MD Mutation436

check the trajectory

We checked the trajectory and got following results:

Reading frame       0 time    0.000   
# Atoms  96555
Precision 0.001 (nm)
Last frame       2000 time 10000.000   

Furthermore, we got some detailed results about the different items during the simulation.

Item	#frames	Timestep (ps)
Step	2001	5
Time	2001	5
Lambda	0	-
Coords	2001	5
Velocities	0	-
Forces	0	-
Box	2001	5

The simulation finished on node 0 Fri Aug 26 08:40:07 2011.

Time
Node (s)	Real (s)	%
34860.474	34860.474	100%
9h41:00

The complete simulation needs 9 hours and 41 minutes to finishing.

Performance
Mnbf/s	GFlops	ns/day	hour/ns
818.560	60.105	24.785	0.968

As you can see in the table above, it takes about 1 hour to simulat 1ns of the system. So therefore, it would be possible to simulate about 25ns in one complete day calculation time.

Back to [Tay-Sachs Disease].

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
System	Water
Protein	Ion
Backbone	NA
MainChain+H	CL
SideChain

Figure 1 shows the visualization with ngmx:

Figure 1: Visualisation of the MD simulation for Mutation 436 with ngmx

Furthermore, we also want to visualise the structure with pymol, which can be seen on Figure 2.

Figure 2: Visualisation of the MD simulation for mutation 436 with pymol

Back to [Tay-Sachs Disease].

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.

Figure 3: Movie of the motion of mutation 436 in stick view.

Figure 4: Movie of the motion of mutation 436 in cartoon view

On Figure 3 and Figure 4, we can see that motion of the protein over time, which was created by the MD simulation.

Back to [Tay-Sachs Disease].

energy calculations for pressure, temperature, potential and total energy

Pressure

Average (in bar)	1.0066
Error Estimation	0.014
RMSD	71.218
Tot-Drift	-0.083422
Minimum (in bar)	-219.7197
Maximum (in bar)	238.8288

The plot with the pressure distribution of the system can be seen here:

Figure 5: Plot of the pressure distribution of the MD system.

As you can see on Figure 5, the pressure in the system is most of the time about 1, but there a big outlier with 250 and -250 bar. So therefore we are not sure, if a protein can work with such a pressure.

Temperature

Average (in K)	297.94
Error Estimation	0.0029
RMSD	0.944618
Tot-Drift	0.00834573
Minimum (in K)	294.63
Maximum (in K)	300.83

The plot with the temperature distribution of the system can be seen here:

Figure 2: Plot of the temperature distribution of the MD system.

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 6 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 relativly cold for a protein to work, because the temperature in our bodies is about 36°C.

Potential

Average (in kJ/mol)	-1.28165e+06
Error Estimation	100
RMSD	1080.9
Tot-Drift	-714.814
Minimum (in kJ/mol)	-1.2852e+06
Maximum (in kJ/mol)	-1.2771e+06

The plot with the potential energy distribution of the system can be seen here:

Figure 3: Plot of the potential energy distribution of the MD system.

As can be seen on Figure 3, the potential engery of the system is between -1.2771e+06 and -1.2852e+06, which is a relativly 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.

Total energy

Average (in kJ/mol)	-1.0519e+06
Error Estimation	100
RMSD	1322.68
Tot-Drift	-708.38
Minimum (in kJ/mol)	-1.0557e+06
Maximum (in kJ/mol)	-1.0463e+06

The plot with the total energy distribution of the system can be seen here:

Figure 4: Plot of the total energy distribution of the MD system.

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 -1.05e+06 and -1.051e+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.

Back to [Tay-Sachs Disease].

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.

Figure 6: Plot of the minimum distance between periodic boundary cells.

Average (in nm)	2.415
Minimum	1.408
Maximum	4.096

As you can see on Figure 6, there is a huge difference between the different time steps and distances. The highest distance is 4.096 nm, whereas the smallest distance is only 1.408 nm. Therefore, there are some states during the simulation in which atoms are close together if they interact and there are some states in which the atoms who interact are far away. Because of the huge bandwidth of minimum distance we can conclude, that the protein is flexible

Back to [Tay-Sachs Disease].

