- 1 check the trajectory
- 2 Visualize in pymol
- 3 Create a movie
- 4 energy calculations for pressure, temperature, potential and total energy
- 5 minimum distance between periodic boundary cells
- 6 RMSF for protein and C-alpha and Pymol analysis of average and bfactor
- 7 Radius of gyration
- 8 solvent accesible surface area
- 9 hydrogen-bonds
- 10 Ramachandran plot
- 11 RMSD matrix
- 12 cluster analysis
- 13 internal RMSD
check the trajectory
We checked the trajectory and got following results:
Reading frame 0 time 0.000 # Atoms 96543 Precision 0.001 (nm) Last frame 2000 time 10000.000
Furthermore, we got some detailed results about the different items during the simulation.
The simulation finished on node 0 Thu Sep 15 23:45:08 2011
|Node (s)||Real (s)||%|
The complete simulation needs 6 hours and 13 minutes to finishing.
As you can see in the table above, it takes about half an hour to simulate 1ns of the system. So therefore, it would be possible to simulate about 40ns in one complete day calculation time.
Visualize in pymol
First of all, we visualized the simulation with with ngmx, because it draws bonds based on the topology file. ngmx gave the user the possibility to choose different parameters. Therefore, we decided to visualize the system with following parameters:
|Group 1||Group 2|
Figure 1 shows the visualization with ngmx:
Furthermore, we also want to visualise the structure with pymol, which can be seen on Figure 2.
Create a movie
Next, we want to visualize the protein with pymol. Therefore, we extracted 1000 frames from the trajectory, leaving out the water and jump over the boundaries to make continouse trajectories.
The program asks for the a group as output. We only want to see the protein, therefore we decided to choose group 1.
Here you can see the movie in stick line and cartoon modus.
On Figure 3 and Figure 4, we can see that motion of the protein over time, which was created by the MD simulation.
energy calculations for pressure, temperature, potential and total energy
|Average (in bar)||1.00711|
The plot with the pressure distribution of the system can be seen here:
As you can see on Figure 5, the pressure in the system is most of the time about 0, but there a big outlier with about 232 and about -217 bar. So therefore we are not sure, if a protein can work with such a pressure.
|Average (in K)||297.94|
|Minimum (in K)||294.82|
|Maximum (in K)||301.31|
The plot with the temperature distribution of the system can be seen here:
As you can see on Figure 2, most of the time the system has a temperature about 298K. The maximal difference between this average temperature and the minimum/maxmimum temperature is only about 7 K, which is not that high. But we have to keep in mind, that only some degree difference can destroy the function of a protein. 298 K is about 25°C, which is relatively cold for a protein to work, because the temperature in our bodies is about 36°C.
|Average (in kJ/mol)||-1.2815e+06|
|Minimum (in kJ/mol)||-1.2853e+06|
|Maximum (in kJ/mol)||-1.2778e+06|
The plot with the potential energy distribution of the system can be seen here:
As can be seen on Figure 3, the potential energy of the system is between -1.2853e+06 and -1.2778e+06, which is a relatively low energy. Therefore this means that the protein is stable. So we can suggest, that the protein with such a low energy is able to function and is stable and therefore, our simulation could be true. Otherwise, if the energy of the simulated system is too high, we can not trust the results, because the protein is too instable to work.
|Average (in kJ/mol)||-1.05177e+06|
|Minimum (in kJ/mol)||-1.05599e+06|
|Maximum (in kJ/mol)||-1.04718e+06|
The plot with the total energy distribution of the system can be seen here:
As we can see on Figure 4 above, the total energy of the protein is a little bit higher than the potential energy of the protein. In this case, the energy is between -1.05599e+06 and -1.04718e+06. But these values are already in a range, where we can suggest that the energy of the protein is low enough so that this one can work.
minimum distance between periodic boundary cells
Next we try to calculate the minimum distance between periodic boundary cells. As before, the program asks for one group to use for the calculation and we decided to use only the protein, because the calculation needs a lot of time and the whole system is significant bigger than only the protein. So therefore, we used group 1.
