Normal mode analysis GLA

^{by Benjamin Drexler and Fabian Grandke}

Introduction

Normal mode analysis (NMA) is used to examine global movements of proteins. A normal mode is pattern of motion in which all parts move in phase and with the same frequency<ref name=wiki_nma>http://en.wikipedia.org/wiki/Normal_mode</ref>. For this, the atoms of the protein (all atoms or only C-alpha atoms) are converted into point masses and connected by springs. The results of normal mode analysis can be used to determine flexible regions of a protein.

In this task, we apply several webservers to calculate the normal modes of the protein α-galactosidase A and discuss their results. In addition, a comparison of an all-atom approach to a elastic network method is carried out.

Methods

The following sections give a brief explanation about the methods and information about their usage.

WEBnm@

The normal mode analysis webserver WEBnm@ was published by Siv Midtun Hollup, Gisle Salensminde and Nathalie Reuter in 2005<ref name=webnma>Siv Midtun Hollup, Gisle Salensminde and Nathalie Reuter. "WEBnm@: a web application for normal mode analyses of proteins". BMC Bioinformatics 2005, 6:52. PubMed</ref>. It allows the calculation of the normal modes and offers serveral types of analyses, i.e. deformation energy, animation of the vibration, atomic squared displacements and vector field analysis.

Usage

• Webserver: http://apps.cbu.uib.no/webnma/home
• Input
  • PDB structure (ID or file)
  • Specification of chains
• Output
  • Animation of vibration
  • Deformation energy
  • Squared atomic displacements

ElNemo

Karsten Suhre and Yves-Henri Sanejouand published the webserver ElNemo in 2004<ref name=elnemo>Karsten Suhre and Yves-Henri Sanejouand. "ElNémo: a normal mode web server for protein movement analysis and the generation of templates for molecular replacement". Nucleic Acids Res. 2004 Jul 1;32(Web Server issue):W610-4. PubMed</ref>. It is used for the calculation of normal modes and is able to process very large proteins due to a building block approximation. This is, several residues are grouped into a single super residue.

Usage

• Webserver: http://www.igs.cnrs-mrs.fr/elnemo/start.html
• Input
  • PDB structure (file or pasted sequence)
  • Number of modes to calculate (the trivial modes 1 to 6 are excluded in this number)
  • Range of perturbation (DQMIN, DQMAX and DQSTEP)
  • Cutoff used to dentify elastic interactions
• Output
  • Animation of the vibration
  • Distance fluctations between the C-alpha atoms
  • Mean square displacement of all C-alpha atoms

Anisotropic Network Model

Anisotropic network model (ANM) is an elastic network and was introduced by Doruker et al. and Atilgan et al. in 2000<ref name=anm_doruker>Doruker P, Atilgan AR, Bahar I. "Dynamics of proteins predicted by molecular dynamics simulations and analytical approaches: application to alpha-amylase inhibitor.". Proteins. 2000 Aug 15;40(3):512-24. PubMed</ref><ref name=anm_atilgan>Atilgan AR, Durell SR, Jernigan RL, Demirel MC, Keskin O, Bahar I. "Anisotropy of fluctuation dynamics of proteins with an elastic network model.". Biophys J. 2001 Jan;80(1):505-15. PubMed</ref>. The ANM webserver is used to calculate the global modes and was published by Eyal et al. in 2006<ref name=anm_eyal>Eyal E, Yang LW, Bahar I. "Anisotropic network model: systematic evaluation and a new web interface.". Bioinformatics. 2006 Nov 1;22(21):2619-27. Epub 2006 Aug 23. PubMed</ref>. The nodes are represented by the C-alpha atoms and the calculation is based on the spring force constant γ.

Usage

• Webserver: http://ignmtest.ccbb.pitt.edu/cgi-bin/anm/anm1.cgi
• Input
  • PDB structure (ID or file)
  • Cutoff for interactions
  • Distance weight for interactions
• Output
  • Animation of the vibration
  • Fluctuation profiles
  • Inter-residue distance fluctuations
  • Deformation energies

oGNM

oGNM (online Gaussian Network Model) is a webserver to calculate normal modes of biologically functional units (e.g. proteins)<ref name=ognm>Yang, L.-W., Rader, A.J., Liu, X., Jursa, C.J., Chen S.C., Karimi, H, Bahar, I. "oGNM: A protein dynamics online calculation engine using the Gaussian Network Model". Nucleic Acids Res, 34, W24-31, 2006 PubMed</ref>. It was published by Yang et al. in 2006. The calculation times is reduced due to the employment of the Lanczos algorithm to calculate the eigenvalues.

Usage

• Webserver: http://ignm.ccbb.pitt.edu/Online_GNM.htm
• Input
  • PDB structure (ID or file)
  • Cutoff
• Output
  • Mobility diagram
  • Several plots about the fluctuations

NOMAD-Ref

The webserver NOMAD-Ref was published by Landahl et al. in 2006<ref name=nomad>Lindahl E, Azuara C, Koehl P, Delarue M. "NOMAD-Ref: visualization, deformation and refinement of macromolecular structures based on all-atom normal mode analysis". Nucleic Acids Res. 2006 Jul 1;34(Web Server issue):W52-6. PubMed</ref>. It uses the Elastic Network Model (ENM) to calculate the normal modes of proteins.

