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 Friday August 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 runtime.

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 simulate 1 nano second (ns) of the system. So therefore, it would be possible to simulate about 25ns in one complete day calculation time.

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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: Visualization of the MD simulation for Mutation 436 with ngmx

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

Figure 2: Visualization of the MD simulation for mutation 436 with PyMol

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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 continuous 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.

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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 outliers 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 6: Plot of the temperature distribution of the MD system.

As you can see on Figure 6, most of the time the system has a temperature about 298K. The maximal difference between this average temperature and the minimum/maximum 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 relatively 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 7: Plot of the potential energy distribution of the MD system.

As can be seen on Figure 7, the potential energy of the system is between -1.2771e+06 and -1.2852e+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.

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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 8: Plot of the total energy distribution of the MD system.

As we can see on Figure 8 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.

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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 9: 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 9, 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

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RMSF for protein and C-alpha and PyMol analysis of average and b-factor

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 flexible 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 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)
Perspective two
Figure 13: Alignment of the original structure (green) and the calculated average structure (turquoise)	Figure 14: Alignment of the original structure (green) and the calculated structure with high B-Factor values (turquoise)	Figure 15: 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 compared to the original structure from PDB (Figure 11 and Figure 13). The average structure is not that similar (Figure 10 and Figure 13). But we know, that the regions with high B-factor values 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 16:

Figure 16: 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 17), and the other region at position 440 (Figure 18). 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 17: Part of the alignment between the original structure and the average structure between residue 140 and 160.

Figure 18: 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 19 and Figure 20). 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 19: Part of the alignment between the original structure and the average structure between residue 140 and 160. High B-Factor value -> bright color

Figure 20: 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. Hence, 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 very different positions 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.

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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 to the original structure.

original & average	original & B-Factors	average & B-Factors
Perspective one
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)
Perspective two
Figure 24: Alignment of the original structure (green) and the calculated average structure of the c-alpha atoms (turquoise)	Figure 25: Alignment of the original structure (green) and the calculated structure with high B-Factor values of the c-alpha atoms (turquoise)	Figure 26: 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

The structure alignments and the according RMSD delivers the same results as in the section above. The RMSD of the alignment between the structure with high B-factor and the original one is the smallest one which indicates that this structures align best (Figure 22 and Figure 25). This was expected, because we used twice the same model, but in this case we neglected the residues of the atoms. But the backbone of the protein remains the same. The other two models (Figure 21, Figure 23, Figure 24 and Figure 26) 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 27:

Figure 27: 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. Having a closer look at the protein it can be seen that the position of the beta sheets differ extremely between the two models. The other peak at position 440 could not be found in the plot. Looking at the pictures above, we can see that the backbones of the two different models not differ extremely. This means that the position of the residues differ a lot, which is not important for us, because we do not regard side chains.

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Radius of gyration

Next, we want to analyze the radius of gyration. Therefore we use g_gyrate and use only the protein for the calculation.

Figure 28: Plot with the distribution of the radius of gyration over time

Figure 29: 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 28 shows the radius of gyration over the simulation time. The radius of gyration is the RMS distance from the outer parts of the protein to the protein center or gyration axis. The plot displays that the average radius is about 2.4 with some fluctuation. This indicates that the protein is flexible. Furthermore, the fluctuation is a periodic curve which shows the loss and the gain of space the protein needs. This suggest that the protein pulsates.

If we have a further look at the radius of the different axis (Figure 29), we can see, that the radius of the x coordinates is the only consistent one at about 2nm during the simulation. The radius of the z axis shows deflection at the end of the simulation where it decreases. 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. This shows that the motions in x direction, the motion in z direction at the beginning and motion in y direction at the end of the simulation has most influence on the whole gyration radius.

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solvent accessible surface area

Next, we analyzed the solvent accessible surface area of the protein, which is the area of the protein which has contacts with the surrounding environment, mainly water.

First of all, we have a look at the solvent accessibility of each residue, which can be seen on Figure 27.

Figure 30: Solvent accessibility area of each residue in the protein

Figure 31: Solvent accessibility 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 nm²)	0.553
Minimum (in nm²)	0.003
Maximum (in nm²)	2.005

The average area per residue during the trajectory is between 0 and 2nm², which can be seen on Figure 30. Most of the residues have an area about 0.5nm². From this it follows that there are mainly sparse moving residues during the complete simulation with some exceptions where the residues are very flexible. In Figure 31, you can additionally see the standard deviation, which is very low and which indicates that there are no big outliers in there. This means that there is no big deviation from the average area and that the residues behave in the same way during the trajectory.

Besides, we can analysis the position of the residues within the protein based on the solvent accessibility. First, we can see in the Figure 30 that the first 100 and the last 100 residues have an average solvent accessibility of 0 which means that these residues are always completely in the interior of the protein. Most of the residues have a solvent accessibility about 0.5nm², and there are only some outliers with an accessibility of more than 1.5nm². This means that there are some residues which are almost always on the surface, a lot of residues which are partly or temporarily on the surface and a lot of residues which are never on the surface. Looking at Figure 31, we can see that the standard deviation is relatively low. This means that there are no system states in which any residues with low or no solvent accessibility get complete accessible to the surface. If the standard deviation would be very high, it would indicate that there are some very unusual states in the simulation which is not the case in our simulation.

