Normal Mode Analysis of Glucocerebrosidase

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Elastic and Gaussian Network Models


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 11: Normal Mode 1 calculated with ANM
Figure 12: Normal Mode 2 calculated with ANM
Figure 13: Normal Mode 3 calculated with ANM
Figure 14: Normal Mode 4 calculated with ANM
Figure 15: Normal Mode 5 calculated with ANM
Inter Distance Analysis and Deformation Analysis
Figure 16a: Distance Matrix - Mode 1

Figure 16b: Deformation Energy - Mode 1
Figure 17a: Distance Matrix - Mode 2

Figure 17b: Deformation Energy - Mode 2
Figure 18a: Distance Matrix - Mode 3

Figure 18b: Deformation Energy - Mode 3
Figure 19a: Distance Matrix - Mode 4

Figure 19b: Deformation Energy - Mode 4
Figure 20a: Distance Matrix - Mode 5

Figure 20b: Deformation Energy - Mode 5
B-factors/mode fluctuations
Figure 21: B-factors/mode fluctuations - Mode 1
Figure 22: B-factors/mode fluctuations - Mode 2
Figure 23: B-factors/mode fluctuations - Mode 3
Figure 24: B-factors/mode fluctuations - Mode 4
Figure 25: B-factors/mode fluctuations - Mode 5


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.



  • 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


also available here:

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5
Figure x
Figure x
Figure x
Figure x
Figure x
Mobility-Color-Coded Ribbon Diagram for modes 1 to 5. Red means high mobility, blue low mobility.
Fluctuations per residue for modes 1 to 5
Figure x
Figure x
Figure x
Cross-correlation plot for mode 1 to 5
Figure x


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, so the interesting ones are mode 7-11. For each mode we have three figures:

  • a) shows the motion of the protein - for modes 1-6 there are no real motions because these are rigid
  • b) shows the elastic net together with the protein
  • c) shows the rmsd per residue

Mode 1 Mode 2 Mode 3 Mode 4
Figure 45a

Figure 45b

Figure 45c
Figure 46a

Figure 46b

Figure 46c
Figure 47a

Figure 47b

Figure 47c
Figure 48a

Figure 48b

Figure 48c

Mode 5 Mode 6 Mode 7 Mode 8
Figure 49a

Figure 49b

Figure 49c
Figure 50a

Figure 50b

Figure 50c
Figure 51a

Figure 51b

Figure 51c
Figure 52a

Figure 52b

Figure 52c
Mode 9 Mode 10 Mode 11
Figure 53a

Figure 53b

Figure 53c
Figure 54a

Figure 54b

Figure 54c
Figure 55a:

Figure 55b

Figure 55c



Comparison of All-atom NMA to Elastic Network NMA

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

1BPT at 600 K

Figure 55
Figure 56
Figure 57
Figure 58

1BPT at 2000 K

Figure 59
Figure 60
Figure 61
Figure 62

Elastic Network NMA

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

Figure 63
Figure 64
Figure 65
Figure 66

Comparison NMA / MD