Difference between revisions of "Team:UCopenhagen/Model"

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<h1>Modelling and design of chamber</h1>
  
  
<div class="column full_size judges-will-not-evaluate">
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<h2>Introduction</h2>
<h3>★  ALERT! </h3>
+
<p>This page is used by the judges to evaluate your team for the <a href="https://2018.igem.org/Judging/Medals">medal criterion</a> or <a href="https://2018.igem.org/Judging/Awards"> award listed below</a>. </p>
+
<p> Delete this box in order to be evaluated for this medal criterion and/or award. See more information at <a href="https://2018.igem.org/Judging/Pages_for_Awards"> Instructions for Pages for awards</a>.</p>
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</div>
+
  
  
<div class="clear"></div>
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<p>
 +
The final product of PharMARSy, <strong><em>Protein Printer</em></strong>  would be a device that allows for growth of bacteria in one chamber and secretion of pure protein into another. The chambers would be divided by a biomimetic membrane, which serves two purposes: it should allow for bacteria to secrete the protein through membrane into collection chamber using injectosome - a syringe-like protein structure, but at the same time it should be robust enough to prevent bacteria to crossing into lower chamber thus contaminating the protein solution.
 +
</p>
 +
<p>
 +
The design of the chamber should therefore fulfill the following criteria:
 +
</p><ul>
  
 +
<li>Simplicity of handling: easy to open, easy to safely close
 +
<li>Allow for fixation of membrane without breaking it (sufficient control over applied pressure)
 +
<li>Prevent mixing of media from different chambers
 +
<li>Allow for fluidic system / stirring / sample taking</li></ul>
  
<div class="column full_size">
 
<h1> Modeling</h1>
 
  
<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>
 
  
</div>
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<p>
<div class="clear"></div>
+
Due to popularity of 3D printing and its relative accessibility we decided to print our own prototype. But it had to be designed first.
 +
</p>
 +
<h2>Design of our first <em>Bacta_tank</em> prototype</h2>
  
<div class="column full_size">
+
 
<h3> Gold Medal Criterion #3</h3>
+
<p>
 +
The first design of the chamber was made before deciding on what type of membrane to use. It was therefore crucial to keep the design open for changes and later modifications.
 +
</p>
 
<p>
 
<p>
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.
+
A general concept was disk-like plastic container allowing for delicate handling of the presumably fragile membrane (fig 1).
<br><br>
+
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>
 
</p>
 +
<img src="https://static.igem.org/mediawiki/2018/4/40/T--UCopenhagen--Bactatank_first_design.png" alt="First design">
 +
  
 
<p>
 
<p>
Please see the <a href="https://2018.igem.org/Judging/Medals"> 2018
+
<strong>Figure 1:</strong> First design.
Medals Page</a> for more information.  
+
 
</p>
 
</p>
</div>
+
<p>
 +
It was realised that the membrane will have to be somehow held in place, to prevent leakage and to allow for stirring of the media above it. The  design was therefore improved to address that problem. One solution was to include another part that would hold the membrane in place as can be seen in figure 2 and 3.
 +
</p>
 +
 
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/4/4f/T--UCopenhagen--BT2.jpeg/800px-T--UCopenhagen--BT2.jpeg" alt="Multicomponent design" style="width:45%">
  
<div class="column two_thirds_size">
 
<h3>Best Model Special Prize</h3>
 
  
 
<p>
 
<p>
To compete for the <a href="https://2018.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://2018.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.  
+
<strong>Figure 2</strong>: Multicomponent design - <em>Bacta_tank1</em> offers more yet at the cost of simplicity. It served as a template for further development, but was never printed.
<br><br>
+
You must also delete the message box on the top of this page to be eligible for the Best Model Prize.
+
 
</p>
 
</p>
 +
<p>
  
</div>
+
<img src="https://static.igem.org/mediawiki/2018/thumb/8/86/T--UCopenhagen--BT3.jpeg/800px-T--UCopenhagen--BT3.jpeg" alt="Bacta_tank2, middle part" style="width:45%">
 +
 
 +
<p>
 +
<strong>Figure 3:</strong> Bacta_tank2, middle part.
 +
</p>
 +
 
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/c/c5/T--UCopenhagen--BT4.jpeg/800px-T--UCopenhagen--BT4.jpeg" alt="Bacta_tank2, upper part" style="width:45%">
  
