Difference between revisions of "Team:Aalto-Helsinki/Modeling micelle"
m (previos page -> parent page) |
m |
||
(16 intermediate revisions by 4 users not shown) | |||
Line 49: | Line 49: | ||
#sidenav { display: none; } | #sidenav { display: none; } | ||
} | } | ||
+ | /* Background pic */ | ||
+ | .compscreens { | ||
+ | background-repeat: repeat-y; | ||
+ | background-image: url("https://static.igem.org/mediawiki/2015/1/11/Aalto-Helsinki_modeling_background.png"); | ||
+ | background-size: 100%; | ||
+ | } | ||
</style> | </style> | ||
Line 60: | Line 66: | ||
− | + | <div class="compscreens"> | |
<div class="inner-container"> | <div class="inner-container"> | ||
Line 71: | Line 77: | ||
<figure style="margin-bottom:2%;"> | <figure style="margin-bottom:2%;"> | ||
− | <img src="https://static.igem.org/mediawiki/2015/a/a2/Aalto-Helsinki_hbd_pathway_car_ado_butyraldehyde.png" style="max-width:100%;" /> | + | <a href="https://static.igem.org/mediawiki/2015/a/a2/Aalto-Helsinki_hbd_pathway_car_ado_butyraldehyde.png"><img src="https://static.igem.org/mediawiki/2015/a/a2/Aalto-Helsinki_hbd_pathway_car_ado_butyraldehyde.png" style="max-width:100%;" /></a> |
<figcaption><b>Figure 1:</b> Propane pathway</figcaption> | <figcaption><b>Figure 1:</b> Propane pathway</figcaption> | ||
</figure> | </figure> | ||
− | <p>The product of second to last enzyme of our pathway, butyraldehyde, is toxic to the cell. Because of that and about 15 naturally occurring butyraldehyde-consuming enzymes in the cell it is essential for the propane production that | + | <p>The product of second to last enzyme of our pathway, butyraldehyde, is toxic to the cell. Because of that and about 15 naturally occurring <a href="http://www.nature.com/ncomms/2014/140902/ncomms5731/full/ncomms5731.html#ref29" target="_blank">butyraldehyde-consuming enzymes</a> in the cell, it is essential for the propane production that butyraldehyde goes swiftly to the enzyme we want it to go to, ADO. As the solution to this our team wanted to put CAR and ADO close together in a micelle so butyraldehyde would go to ADO with a higher probability than to any other competing enzyme in the cell.</p> |
− | <p>We have made a <a href="https://2015.igem.org/Team:Aalto-Helsinki/Modeling_synergy">model of effectiveness of having enzymes close together</a>, but our team also wanted to know if the micelle structure was possible in the first place. We know | + | <p>We have made a <a href="https://2015.igem.org/Team:Aalto-Helsinki/Modeling_synergy">model of effectiveness of having enzymes close together</a>, but our team also wanted to know if the micelle structure was possible in the first place. <a href="http://www.nature.com/nmat/journal/v14/n1/full/nmat4118.html" target="_blank">We know</a> that it is possible to form the micelle without any proteins at the end and with green fluorecent protein (GFP), but could CAR and ADO be part of this kind of structure? </p> |
</section> | </section> | ||
Line 94: | Line 100: | ||
<h4 id="micellestructure">Micelle structure</h4> | <h4 id="micellestructure">Micelle structure</h4> | ||
− | <p>The micelle is formed by amphiphilic proteins that have both hydrophilic and hydrophobic parts. At the end of the hydrophilic part there is a short | + | <p>The micelle is formed by amphiphilic proteins that have both hydrophilic and hydrophobic parts. At the end of the hydrophilic part there is a short (8 aa) oligopeptide linker that attaches CAR or ADO to the amphiphilic part.</p> |
Line 102: | Line 108: | ||
</figure> | </figure> | ||
− | <p> | + | <p>As the bilayer structures formed by amphiphilic proteins <a href="http://www.nature.com/nmat/journal/v14/n1/full/nmat4118.html" target="_blank">have been reported</a> to be 10 nm thick, we can deduce that the amphiphilic proteins are 5 nm long, 2.5 nm for both hydrophilic and hydrophobic parts. The linker consists of eight amino acids (GSPTGAST), and for each amino acid, the maximum lenght is 0.38 nm. From this we can calculate that at most the length of one linker is 2.8 nm. If the linker would form an α-helical structure, then the <a href="https://books.google.fi/books?id=2yRDWkHhN9QC&lpg=PA9&ots=mQiHtY9-W_&dq=length%20of%20extended%20peptide%20bond&hl=sv&pg=PA14#v=onepage&q&f=false" target="_blank" style="padding:0;">length for one amino acid</a> would be about 0.15 nm so one 8 amino acid linker would be 1.2 nm long. However, we can estimate that the linkers are rather straight, since running the structure in <a href="http://mobyle.rpbs.univ-paris-diderot.fr">peptide structure prediction software</a> doesn't yield strong folding or helical structure. Thus we predict our linker lenght to be 2.8 nm. CAR uses two subsequent linkers whereas ADO uses one. </p> |
