Normal mode analysis HEXA

Webnma

General information

The WEBnma (Webtool for Normal Mode Analysis) is a webtool which allows the user to run a normal mode analysis of its protein. It is public available [here]. This tool offers two different analysis modes (single analysis and comparative analysis). We used the single analysis mode. Therefore, we upload our PDB file, but it is also possible to paste only the PDB id of the protein. Furthermore, it is possible to declare which chain of the protein should be analysed. We pasted our e-mail adress and used the standard parameter for the analysis.
As a result we got a plot with normalized squared atomic displacments for each model. Furthermore, we got pictures of the motion of the protein, which can be seen in the result section.

Results

We analysed the five models with the lowest energy values. Webnma calculates fourteen different models with following energy values:

Mode Index	Deformation Energy
7	1041.88
8	1318.21
9	1738.30
10	2841.31
11	3135.09
12	4100.18
13	3911.06
14	5337.50
15	5741.69
16	6513.85
17	6081.05
18	6882.96
19	7514.14
20	7943.67

We took the first five models (7, 8, 9, 10, 11), because they have the lowest energy of all models.

Here you can see the normalized squared atomic displacments of our models:

model 7	model 8	model 9	model 10	model 11
Figure 1: Normalized squared atomic displacments of model 7	Figure 2: Normalized squared atomic displacments of model 8	Figure 3: Normalized squared atomic displacments of model 9	Figure 4: Normalized squared atomic displacments of model 10	Figure 5: Normalized squared atomic displacments of model 11

Here you can see the motion of our analyses.

model 7	model 8	model 9	model 10	model 11
Figure 6: Normalized squared atomic displacments of model 7	Figure 7: Normalized squared atomic displacments of model 8	Figure 8: Normalized squared atomic displacments of model 9	Figure 9: Normalized squared atomic displacments of model 10	Figure 10: Normalized squared atomic displacments of model 11

Discussion

If we look at the squared atomic displacments of our models we can see that almost every model has a peak at the same place.

Here is an overwiew, where are the peaks of the models:

model 7		model 8		model 9		model 10		model 11
position of the peak	value of the peak	position of the peak	value of the peak	position of the peak	value of the peak	position of the peak	value of the peak	position of the peak	value of the peak
250	3.0	10	0.8	10	0.7	250	8	20	0.6
290	1.5	12	0.8	15	0.7			220	0.8
300	1.5	60	1.3	50	0.8			310	0.9
310	1.5	90	1.0	110	1.8			315	0.9
		110	0.6	190	0.6			350-380	~1.2
		115	0.6	250	0.7			405	1.5
		250	2.0	310	1.2			500	0.9
		300	1.0

As listed in the table above, each model has a different amount of peaks and also the values differ extremly. Therefore, if you look at the plots (Figure 1 to 5) you have to keep in mind, that the axis are not equal in each model. In out case, model 8 (Figure 2) has the most peaks, whereas model 10 (Figure 4) has only one peak, but this peak has the highest value of the peaks in the models.
Model 7 (Figure 1) has four points in the structure where the peak is very high. These points are located near to each other, which means that there is a very flexible region in the protein. If we look at Figure 6 which presents the motion of model 7 we can see that the highest helix is very flexible, which is probably the region in the protein where the peaks are very high. The rest of the protein moves, because of the hugh movement of this helix.
Model 8 (Figure 2) contains a lot of flexible regions, which are not located next to each other. Therefore, the protein moves at different locations. This means, that there are several independent movements and not only one motion which forces the rest of the protein to move. If we have a look at the visualization in Figure 7, we can see that there are some regions which move indenpently, like the two helices on the right botton or the highest helix, which move from right to left and back.
Model 9 (Figure 3) has also a lot of peaks in the plot. The peaks are very similar to the one of model 8, which means these two models should move in a very similar way. This is the case, as can be seen in Figure 8. Model 9 displays lower movement, than model 8, but the direction of the movement and the regions are the same. The reason therefore is that model 8 has some additional regions which are flexbile.
Model 10 (Figure 4) has only one very high peak at the region around residue 250. By a look at Figure 9 it can be seen that the highest helix shows an extensive movement, which force the rest of the protein to move with it. This motion is similar to the one of model 7, but more concentrated on the helix at residue 250.
The last model, model 11 (Figure 5) displays a lot of peaks as well and one extremly flexible region. The protein moves around the ring which is shown in Figure 10. The complete protein wobble around this ring, which is a similar to the movement of model 8, but here this movement is more pronounced.