Usage

• Webserver: http://lorentz.dynstr.pasteur.fr/nma/submission.php
• Input
  • PDB structure (file)
  • Number of modes to calculate (the first six trivial modes included)
  • Distance weight
  • Cutoff
  • Average RMSD in output trajectories
  • Method to solve the matrix
• Output
  • PDB structure with trajectories
  • cRMS-plot

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

The NOMAD-Ref website also provides an alternative to calculate the normal modes. In contrast to the methods which were described ealier this method is not based on elastic network. It uses Gromacs and is a force field-based approach.

Usage

• Webserver: http://lorentz.dynstr.pasteur.fr/gromacs/nma_submission.php
• Input
  • PDB structure (file)
    • The file may contain only lines that begin with ATOM
  • Number of modes to calculate (the first six trivial modes included)
  • Temperature
• Output
  • PDB structure with trajectories

Results & Discussion

α-galactosidase A

We applied five webserver (WEBnm@, ElNemo, ANM, oGNM and NOMAD-Ref) with the protein α-galactosidase A. We used the PDB structure 1R47 as input and restricted the computation to chain A. The results for the modes 7 to 12 are discussed in the following sections.

Supplementary animations and plots are provided on this page: Supplementary Page

Mode 7

WEBnm@	ElNemo	ANM	oGNM	NOMAD-Ref

The results of the webservers display a high degree of consensus. Especially the beta strands on the right side show a strong movement in the down direction. This movement can also be expressed as a twist movement which is the strongest in the results of ANM, ElNemo and NOMAD-Ref. It seems like that there is also a fluctuation of a large part on the left side which could be driven by the twist movement on the right side.

These obversations in the animations can also be seen in the presentation of oGNM that highlights the beta strands on the right side and also indicates some sort of flexibility on the left side. It is very likely that these flexibility results in a motion which is similar to the movement of the results of the other webservers.

Mode 8

WEBnm@	ElNemo	ANM	oGNM	NOMAD-Ref

Similar to mode 7, there is a strong type of twist movement in the outer parts of the molecule for the most part of the results. This time the fluctuation goes upwards on the right side in the results of ANM, ElNemo and WEBnm@. These three results differ only in the fluctuations of the left side. The range of motion decreases from high (ANMN) to almost none (WEBnm@).

The mode 8 of NOMAD-Ref is very similar to the mode 7. Mode 8 shows an increase of flexibility which is especially the case for the left part. The result of NOMAD-Ref is similar to the three results of ANM, ElNemo and WEBnm@, but the right side moves slightly in a different direction.

The presentation of oGNM differs totally from the other results. oGNM predicts that the most flexible regions are alpha-helices on the upper and lower part. These areas barely move in the results of the other webservers.

Mode 9

WEBnm@	ElNemo	ANM	oGNM	NOMAD-Ref

Again, we have the most kind of movement in the outer parts of the molecule and the five results exhibit a high degree of consensus. This time, the fluctuation resembles more the movement of a hinge than a twist movement. This is especially observable for the results of ANM and NOMAD-Ref, because the range of motions seems to be bigger than in the results of WEBnm@ and ElNemo.

The presentation of oGNM also indicates a flexible region of an alpha-helix in the middle, which is also noticeable in the results of ElNemo, ANM and NOMAD-Ref.

Mode 10

WEBnm@	ElNemo	ANM	oGNM	NOMAD-Ref

The results of ElNemo, ANM and NOMAD-Ref display some kind of twist movement in the outer parts of the molecule. This twist movement is achieved by the flexibility of three small areas in the result of ANM and probably also in the result of ElNemo, whereas the result of NOMAD-Ref seems to be more global. That is, the range of motion seems to be the biggest for NOMAD-Ref and the smallest for ElNemo.

A totally different kind of motion is displayed by the result of WEBnm@. The result shows some sort of a stretch motion in the horizontal axis with the right part being the most flexible one.

oGNM indicate flexible regions in alpha-helices in the upper and lower part of the molecule. This is very similar to mode 8, but this time the flexibility is lower which can be seen by the less intense red. Just like at mode 7, the result shows distinction to the result of the other webservers.

Mode 11

WEBnm@	ElNemo	ANM	oGNM	NOMAD-Ref

It is very tough to recognize a clear trend in the movements for this mode. The result of ANM shows the same stretching motion like mode 10 of WEBnm@. It could be the case that the molecule undergoes the same fluctuations in the result of ElNemo, but it is not that noticeable.

The result of WEBnm@ is very similar to the twist motion of mode 10 of ElNemo, ANM and NOMAD-Ref.

The presentation of oGNM is tough to interpret. There are two very flexible regions, i.e. a coil on the left side and a coil and a part of a beta strand on the right side. We do not assume that these flexible regions result in a motion witch is similar to a mode of the other webservers.

