Normal Mode Analysis of Glucocerebrosidase

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Nomal mode analysis (NMA) is a time-independent method to calculate vibrational modes and protein flexibility and therefore helps to describe slow large-amplitude/ low-frequency motions. These motions describe conformational changes which are essential for the protein function. Each NMA technique uses harmonic approximations and neglect solvent damping. For the analysis atoms are modeled as point masses connected by springs, which represent the interatomic forces. The normal mode describes a pattern of motion in which all parts of the system (all atoms or only Cα atoms) move with the same frequency and in phase. These modes are no actual protein motions, but can give insight in the possible movements and regions of flexibility. <ref> Alexandrov et al., Normal modes for predicting protein motions: A comprehensive database assessment and associated Web tool. 2004. Protein Science, Vol. 14 </ref> Normal modes can either be calculated with all atoms or can be restrained to Cα atoms only.

In this section different normal mode analyses were carried out for glucocerebrosidase (2NT0). Furthermore, the difference between all-atom and elastic network normal mode analysis gets illustrated on a small protein (1BPT).

Additional modes and figures, which are not addressed in this discussion, are located in the supplementary data page.

Elastic and Gaussian Network Models

The Elastic Network Model is a particular type of NMA in which the springs connecting each node to the neighbouring nodes are of equal strength and only the atom pairs within a cutoff distance get considered. In the Gaussian Network Model the proteins are represented by point masses of the Cα atoms and a harmonic approximation is used to model the interactions between point masses.


WEBnm@ is a web-server which provides automated computation and analysis of low-frequency normal modes of proteins. For an input structure file in PDB format, the normal modes are calculated and a series of automated calculations (normalized squared atomic displacements, vector field representation and an animation of the first six vibrational modes). Additional to the single analysis (calculating lowest frequency normal modes for one protein), the server offers a comperative analysis. In this analysis, the normal modes of a set of aligned sequences are calculated and compared. This feature is still under development. <ref>Hollup SM, Sælensminde G, Reuter N. WEBnm@: a web application for normal mode analysis of proteins BMC Bioinformatics. 2005 Mar 11;6(1):52 </ref>


  • Webserver:
  • Input:
    • Single Analysis: structure file in PDB format
    • Comparative Analysis: structure files in PDB format and sequence files in fasta format


Figure 1 to 5 show the first five vibrational modes (modes 7 to 11) calculated with WEBnm@ for the structure of glucocerebrosidase (2NTO). On the left side of each figure the vectors are shown, whereas the movement is illustrated to the right.
The atomic displacement of the different models is shown in the following pdf file: File:Webnma atomic displacement glucocerebrosidase.pdf. The plots show the normalized square of the displacement of each Calpha atom, whereof the highest values correspond to the most displaced regions.

Figure 1: Normal Mode 7 calculated with WEBnm@
Figure 2: Normal Mode 8 calculated with WEBnm@
Figure 3: Normal Mode 9 calculated with WEBnm@
Figure 4: Normal Mode 10 calculated with WEBnm@
Figure 5: Normal Mode 11 calculated with WEBnm@


Having a look at the atomic displacements, one can see that modes 7, 9, 10 and 11 have peaks and high values all over the protein. This indicates, that most parts of glucocerebrosidase are flexible. Mode 8 describes instead local flexibilities at the N- and C- terminus of the protein. The movement consists movements and displacements of the different domains. These movements consist of streching, bending, twisting, attraction or repulsion of the different glucocerebrosidase domains.


ElNémo is a web-server based on the Elastic Network Model. The tool computes, visualizes and analyses low-frequency normal modes of large macro-molecules. Any size of proteins can be treated as ElNémo uses a 'rotation-translation-block' approximation. <ref>K. Suhre & Y.H. Sanejouand, ElNemo: a normal mode web-server for protein movement analysis and the generation of templates for molecular replacement. Nucleic Acids Research, 32, W610-W614, 2004. </ref>


  • Webserver:
  • Input:
      • structure file in PDB format
      • supplementary options for NMA calculation (number of normal modes to be calculated, minimum and maximum perturbation and stepsize between DQMIN and DQMAX)
      • options for computing the eigenmodes (NRBL and cutoff to identify elastic interactions)


Figure 6 to 9 show for each of the five first vibrational normal modes calculated with ElNémo three different perspectives.