<p>One problem we are facing here is that we need some sort of approximations for the enzymes’ radii. Since we don’t know the exact three-dimensional structure of the proteins, we approximated the enzymes as perfect spheres. | <p>One problem we are facing here is that we need some sort of approximations for the enzymes’ radii. Since we don’t know the exact three-dimensional structure of the proteins, we approximated the enzymes as perfect spheres. | ||
− | If we assume that our enzymes have a density that is common to enzymes, our task becomes easier. | + | If we assume that our enzymes have a density that is common to enzymes, our task becomes easier. <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055910/">The average density of proteins</a> is 1.37 g/ml. Because we want to calculate the volume, and in effect, their radius, we invert this value, thus getting 0.73 ml/g.</p> |
<p>Using some clever calculation, we get that the relationship between mass and volume for proteins is | <p>Using some clever calculation, we get that the relationship between mass and volume for proteins is | ||
Line 131: | Line 137: | ||
</div> | </div> | ||
</div> | </div> | ||
− | |||
− | |||
Line 144: | Line 148: | ||
and for ADO | and for ADO | ||
\[ \Omega_{cone\text{-}ADO} = 2\pi \left( 1-\cos\left( \arctan\left(\frac{2}{9.8}\right)\right) \right) \approx 0.127 \text{ sr}.\]</p> | \[ \Omega_{cone\text{-}ADO} = 2\pi \left( 1-\cos\left( \arctan\left(\frac{2}{9.8}\right)\right) \right) \approx 0.127 \text{ sr}.\]</p> | ||
− | |||
− | |||
<p>This means that there would be at most 40 of both ADO and CAR, totalling 80 fusion proteins in one micelle by this method of calculation.</p> | <p>This means that there would be at most 40 of both ADO and CAR, totalling 80 fusion proteins in one micelle by this method of calculation.</p> | ||
<p>However, when approximating enzymes with spheres it is not possible for them to fill the whole surface of the micelle; there will always be gaps. This is why it might be better to approximate the solid angle these complexes of amphiphilic proteins and enzymes by using pyramids instead of cones. </p> | <p>However, when approximating enzymes with spheres it is not possible for them to fill the whole surface of the micelle; there will always be gaps. This is why it might be better to approximate the solid angle these complexes of amphiphilic proteins and enzymes by using pyramids instead of cones. </p> | ||
− | |||
− | |||
<p>The solid angle \( \Omega\) for this kind of structure can be calculated by | <p>The solid angle \( \Omega\) for this kind of structure can be calculated by | ||
Line 187: | Line 187: | ||
<h4>Micelle structure</h4> | <h4>Micelle structure</h4> | ||
+ | |||
+ | <figure style="float:right;margin-left:20px;"> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/e/e4/Aalto-Helsinki_micelle_circle_approach_2.png" style="width:200px;"/> | ||
+ | <figcaption><b>Figure 7:</b><br/>2d simplification of the micelle</figcaption> | ||
+ | </figure> | ||
<p>In the first approach we didn't take into account anything else from amphiphilic proteins than the lengths. However we can calculate the width of the protein a bit similarly as we calculated the sizes of the enzymes.</p> | <p>In the first approach we didn't take into account anything else from amphiphilic proteins than the lengths. However we can calculate the width of the protein a bit similarly as we calculated the sizes of the enzymes.</p> | ||
Line 192: | Line 197: | ||
<p>We know that the length of the amphiphilic proteins is 5 nm. If we assume their density to be that of other proteins and assume that they are roughly cylinder-shaped, we can calculate the radius for the cylinder.</p> | <p>We know that the length of the amphiphilic proteins is 5 nm. If we assume their density to be that of other proteins and assume that they are roughly cylinder-shaped, we can calculate the radius for the cylinder.</p> | ||
− | <p> | + | <p>The mass of amphiphilic protein is <a href="" target="_blank">18600 daltons</a>. Considering that the protein consists of two domains of roughly similar size (9300 Da) and from <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3055910/" targe="_blank">equation</a> |