In general, all models show relatively similar movements. Especially, the helices at the bottom right and at the top are very flexible, which is consistent in each model.

The Normal mode analysis is just a coarse approximation of the movememnt of the protein. But we think that it is pretty sure, that these three helices are really flexible, because this is the consensus of all different models. Therefore, we suggest, that the protein wobbles around the ring with movements of these helices.

El Nemo

General information

ELNemo is a Webinterface to compute Normal Modes by using The Elastic Network Model. The Webserver is available [here].
As input we uploaded our PDB file. Optional it is possible to assign a job name. We changed the parameters according to the task description. As output we got a fluctuation matrix for each model and also three different pictures of the protein motions from different perspectives.

Results

Here you can see the CA distance fluctuations for the different modes:

This matrix displays the maximum distance fluctuations between all pairs of CA atoms and between 
the two extreme conformations that were computed for this mode (DQMIN/DQMAX). Distance increases are
plotted in blue and decreases in red for the strongest 10% of the residue pair distance changes. 
Every pixel corresponds to a single residue. Grey lines are drawn every 10 residues, yellow lines
every  100 residues (counting from the upper left corner).

model 7	model 8	model 9	model 10	model 11
Figure 11: Fluction matrix between the two different modes from model 7	Figure 12: Fluction matrix between the two different modes from model 8	Figure 13: Fluction matrix between the two different modes from model 9	Figure 14: Fluction matrix between the two different modes from model 10	Figure 15: Fluction matrix between the two different modes from model 11

El Nemo provides three different animated gif to the user, which show the motions of the protein. Furthermore, we created another animated gif. Therefore, we received four different anmiated gifs which we listed in one line for one model.

Model 7:

picture from us	picture 1 from ElNemo	picture 2 from ElNemo	picture 3 from ElNemo
Figure 16: Motions of Model 7 from El Nemo, which is generated by ourselfs	Figure 17: Picture 1 of the motions of Model 7 from El Nemo, which is generated by the program	Figure 18: Picture 2 of the motions of Model 7 from El Nemo, which is generated by the program	Figure 19: Picture 3 of the motions of Model 7 from El Nemo, which is generated by the program

Model 8:

picture from us	picture 1 from ElNemo	picture 2 from ElNemo	picture 3 from ElNemo
Figure 20: Motions of Model 8 from El Nemo, which is generated by ourselfs	Figure 21: Picture 1 of the motions of Model 8 from El Nemo, which is generated by the program	Figure 22: Picture 2 of the motions of Model 8 from El Nemo, which is generated by the program	Figure 23: Picture 3 of the motions of Model 8 from El Nemo, which is generated by the program

Model 9:

picture from us	picture 1 from ElNemo	picture 2 from ElNemo	picture 3 from ElNemo
Figure 24: Motions of Model 9 from El Nemo, which is generated by ourself	Figure 25: Picture 1 of the motions of Model 9 from El Nemo, which is generated by the program	Figure 26: Picture 2 of the motions of Model 9 from El Nemo, which is generated by the program	Figure 27: Picture 3 of the motions of Model 9 from El Nemo, which is generated by the program

Model 10:

picture from us	picture 1 from ElNemo	picture 2 from ElNemo	picture 3 from ElNemo
Figure 28: Motions of Model 10 from El Nemo, which is generated by ourself	Figure 29: Picture 1 of the motions of Model 10 from El Nemo, which is generated by the program	Figure 30: Picture 2 of the motions of Model 10 from El Nemo, which is generated by the program	Figure 31: Picture 3 of the motions of Model 10 from El Nemo, which is generated by the program

Model 11:

picture from us	picture 1 from ElNemo	picture 2 from ElNemo	picture 3 from ElNemo
Figure 32: Motions of Model 11 from El Nemo, which is generated by ourself	Figure 33: Picture 1 of the motions of Model 11 from El Nemo, which is generated by the program	Figure 34: Picture 2 of the motions of Model 11 from El Nemo, which is generated by the program	Figure 35: Picture 3 of the motions of Model 11 from El Nemo, which is generated by the program

Discussion

This method provides a fluctation matrix and also some pictures of the motion. The fluctation matrix visualize if two residues come closer together (red) or are more distant (blue) during the motion. So it is possible, to see which residue of the protein behaves in which way. Furthermore, we got some pictures of the motion in different perspectives, which it made easy to get an imagination of how the protein moves.

