Normal mode analysis Gaucher Disease

Introduction

The protein function often depends on its conformation and dynamical properties. To get a complete picture of the dynamic properties of proteins, the traditional de novo method is known to be Molecular dynamics (MD) simulation. These simulations consider both harmonic and anharmonic motions, and can provide insights into the dynamic of proteins. By taking into account all atoms of a protein, MD simulations shed also light on small motions. However, fine grained MD simulations are computationally very costly which restricts their use to rather short time frames.

An alternative method is Normal mode analysis (NMA) which has become a popular and often used theoretical tool in the study of functional motions in enzymes, viruses, and large protein assemblies<ref name="NMA1">Eric C Dykeman and Otto F Sankey.(2010). Normal mode analysis and applications in biological physics. JOURNAL OF PHYSICS.</ref>. NMA is based on a physical theory about the motion of an oscillation system where all parts within the system move sinusoidally with the same frequency and with a fixed phase relation. By using it to study the protein dynamical motion, the atoms are considered as point masses connected by springs to simulate the inter-atomic forces. NMA uses only harmonic approximations and anharmonic motions are neglected. <ref name="NMA2">Adam D. Schuyler, Gregory S. Chirikjian.(2003). [http://custer.lcsr.jhu.edu/wiki/images/7/76/Schuyler03.pdf Normal mode analysis of proteins: a comparison of rigid cluster modes with Cα coarse graining]. Journal of Molecular Graphics and Modelling.</ref>. Thus, the simulations are not as detailed as MD simulations. Instead, a normal mode refers to the harmonic motion of larger parts of a protein such as domains. Since the normal models can be computed efficiently by matrix decomposition, motions can be simulated over a larger time frame compared to MD simulations. The shape of each normal mode is determined by an eigenvector whose eigenvalue corresponds to the frequency of the normal mode. Normal modes are numbered by their frequency and the lowest frequency mode 7 is often closets to the biological motion of an protein.

In this task, we used different normal mode analysis servers to study the normal modes of chain A of glucocerebrosidase (2nt0).

Technical details are reported in our protocol.

WEBnm@

The WEBnm@ web server provides automated computation and analysis of low-frequency normal modes for proteins. After getting results, the users are thought to have a first glance if the protein contains large amplitude movements and therefore is worth to apply further analyses. WEBnm@ employs the MMTK package (K. Hinsen, J.Comput.Chem., 2000) to calculate the normal modes and only the C-alpha atoms are used. Variety of analysis tools are available:

• Deformation Energies of each mode, eigenvalues
• Atomic displacements and normalized squared fluctuations
• Visualization of the modes
• Correlation matrix

Deformation Energies

For each mode, the deformation energies were given to show the associated energy. And the corresponding eigenvalues indicated the frequency of the motion. <xr id="tab:defor_enery"/> presents the values of the deformation energy for modes 7 to 20 and <xr id="fig:Eigenvalues_plot"/> shows us the the eigenvalues of each mode. The energy values and eigenvalues are increased in modes 7 to 20.

</figtable>

</figure>

The deformation energy for modes 7 to 20
for protein structure 2NT0 chain A from Webnma@.

The Eigenvalues Plot for for protein structure 2NT0 chain A from Webnma@.

<figtable id="tab:defor_enery"> Mode Index Deformation Energy 7 1663.91 8 2377.48 9 2720.71 10 5191.86 11 5033.67 12 6174.70 13 6360.72 14 6698.31 15 9791.69 16 9534.10 17 10022.74 18 11137.44 19 11592.80 20 12045.03

<figure id="fig:Eigenvalues_plot">

Atomic Displacement

In <xr id="fig:atom_disp_7to12"/>, we see the normalized square of the displacement of each C-alpha atom for modes 7 to 12. The sum of that value of all the residues is 100. The cluster of peaks there reflects the region in strong motion and the individual peak shows the local flexibility.

