Canavan Disease: Task 10 - Normal Mode Analysis

Normal Mode Analysis is a way to predict the dynamics behind a protein. Here elastic network models are used, since they are very memory reducing.

Background

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Eigenvalues of WEBnm@ starting with mode 7

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There are several servers available, which can give some indication of the movement and dynamics within the protein. There are three main approaches to do this:

• Molecular Dynamics (MD)
• Normal Mode Analysis (NMA)
• Elastic Network Models

The main problem within Molecular Dynamics is the CPU-Power. The calculation of dynamics behind a protein depends on the timespan (micro-, nano-, pico or even femtoseconds). The smaller the timespan is chosen the better gets the prediction in the end, but on costs of CPU Power.
A much faster approach is Normal Mode Analysis (Reference). Always the lowest energy levels show the formations the protein can make. To calculate the modes, a Hessian Matrix is internally calculated, since its eigenvectors represent the normal modes. Those with the lowest frequencies (soft modes) are the best normal modes, since it descrobes the largest movements. The eigenvalues ot the vectors are the squares of frequencies (compare <xr id="eigen"></xr>). There are also zero-frequency modes, which represent the global movement of the protein (in WEBnm@ and NOMAD the first six). As it can be seen in the results of WEBnm@, the deformation energies, which represent the low-frequency movements are increasing with increasing mode. Taking Elastic Network Models into account (as NOMAD do), the calculation in finding the best energy level to start, is much easier. An elastic network represents a set of harmonic potentials between atoms. The CPU-Power is not affected as much as in Molecular Dynamics, the prediction on the other hand is not as distinctive as in Molecular Dynamics.

For this Task two servers WEBnm@ and NOMAD were used to calculate normal modes of aspartoacylase using the PDB-structure 2O4H. The severs provide different possibilities calculating the nomal modes. <xr id="servers"></xr> gives an overview of the differences and similarities between the servers:

<figtable id="servers">

Differences and Similarities in WEBnm@ and NOMAD
Comparison	Webnm@	NOMAD
Background (see References)	WEBnm@ is using the MMTK package: MMTK calculates the low-frequence domain movements using an approximate normal mode calculation method by Hinsen et al. 200 modes are calculated for proteins with less than 1200 residues. Proteins with more than 1200 residues (N>1200) will bring N/6 modes. Only the lowest frequency modes should be taken into account. Therefore WEBnm@ presents the modes 7-12 to its users.	NOMAD makes its calculation using Elastic Network Models (or classical force fields): The Elastic Network Models (ENM) bring the advantage that a prior energy minimization to find the eigenvectors in the Hessian Matrix is not needed. The ENMs represent a set of harmonic potentials between atoms. This state represents the global minimum. Up to 160 modes are allowed to be calculated. The user has the possibility to choose how many modes.
	Calculation implies the use of the Hessian Matrix, since its eigenvectors represent the normal modes. The first 6 (zero-frequency) modes represent the global rotation and translation of the protein
Which part of the structure is taken into account for the calculation?	C-alpha atoms only
	-	2 further options: all atoms, sidechains only
Which analysis tools are available?	visualization, fluctuations, eigenvalues
	deformation energies, atomic displacements, correlation matrix	frequencies, overlap coefficients, structure minimization using GROMACS (only structures with less than 3000 atoms)
What options do I have?	choosing chain of protein, Comparative Analysis	Number of modes to calculate (first six ones are translation and rotation), distance weight (for elastic constant), ENM Cutoff (for mode calculation), Average Rmsd (in output trajectories)

Comparison of the servers WEBnm@ and NOMAD.

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WEBnm@

This section shows the result of WEBnm@. The first column decribes the mode. The second shows a vector-like representation on aspartoacylase. The third is the movement and at last diplayes id the atomic disreplacement/fluctuation curve. The atomic disreplacement / fluctuation curve always shows which atoms do a major movement (not considered directions):

Mode 7: Deformation Energy: 1429.83 Hinge movement of two rigid protein parts, the bottom left loop region and the upper right helix and sheet region.
Mode 8: Deformation Energy: 1740.31 A small hinge movement between the bottom left loop region and the rest of the protein additionally to a inwards turning movement of th loop region.
Mode 9: Deformation Energy: 2545.68 The bottom left loop region and the upper right helix/sheet region describe a hinge movement that is orientated towards the back of the visible plane.
Mode 10: Deformation Energy: 3584.30 The motion visible for mode 10 is best described as at form of the protein tightening itself around the binding site. During that process the most felxible part seems to be the loop region in the bottom left area of the image.
Mode 11: Deformation Energy: 4202.00 Mode 11 describes a breathing movement of the upper part of the protein. The lower left loop region is contrary to the other modes a more rigid part of the protein.
Mode 12: Deformation Energy: 5480.10 In mode 12 a combined breathing and streching of the whole protein is visible. The area around the binding site seems to be almost unaffected and very rigid, whereas the surface parts of the protein are mor flexible.