  
<div class="column third_size">
 
<div class="highlight decoration_A_full">
 
<h3> Inspiration </h3>
 
 
<p>
 
<p>
Here are a few examples from previous teams:
+
<strong>Figure 4</strong>: Bacta_tank2, upper part.
 +
</p>
 +
<p>
 +
However all of the models described above are relatively complicated for handling, and not that easy to manufacture with 3D printers techniques available to us. If possible, we were aiming at designing a prototype that would be easy to produce and easy to handle.
 +
</p>
 +
<p>
 +
A radically new design was needed - simpler and smaller.
 +
</p>
 +
<p>
 +
The inspiration came from the very thing that we were trying to get rid of: the screws. Why having external, metal screws if one can design chamber components to be "big hollow screws?"
 +
</p>
 +
<p>
 +
Inclusion threads inside the walls of chamber components meant that parts can be simply screwed one into another, eliminating any need of external holders or screws. Admittingly somewhat a challenge for a designer and a test of precision for 3D printer, at least it would be very simple for the end-user.
 +
</p>
 +
<p>
 +
It is relatively simple to design a 2 components system where only 2 threads are used, however when having thread on both sides of the middle part (coloured blue in Figure 6), one has to pay attention not to "slice" with the threads through the walls of the body of the component. To make screwing easier, a hexagon extension was envisioned at the top of two upper parts allowing for use of tools if necessary. 
 +
</p>
 +
<p>
 +
An example of cross section can be seen in the following illustration (Figure 5).
 
</p>
 
</p>
<ul>
 
<li><a href="https://2016.igem.org/Team:Manchester/Model">2016 Manchester</a></li>
 
