Team:Potsdam/Model
Simulation for our Team by Eindhoven
Team Eindhoven’s project and our LLPs project have a lot of similarities (see our collaboration for more information). Apart from experimenting with their idea they also used a newly designed and a rule-based model system to simulate their experiments outcome more accurately. Through our collaboration they agreed to helping us modelling our system for a better insight into the protein-protein interactions during LLPs.
The first approximation was the concentration of our protein in the yeast cells. Team Eindhoven found a rough estimation of a range, which was 0.1 - 1.4 μM. They therefore set the initial concentration to be 0.5 μM, which lies somewhere in between. For the association rate, we took the same as team Eindhoven used for their simulation, namely 10-5 as found in the paper of Schlosshauer [1].
The known information of the system includes the molecular weight of the protein, being 60.4 kDa and the droplet size, with an average diameter of 1.19 μm, measured by fluorescence microscopy. The weight of a single molecule can be used to approximate the volume of a single molecule with Protein Volume = 1.21 * Molecular Weight [2]. This leads us to a volume of 73.084 Å3 per molecule. As 10 Å = 1 nm this means that 73.084 Å3 = 73.1*10-3 nm3 per molecule.
Like the formula for the volume of the protein, there is a formula for the volume of spheres, which is more generally known, and defined as Volume Sphere = 4/3π * r3. Using this formula, we got a volume of 0.88 μm3 = 0.88 * 109 nm3. When dividing the volumes, you would think that this means that there are about 1,2 * 107 proteins in one droplet. However, this is not quite the case, as you have to take into account that sphere packing has a lower density and that there are different ways of packing, and we don’t know which is applicable yet. If we assume there is a surrounding of 4 molecules, as in a tetrahedral lattice, there are only 4,1 * 106 molecules that should fit in the droplets.
Because simulating that many molecules takes a lot of computer memory, which Eindhoven didn’t have, they rescaled the system. A yeast cell has a volume of 42 ± 2 μm3 [3] and they used a simulation box with the size of 10 μm3. If we rescale the measured droplet size, which is 2% of the yeast volume, we expect to have cluster that also have a size of 2% of the initial amount of molecules. This would indicate that the simulated complexed would have an average size of somewhere around 60 molecules, as the initial amount of molecules was 3010. In the table below you can see what the results of the simulation for different valences are, and that the average complex size of 60 lies between a valency of 3 and of 4.
We used disordered regions that can interact with itself, the valency is not specified and indeed can differ for each protein.
Table 1: Results of the simulation performed by iGEM TU Eindhoven 2017
| Valency 2 | Valency 3 | Valency 4 | Valency 5 | |
|---|---|---|---|---|
| Average Complex Size | 2.7 | 18.0 | 250.8 | 1505 |
| Total Amount of Complexes | 1117 | 167 | 12 | 2 |
Table 2: Densities for different types of sphere packing
| Description | Cubic Close Packing | Hexagonal Lattice | Cubic Lattice | Tetrahedral Lattice |
|---|---|---|---|---|
| Formula | 32 | 33 | 6 | 316 |
| Value | 0,74 | 0,60 | 0,52 | 0,34 |
Really unnecessary and complicated solution to stop the graphs from sliding down the site
[1] Schlosshauer M, Baker D. Realistic protein-protein association rates from a simple diffusional model negleting long-range interactions, free energy barriers, and landscape ruggedness. Protein Science (2004) 13:1660-1669
[2] Harpaz, Gerstein and Chothia (1994) Structure 2, 641-649 (issue of July 15),
http://biotools.nubic.northwestern.edu/proteincalc.html#vol
[3] Cell Biology by the Numbers - Ron Milo, Rob Phillips
Edition: 1st Author(s): Ron Milo, Rob Phillips ISBN: 9780815345374 Format: Paperback Publication Date:December 07, 2015 Content Details:358 pages | 181 illustrationsLanguage:English
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