Since aspartoacylase has a bound zinc ion, a comarison using a structure without the ligand was necessary. Therefore the ligand was deleted from the PDB-structure. To check for differences the correlation matrix (<xr id=correlation></xr>) and the normalized fluctuation of the protein (<xr id=fluctuation></xr>) were compared with the ones build for the structure without the ligand. There was no difference. This may be due to the fact, that the Zinc is important for the function however not important as a stabilizing factor, and the stabilazation that occurs at the active site is determined by secodnary structure elements.

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The correlation matrix over all modes calculated by Webnm@ for 2O4H. The matrix displays the movemnt correlation between residues.

The normalized fluctuation for all modes of 2O4H. This graph summuarizes which parts of the protein have a high and low movement fluctuation within the protein.

<figure id="correlation">

<figure id="fluctuation">

NOMAD

Since there was a problem using the server, elNemo could not be taken into account. Therefore NOMAD was chosen to predict normal modes.
NOMAD has the possibility to choose whether the prediction should be calculated on the backbone, only on sidechains, or on all atoms. Here the calculation was done for all atoms. The result for modes 7 to 12 are shown below. The first column describes the mode, the second shows the movement and the third displays the fluctuation curve. As in WEBnm@ the atomic disreplacement / fluctuation curve always shows which atoms do a major movement (not considered directions). Other than in WEBnm@ here all atoms were taken into account.

Mode 7: The motion of the protein completely centres around the binding pocket. Overall it is a seesawing motion of all parts towards the centre with the most flexible part being the lower left loop region. The secondary structure elements are the most rigid parts.
Mode 8: In mode 8 a hingelike motion is detectable, that is centring around the active site of the protein, and looks like a clamming of the protein to the potential substrate. The outer loopregions are the most flexible parts of the protein, whereas the secondary structure elements are the most stable.
Mode 9: Mode 9 is sort of a combination of the clamming movement of mode 8 and the seesaw movement of mode 7. Again the motion seems centred around the binding pocket of the protein.
Mode 10: This mode has like mode 8 a hinge like motion with the difference to mode 8 being that he imaginary plane that defines the hinge movement is orientated differently. As with the other modes the motion is centred around the binding pocket and the most flexible part is the loop region in the bottom left.
Mode 11: The motion of model 11 is best described as if two planes of the protein are moved into opposite directions. Centre of the motion, the most flexible and rigid parts of the protein are the same as with the other modes.
Mode 12: Mode 12 combines the clamming motion of mode 8 and 10 with a breathing of the protein. Interpreting this motion tends to give the same result as before, with motion surrounding the active site, and the loop regions being the most flexible.

Comparison

Comparing all modes calculated by both methods demonstrates that the least motion happens at the binding pocket of the protein. This is visually detectable from the pymol representation of the modes as well as from the corresponding fluctuation curves. Especially the normalized fluctuation curve over all modes highlights this observation. Additionally it can be seen that the most flexible part of the protein is the loop region ranging approximately form residue 225 to residue 270. Although comparing the corresponding modes by Webnm@ and Nomad does not always result in the same motion, the fluctuation curves do correlate. Looking at the lower numbered modes it may be assume that there are two domains one being the loop region. However this clear separation of movement blurs into an overall movement of the protein if looking at the higher numbered modes. Therefore it can be assumed that the protein has no separate multiple domains but is made up out of only one domain. Comparing this assumption with the annotations in Pfam and CATH the one domain theory can be validated.

References

official papers:

• WEBnm@
• NOMAD

Tasks

• Link to Task 01: Canavan Disease
• Link to Task 02: Alignments
• Link to Task 03: Sequence-based Predictions
• Link to Task 04: Structural Alignments
• Link to Task 05: Homology Modelling
• Link to Task 06: Protein Structure Prediction from Evolutionary Sequence Variation
• Link to Task 07: Researching SNPs
• Link to Task 08: Sequence-based Mutation Analysis
• Link to Task 09: Structure-based Mutation Analysis
• Link to Task 10: Normal Mode Analysis