<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>
 
</ul>
 
</div>
 
</div>
 
  
 +
<img src="https://static.igem.org/mediawiki/2018/c/c5/T--UCopenhagen--BT5.jpeg" alt="Bacta_tank2, upper part" style="width:45%">
 +
<p>
 +
<strong>Figure 5:</strong> A cross section of design for Bacta_tank3. Components can be seen to fit nicely and a simulation was performed many times to check for any issues prior to printing.
 +
 +
</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/e/e7/T--UCopenhagen--BT6.jpeg" alt="Another view of the Bacta_tank3" style="width:45%">
 +
 +
 +
<p>
 +
<strong>Figure 6</strong>: Another view of the Bacta_tank3 design, both assembled and disassembled.
 +
</p>
 +
<p>
 +
As can be seen on the picture, including threads considerably simplified the use of "Bacta tank". The membrane would be placed between the upper and middle part, and protein wouldl be collected in the lowest chamber, while bacteria culture would be cultured in the utmost top. The threads allow for customisation of the volume of collection buffer in collection chamber, while also allowing for careful fixation of the membrane between upper two parts.</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/a/a4/T--UCopenhagen--BT7.jpeg/800px-T--UCopenhagen--BT7.jpeg.png" alt="Rendering" style="width:45%">
 +
 +
<p>
 +
<strong>Figure 7</strong>: Rendering tool in Autodesk Fusion 360 program allows for different materials to be "tested" for visual appearance prior to actual production. Of course printing in glass or aluminium was beyond our capabilities.
 +
</p>
 +
<h2>Technical details</h2>
 +
 +
 +
<p>
 +
The drawing of the chamber design was done in Fusion 360, a cloud-based CAD/CAM/CAE tool for collaborative product development, using an educational licence. The version used was 2.0.4126:
 +
</p>
 +
<p>
 +
The drawing was then exported into Ultimaker Cura, an open access program for preparing the model for 3D printing.
 +
</p>
 +
<p>
 +
All chamber components were printed Ultimaker 2+, using PLA filament (polylactic acid), with filament diameter of 2.85mm and Marine Blue color, with disabled support, enabled print cooling and adhesion plate type "Brim".
 +
</p>
 +
<h2>Future improvements</h2>
 +
 +
 +
<p>
 +
Of course PLA polylactic acid is probably not the best material for growing bacteria in. At least some painting could be used after printing the model.
 +
</p>
 +
<p>
 +
The device that was envisioned for astronauts to take on their space voyages would be of course far more advanced. It should be hermetically closed with double walls and multiple inlets/outlets allowing for manipulation of liquids and monitoring of parameters. It should also be enclosed in one more contamination containment chamber (the principle similar to what they currently use in nuclear power plants) which would protect the crew from the spillage of biohazard material in case of accidents. The fluidic system should allow for uninterrupted sampling both of the bacteria culture and of the protein solution. Bacteria could mutate due to exposure to mutagenic cosmic radiation so checking the genome of bacteria prior to start of protein production could be a good idea. On the other hand a samples from protein solution could be analysed either via capillary electrophoresis on a microfluidic device or some other method that would confirm the required purity and "quality" of the protein prior to use on the patient.
 +
</p>
 +
<p>
 +
Finally, the chamber must withstand the disinfection between changing the bacterial strains when different proteins are needed. The most vulnerable part in this case would probably be the membrane, so a system that allows for changing of the membrane is a much better solution than the system with fixed one. This would also considerably extend the useability of the system, since a membrane that wears out could be easily changed.
 +
</p>
 +
<h2>Pictures from real process:</h2>
 +
 +
 +
<p>
 +
<strong><em>A special note to the 3D printing enthusiasts. As the principal idea of 3D printing is accessibility to everyone (who has access to the 3D printer) and sharing, many designs can be found online. This is the case also with our design. If you are interested into our Bacta_tank3.0 and would like to print it on your own, please feel free to contact us and we will readily share our knowledge with you. We are also welcoming any suggestions from the more experienced printer-maestros, since we are very much aware that there is plenty of room for improvement.</em></strong>
 +
</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/f/fc/T--UCopenhagen--BT8.jpeg/320px-T--UCopenhagen--BT8.jpeg" alt="Ultimaker 2">
 +
 +
<p>
 +
<strong>Figure 8:</strong> Ultimaker 2+ that was used for printing. The blue duct tape was used due to problems with sticking to the baseplate.
 +
</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/f/ff/T--UCopenhagen--BT9.jpeg/800px-T--UCopenhagen--BT9.jpeg" alt="Initial layer" style="width:45%">
 +
 +
<p>
 +
<strong> Figure 9:</strong> The initial layer is usually the hardest. A blue adhesive tape tends to solve the problem, especially if combined with the hair conditioner sprayed just before printing.