Figure 6: Normal Mode 7 calculated with ElNémo
Figure 7: Normal Mode 8 calculated with ElNémo
Figure 8: Normal Mode 9 calculated with ElNémo
Figure 9: Normal Mode 10 calculated with ElNémo
Figure 10: Normal Mode 11 calculated with ElNémo


The normal modes obtained with ElNémo seem to describe the same movements as the resulting normal modes of Webnm@. Most of the movement seems to be between the different domains. As observed in the results of Webnm@ the movements consists of stretching, bending, attraction, repulsion and twisting.

Anisotropic Network Model

The ANM Webserver provides NMA Analysis with the anisotropic network model (ANM) which is an elastic network (EN) introduced in 2000. It is a very fast method which predicts the global modes. The ANM adopts a uniform force constant γ to all springs and nodes are refered as the Cα atoms.<ref>Anisotropic network model: systematic evaluation and a new web interface, Eyal E, Yang LW, Bahar I. Bioinformatics. 22, 2619-2627, (2006)</ref>



After submitting the job you get a results page where you can analyze the different normal modes more precisely. You can change the amplitude and the frequency of the motions, you can visualize the vectors and change the appearance of the protein. Furthermore you have several possibilities to choose:

  • download files
  • create PDB (motion)
  • create PyMol script
  • get anisotrpic temp. factors
  • B-factors/mode fluctuations
  • Eigenvalues
  • Correlations
  • Distance fluctuations and deformation energy
  • GNM

The movement, distance fluctuations, the deformation energy per position and mode fluctuations are shown for five different modes in the following figures. Additional modes can be found here.
At the end you can see the Cα anisotropic temperature factors as ellipsoids calculated in different ways.

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5
Figure 11a: Normal Mode 1 calculated with ANM
Figure 12a: Normal Mode 2 calculated with ANM
Figure 13a: Normal Mode 3 calculated with ANM
Figure 14a: Normal Mode 4 calculated with ANM
Figure 15a: Normal Mode 5 calculated with ANM
Inter Distance Analysis and Deformation Analysis
Figure 11b: Distance Matrix - Mode 1

Figure 11c: Deformation Energy - Mode 1
Figure 12b: Distance Matrix - Mode 2

Figure 12c: Deformation Energy - Mode 2
Figure 13b: Distance Matrix - Mode 3

Figure 13c: Deformation Energy - Mode 3
Figure 14b: Distance Matrix - Mode 4

Figure 14c: Deformation Energy - Mode 4
Figure 15b: Distance Matrix - Mode 5

Figure 15c: Deformation Energy - Mode 5
B-factors/mode fluctuations
Figure 11d: B-factors/mode fluctuations - Mode 1
Figure 12d: B-factors/mode fluctuations - Mode 2
Figure 13d: B-factors/mode fluctuations - Mode 3
Figure 14d: B-factors/mode fluctuations - Mode 4
Figure 15d: B-factors/mode fluctuations - Mode 5
Cα anisotropic temperature factors as ellipsoids
purely computational refined by experimental b-factors
Rastep Povscript Rastep Povscript
Figure 16a: Cα anisotropic temperature factors as ellipsoids, purely computational
Figure 16b: Cα anisotropic temperature factors as ellipsoids, refinde by experimental b-factors
Figure 17a: Cα anisotropic temperature factors as ellipsoids, purely computational
Figure 17b: Cα anisotropic temperature factors as ellipsoids, refinde by experimental b-factors


In each of the five best normal modes obtained, the whole protein seems to be in motion. This is confirmed by the various peaks in the mode fluctuations and the deformation energy plots. Various movements can be observed: twisting, turning, repulsion, attraction and bending. We can also see that the areas, which stand out in the B-factors/mode fluctuations and the Cα anisotropic temperature factors (figures 16 and 17) are the ones, which move the most at the normal modes.

Mode 1

For mode 1 (figures 11a-d) you can see repulsion and attraction. The upper and the lower part are moving very strong. Therefore the core of the protein is also a bit in motion. Looking at the deformation energy you can also see that the protein is in motion. Especially in the B-factors/mode fluctuations diagram you can see where the motion comes from. The distance matrix shows the large inter-residue fluctuations as blue. For this case you can see that residues with a greater distance show larger fluctuations.

