Normal Mode Analysis of Glucocerebrosidase

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Introduction

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).

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@

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>

Usage

  • Webserver: http://apps.cbu.uib.no/webnma/home
  • Input:
    • Single Analysis: structure file in PDB format
    • Comparative Analysis: structure files in PDB format and sequence files in fasta format


Results

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@

Discussion

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

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>

Usage

  • Webserver: http://www.igs.cnrs-mrs.fr/elnemo/start.html
  • 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)

Results

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


Discussion

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>

Usage

Results

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
Cα anisotropic temperature factors as ellipsoids
purely computational refined by experimental b-factors
Rastep Povscript Rastep Povscript
Figure 41: Cα anisotropic temperature factors as ellipsoids, purely computational
Figure 42: Cα anisotropic temperature factors as ellipsoids, refinde by experimental b-factors
Figure 43: Cα anisotropic temperature factors as ellipsoids, purely computational
Figure 44: Cα anisotropic temperature factors as ellipsoids, refinde by experimental b-factors


Discussion

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.

Mode 1

For mode 1 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 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 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 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 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

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.

Usage

  • Webserver: http://ignm.ccbb.pitt.edu/Online_GNM.htm
  • 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

Results

[The results are also available at http://ignm.ccbb.pitt.edu/ognm/795639148/temp/index.htm]

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


Mobility-Color-Coded Ribbon Diagram
Figure x: Mode 1
Figure x: Mode 2
Figure x: Mode 3
Figure x: Mode 4
Figure x: Mode 5
Fluctuations per residue for modes 1 to 5
Figure x
Figure x
Figure x
Cross-correlation plot for mode 1 to 5
Figure x

Discussion

TODO

NOMAD-Ref

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.

Usage

Results

Modes 1-6 are rigid body motions, so the interesting ones are mode 7-11. For each mode we have two figures:

  • a) shows the motion of the protein - for modes 1-6 there are no real motions because these are rigid
  • c) shows the rmsd per residue
Mode 7 Mode 8 Mode 9 Mode 10 Mode 11
Figure 51a:

Figure 51c:
Figure 52a:

Figure 52c
Figure 53a

Figure 53c
Figure 54a

Figure 54c
Figure 55a:

Figure 55c

Discussion

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.

Discussion

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 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


Discussion

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

TODO

References

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