 +
</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/a/af/T--UCopenhagen--BT10.jpeg/800px-T--UCopenhagen--BT10.jpeg" alt="Body printed" style="width:45%">
 +
 +
<p>
 +
<strong>Figure 10:</strong> After first layer is printed, the worst is over and the rest of the body can be printed without supervision.
 +
</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/5/55/T--UCopenhagen--BT11.jpeg/450px-T--UCopenhagen--BT11.jpeg" alt="Top view">
 +
 +
<p>
 +
<strong> Figure 11: </strong> Top view
 +
</p>
 +
 +
<img src="https://static.igem.org/mediawiki/2018/thumb/e/ed/T--UCopenhagen--BT12.jpeg/450px-T--UCopenhagen--BT12.jpeg" alt="Finished printing">
 +
<p>
 +
<strong>Figure 12: </strong> Right after finished printing, a careful removal of the object follows.
 +
</p>
 +
 +
<h2> Calculations </h2>
 +
<head>
 +
  <meta charset="utf-8">
 +
  <meta name="viewport" content="width=device-width">
 +
  <title>MathJax example</title>
 +
  <script type="text/javascript" async
 +
  src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-MML-AM_CHTML" async>
 +
</script>
 +
</head>
 +
<body>
 +
<p>To support our predictions for the chamber size, we made simple approximations for how the cells could bind to the membrane. The outcome of different membrane sizes, cell secretion rates and the needed size for specific proteins can then be evaluated. Previously experiments with the secretion of a SipA protein has been conducted. Here a secretion rate of in the magnitude 60 molecules per cell per second was found.[1] The resulting production rate is then found. Here we assume a membrane size of 4 square centimeter, a <i>E. coli</i> attachment surface of 2 <span style="font-weight: 400;">&mu;</span>m^2 and we know the molecular weight of SipA is 74 kDa
 +
$$N_{cells} = {0.0004m^2 \over 2*10^{-12}m^2}R_{bind}$$
 +
$${dN_{produced} \over dt} = N_{cells}*SecRate$$
 +
$$ProdRate = {dN_{produced} \over dt}*74kDa=1.47 {ng \over s}$$
 +
Which is for 4 square centimeter. The production rate per square centimeter is then  \(ProdRate = 0.368 {ng \over s}\)
 +
 +
We can then calculate the membrane size needed to produce the amount of insulin needed to maintain the health of an astronaut suffering of Type 1 Diabetes Mellitus, which is 0.5 to 1 U per kg per day.[2] The molecule that is used as an example is Novorapid Insulin Aspart, with a weight of 100/3.5mg,[3] on a person of 70 kg
 +
$$ M_{Aspart,daily} = {70 {U  \over day} \over M_{Aspart}}=2.45 {mg \over day}$$
 +
$$ A_{membrane} = {M_{Aspart,daily}  \over ProdRate_{daily}}= 76.92 cm^2 $$
 +
Contour plotting the production rate as a function of secretion rate and binding factor, \(R_{bind}\) and finding the coefficients needed, allows us to evaluate the design in accordance to the needed production of Aspartan. Below is the plots of 3 different membrane sizes,</p>
 +
<figure>
 +
    <img src="https://static.igem.org/mediawiki/2018/6/61/T--UCopenhagen--PR5cm2.jpeg" alt="Finished printing" style="width:45%">
 +
    <figcaption><strong>Figure 13:</strong> Membrane of \(5 cm^2\), the black line represents the contour needed to produce insulin enough for one person for one day </figcaption>
 +
</figure>
 +
<figure>
 +
    <img src="https://static.igem.org/mediawiki/2018/c/c4/T--UCopenhagen--PR10cm2_3d.jpeg" alt="Finished printing" style="width:45%">
 +
    <figcaption><strong>Figure 14:</strong> Membrane of \(5 cm^2\), the black line represents the contour needed to produce insulin enough for one person for one day </figcaption>
 +
</figure>
 +
<figure>
 +
    <img src="https://static.igem.org/mediawiki/2018/7/76/T--UCopenhagen--PR10cm2%281%29.jpeg" alt="Finished printing" style="width:45%">    <figcaption><strong>Figure 15:</strong> Membrane of \(10 cm^2\), the transparent plane represents the rate needed to produce insulin enough for one person for one day </figcaption>
 +
</figure>
 +
<figure>
 +
    <img src="https://static.igem.org/mediawiki/2018/2/2b/T--UCopenhagen--PR20cm2.jpeg" alt="Finished printing" style="width:45%">
 +
    <figcaption><strong>Figure 15: </strong>Membrane of \(20 cm^2\), the black line represents the contour needed to produce insulin enough for one person for one day </figcaption>
 +
</figure>
 +
<p>With this we are able to conclude that the size of the physical model to produce enough protein for one person is achievable! In the future, focus on modeling secretion rates across membranes would be an ideal way to evaluate experiments with injectisome binding to membranes. </p>
 +
<p>
 +
References:
 +
</p>
 +
<p>
 +
[1] M. C. Schlumberger, A. J. Müller, K. Ehrbar, B. Winnen, I. Duss, B. Stecher, and W. Hardt. Real-time imaging of type III secretion: Salmonella SipA injection into host cells. 2005 Aug 30; 102(35): 12548–12553. </p>
 +
<p>
 +
[2] B. HIRSCH, M.D., University of Washington School of Medicine, Seattle, Washington. (2006) Type 1 Diabetes Mellitus and the Use of Flexible Insulin Regimens. Am Fam Physician. 1999 Nov 15;60(8):2343-2352. </p>
 +
<p>[3] EMC Website <a hef="https://www.medicines.org.uk/emc/product/4779/smpc"><span>Here</span></a>
 +
</body>
 