Mode 2

In mode 2 (figures 12a-d) only the upper part shows repulsion and attraction. But this influences also the rest of the protein which is in motion. The lower part responds very strong to the movement of the upper part. The distance matrix is very similar to that of mode 1. The reason is that the movement is also very similar. But the deformation energy differs. The maxima are at the end at positions 344 til 393 and at 442. The last one is in the upper part of the protein, 344 til 393 in the middle.

Mode 3

Mode 3 (figures 13a-d) shows also attraction and repulsion but this time with the beta barrels. Therefore also the alpha helices are moving. The distance matrix shows more large inter-residue fluctuations than in mode 1 and 2. Also the deformation energy differs. You can see the maxima at the beginning between position 50 and 99 and at position 344 and 393. The last two ones are positioned at loops which are in very strong motion.

Mode 4

Mode 4 (figures 14a-d) shows many movements. It is like pulsation. The protein is contracting and extending. Only the core is almost without motion. The distance matrix shows many large inter-residue fluctuations, but low inter-residue fluctuations for residues that are very near or very far away. The deformation energy shows one maximum between position 50 and 99 and some little maxima between 246 and 393. This also reflects that there are many different movements.

Mode 5

Mode 5 (figures 15a-d) shows bending and turning and also a bit twisting at the upper part. The beta sheets are the elements that are responsible for the moving. They show the most motion. The rest of the protein just responds. The distance matrix shows that most of the residues have small inter-residue fluctuations. For the deformation energy we can see the maxima at the beginning of the sequence at positions 1 to 50 and also some small maxima at the end.


oGNM is a tool which calculates the equilibrium dynamics of proteins using the Gaussian Network Model. Futhermore it provides a database (iGNM) with precalculated PDB results.


  • Webserver:
  • Input:
    • structure file in PDB format or PDB id
    • number of nodes to represent a nucleotide
    • cutoff distances for amino acids and nucleotide pairs
    • preferred visualization engine


[The results are also available at]

The figure below show a mobility-color-coded ribbon diagram for modes 1 to 5 where red describes regions of high mobility and blue regions of low mobility.

Mobility-Color-Coded Ribbon Diagram
Figure 18: Mode 1
Figure 19: Mode 2
Figure 20: Mode 3
Figure 21: Mode 4
Figure 22: Mode 5
Fluctuations per residue for modes 1 to 5
Figure 23: Fluctuations per residue for mode 1 and 2
Figure 24: Fluctuations per residue for mode 3 and 4
Figure 25: Fluctuations per residue for mode 5, 6 and 7
Cross-correlation plot for mode 1 to 5
Figure 26:
Cross-correlation plot for mode 1 to 5


oGNM shows which parts of the protein are able to move and where the protein is most dynamic. In the upper part the Mobility-Color-Coded Ribbon Diagrams, diagrams with the fluctuations per residue and a cross-correlation plot for mode 1 to 5 are shown. In the last one you can see that only for residues that are very near or very far the correlation is high.

Mode 1

In mode 1 (figure 18) you can see that the beta sheets at the exterior of the protein are the most dynamic. The inner part is colored blue and therefore not mobile. Compared to the normal modes of other tools it is what we have seen. Also the diagram with the fluctuations (figure 23) per residue shows that positions 300 to 400 has the fewest mobility which is the middle or the core of the protein.

Mode 2

In mode 2 (figure 19) there are only two small red parts with high mobility, one part of an alpha helix and a beta sheet. Both are at the exterior of the protein. But there are more parts with medium mobility. All the exterior elements are colored light blue. The diagram with the fluctuations (figure 23) also shows that there are more moving parts.

Mode 3

Mode 3 (figure 20) has some little helix parts that are red and several beta sheet and also helix parts that are colores rosy. There are little flexible parts at the left and right side of the protein and one larger part in the middle. This is also shown in the diagram with the fluctuations (figure 24), where the maximum occurs between position 300 and 350.

Mode 4

Mode 4 (figure 21) shows only two little red loops and a few rosy parts. But the bigger part of the protein is colored blue. This seems to be a mode with few motion. Interestingly the diagram with the fluctuations (figure 24) shows a maximum of 0.065 at position 350, which is very high. This is exactly the red colored loop.