+ | \[M (Da) = 825 * V (nm3)\] | ||
+ | we get for volume \(V = 11.3\; \text{nm}^3\). Now for radius \(r\) of amphiphilic proteins, we get \[ r = \sqrt{\frac{V}{h \cdot \pi}} \approx 0.85 \; \text{nm}, \] where \(h\) is the length of the cylinder. </p> | ||
− | <p>Now that we approximate the amphiphilic proteins as a cylinder there will be empty space in the middle of the micelle. | + | <p>Now that we approximate the amphiphilic proteins as a cylinder there will be empty space in the middle of the micelle. This shouldn't be a problem since in real world there are many non-polar molecules in the cell that are ready to take that space</p> |
− | <p>Now that we think that there is empty space in the middle of the micelle we must calculate the radius of it. This can be calculated with similar triangles from ADO fusion protein. See | + | <p>Now that we think that there is empty space in the middle of the micelle we must calculate the radius of it. This can be calculated with similar triangles from ADO fusion protein. See figures 8 and 9 below.</p> |
− | < | + | |
+ | <div class="row"> | ||
+ | <div class="col-md-6 vcenter"> | ||
+ | <figure style="margin-left:100px;"> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/f/ff/Aalto-Helsinki_New_CAR_with_width.png" style="width:280px;" /> | ||
+ | <figcaption style="margin-top:2%;"><b>Figure 8:</b> CAR fusion protein</figcaption> | ||
+ | </figure> | ||
+ | </div> | ||
+ | |||
+ | <div class="col-md-5 vcenter"> | ||
+ | <figure style="margin-left:80px;"> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/1/12/Aalto-Helsinki_New_ADO_with_width.png" style="width:260px;" /> | ||
+ | <figcaption style="margin-top:2%;"><b>Figure 9:</b> ADO fusion protein</figcaption> | ||
+ | </figure> | ||
+ | </div> | ||
+ | </div> | ||
Line 211: | Line 233: | ||
\[\Omega_{pyramid\text{-}ADO} = 4\arcsin\left( \sin\left(\arctan\left( \frac{2}{17.04} \right) \right) ^2 \right) \approx 0.0544 \text{ sr}\] and thus we could fit \( (4\pi)/(0.1048+0.0544)\approx 78\) of both CAR and ADO in one micelle, 156 in total.</p> | \[\Omega_{pyramid\text{-}ADO} = 4\arcsin\left( \sin\left(\arctan\left( \frac{2}{17.04} \right) \right) ^2 \right) \approx 0.0544 \text{ sr}\] and thus we could fit \( (4\pi)/(0.1048+0.0544)\approx 78\) of both CAR and ADO in one micelle, 156 in total.</p> | ||
− | <p>With overlapping structure explained before, we had to check whether we would need to make any changes into this approach. We calculated the angle \(\gamma\) from | + | |
+ | <div class="row"> | ||
+ | <div class="col-md-6 vcenter"> | ||
+ | <figure style="margin-left:100px; margin-bottom:3%;"> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/e/e5/Aalto-Helsinki_CAR_and_ADO_with_width.png" style="width:200px;" /> | ||
+ | <figcaption style="margin-top:2%;"><b>Figure 10:</b> Overlapping structure</figcaption> | ||
+ | </figure> | ||
+ | </div> | ||
+ | |||
+ | <div class="col-md-5 vcenter"> | ||
+ | <figure style="margin-left:80px;"> | ||
+ | <img src="https://static.igem.org/mediawiki/2015/f/f2/Aalto-Helsinki_lower_Micelle_parts_w_angles.png" style="width:260px;" /> | ||
+ | <figcaption style="margin-top:2%;"><b>Figure 11:</b> Amphiphilic proteins in overlapping structure</figcaption> | ||
+ | </figure> | ||
+ | </div> | ||
+ | </div> | ||
+ | |||
+ | <p>With overlapping structure explained before, we had to check whether we would need to make any changes into this approach. We calculated the angle \(\gamma\) from figure 10 and compared it to \(\beta\) from figure 11. The latter is bigger with \(\beta = 2 \tan\left(\tfrac{0.85}{7.24}\right) \approx 0.236\). This yields us \[\Omega_{CAR\&ADO} = 4\arcsin\left( \sin\left( 2 \tan \left(\tfrac{0.85}{7.24} \right) \right) ^2 \right) \approx 0.2186 \text{ sr}\] and thus about \( (4\pi)/0.2186\approx 57\) CAR fusion proteins and about 114 ADO fusion proteins making the whole micelle size 171.</p> | ||
+ | |||
<h4 id="adocar">Calculations for GFP</h4> | <h4 id="adocar">Calculations for GFP</h4> | ||
Line 227: | Line 267: | ||
<h2 id="discussion">Discussion</h2> | <h2 id="discussion">Discussion</h2> | ||