</html>
 
</html>

Latest revision as of 19:38, 17 October 2018

Modelling and design of chamber

Introduction

The final product of PharMARSy, Protein Printer would be a device that allows for growth of bacteria in one chamber and secretion of pure protein into another. The chambers would be divided by a biomimetic membrane, which serves two purposes: it should allow for bacteria to secrete the protein through membrane into collection chamber using injectosome - a syringe-like protein structure, but at the same time it should be robust enough to prevent bacteria to crossing into lower chamber thus contaminating the protein solution.

The design of the chamber should therefore fulfill the following criteria:

  • Simplicity of handling: easy to open, easy to safely close
  • Allow for fixation of membrane without breaking it (sufficient control over applied pressure)
  • Prevent mixing of media from different chambers
  • Allow for fluidic system / stirring / sample taking

Due to popularity of 3D printing and its relative accessibility we decided to print our own prototype. But it had to be designed first.

Design of our first Bacta_tank prototype

The first design of the chamber was made before deciding on what type of membrane to use. It was therefore crucial to keep the design open for changes and later modifications.

A general concept was disk-like plastic container allowing for delicate handling of the presumably fragile membrane (fig 1).

First design

Figure 1: First design.

It was realised that the membrane will have to be somehow held in place, to prevent leakage and to allow for stirring of the media above it. The design was therefore improved to address that problem. One solution was to include another part that would hold the membrane in place as can be seen in figure 2 and 3.

Multicomponent design

Figure 2: Multicomponent design - Bacta_tank1 offers more yet at the cost of simplicity. It served as a template for further development, but was never printed.

Bacta_tank2, middle part

Figure 3: Bacta_tank2, middle part.

Bacta_tank2, upper part

Figure 4: Bacta_tank2, upper part.

However all of the models described above are relatively complicated for handling, and not that easy to manufacture with 3D printers techniques available to us. If possible, we were aiming at designing a prototype that would be easy to produce and easy to handle.

A radically new design was needed - simpler and smaller.

The inspiration came from the very thing that we were trying to get rid of: the screws. Why having external, metal screws if one can design chamber components to be "big hollow screws?"

Inclusion threads inside the walls of chamber components meant that parts can be simply screwed one into another, eliminating any need of external holders or screws. Admittingly somewhat a challenge for a designer and a test of precision for 3D printer, at least it would be very simple for the end-user.

It is relatively simple to design a 2 components system where only 2 threads are used, however when having thread on both sides of the middle part (coloured blue in Figure 6), one has to pay attention not to "slice" with the threads through the walls of the body of the component. To make screwing easier, a hexagon extension was envisioned at the top of two upper parts allowing for use of tools if necessary.

An example of cross section can be seen in the following illustration (Figure 5).

Bacta_tank2, upper part

Figure 5: A cross section of design for Bacta_tank3. Components can be seen to fit nicely and a simulation was performed many times to check for any issues prior to printing.

Another view of the Bacta_tank3

Figure 6: Another view of the Bacta_tank3 design, both assembled and disassembled.

As can be seen on the picture, including threads considerably simplified the use of "Bacta tank". The membrane would be placed between the upper and middle part, and protein wouldl be collected in the lowest chamber, while bacteria culture would be cultured in the utmost top. The threads allow for customisation of the volume of collection buffer in collection chamber, while also allowing for careful fixation of the membrane between upper two parts.

Rendering

Figure 7: Rendering tool in Autodesk Fusion 360 program allows for different materials to be "tested" for visual appearance prior to actual production. Of course printing in glass or aluminium was beyond our capabilities.

Technical details

The drawing of the chamber design was done in Fusion 360, a cloud-based CAD/CAM/CAE tool for collaborative product development, using an educational licence. The version used was 2.0.4126:

The drawing was then exported into Ultimaker Cura, an open access program for preparing the model for 3D printing.

All chamber components were printed Ultimaker 2+, using PLA filament (polylactic acid), with filament diameter of 2.85mm and Marine Blue color, with disabled support, enabled print cooling and adhesion plate type "Brim".

Future improvements

Of course PLA polylactic acid is probably not the best material for growing bacteria in. At least some painting could be used after printing the model.

The device that was envisioned for astronauts to take on their space voyages would be of course far more advanced. It should be hermetically closed with double walls and multiple inlets/outlets allowing for manipulation of liquids and monitoring of parameters. It should also be enclosed in one more contamination containment chamber (the principle similar to what they currently use in nuclear power plants) which would protect the crew from the spillage of biohazard material in case of accidents. The fluidic system should allow for uninterrupted sampling both of the bacteria culture and of the protein solution. Bacteria could mutate due to exposure to mutagenic cosmic radiation so checking the genome of bacteria prior to start of protein production could be a good idea. On the other hand a samples from protein solution could be analysed either via capillary electrophoresis on a microfluidic device or some other method that would confirm the required purity and "quality" of the protein prior to use on the patient.