The first model (model 7) has almost the same amount of residues that come closer together and which are more distinct. If we have a look at the pictures in Figure 16, we can see, that the whole protein moves. In the first perspective of ELNemo (Figure 16) we can see, that the protein pulsates. Especially one helix shows an up and down movement, which cause the rest of the protein motion. Only the ring in the middle of the protein is relativly stable and shows only low motion.
The second model (model 8) has a different fluctation matrix (Figure 12). At the beginning of the protein the residues are more distant, whereas, at the end of the protein the residues come closer together. In the pictures (Figure 20-23) we can see that, like before, the upper helix shows a strong motion. Furthermore, the lower sheets show stronger motion as well like in the model before. In general this model shows higher motion than the one before. This can be seen for example at the ring, which moves clearly more than the ring from model 7. Again, like before, the protein seems to pulsate.
Although the fluctation matrix of model 9 (Figure 13) is different to the one of model 8, the motion seems to be very equal. In the matrix it can be seen, that the residues just come closer together. There are almost no residues, which get a greater distance to the residues than the one in their QMIN state. Looking at the pictures (Figure 24-27) it can be seen that the motion of model 9 and model 8 is quite similar. Model 9 only shows a bit less motion in the first helix, but the general movement ist equal. Here again, the protein seems to pulsate around the ring.
In model 10 almost all residues come closer together or keep their distance. This matrix (Figure 14) is really different to the other matrices before. Therefore, we suggest, that the protein motion is different to the already discussed models. By a look at the pictures (Figure 28-31) we can see that this assumption is correct. The protein shows a more complex motion than the models before. The protein still contains the movement of the helix at the top, but this motion is very small. Otherwise, the complete protein puslate, but the pulsation is more distinct than before. The whole protein seems to pulste twice, which could not be seen in the other models.
The last model has a fluctation matrix (Figure 15) which is most similar to the one of model 10 (Figure 14). There are less residues which come closer together, but as before, there are no residues which enlarge the distance. So we suggest, that the motion has to be similar to the one of model 10, although the motion should not be so pronounced like by model 10. If we look at the pictures (Figure 32-35), we can see, that this is true. The protein shows less motion and especially the pulsation seems to be low. Only if we look at Figure 33, we can see, that the protein has a hugh pulsation, but the direction is different to the models before.

In general, we can say, that the ring in the middle of the protein is stable and the protein pulsate around them. The different models show different possible occurences of this motion. The top helix is a very flexible one, which has a motion in all different models. Futhermore, each model show pulsation, so we can suggest, that the upper helix moves and the protein pulsate around their center, which is a ring here. All models show similar motions, especially the motion of the upper helix and the lower sheets, which are flexible in each model. So therefore, we can get a coarse imagination of how this protein moves and which parts of the protein are the most important ones for motion.

Anisotropic Network Model web server

General information

The Anisotropic Network Model web server can be found [here].
In the web interface, we uploaded our PDB file and chose the chain for which the analysis should be done. Furthermore, we changed the parameters according to the task description.
As an output we received a plot of the real occuring and calculated B-factor values. Furthermore, we got a visualization of motion for each model. Very nice is, that there are arrows in the picture which shows the direction of the motion. So therefore, it is very easy to reconstruct the motion directions.

Results

Here you can see the B-factor distribution of the real occuring B-factors (black) and the calulated B-factors (blue).

model 1	model 2	model 3	model 4	model 5
Figure 36: Distribution of the occuring B-factors and the calculated B-factors in Model 1	Figure 37: Distribution of the occuring B-factors and the calculated B-factors in Model 2	Figure 38: Distribution of the occuring B-factors and the calculated B-factors in Model 3	Figure 39: Distribution of the occuring B-factors and the calculated B-factors in Model 4	Figure 40: Distribution of the occuring B-factors and the calculated B-factors in Model 5