Here you can see the result of this analysis.
|Average (in nm)||3.139|
As you can see on Figure 6, there is a huge difference between the different time steps and distances. The highest distance is up to 4 nm, whereas the smallest distance is only about 2nm. So in general the distances between the parts of the protein which interact with each other are between 2 and 4nm, which is not that near. Because of the jumping curve in the plot we can conclude, that the protein is flexible, because the minimum distance of the interaction is always different which means, that atoms which were in contact lost it and therefore the minimum distance decrease or increase.
RMSF for protein and C-alpha and Pymol analysis of average and bfactor
First of all, we calculate the RMSF for the whole protein.
The analysis produce two different pdb files, one file with the average structure of the protein and one file with high B-Factor values, which means that the high flexbile regions of the protein are not in accordance with the original PDB file.
To compare the structure we align them with pymol with the original structure.
|original & average||original & B-Factors||average & B-Factors|
The structure with the high B-factors is the most similar structure (Figure 8 and Figure 11) compared with the original structure from PDB (Figure 7 and Figure 10). The average structure is not that similar (Figure 10 and Figure 12). But we know, that the regions with high B-Factors are very flexible, and therefore in the structure downloaded from the PDB, the protein is in another state, because of its flexible regions. Therefore, because of the low RMSD between the high B-factors structure and the original structure we can see, that the simulation predicts the structure quite good.
Furthermore, we got a plot of the RMSF values of the protein, which can be seen in Figure 13:
There are a lot regions with high B-factor values. The highest B-factor value can be found on position 150 (Figure 14), but there are also high values on position 110 (Figure 13), 290 (Figure 16), 320 (Figure 17), 410 (Figure 18), 460 (Figure 19) and 490 (Figure 20). If we compare the picture of the original and the average structure, we can see that most of the regions build a very good alignment, whereas some regions vary in their position. Therefore, we want to compare, if these regions are the regions with very high B-factor values.
As we can see in the pictures above (Figure 14 - Figure 20),we can see that there is always a little difference between the two structures. Therefore, this regions seem to be flexible.
Furthermore, we visualized the B-factors with the pymol selection B-factor method. We calculated the B-factors for the blue protein (Figure 21 - Figure 27). If you see red, this part of the protein is very flexible. The brighter the color, the higher is the flexibility of this residue.
In Figure 21 and Figure 22, the color of the protein is turquoise, which shows that there is a relatively high B-factor value. Figure 23 is also colored in turquoise. The pictures which show the center of the protein (Figure 24 - Figure 26) also show only a dark blue protein which means that there is a low B-factor value and therefore the plot or the picture are wrong. The last picture (Figure 27) shows us that there is a high B-factor value in the chain.
Now we repeat the analysis done for the protein for the C-alpha atoms of the protein. Therefore, we followed the same steps as in the section above.
To compare the structure we align them with pymol with the original structure.
|original & average||original & B-Factors||average & B-Factors|
As in the section above, the RMSD between the structure with high B-factor values and the original structure is the most similar (Figure 19 and Figure 22). This was expected, because we used twice the same model, but in this case we neglecte the residues of the atoms. But the backbone of the protein remains the same. The other two models (Figure 18, Figure 20, Figure 21 and Figure 23) have nearly the same RMSD value and therefore there are equally.
Furthermore, we got a plot of the RMSF values of the protein, which can be seen on Figure 34:
In this case, there are only three high peaks at position 150, 280 and 310. By comparison to figure 13, these high peaks can also be found in this plot. Furthermore, it was possible to observe these high B-factor values in the pictures.
Radius of gyration
Next, we want to analyse the Radius of gyration. Therefore we use g_gyrate and use only the protein for the calculation.
|Rg (in nm)||RgX (in nm)||RgY (in nm)||RgZ (in nm)|
Figure 35 shows the radius of gyration over the simulation time. The Radius of gyration is the RMS distance of its parts from its center or gyration axis. On the plot it could be seen, that the average radius is about 2.4, but there are big differences, which means, that the protein is flexible. The distance between the different parts of the protein and the center differs so the protein seems to pulsate, because there is a periodic curve which shows the loss and the gain of space the protein needs. But over time, the radius grows, so in the beginning the protein has a radius about 2.39, whereas in the end of the simulation the radius is about 2,43.