RMSF for protein and C-alpha and Pymol analysis of average and bfactor

Protein

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
Perspective one
Figure 7: Alignment of the original structure (green) and the calculated average structure (turquoise)	Figure 8: Alignment of the original structure (green) and the calculated structure with high B-Factor values (turquoise)	Figure 9: Alignment of the structure with high B-Factor values (red) and the calculated average structure (blue)
Perspective two
Figure 10: Alignment of the original structure (green) and the calculated average structure (turquoise)	Figure 11: Alignment of the original structure (green) and the calculated structure with high B-Factor values (turquoise)	Figure 12: Alignment of the structure with high B-Factor values (red) and the calculated average structure (blue)
RMSD
1.525	0.348	1.671

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:

Figure 13: Plot of the RMSF values over the whole protein.

There are two regions with very high B-factor values. One region at position 150 (Figure 14), and the other region at position 440 (Figure 15). 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.

Figure 14: Part of the alignment between the original structure and the average structure between residue 140 and 160.

Figure 15: Part of the alignment between the original structure and the average structure between residue 430 and 450.

Furthermore, we visualized the B-factors with the pymol selection B-factor method. We calculated the B-factors for the blue protein (Figure 16 and Figure 17). If you see red, this part of the protein is very flexible. The brighter the color, the higher is the flexibility of this residue.

Figure 16: Part of the alignment between the original structure and the average structure between residue 140 and 160. High B-Factor value -> bright color

Figure 17: Part of the alignment between the original structure and the average structure between residue 430 and 450. High B-Factor value -> bright color

In the second picture, you can see, that the color is dark blue. Therefore a peak lower than 0.3 do not mean that there is high flexibility. Therefore, our protein has only one very flexible region and this is around residue 140.

As you can see in the pictures above, especially in the first picture, which is the part with the highest peak in the plot, the structures have a very different position and the alignment in this part of the protein is very bad, although the rest of the alignment is quite good. This also explains the relatively high RMSD values, because of the different positions of the flexible parts of the protein.

C-alpha

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
Perspective one
Figure 18: Alignment of the original structure (green) and the calculated average structure of the c-alpha atoms (turquoise)	Figure 19: Alignment of the original structure (green) and the calculated structure with high B-Factor values of the c-alpha atoms (turquoise)	Figure 20: Alignment of the structure with high B-Factor values of the c-alpha atoms (red) and the calculated average structure of the c-alpha atoms (blue)
Perspective two
Figure 21: Alignment of the original structure (green) and the calculated average structure of the c-alpha atoms (turquoise)	Figure 22: Alignment of the original structure (green) and the calculated structure with high B-Factor values of the c-alpha atoms (turquoise)	Figure 23: Alignment of the structure with high B-Factor values of the c-alpha atoms (red) and the calculated average structure of the c-alpha atoms (blue)
RMSD
1.324	0.277	1.334

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 24:

Figure 24: Distribution of the b-factor values by only regarding the backbone of the protein.

In this case, there is only one high peak at position 150. By observing the whole protein, it was possible to see, that the position of the beta sheet differs extremely between the two models. The other peak at position 440 could not be found in the plot. By a look at the picture above, we can see that the backbone do not differ extremely between the two models. Therefore, in this case the position of the residues has to be very different, which is not important in our case, because we do not regard side chains.

Back to [Tay-Sachs Disease].

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.

Figure 25: Plot with the distribution of the radius of gyration over time

Figure 26: Plot with the distribution of the radius of gyration over time for each axis

	Rg (in nm)	RgX (in nm)	RgY (in nm)	RgZ (in nm)
Average	2.408	2.094	1.853	1.929
Minimum	2.344	1.986	1.581	1.618
Maximum	2.436	2.179	2.102	2.212

Figure 25 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.

If we have a look also to the radius of the different axis (Figure 26), we can see, that only the radius of the x coordinates is mostly consistent around 2nm during the whole simulation. The radius of the z axis shows more deflection than the x coordinates values and decreae during the simulation. Especially at the end of the simulation, the Rg values for z are very low. The y axis values, however, increase during the simulation, but do not reach the values of the x axis. So, therefore, we can see, that most of the Radius of gyration is because of motions in x and at the beginning in z and at the end in y direction.

Back to [Tay-Sachs Disease].

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 27.

Figure 27: Solvent accesibility area of each residue in the protein

Figure 28: Solvent accesibility area of each residue in the protein with standard deviation

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)	0.553
Minimum (in nm^2)	0.003
Maximum (in nm^2)	2.005

The average area per residue during the trajectory is between 0 and 2nm^2, as can be seen on Figure 27. Most of the residues have an area about 0.5nm^2. So therefore, there are some very flexible residues, but most of the residues only move a little bit during the complete simulation. In Figure 28, you can also see the standard deviation, which is very low, so therefore in there are no big outlier, which means that there is no big deviation from the average area and the residues behave in the same way during the trajectory. Furthermore, it is also possible to look at the solvent accesibility of each atom of the complete protein, which can be seen on Figure 29 and Figure 30.
We can see on the Figure 27 that the first 100 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, 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 28, 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.