And in <xr id="fig:fluc_plot"/>, we see the normalized the fluctuation of each C-alpha atom for all modes. The sum of that value of all the residues is 100. This fluctuation values are calculated by summing all the atomic displacements from each mode which takes their eigenvalues as weight value. They indicate the normalized temperature factors.

Looking at the displacement plots, in the modes 7, 9, 10 and 11, there are peaks showing throughout the whole protein which suggest that the most parts of this protein are flexible. In mode 8, two individual peaks showing local flexibility at each end of the protein can be found.

</figure>

</figure>

The Atomic displacements plots for modes 7 to 12 for protein structure 2NT0 chain A from Webnma@.

The normalized squared fluctuations for all modes for protein structure 2NT0 chain A from Webnma@.

<figure id="fig:atom_disp_7to12">

<figure id="fig:fluc_plot">

Correlation Matrix

In <xr id="fig:corr_matr"/>, we can see the correlation matrix which presents the correlated movement of the C-alpha atoms of the protein. Each cell shows the isotropic correlation of two residues in the protein on a range from -1 (anti-correlated) via 0 (uncorrelated) to 1 (correlated). Similar to the displacement plots(<xr id="fig:atom_disp_7to12"/>) and fluctuation plot(<xr id="fig:fluc_plot"/>),here we can find again that the red areas around the diagonal indicate that there exist motions throughout the complete protein. And the the region around 0-100 residues and the region around 350-500 residues are somehow relative strongly correlated which reveals a type of isotropic motion of these two regions.

<figure id="fig:corr_matr">

The correlation matrix for protein structure 2NT0 chain A from Webnma@. Each cell in the plot shows the isotropic correlation of two residues in the protein on a range from -1 (anti-correlated) via 0 (uncorrelated) to 1 (correlated).

</figure>

ElNemo

elNémo is the Web-interface to create the Elastic Network Model which is a fast and simple tool to compute the low frequency normal modes of a protein. It was developed by Yves-Henri Sanejouand and co-workers in 1996.

elNémo allows the user to get the low frequency normal modes for a given protein structure in PDB format. There are different analysis tools available:

• compare the collectivity of the modes
• view 3-D animations of the protein movement for each mode
• identify those residues that have the largest distance fluctuations in a given mode.
• Compare B-factors derived from the normal mode decomposition and measured B-factors gives an indication on differences in protein flexibility of the free protein and the protein in a crystallographic environment.

If two conformations of the same protein are uploaded, the user will see the contribution of each mode to the conformational changes (overlap between a protein motion and a normal mode). If two homologous proteins are uploaded, the root mean square distance (RMSD) between all residues and the number of residues that are closer than 3A as a function of mode and perturbation can be computed.

<figure id="fig:elne_model7">

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  Normal Mode 7

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  Normal Mode 7: view of X axis

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  Normal Mode 7: view of Y axis

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  The distance fluctuations between all C-alpha atoms.

The model 7 </figure>

<figure id="fig:elne_model8">

• 

  Normal Mode 8

• 

  Normal Mode 8: view of X axis

• 

  Normal Mode 8: view of Y axis

• 

  The distance fluctuations between all C-alpha atoms.

The model 8 </figure>

<figure id="fig:elne_model9">

• 

  Normal Mode 9

• 

  Normal Mode 9: view of X axis

• 

  Normal Mode 9: view of Y axis

• 

  The distance fluctuations between all C-alpha atoms.

The model 9 </figure>

<figure id="fig:elne_model10">

• 

  Normal Mode 10

• 

  Normal Mode 10: view of X axis

• 

  Normal Mode 10: view of Y axis

• 

  The distance fluctuations between all C-alpha atoms.

The model 10 </figure>

<figure id="fig:elne_model11">

• 

  Normal Mode 11

• 

  Normal Mode 11: view of X axis

• 

  Normal Mode 11: view of Y axis

• 

  The distance fluctuations between all C-alpha atoms.

The model 11 </figure>

References

<references/>