n=Hill coefficient ,k31=activation constant, k41=mRNA degradation rate ,mRNA[t]=total amount of coat protein mRNA, dP/dt=change of the total amount of protein in a certain time interval, P[t]=total amount of coat protein, k12=expression constant, k22=protein degradation rate}</font>
+            <br>
+            <br>
+            <center><img class="something" src="https://static.igem.org/mediawiki/2016/0/02/T--Freiburg--Modeling36.png"> </center> <font color="#01afb7"> <b>Figure 13: Increase of coat protein mRNA (blue line graph) and Protein (yellow line graph).</b>
+<br><br>
+{k11= 0.1, k21= 2, k31= 1.5, k41= 0.1, k12= 2, k22= 0.1, v= 1, n= 2, a= 2, mRNA[0] = 0, P[0] = 0, time in hours, concentration in mM
+}</font>
+            <br>
+            <br>
+            <br>
+            <br> </div>
+    </div>
+    <div class="color8">
+        <div class="para_center_Quellen"> 1. Guarner, F. , Malagelada, J. , Gut flora in health and disease , 6 Feburary 2003, p. 512
+            <br> 2. De Vrese, M. , Schrezenmeir, J. , Probiotics, Prebiotics, and Synbiotics, 07 May 2008, Volume 111 of the series Advances in Biochemical Engineering/Biotechnology pp 1-66
+            <br> 3. Benson, A.K. , Individuality in gut microbiota composition is a complex polygenic trait shaped by multiple environmental and host genetic factors, 10 June 2010 18933–18938, doi: 10.1073/pnas.1007028107
+            <br> 4. Hayes, P. , Irritable Bowel Syndrome: The Role of Food in Pathogenesis and Management, 2014 Mar; 10(3): 164–174.
+            <br> 5. Guarner, F., Rerdigon, G., Should yoghurt cultures be considered probiotic?, 17 Januaey 2005, British Journal of Nutrition (2005), 93, 783–786
+            <br> 6. Health and Nutritional Properties of Probiotics in Food including Powder Milk with Live LacticAcid Bacteria - Food and Agriculture Organization of the United Nations, 4 october 2001
+            <br> 7. Ouwehand, A. C. , Salminen, S. , Probiotics: an overview of beneficial effects, August 2002, Volume 82, Issue 1, pp 279–289
+            <br> 8. Duc, Le H., Characterization of Bacillus Probiotics Available for Human Use, 20 December 2003, APPLIED AND ENVIRONMENTAL MICROBIOLOGY, Apr. 2004, p. 2161–2171
+            <br> 9. Qin, J. , Li, R. , A human gut microbial gene catalogue established by metagenomic sequencing, Nature 464, 59-65 (4 March 2010)
+            <br> 10. de Boer Sietske, A. & Diderichsen, B. Appl Microbiol Biotechnol (1991) 36: 1. doi:10.1007/BF00164689
+            <br> 11. Buchanan, R.L , Whiting , R.C, When is simple good enough: a comparison of the Gompertz, Baranyi, and three-phase linear models for fitting bacterial growth curves , doi:10.1006/fmic.1997.0125
+            <br> 12. Errington, J. , Bacillus subtilis Sporulation: Regulation of Gene Expression and Control of Morphogenesis , MICROBIOLOGICAL REVIEWS, Mar. 1993, p. 1-33
+            <br> 13. Driks, A., Bacillus subtilis Spore Coat , Microbiol. Mol. Biol. Rev. March 1999 vol. 63 no. 1 1-201 March 1999
+            <br> 14. Zwietering, M. H., et al. "Modeling of the bacterial growth curve." Applied and environmental microbiology 56.6 (1990): 1875-1881.
+            <br> 15. Gompertz, B., On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies, 18.10.2016 Philosophical Transactions of the Royal Society of London, Vol. 115 (1825), pp. 513- 583
+            <br> 16. CHEN, T., MODELING GENE EXPRESSION WITH DIFFERENTIAL EQUATIONS, Published in 1999 Pacic Symposium of Biocomputing
+            <br> 17. Errington, J. E. F. F. E. R. Y. "Bacillus subtilis sporulation: regulation of gene expression and control of morphogenesis.", Microbiological reviews 57.1 (1993): 1-33. </div>
+    </div>