Figure 29: Solvent accesibility of each atom of the complete protein.

Figure 30: Solvent accesibility of each atom of the complete protein with standard deviation.

As before, the residues at the beginning and the end with a value of 0 are ignored.

Average (in nm^2)	0.032
Minimum (in nm^2)	0
Maximum (in nm^2)	0.558

In Figure 29 the average area per atom is ploted, which shows a similar picture as on Figure 27. 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. There is a huge number of atoms which have an area of about 0nm^2. As before, the standard deviation is not that high (Figure 30). It is a little bit higher than on Figure 28, but that was expected, because this Figure is more detailed and the scale is smaller, but in general Figure 29 and Figure 30 confirm the results of Figure 27 and Figure 28.

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.

Figure 31 shows how much of the area of the protein is accesibile to the surface during the complete simulation. As we saw before, by the gyration radius of the protein, the values differ during the simulation, which shows, that the protein is flexible.

Figure 31: Area of the protein which is accesible to the surface during the simulation.

Figure 32: Area of the protein which is accesible to the surface during the simulation with standard deviation.

Average (in nm^2)	138.727
Minimum (in nm^2)	127.066
Maximum (in nm^2)	146.571

On Figure 31 and Figure 32 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 140nm^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 accessibility 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.

Back to [Tay-Sachs Disease].

hydrogen-bonds

In this case, we differ between hydrogen-bonds between the protein itselfs 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 differ extremely over the time.

Figure 33: Number of hydrogen-bonds in the protein over simulation time

Figure 34: Number of hydrogen-bonds and the possible hydrogen-bonds in the protein over simulation time

	bonds in the protein	possible bonds in the protein
Average	319.787	1534.866
Minimum	292	1483
Maximum	356	1584

On Figure 33 you can see the bonds between the protein. Here you can see that the number differs between 300 bonds and 355. Most of the time, the protein has between 320 and 330 hydrongen-bonds.

If we look at Figure 34, 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.

Figure 35: Number of hydrogen-bonds between the protein and the surronding water.

Figure 36: Number of hydrogen-bonds and the possible hydrogen-bonds between the protein and the surronding water.

	bonds between protein and water	possible bonds between protein and water
Average	853.403	999.847
Minimum	778	905
Maximum	907	1106

If we have a look at the number of bonds between the protein and the water, which are visualized on Figure 35, 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 860 bonds with the water.

On Figure 36 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 is significantly lower than on Figure 34. 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.

This 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.

Back to [Tay-Sachs Disease].

Ramachandran plot

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.

Figure 37: Ramachandran Plot of the wild type.

As we can see on Figure 37, 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.

RMSD matrix

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.

Figure 38: RMSD matrix of our structures during the simulation

As you can see on Figure 38, 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. Therefore, we can conclude, that we do not find very similar structures during the simulation and our protein shows different structures by moving around.

Back to [Tay-Sachs Disease].

cluster analysis

Next, we started a cluster analysis. First of all, we found 231 different clusters.

We visualized all of these cluster structres in Figure 39:

Figure 39: Visualisation of the 231 different clusters

Next we aligned some structures of the cluster and measured the RMSD:

Cluster 1	Cluster 2	RMSD
cluster 1	cluster 2	0.880
cluster 1	cluster 5	0.068

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. Therefore, we can see that the different structures of the simulation are very similar.

To have a better insight into the distribution of the RMSD value between the different clusters, we visualize the distribution in Figure 40.

Figure 40: Distribution of the RMSD value over the different clusters

On Figure 40, it is possible to see, that the distribution is a gaussian distribution, with the highest peak at 0.18 Angstrom. This means, that most of the structures have a RMSD about 0.18 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.

Back to [Tay-Sachs Disease].

internal RMSD

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.

Figure 41: Plot of the distance RMS values in the protein.

Average (RMSD in nm)	0.242
Minimum (RMSD in nm)	0.141
Maximum (RMSD in nm)	0.409

As we can see on Figure 41, at the beginning of our simulation the RMSD is relatively small, but it decreases almost the complete simulation. Only at Time 6000 there is a vally in the plot. The internal RMSD is in the end at 0.25 Angstorm, which is not relatively high. Therefore the protein is big distances in it self.

Back to [Tay-Sachs Disease].