Mode 5

Mode 5 (figure 22) has some loops and parts of beta sheets that are colored red. Near them are some rosy parts but again the biggest part of the protein is colored blue. Looking at the diagram with the fluctuations (figure 25) there are peaks at the beginning and the end, which are the exterior parts which are colored red or rosy.


NOMAD-Ref is a webserver for normal mode analysis. By simplifying the potential energy between atoms all atoms can be used. This is possible by using the Tirion calculation of normal modes.<ref>Tirion, Monique M. Large Amplitude Elastic Motions in Proteins from a Single-Parameter, Atomic Analysis. Phys Rev Lett, 77, 1905--1908 (1996).</ref> NOMAD-Ref provides pdb-files for pymol and the elastic network of different normal modes, a graph with the RMSD values per residue and a modes.dat file with gives information about the frequency of the modes and the eigenvectors.



Modes 1-6 are rigid body motions (can be found here), and modes 7 to 11 describe the best five vibrational modes. Each mode is represented by two figures:

  • animation of the protein motion
  • cRMS per residue plot
Mode 7 Mode 8 Mode 9 Mode 10 Mode 11
Figure 27a: Mode 7

Figure 27b: cRMS per residue
Figure 28a: Mode 8

Figure 28b: cRMS per residue
Figure 29a: Mode 9

Figure 29b: cRMS per residue
Figure 30a: Mode 10

Figure 30b: cRMS per residue
Figure 31a: Mode 11

Figure 31b: cRMS per residue


Mode 7 to 9 show a movement all over the protein (see plots for rmsd per residue), whereas Mote 10 and 11 have a high flexibility at the N-terminus of the protein.

Mode 7

Mode 7 shows repulsion and attraction. It seems as the upper and the lower part of the protein are moving to each other and then apart. The plot with the cRMS per residue has the maxima at the beginning and at the end of the sequence. At position 2500 there is also one maximum.

Mode 8

Mode 8 has a twisting motion. The whole protein moves, it looks like bending and turning. The plot with the cRMS per residue shows its maximum at position 3500, which is at the upper part of the protein.

Mode 9

In mode 9 there is again repulsion and attraction. It looks very similar to mode 7. But the plot with the cRMS per residue differs. At position 3500 again there is a huge maximum. The rest seems to be the same.

Mode 10

As already mentioned in mode 10 one can see primarily the N-terminus which is moving. The rest of the protein also moves because of this motion. The plot with the cRMS per residue cannot be interpreted well because there is one maximum at position 2500 which is very high (2000 Angstrom) and so the rest cannot be seen.

Mode 11

Also in mode 11 the N-terminus is the most flexible part of the protein. There is also a twisting motion of the protein. The plot with the cRMS per residue also shows a maximum at position 3500 and a little peak at position 2500.


Comparison of All-atom NMA to Elastic Network NMA

All-atom NMA considers each atom for the calculation of the modes, not only the Cα atoms and is therefore quite time conusming. In this section, all-atom normal mode analyses are compared to the normal modes based on elastic networks. Instead of glucocerebrosidase (our main protein of interest) 1BPT was chosen, as it is quite small and therefore enables a quite fast all-atom normal mode analysis.

All-Atom NMA

The all-atom normal mode analysis was carried out two times with two different temperatures (600 and 2000 K). The temperature was modified as low frequencies dynamics of proteins are temperature dependent and it would therefore be interesting to see the differences.

1BPT at 600 K

Figure 32a
Figure 33a
Figure 34a
Figure 35a

1BPT at 2000 K

Figure 32b
Figure 33b
Figure 34b
Figure 35b

Elastic Network NMA

The following images show the normal modes 7 to 10 for 1BPT created with Nomad-Ref.

Figure 32c
Figure 33c
Figure 34c
Figure 35c


The modes caluclated at 2000 K are slightly bigger than the ones calculated with a temperature of 600 K. The directions of the movements are the same with both temperatures. This shows that the motions get more anharmonic with higher temperatures. The visual inspectation of the different modes suggests that modes 2 - 4 of all-atom and elastic network describe the same motion, whereof the elastic network modes have the biggest movement range. Mode 1 of the elastic normal mode analysis seems to be rigid apart from one flexible loop. In the all-atom mode mor parts of the protein are flexible.

Comparison NMA / MD