If we have a look also to the radius of the different axis on Figure 36, we can see, that the radius of the x coordinates is most similar during the whole simulation. The radius of the z axis shows more deflection than the x coordinates values, but both values are in a similar range. The y axis values, however, is significant lower so therefore, there is less different between the positions of the y axis values. Especially at the end of the simulation, the Rg values for y are very low. So, therefore, we can see, that most of the Radius of gyration is because of motions in x and z direction and not so much about motions in y direction.
solvent accesible surface area
Next, we analysed the solvent accesible surfare area of the protein, which is the area of the protein which has contacts with the surronding environment, mainly water.
First of all, we have a look at the solvent accesibility of each residue, which can be seen on Figure 36.
The following table list the average, minimum and maximum values of the Solvent accessibility for each residue in the protein. The residues at the beginning and at the end of the simulation which have a value of 0 are ignored.
|Average (in nm^2)||0.537|
|Minimum (in nm^2)||0.004|
|Maximium (in nm^2)||2.058|
The solvent accessibility area is the area of each residue which is accessible to the surface of the protein. In Figure 37 and Figure 38 we can see the average solvent accessibility of each residue over the complete simulation. Therefore, this means, that each residue can be more or less on the solvent in each state of the simulation.
We can see on the Figure 37 that the first 89 and the last 100 residues have an average solvent accessibility of 0, therefore, this means these residues are always completely in the interior of the protein. A lot of residues have a solvent accessibility about 0.5nm^2, and there are only some outlier with an accessibility of more than 1.5nm^2. So therefore, there are some residues which are almost always on the surface, a lot of residues which are partly or temporarly on the surface and also a lot of residues which are never on the surface. If we look at Figure 38, we can see that the standard deviation is relatvely low, which means that there are no states of the system in which some residues with low or no solvent accessibility are complete accessible to the surface. If the standard deviation would be very high, it could be possible that there are states in the simulation which are very unusual. But this is not the case in our simulation.
As before, we only regard the atoms with an area of more than 0 in the following table.
|Average (in nm^2)||0.031|
|Minimum (in nm^2)||0|
|Maximum (in nm^2)||0.560|
In Figure 39 the average area per atom is ploted, which shows a similar picture as on Figure 37, but at the beginning there are no atoms with no surface accessibility. In general the atoms have not that big area as the residues, which is clear, because the area of the residues consist of the area of the single atoms which belong to this residue. As before, the standard deviation which is plotted in Figure 40, is not that high. It is a little bit higher than on Figure 38, but that was expected, because this Figure is more detailed and the scale is smaller, but in general Figure 39 and Figure 40 confirm the results of Figure 37 and Figure 38. At the end of the plot, there are a lot of atoms which have a surface accessibility area of 0, which is consistent with the result of the residues. But at the beginning of the plot, there are no atoms which have no surface accessibility area. But there are a lot of atoms with low or no accessibility area in the plot and we know, that gromacs is a non-deterministic algorithm. Therefore, this result should be consistent with the results of the different residues.
|Average (in nm^2)||135.036|
|Minimum (in nm^2)||129.084|
|Maximum (in nm^2)||142.218|
On Figure 41 and Figure 42 we can see the solvent accessibility surface of the protein during the simulation. The surface accessibility of the hydrophobic residues has an area of about 135nm^2, which is relatively consistent during the complete simulation. If we have a closer look to the distribution of the different pysiocochemical properties and the surface accessibilit of them that the area of the hydrophobic amino acids is larger than the are of the hydrophilic amino acids. This is really surprising, because in general hydrophobic amino acids prefer a location in the core of the protein and not on the surface.
In this case, we differ between hydrogen-bonds between the protein itself and bonds between the protein and the water.
As before, it is possible to see in the plot, that the protein is flexible, because the number of bonds differs extremely over the time.