Mode 12

WEBnm@	ElNemo	ANM	oGNM	NOMAD-Ref

A distinct coil region on the left side shows a very high amount of motion in the result of ANM. This movement can also be observed in the result of ElNemo. The presentation of oGNM is almost entirely blue which suggest an rigid molecule. Only the coil on the left side and a coil region on the right side have a red color and this fits very well with the observed motions in the result of ANM and ElNemo.

The result of NOMAD-Ref displays the twist movement which was also observed in ealier modes and it covers a very wide range of motion.

The molecule in the result of WEBnm@ undergoes a stretching motion which is very similar to the movement in the mode 10 of WEBnm@.

Discussion

First of all, we discuss a general observation about the results. It was noticeable that the higer the examined mode is the more divergent the results get. But it was still possible to see similarities between the results of the different webservers. Not only in the same mode, but also in nearby modes. This is not surprising, since the higher the mode gets the more degrees of freedom are available and hence it gets more complex.

The most abundant type of motion was a twist movement of the molecule. This is, the left and the right parts move in opposite directions. It is tough to connect this sort of movement with the biological meaning of the protein. It is somehow noteworthy that the region where the ligand of the proteins binds (referring to the animations, this region is nearby some beta-strands on the left side, see figure 1) was rarely involved in the movements.

Figure 1: α-galactosidase A (blue) in cartoon representation and the ligand (red) in sticks representation. (A) This perspective was used for the presentation of the results of the normal modes. (B) A close-up of the ligand in the protein.

Bovine Pancreatic Trypsin Inhibitor

We applied an all-atom method to calculate the normal modes. The calculation of NOMAD uses Gromacs and is force field-based. The method is limited to small proteins (2000 atoms). Bovine pancreatic trypsin inhibitor (BPTI) has a length of 58 amino acids and was used as an input (PDB structure 1BPT).

The calculation was carried out with a temperature setting of 600K and 2000K, respectively. In the following sections, we discuss the results and compare them to the results of the webserver NOMAD-Ref which is based on an elastic network approach.

Mode 7

All-Atom NMA (600K)	All-Atom NMA (2000K)	NOMAD-Ref

The only difference between the two all-atom (600K and 2000K) results is the larger range of motion of the 2000K result and this is probably due to the higher temperature. We expect to observe this also in all the following modes. The most flexible region is a coil in the lower front part and all the other fluctuations seem to be induced by the movement of this coil.

This coil is also the most flexible part in the result of NOMAD-Ref. It undergoes a stretching movement in the horizontal axis. Similar to the all-atom results, this stretching of the coil region seems to induce the other movements of the molecule. Overall this result displays a much higher degree of flexibility.

Mode 8

All-Atom NMA (600K)	All-Atom NMA (2000K)	NOMAD-Ref

The results of the all-atom method shows a movement of the coil region in the lower front and a slight movement of the alpha-helix in the top. Due to these fluctuations, the distance between these regions increases. The result of NOMAD-Ref shows a very similar motion of these two regions, but only exaggerated. Hence the whole molecules seems to be involved in the movement.

Mode 9

All-Atom NMA (600K)	All-Atom NMA (2000K)	NOMAD-Ref

In the result of the all-atom methods, the coils in the lower front move down, whereas the remains of the molecule stay at the same place. This movement is exaggerated in the result of NOMAD-Ref. One beta-strand in the lower left back is also involved in the down motion and all the other parts move upwards.

Mode 10

All-Atom NMA (600K)	All-Atom NMA (2000K)	NOMAD-Ref

Once again, the most flexible region is the coil region in the lower front of the all-atom result, but this time the beta-strand on the left and the alpha-helix in the back seem to be also involved. Overall the fluctuations of the molecule looks like breathing motion.

This time it is not possible to recognize a similar movement in the result of NOMAD-Ref. In this result, the molecule acts like a seesaw with every part being involved in the movement.

Mode 11

All-Atom NMA (600K)	All-Atom NMA (2000K)	NOMAD-Ref

The results of mode 11 are similar to mode 9 for the all-atom methods. The difference is bigger between the results of NOMAD-Ref. In contrast to the results of mode 9, a larger part of the coil region is also involved in the upward motion and overall the fluctuations become more lateral.

Mode 12

All-Atom NMA (600K)	All-Atom NMA (2000K)	NOMAD-Ref

For the results of the all-atom methods, there is no especially flexible region, but there are slight fluctuations in almost every part of the molecule. This is also true for the result of NOMAD-Ref, but the movements become exaggerated once again. The most flexible part are the coil regions and the beta strands in the lower front and their fluctuions resemble some sort of twist movement.

Discussion

The differences are very small between the results with a temperature of 600K or 2000K, respectively. The range of motion increases with a temperature of 2000K, which is due to the higher temperature. In comparison to the results of the elastic network method (NOMAD-Ref), it is often the case that it is possible to recognize the same type of movements in both results. The all-atom results seem to describe the movements finer, whereas the results of NOMAD-Ref exaggerate the fluctuations. So it could be the case that the motions of the all-atom approach represent the reality more realistic. On the other hand, it is easier to identify the most flexible regions in the results of an elastic network method which is a purpose of a normal mode analysis.

References

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