The following table displays the motion of protein for the different models:

model 1	model 2	model 3	model 4	model 5
Figure 41: Calculated motion of the NMA model 1	Figure 42: Calculated motion of the NMA model 2	Figure 43: Calculated motion of the NMA model 3	Figure 44: Calculated motion of the ANM model 4	Figure 45: Calculated motion of the ANM model 5

Discussion

This method provides a distribution of the real occuring B-factors and of the calculated B-factors. By comparing both values we can see which parts of the protein are flexible. A high B-factor value means a high flexbility of this residue. If we look at the plots in detail, on the first view all values seem to be very similar. Each model has four very high peaks at the same place, but at the rest of the protein the values differ between the different models. All models have also big peaks at the beginning of the protein, which was expected, because the beginning and the end of a protein are often very flexbile (therefore, most methods which predict disordered regions predict them at the beginning or the end of the protein).

The first model has only one loop which shows strong motion and therefore the rest of the protein follows the motion of this loop. It seems that the whole protein contract and strecht. This motion is caused by the motion of the flexible loop.
The second model shows a complexer motion, with not only one motion center. There are two contrary motions. As before, the loop moves from right to left. But at the other side of the protein, there is a second loop which also moves forward and backward. These two loops move in the same time to the same direction. Therefore, it seems that the protein build a deeper curve by moving the two loops. The rest of the protein follows the motion of these two loops. Only the ring does not change its structure in a very obvious way.
In the third model there are again two loops which moves. They are the same loops as before. But this time, the loops move contrary. If one loop moves forward, the other loop moves backward. Therefore, the rest of the protein has not to move that much as in model 2. The ring again is very stable and does not change its structure.
The forth model has only one loop which moves. But in this case not only the loop moves, but also the associated helix. This cause a stronger movement of the whole protein as in model 1. This is the first case in which the ring also moves itselfs. So in this case the loops, which build the ring, come closer together.
The last model, we look at, has three different motions. The two loops from model 2 and 3 moves again. But there is also a helix which moves. Compared to the other models, this model shows the strongest motion and the whole protein seems to be very unstable. Also the ring shows a lot of motion.

In general there are two parts of the protein which seems to be in almost all models the center of the motion. The last model is very unstable and therefore, we do not suggest that this is the real motion of the protein. We suggest, that especially the two loops are the center of the motion and the rest of the proteins follows the motion. It was not possible to decide if both loops moves in the same or in contrary directions, because these models are just coarse approximations of the protein motion and both cases could be the real motion. But in sum we can suggest, that the protein has two loops which act as motion center, the ring does not move that much and keeps its structure and the rest of the protein follows the motion of the two motion centers.

oGNM – Gaussian network model

General information

The Gaussian network model (oGNM) web server can be found [here].

The oGNM is an online server which can calculates the essential dynamics of PDB structures and of user-modified or unrealesed structures. The method is based on an Elastic Network (EN) model called the Gaussian Network Model (GNM). The online server was an enlargment of the already existing database iGNM which also uses the GNM and which contains already a lot of PDB structures. The advantages of the server compared to iGNM or other normal mode analysis tools is that the calculation is very fast and a result is received in a few seconds. Furthermore, it is not limitied in size which means it is not necessary to use really small structures like in other normal mode analysis methods.
For the calculation the method uses a network model that represents the biomolecular structure. This network can be identified by the alpha-carbon atoms and some other selected atoms on nucleotides. Furthermore, they assume that the fluctuations of the nodes are isotropic and Gausian. Therefore, there are different parameters which can be selected before the calculation: number of model nodes to represent a nucleotide (1 or 3) and the interaction cutoff distance for nucleotide and amino acid pairs (the c-alpha cutoff is the average of this two cutoffs).
The method delivers plenty of different output files, like the Eigenvalues and the Kirchoff matrix which play a role in the calculation as well as the 20 slowest modes which is part of the results. Furthermore, there are three main representive results which displays the fluctuation and the mobility of the structure as well as cross-correlation plot between the desired modes.

(Sources: [Paper] and [Webserver])

Results

Full diversity of the received output can be seen [here]. For the analysis of the result we decided to display only the three main visualizations.

