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). 2nt0_A is has N=496 residues such that there are altogether 3N-6=1482 normal modes. Each mode is defined by an eigenvector and its corresponding eigenfrequency. The eigenvector contains the amplitude and direction of motion for each atom. In mode i, all N atoms oscillate at the same frequency.

Technical details are reported in our protocol.

WEBnm@

Introduction

WEBnm@<ref name="webnma">Siv Hollup, Gisle Salensminde, and Nathalie Reuter. WEBnm@: a web application for normal mode analyses of proteins. BMC Bioinformatics, 6(1):52+, 2005.</ref> is a web server for automatically computing and analysing low-frequency normal modes of proteins. WEBnm@ is based on the Elastic Network Model (ENM) and only takes into account the C-alpha atoms. For computing the 200 lowest frequency mode, WEBnm@ employs the MMTK package[1]. The server offers various methods for investigating the resulting normal modes:

Visualization of the modes
Deformation Energies
Atomic displacements and normalized squared fluctuations
Correlation matrix for investigating the which residue movements are correlated

Deformation Energies

The deformation energy is the potential energy of the motion described by a normal mode. <xr id="tab:defor_enery"/> lists the deformation energy of mode 7 to 20 and <xr id="fig:Eigenvalues_plot"/> shows the respective eigenvalue which corresponds to the frequency of the mode. The deformation energy is positive correlated with the eigenvalue, i.e. modes with a higher frequency also exhibit a higher deformation energy.

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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

The deformation energy of mode 7 to 20
of protein structure 2NT0 chain A computed by Webnm@.

Normal mode eigenvalues of 2NT0 chain A computed by Webnma@.

Correlation Matrix

<xr id="fig:corr_matr"/> depicts correlated motions of C-alpha. Each cell shows the isotropic correlation of two residues in the protein from -1 (anti-correlated) over 0 (uncorrelated) to 1 (correlated). The red areas along the diagonal suggest smaller local correlations. In addition, the N terminal region (1-100) is correlated with the C terminal region (350-500), that is, the beginning and the end of the protein exhibit similar motions.

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).

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Atomic Displacement

<xr id="fig:atom_disp_7to12"/> shows the normalized square of the displacement of each C-alpha atom for mode 7 to 12. Narrow peaks denote local movements whereas broad peaks indicate larger flexible protein regions. <xr id="fig:fluc_plot"/> depicts the normalized fluctuation of each C-alpha atom calculated by averaging over the atomic displacements of all modes which are weighted by their eigenvalue.

Except for mode 9 and mode 10, the most flexible regions are at the beginning and at the end of the protein. All modes have clear peaks around range 55-65 and 439-442, which are also pronounces in <xr id="fig:fluc_plot"/>. Furthermore, these two regions seem to be correlated (<xr id="fig:corr_matr"/>). We therefore visualized residue 55-65 and 439-442 (<xr id="fig:webnma_displacement"/>) and found that they are part of two loop regions on the surface. These two loop regions are significantly more flexible than other parts of the protein such as the active site residues E235 and E340 which both exhibit small displacement values for most modes.

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

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</figure> </figure>

The normalized squared fluctuations for all modes for protein structure 2NT0 chain A from Webnma@.
<figure id="fig:fluc_plot">
<figure id="fig:webnma_displacement">

Mode Visualization

Animation of normal mode 7
Vectors of normal mode 7
Mode 7 exhibits a bending movement.

The visualization of mode 7 and the vectors showing the direction of the movements. </figure>

Animation of normal mode 8
Vectors of normal mode 8
In Mode 8, loop regions are moving most. The amplitude is smaller compared to mode 7.

The visualization of mode 8 and the vectors showing the direction of the movements. </figure>

Animation of normal mode 9
Vectors of normal mode 9
Mode 9 exhibits a shearing moving of the two protein domains.

The visualization of mode 9 and the vectors showing the direction of the movements. </figure>

Animation of normal mode 10
Vectors of normal mode 10
For mode 10, also alpha helical regions in the middle of the protein are moving with a small amplitude.

The visualization of mode 10 and the vectors showing the direction of the movements. </figure>

Animation of normal mode 11
Vectors of normal mode 11
In mode 11, all parts of the protein a slightly moving similar to mode 10.

The visualization of mode 11 and the vectors showing the direction of the movements. </figure>

Animation of normal mode 12
Vectors of normal mode 12
Mode 12 exhibits a hinge like movements which displaces in particular loop region 55-65.

The visualization of mode 11 and the vectors showing the direction of the movements. </figure>

Comparison of different conformations

To do: compare different conformations, for example: 2NT0 and 3GXI.

ElNemo

Introduction

elNémo<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 Research, 32(suppl 2):W610–W614, July 2004.</ref> is a normal mode web server for protein movement analysis. Just as Webnm@, ElNeno employs the Elastic Network Model (ENM) for computing the lowest frequency modes. Interaction forces are computes between C-alpha atoms only and a cut-off distance (default 8 A) specifies the number of neighbouring atoms which are taken into account in the computations. The cut-off distance can be arbitrarily adjusted by the user and is a trade-off between runtime and approximation accuracy. ElNema further employs the Rotational Translation Block (RTB) algorithm for speeding up the calculations by grouping a several residues to super residues. The ElNemo web-interface takes a PDB structure as input and computes the 100 lowest frequency modes which can be investigated in different ways:

viewing 3-D animations of the protein movement for each mode
comparing the collectivity of the modes
identifying residues that have the largest distance fluctuations in a given mode.
comparing B-factors derived from the normal mode decomposition to experimentally determined B-factors for analysing to which extend their flexibility differs

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 as well as the number of residues that are closer than 3A to the function of mode and perturbation can be computed.

Mode Visualization and distance fluctuation

In the following figures, the visualization of model 7 to 11 and their distance fluctuation are shown. The structure is presented from three different orthologuous viewpoints where the secondary structures are determined from the C-alpha atom positions of the uploaded protein (N-terminal blue, C-terminal red). In the distance fluctuation map, each cell measures the relative movement between a pair of residues. One can find the rigid and the flexible regions of the protein, as well as their relative movements. The regions where amino acid residues move as rigid bodies are shown in black whereas flexible segments are colored blue or red. The blue parts indicate where the distance between two C-alpha atoms increases significantly, and the red parts where the distance decreases.

Normal Mode 7: view through Z axis
Normal Mode 7: view through X axis
Normal Mode 7: view through Y axis
The distance fluctuations between all C-alpha atoms.
Mode 7 presents a bending and stretching movement.

The visualization of mode 7 and its distance fluctuation. </figure>

Normal Mode 8: view through Z axis
Normal Mode 8: view through X axis
Normal Mode 8: view through Y axis
The distance fluctuations between all C-alpha atoms.
Mode 8 presents a bending and stretching movement as similar to mode 7 but towards different direction.