Difference between revisions of "Team:Aalto-Helsinki/Modeling micelle"
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If we assume that our enzymes have a density that is common to enzymes, our task becomes easier. Based on this paper, the average density of proteins 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> | If we assume that our enzymes have a density that is common to enzymes, our task becomes easier. Based on this paper, the average density of proteins 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 \[V(nm^3)=\frac{0.73\tfrac{nm^3}{g}10^{21}\tfrac{nm^3}{cm^3}}{6.023\cdot 10^-3 \tfrac{nm^3}{Da}} M(Da).\] We can calculate the radius by \[r_{min} = \left( \frac{3V}{4\pi} \right)^{1/3}\] if we know the volume of a sphere, so we get that | + | <p>Using some clever calculation, we get that the relationship between mass and volume for proteins is \[V(nm^3)=\frac{0.73\tfrac{nm^3}{g}10^{21}\tfrac{nm^3}{cm^3}}{6.023\cdot 10^-3 \tfrac{nm^3}{Da}} M(Da).\] We can calculate the radius by \[r_{min} = \left( \frac{3V}{4\pi} \right)^{1/3}\] if we know the volume of a sphere, so we get that \( R_{min}=0.066\cdot M(Da) \).</p> |
<p>The mass of CAR is <a href = "http://www.uniprot.org/uniprot/B2HN69">127 797 DA</a> and the mass of ADO is <a href="http://www.rcsb.org/pdb/explore/explore.do?structureId=4KVS">27 569.15 Da</a>. Now the radius would be 3,5 nm for CAR and 2 nm for ADO. The mass of Gfp is 26 890 Da, which makes its radius roughly 2 nm.</p> | <p>The mass of CAR is <a href = "http://www.uniprot.org/uniprot/B2HN69">127 797 DA</a> and the mass of ADO is <a href="http://www.rcsb.org/pdb/explore/explore.do?structureId=4KVS">27 569.15 Da</a>. Now the radius would be 3,5 nm for CAR and 2 nm for ADO. The mass of Gfp is 26 890 Da, which makes its radius roughly 2 nm.</p> | ||
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<h2 id="adocar">Calculations for Ado and Car</h2> | <h2 id="adocar">Calculations for Ado and Car</h2> | ||
− | <p>We can estimate how many amphiphilic proteins we can theoretically fit in one micelle by calculating how big solid angles they take with attached enzymes. The easiest way to estimate the solid angles is to think the amphiphilic proteins linked with enzymes as cones. We can calculate the solid angle | + | <p>We can estimate how many amphiphilic proteins we can theoretically fit in one micelle by calculating how big solid angles they take with attached enzymes. The easiest way to estimate the solid angles is to think the amphiphilic proteins linked with enzymes as cones. We can calculate the solid angle \( \Omega \) for these by \[ \Omega = 2\pi \left( 1-\cos(\theta) \right), \] where $\theta$ is half of the apex angle. So for CAR we get \[ \Omega_{cone-CAR} = 2\pi \left( 1-\cos\left( \arctan\left(\frac{3.5}{14.1}\right)\right) \right) \approx 0.185 \text{ rad} \] and for ADO \[ \Omega_{cone-ADO} = 2\pi \left( 1-\cos\left( \arctan\left(\frac{2}{9.8}\right)\right) \right) \approx 0.127 \text{ rad}.\]</p> |
<p style="color:gray">--picture of this cone-like structure--</p> | <p style="color:gray">--picture of this cone-like structure--</p> | ||
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<p style="color:gray">--picture of pyramid structure--</p> | <p style="color:gray">--picture of pyramid structure--</p> | ||
− | <p>The solid angle | + | <p>The solid angle \( \Omega\) for this kind of structure can be calculated by \[\Omega = 4\arcsin\left( \sin\left(\theta\right) ^2 \right),\] where \( \theta\) is again half of the apex angle. This yields us \[\Omega_{pyramid-CAR} = 4\arcsin\left( \sin\left(\arctan\left( \frac{3.5}{14.1} \right) \right) ^2 \right) \approx 0.232 \text{ rad}\] and \[\Omega_{pyramid-ADO} = 4\arcsin\left( \sin\left(\arctan\left( \frac{2}{9.8} \right) \right) ^2 \right) \approx 0.16 \text{ rad}.\] </p> |
<p>By this method of calculation we could get at most 32 of both fusion proteins in one micelle.</p> | <p>By this method of calculation we could get at most 32 of both fusion proteins in one micelle.</p> |
Revision as of 09:03, 4 August 2015