Here you can see the mobility profiles. This plots can be used for the comparitive analysis of the different mode profiles. On the x-axis are the residues of chain A and the y-axis displays the according fluctuation. The first five pictures display the modes 7-11 on their own and the last picture displays all modes together.

mode 7	mode 8	mode 9	mode 10	mode 11	all modes
Fluctuation of mode 7	Fluctuation of mode 8	Fluctuation of mode 9	Fluctuation of mode 10	Fluctuation of mode 11	Fluctuation of the modes 7-11

In the next picture display the mobility of the different modes. The mobility goes from blue to red, where blue means little mobility and red means high mobility.

mode 7	mode 8	mode 9	mode 10	mode 11
Calculated mobility of mode 7	Calculated mobility of mode 8	Calculated mobility of mode 9	Calculated mobility of mode 10	Calculated mobility of mode 11

Here you can see the cross-correlation plot of mode 7-11. The colors of the plot go from dark red to dark blue whereas dark red colored parts are indicating a positive correlation of motion between the different modes. Contrary the dark blue parts display negative correlated motions.

Cross-correlation plot of mode 7-11

Discussion

Looking at the mobility profile, one can see that there are two different peeks for the fluctuation that stands out. The first peek is around residue 150. There, the fluctuation jump betwenn 0.2 and 0.7 in different modes. This peek can be seen in mode 7 and 9 where it is the only existing peek as well as in mode 8 and 11. The other outstanding peek ist the one around residue 525, which can be seen in mode 8, 9 and 10. There the fluctuation differs between 0.1 and 0.4 in the different modes. The only exception is mode 10 which is the only one which has many different peeks at very low fluctuation level under 0.1. Furthermore, the other modes contain also some other small fluctuation peeks. However, the last figure which contains all different fluctuation plots displays also this two outstandig peeks at residue 150 and 525. This indicates that at this two residues the fluctation is probably the highest and that there are some more residues which have a low fluctuation.

The 3D visualization of the chain A of hexosaminidase with the corresponding mobility deliver similar results. Mode 7, 8 (rotation here differs a bit which makes it in this case hard to see), 9 and 11 show arised mobility in the beta-sheets which are here on the left side. Mode 7, 8 and 11 are more and darker red colored which means there they have a higher mobility. Looking at the only colored part in mode 9 (white) it agrees with the red darkest part in mode 7 and 11. This is similar to the mobility profiles where all this modes have the highest peek at residue 150. Contrary, Mode 8 and 10 have some other parts which have also higher mobility. In mode 8 part of the helices on the right side have high mobility. In mode 10 most alpha-helices on the right side have high mobility. This agrees also with the mobilit profile where mode 10 displays many fluctuations whereas mode 8 has only one peek aroud resiude 525.

Therefore, both the mobility profile as well as the 3D visualization show evidence that there are two parts in chain A which have higher mobility. This two parts are around ther residues 150 and 525. In the 3D-visualization the parts complies with the right and on the left 'ends'.

The cross-correlation plot displays the correlated motion of the modes 7-11. There are three boxes around the diagonal which are outstanding. This box contains regions of dark blue and dark red which means there are positive and negative corelation present. The rest of the correlation plot displayd mostly no outstanding correlation. This means that there is no motion correlation of two completly different parts of the structure regarding this different modes. This agrees with the plots and the 3D visualization described above where the motion is consistent between the different modes.

NOMAD-Ref

General information

The Normal Mode Analysis, Deformation and Refinment (NOMAD-REF) web server can be found [here].

NOMAD-Ref is an online server which provides tools for the normal mode calculation and algorithms that use normal modes for structural refinement or optimization. The Normal Modes were widley calculated by Elastic Network Model (ENM). Furthermore, there exists the option to use classical force fields for the calculation.
In addition to the Normal Mode calculation which is used as the basis, NOMAD-Ref provides three different possibility for further analysis. The first one is the geration of alternative models with correct stereochemistry but large amplitude movements. The next two are two different kinds of refinements: refinement of the models against experimental data (e.g. X-Ray diffraction) and the refinement ot the docking solutions when the receptor is known flexible.
NOMAD-Ref tools can be applied for all PDB-structures, even for very larg proteins it can include all atoms. For the calculation of the normal mode and following visualization different parameters can be choosen. You can select the number of to be calculated, the distance weight parameter (Ångström), the cutoff to use for mode calculation (Ångström) and the average RMSD (Ångström) in output trajectories.