On Figure 43 you can see the bonds between the protein. Here you can see that the number differs between 300 bonds and 360. Most of the time, the protein has between 320 and 340 hydrogen-bonds. If we look at Figure 44, we can see, that there are a lot more possible hydrogen bindings than occurred in real. There are about 1500 pairs of atoms with a distance less than 0.35nm, which is a distance where a hydrogen bond is theoretically possible. So therefore, you can see, that the protein has only a small number of hydrogen bonds, about 20% of all possible hydrogen bonds. Therefore, this protein could be very flexible, because of the small number of hydrogen bonds.
|bonds in the protein||possible bonds in the protein|
If we have a look at the number of bonds between the protein and the water, which are visualized on Figure 45, we can see that there are a lot more bonds between protein and water than in between the protein. The number differs between 800 and 900 and there there are about 3 times more bonds between the protein and the water. Over the simulation time, the number of bonds between water and protein grows in average. But most of the time, the protein has between 840 and 850 bonds with the water. On Figure 46 we can see how many pairs of residues have a distance of less than 0.35 nm, which means these pairs are able to build hydrogen bonds with each other. The distance of possible and real occurring hydrogen bonds, shown in Figure 46, is significantly lower than on Figure 42. So therefore, in this case almost 80% of all possible hydrogen bonds are also real hydrogen bonds. Therefore, we can see that the binding between protein and water is really stable.
|bonds between protein and water||possible bonds between protein and water|
The high number of hydrogen bonds between protein and water is no surprise, because every residue on the surface has contact with water, whereas in the protein there are a lot of amino acids which do not have contact partners, because the other amino acids are too far away.
Now, we want to have a closer look to the secondary structure of the protein during the simulation. Therefore, we used a Ramachandran plot to analyse the phi and psi torsion angles of the backbone to get a better understanding of the secondary structure during the simulation.
As we can see on Figure 47, there are a lot of beta sheets, alpha helices and right-handed alpha helices. The white regions are the regions where no secondary structure can be found, which is right.
Next we analysed the RMSD values. Therefore, we used a RMSD matrix. This is useful to see if there are groups of structures over the simulation that share a common structure. These groups will have lower RMSD values withing their group and higher RMSD values compared to structure which are not in the group.
The following matrix shows the RMSD values of our structures.
As you can see on Figure 48, there is one big group which is colored in green, but it is not possible to find any very dense groups which all have a very low RMSD compared to each other. Only near on the diagonal there are some structures which are colored in cyan, but in general, most of the structures are colored in green which means a RMSD value of about 0.15 Angstrom. So we can see that there are differences of the protein structure during the simulation and therefore we can conclude that this protein is very flexible.
Next, we started a cluster analysis. First of all, we found 225 different clusters.
We visualized all of these cluster structures on Figure 49:
Next we aligned some structures of the cluster and measured the RMSD:
|Cluster 1||Cluster 2||RMSD|
|cluster 1||cluster 2||0.654|
|cluster 1||cluster 5||0.899|
|cluster 30||cluster 100||1.391|
The RMSD values of the different structures are very similar, which can be seen in the picture above. Furthermore, the RMSD values of the different structures of the clusters are very low. But if we align structures which are far away in number, the RMSD value increase, which shows us that over the simulation time the differences between the start structure and the simulated structures increase. Therefore, we can see that the different structures of the simulation are very similar, but over the time they change more and more.
To have a better insight into the distribution of the RMSD value between the different clusters, we visualize the distribution in Figure 50.
On Figure 50, it is possible to see, that the distribution is a gaussian distribution, with the highest peak at 0.2 Angstrom. This means, that most of the structures have a RMSD about 0.2 Angstrom compared to the start structure. This value is not that high, but it is a strong hint, that the protein is flexible during the simulation.
The last point in our analysis is the calculation of the internal RMSD values. This means the distances between the single atoms of the protein, which can us help to obtain the structure of the protein.
|Average (RMSD in nm)||0.238|
|Minimum (RMSD in nm)||4.89e-7|
|Maximum (RMSD in nm)||0.312|
As we can see on figure 51, at the beginning of our simulation the RMSD is relatively small, but it decreases almost the complete simulation. The internal RMSD is in the end at 0.28 Angstorm, which is not relatively high. Therefore the protein has no big distances in it self.