− | <p>The goal of this geometrical model was to understand if it was possible to form micelles which have CAR or ADO at the end of the amphiphilic proteins. The main thing was to prove that the proteins aren’t too big to have an impact on micelle formation, and since we already knew that this arrangement works with green fluorescent protein it was only natural to compare these two | + | <p>The goal of this geometrical model was to understand if it was possible to form micelles which have CAR or ADO at the end of the amphiphilic proteins. The main thing was to prove that the proteins aren’t too big to have an impact on micelle formation, and since we already knew that this arrangement works with green fluorescent protein it was only natural to compare these two.</p> |
− | <p> | + | <p>Based on our calculations the green fluorescent protein (GFP) micelles have upper bound of 78-98 amphiphilic fusion proteins per micelle and the micelles with CAR and ADO 64-111 amphiphilic fusion proteins per micelle (approach I). The number of amphiphilic fusion proteins per micelle is thus about the same with GFP as with CAR and ADO. The GFP micelles have been <a href="http://www.nature.com/nmat/journal/v14/n1/full/nmat4118.html" target="_blank">shown</a> to form , so it would appear possible for CAR and ADO micelles to form as well.</p> |
+ | |||
+ | <p>On approach II the proof is weaker, but the difference of 156-200 and 230-293 isn't so big that the formation should be doubted very much.</p> | ||
<p>It needs to be noted that we didn’t even aim to be accurate in the assembly of ADO and CAR on a spherical surface. The best possible formation is very hard to find in this situation and there wasn’t any need to be that accurate in our calculations. Furthermore, since we don't know what shapes the enzymes or amphiphilic proteins are, we had to estimate.</p> | <p>It needs to be noted that we didn’t even aim to be accurate in the assembly of ADO and CAR on a spherical surface. The best possible formation is very hard to find in this situation and there wasn’t any need to be that accurate in our calculations. Furthermore, since we don't know what shapes the enzymes or amphiphilic proteins are, we had to estimate.</p> | ||
<p>Even though our model seems to prove that the formation of these micelles is possible, there are lots of things we couldn’t take into account that might have effects on micelle formation and make it impossible. We didn't consider any forces that might form between our proteins, thus rendering micelles impossible. It might well be that even though this is geometrically possible in reality micelles can not form. However, finding out the forces between these enzymes might prove to be extremely difficult, which is why we did not pursue that avenue of thought.</p> | <p>Even though our model seems to prove that the formation of these micelles is possible, there are lots of things we couldn’t take into account that might have effects on micelle formation and make it impossible. We didn't consider any forces that might form between our proteins, thus rendering micelles impossible. It might well be that even though this is geometrically possible in reality micelles can not form. However, finding out the forces between these enzymes might prove to be extremely difficult, which is why we did not pursue that avenue of thought.</p> | ||
+ | |||
+ | <p style="margin-bottom:0;padding-bottom:10%;">Although the model doesn't give certain proof of micelle formation, it gives strong enough proof that that we can try this in laboratory.</p> | ||
</section> | </section> | ||
+ | </div> | ||
</div> | </div> | ||
</div></div></div> <!--These are the closing tags for div id="mainContainer" and div id="contentContainer". The corresponding opening tags appear in the template that is {{included}} at the top of this page.--> | </div></div></div> <!--These are the closing tags for div id="mainContainer" and div id="contentContainer". The corresponding opening tags appear in the template that is {{included}} at the top of this page.--> | ||
+ | <p style="margin-bottom:0"> | ||
<!-- Scirpt for beautiful scrolling inside the page: smooth transitions and we show in what section the reader is. --> | <!-- Scirpt for beautiful scrolling inside the page: smooth transitions and we show in what section the reader is. --> | ||
<script src="https://2015.igem.org/Team:Aalto-Helsinki/ResponsiveNavScript?action=raw&ctype=text/javascript"></script> | <script src="https://2015.igem.org/Team:Aalto-Helsinki/ResponsiveNavScript?action=raw&ctype=text/javascript"></script> | ||
− | |||
− | |||
− | |||
− |
Latest revision as of 18:29, 16 September 2015