(Source: [website])

Results

model 7	model 8	model 9	model 10	model 11
Histogram of the cRMS for model 7	Histogram of the cRMS for model 8	Histogram of the cRMS for model 9	Histogram of the cRMS for model 10	Histogram of the cRMS for model 11

model 7	model 8	model 9	model 10	model 11
model 7	model 8	model 9	model 10	model 11

Discussion

The first plots contain the cRMS of the different modes. The cRMS displays the strength of the movement according to the atome. Mode 7, 8 and 10 have an cRMS between 1 and 25 Angstrom. This movements are on the entire length and have some peeks at the beginning, in the middle and at the end. Mode 8 has at the end one outstandig peek which has a very high cRMS at aboutn 25 Angstrom. The rest of the atmos in mode 8 have lower cRMS, like all atoms in mode 7 and 10. This means that mode 8 moves harder at one end.
The other two modes 9 and 11 have one outstandig peek at a very high cRMS at about 250 Angstrom. The rest of the atoms in both modes have a lower cRMS which is equal to the cRMS over all atoms in mode 7, 8 and 10. This follows, that mode 9 and 11 have at one position in the structure a very extrem movement.

A further output of Nomad-Ref were the movies which display the motion. Here we can see, that mode 7, 8 and 10 have some movement at the ends of this structure. Mode 8 and 10 move very similar and seesaws the ends of the structure up and down. In contrast, mode 7 moves the ends to the back which looks like it folds in structure-center direction. The other two modes 9 and 11 also move the ends of the structure, but contain also a extrem movement. Excluding the extrem one, these two modes also display this up and down seesaw like motion.

The movements of all modes correspond exactly with the above discribed plots and indicate motions at both ends of the structure. The outstandig extrem movement of mode 9 and 11 is in our eyes too strong and probably not realistic. In the most modes the movement of the ends is seesaw like up and down. Therefore, we believe that this can probably be a movement of hexosaminidas chain A.

All-atom NMA using Gromacs on the NOMAD-Ref server

General information

The all-atom Gromacs-NMA on the NOMAD-Ref webserver can be found [here].

The all-atome Gromacs-NMA is a normal mode calculation that does not use elastic networks like the other methods provided by Nomad-Ref. In contrast, this method use classical force fields. Therefore, it creates an all-atom topology of the input structure. One disadvantage is that this method takes more time and memory space than the elastic network calculation. Therefore, the size of the structure is limitated to 5000 atoms on the server.

(Source: [website])

Results

For the all-atom NMA we had to use the structure of 1BPT, because chain A of the hexosaminidase was to big. Furthermore, we run the all-atome NMA twice with different temperatures (600K and 2000K).

600K

Here you can see the motion of 1BPT at temperature 600K.

model 7	model 8	model 9
All-atom NMA movement of model 7 at 600K	All-atom NMA movement of model 8 at 600K	All-atom NMA movement of model 9 at 600K

2000K

Here you can see the motion of 1BPT at temprature 2000K.

model 7	model 8	model 9
All-atom NMA movement of model 7 at 2000K	All-atom NMA movement of model 8 at 2000K	All-atom NMA movement of model 9 at 2000K

Comparison to an Elastic Network Calculation

Next, we want to compare the result of All-atom NMA to the elastic network calculation of NOMAD-Ref.

model 7	model 8	model 9
normalized squared atomic displacments of model 7	normalized squared atomic displacments of model 8	normalized squared atomic displacments of model 9

Discussion

Looking at the differenz modes of 1BPT calculatet at 600K and 2000K, one can see that there is no big difference. All modes display a see-saw like movement where the right and left loop-like parts move up to the center. They neither show a difference in speed nor in the way of movement. This suggests that the temperature has no high influence on the motion of 1BPT.

Compared to the Nomad-Ref Elascit Network calculation more differenence can be seen. First of all, mode 7 moves completly different. The ends of this mode do not move up to the center. Instead, the ends are more rigid and the whole body moves. The ends in mode 8 and 9 have a stronger motion, where especially the coil region (green) displays more flexibility. Mode 9 has the most powerfull movement at this coil region.

All in all, all modes,except mode 7 of the elastic network calculation, agree. One remarkable thing is that the movement of the elastic network calculation is in somehow more flexibel. Because all modes have this see-saw like movement of the right and left loop-like parts move, we believe that this is probably the real movement of 1BPT.