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 mehthod is known to be Molecular dynamics (MD) simulation. These simulations consider both harmonic and anharmonic motions, and produce great insights into protein dynamics. When the timescales of the dynamics is short enough, MD is a great tool. However this method is still very computationally consuming.

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, therefore it can not give a very precise simulation as MD does. However, it is still very helpful to describe the low-frequency, large-amplitude motions which are most closely related to protein function<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>.

In this task, we used different normal mode analysis servers to study 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

"Deformation energies and eigenvalues reflect the energy associated with each mode and are inversely related to the amplitude of the motion described by a the corresponding modes. The protein structure moves along all the normal modes at once. A mode should only be interpreted in isolation if it is energetically well separated from other modes. " - from Webnma@

Below are the values of the deformation energy for modes 7 to 20.

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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:Eingenvalues_plot">

Atomic Displacement

" Atomic displacements:

The square of the displacement of each Calpha atom (for modes 7 to 12), normalized so that the sum over all residues is equal to 100.

Highest values correspond to the most displaced regions. On the plots, one should look for cluster of peaks, those identify significantly big regions. Isolated peaks reflect local flexibility and are not relevant. Fluctuations

The square of the fluctuation of each Calpha atom (for all non-trivial modes), normalized so that the sum over all residues is equal to 100.

The fluctuations are the sum of the atomic displacements in each mode weighted by the inverse of their corresponding eigenvalues. These are equivalent to the normalized temperature factors.

Results can be retrieved as plots at the PNG format or raw data (first column: resid, second column: normalized squared atomic displacement/fluctuation) " - from Webnma@

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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@.

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<figure id="fig:fluc_plot">

Correlation Matrix

"The correlation matrix shows the correlated movement of the Calphas in the protein. Both axis denote the Calphas of the protein in sequential order, so that 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). " - from Webnma@

<figure id="fig:corr_matr">

The correlation matrix for protein structure 2NT0 chain A from Webnma@.

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ElNemo

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The model 7 </figure>

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The model 8 </figure>

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The model 9 </figure>

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The model 10 </figure>

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The model 11 </figure>

References

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