Furthermore, it is possible to look at the solvent accessibility of each atom of the complete protein, which can be seen in Figure 32 and Figure 33.

Figure 32: Solvent accessibility of each atom of the complete protein.

Figure 33: Solvent accessibility 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 nm²)	0.032
Minimum (in nm²)	0
Maximum (in nm²)	0.558

In Figure 32 the average area per atom is plotted, which deliver similar results to Figure 30. In general the atoms have not such a big area as the residues. This can be explained easily because the residue area is consisting of the single atom areas which belong to this residue. There are a huge number of atoms which have an area of about 0nm². As before, the standard deviation is not that high (Figure 33). It is a little bit higher than than the one in Figure 31 which was expected, because of the smaller and more detailed scale of this Figure. In general Figure 32 and Figure 33 confirm the results of Figure 30 and Figure 31.

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 for the residues. But at the beginning of the plot, there are no atoms which have no surface accessibility area. However, there are a lot of atoms with low or no accessibility area in the plot. Gromacs is a non-deterministic algorithm and that is why this result should be consistent with the results for the different residues.

Figure 34 shows how much of the area of the protein is accessible 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 34: Area of the protein which is accessible to the surface during the simulation.

Figure 35: Area of the protein which is accessible to the surface during the simulation with standard deviation.

Average (in nm²)	138.727
Minimum (in nm²)	127.066
Maximum (in nm²)	146.571

Figure 34 and Figure 35 display the solvent accessibility surface of the whole protein during the simulation. The surface accessibility of the hydrophobic residues has an area of about 140nm², which is relatively consistent during the complete simulation. The second plot describes the solvent accessibility for different physicochemical properties. It shows that the accessibility of the hydrophobic amino acids is larger than of the hydrophilic amino acids which is unexpected. Normally, hydrophobic amino acids prefer a location in the core of the protein and not on the surface.

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hydrogen-bonds

As a next step we analysis the formed hydrogen bonds within the protein during the simulation. Here, we differ between hydrogen-bonds between the protein itself and bonds between the protein and the water.

The following plots display the number of hydrogen bonds within the protein over the simulation time.

Figure 36: Number of hydrogen-bonds in the protein over simulation time

Figure 37: 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

In Figure 36 you can see the bonds within the protein. Here you can see that the number differs between 300 bonds and 355. Most of the time, the protein has between 310 and 330 hydrogen-bonds. Besides, the number of bonds declines a bit in average over the simulation time. Furthermore, it is possible to see in this plot, that the protein is flexible, because the number of bonds fluctuate extremely over the time.

Figure 37 displays the number of hydrogen bonds that occur during the simulation as well as all residue pairs with a distance smaller than 0.35nm which is the distance where a hydrogen bond is theoretically possible. This plot shows that there exist much more possible hydrogen bindings than occurred in real. Here the number of possible pairs is about 1500 whereas the number of formed hydrogen bond is only between 320 and 330 which is only about 20%. The small number of formed hydrogen bonds can indicate the high protein's flexibility.

The following plots display the number of hydrogen bonds between the protein and the surrounding water over the simulation time.

Figure 38: Number of hydrogen-bonds between the protein and the surronding water.

Figure 39: Number of hydrogen-bonds and the possible hydrogen-bonds between the protein and the surrounding water.

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

Looking at the number of hydrogen bonds formed between the protein and the surrounding water, which is visualized in Figure 38, we can see that there exist much more bonds between protein and water than within the protein. The number differs between 800 and 900 which is about 3 times more than the number within the protein. Besides, the average number of bonds between water and protein increases a bit over the simulation time. However, most of the time, the protein forms between 840 and 860 bonds with the surrounding water.

Figure 39 displays additionally the number of residue pairs with a distance less than 0.35 nm which is the distance where a hydrogen bond is theoretically possible. The number of pairs within 0.35nm is about 1000. Compared to Figure 34 the distance of possible and real occurring hydrogen bonds is significantly lower. In this case it 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 within the protein there are a lot of amino acids which have no contact partners, because of the big underlying distance to another amino acid.

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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 analyze the phi and psi torsion angles of the backbone to get a better understanding of the secondary structure during the simulation.

Figure 40: Ramachandran Plot of the wild type.

As we can see on Figure 40, 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 are consistent to the white regions of the standard ramachandran plot.

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RMSD matrix

Next we analyzed 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 41: RMSD matrix of our structures during the simulation

As you can see on Figure 41, 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.

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cluster analysis

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

We visualized all of these cluster structures in Figure 42:

Figure 42: Visualization 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 43: Distribution of the RMSD value over the different clusters

In Figure 43, 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.

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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 44: 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

Figure 44 shows that the RMSD increases consistent during the whole simulation. At the beginning the RMSD is relatively small and then arises very fast till it reaches a point where it rises slower. Only at Time 6000 there is a valley in the plot. The internal RMSD reaches at the end about 0.25 Angstrom, which is not relatively high. Therefore the protein has a big distances to itself.

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