Finally, the chamber must withstand the disinfection between changing the bacterial strains when different proteins are needed. The most vulnerable part in this case would probably be the membrane, so a system that allows for changing of the membrane is a much better solution than the system with fixed one. This would also considerably extend the useability of the system, since a membrane that wears out could be easily changed.

Pictures from real process:

A special note to the 3D printing enthusiasts. As the principal idea of 3D printing is accessibility to everyone (who has access to the 3D printer) and sharing, many designs can be found online. This is the case also with our design. If you are interested into our Bacta_tank3.0 and would like to print it on your own, please feel free to contact us and we will readily share our knowledge with you. We are also welcoming any suggestions from the more experienced printer-maestros, since we are very much aware that there is plenty of room for improvement.

Ultimaker 2

Figure 8: Ultimaker 2+ that was used for printing. The blue duct tape was used due to problems with sticking to the baseplate.

Initial layer

Figure 9: The initial layer is usually the hardest. A blue adhesive tape tends to solve the problem, especially if combined with the hair conditioner sprayed just before printing.

Body printed

Figure 10: After first layer is printed, the worst is over and the rest of the body can be printed without supervision.

Top view

Figure 11: Top view

Finished printing

Figure 12: Right after finished printing, a careful removal of the object follows.

Calculations

MathJax example

To support our predictions for the chamber size, we made simple approximations for how the cells could bind to the membrane. The outcome of different membrane sizes, cell secretion rates and the needed size for specific proteins can then be evaluated. Previously experiments with the secretion of a SipA protein has been conducted. Here a secretion rate of in the magnitude 60 molecules per cell per second was found.[1] The resulting production rate is then found. Here we assume a membrane size of 4 square centimeter, a E. coli attachment surface of 2 μm^2 and we know the molecular weight of SipA is 74 kDa $$N_{cells} = {0.0004m^2 \over 2*10^{-12}m^2}R_{bind}$$ $${dN_{produced} \over dt} = N_{cells}*SecRate$$ $$ProdRate = {dN_{produced} \over dt}*74kDa=1.47 {ng \over s}$$ Which is for 4 square centimeter. The production rate per square centimeter is then \(ProdRate = 0.368 {ng \over s}\) We can then calculate the membrane size needed to produce the amount of insulin needed to maintain the health of an astronaut suffering of Type 1 Diabetes Mellitus, which is 0.5 to 1 U per kg per day.[2] The molecule that is used as an example is Novorapid Insulin Aspart, with a weight of 100/3.5mg,[3] on a person of 70 kg $$ M_{Aspart,daily} = {70 {U \over day} \over M_{Aspart}}=2.45 {mg \over day}$$ $$ A_{membrane} = {M_{Aspart,daily} \over ProdRate_{daily}}= 76.92 cm^2 $$ Contour plotting the production rate as a function of secretion rate and binding factor, \(R_{bind}\) and finding the coefficients needed, allows us to evaluate the design in accordance to the needed production of Aspartan. Below is the plots of 3 different membrane sizes,

Finished printing
Figure 13: Membrane of \(5 cm^2\), the black line represents the contour needed to produce insulin enough for one person for one day
Finished printing
Figure 14: Membrane of \(5 cm^2\), the black line represents the contour needed to produce insulin enough for one person for one day
Finished printing
Figure 15: Membrane of \(10 cm^2\), the transparent plane represents the rate needed to produce insulin enough for one person for one day
Finished printing
Figure 15: Membrane of \(20 cm^2\), the black line represents the contour needed to produce insulin enough for one person for one day

With this we are able to conclude that the size of the physical model to produce enough protein for one person is achievable! In the future, focus on modeling secretion rates across membranes would be an ideal way to evaluate experiments with injectisome binding to membranes.

References:

[1] M. C. Schlumberger, A. J. Müller, K. Ehrbar, B. Winnen, I. Duss, B. Stecher, and W. Hardt. Real-time imaging of type III secretion: Salmonella SipA injection into host cells. 2005 Aug 30; 102(35): 12548–12553.

[2] B. HIRSCH, M.D., University of Washington School of Medicine, Seattle, Washington. (2006) Type 1 Diabetes Mellitus and the Use of Flexible Insulin Regimens. Am Fam Physician. 1999 Nov 15;60(8):2343-2352.

[3] EMC Website Here