Normal mode analysis (Phenylketonuria)

Summary

In this task we consider normal mode analysis (NMAs). A normal mode is described as a model of movement in an oscillating system. Thereby only harmonic motions can be captured by such analyses as the whole system must move with the same frequency, sinusoidally and with a fixed phase relation. Altogether, there are three types of motions with three atoms: the symmetric stretch, the antisymmetric stretch and the scissoring bend<ref name="molWib"> https://en.wikipedia.org/wiki/Molecular_vibration: Molecular vibration, retrieved August 06, 2013. </ref>. To calculate such motions there is a three step algorithm. First a potential function for the system is generated. After that a matrix is calculated representing the force constants. In the last step this matrix is diagonalized. The eigenvectors then correspond to the normal modes and the eigenvalues to the frequency<ref name="nm"> Dykeman et al. (2010): "Normal Mode Analysis and its applications in biological physics" J. Phys.: Condens. Matter 22 doi:10.1088/0953-8984/22/42/423202</ref>. As a matrix for all atoms would be problematic elastic models are created, where all atoms can be used. The atoms are connected with springs<ref name="elMod"> Altigan et al. (2001): "Anisotropy of Fluctuation Dynamics of Proteins with an Elastic Network Model" Biophysical Journal 80, 505–515 doi:10.1016/S0006-3495(01)76033-X</ref>.
In the following we used two different NMA tools. First we examine our protein PAH with WEBnm@ and then again with elNémo, which uses elastic networks. Provided animations are analysed showing the motions with lowest frequencies. Thereby we search for parts of the protein that move together and therefore indicating domains.

Normal Mode Analysis

Lab journal
For the analysis, we used the pdb structure 1J8U from the task before (Task 9 - Structure-based mutation analysis) for our protein PAH. Theoretically 3N-6 modes can be calculated by the NMA tools, where N represents the number of atoms of the molecule and 6 the degrees of freedom.

WEBnm@

WEBnm@ provides a lot of information about the movement of a protein. First you can look at the "Atomic Displacement Analysis", which shows the normalized increasing or decreasing of the Cα atoms of each residue. Additionally there is a "Mode Visualization and Vector Field Analysis" with which the calculated fluctuation can be viewed as vibration and vectors. Another tool is the "Correlation Matrix Analysis" where you can look at the correlations at the movement between the atoms and see, if parts of the protein move together and therefore might be a domain. Futhermore "Overlap Analysis" is provided. There a comparison with a second conformation of the same protein can be viewed. Last but not least the deformation energy and the eigenvalues are presented. For the calculation of the normal modes WEBnm@ only uses the Cα atoms.<ref name="webnma"> Siv Midtun Hollup, Gisle Salensminde and Nathalie Reuter (2005): "WEBnm@: a web application for normal mode analyses of proteins" BMC Bioinformatics 6:52 doi:10.1186/1471-2105-6-52</ref>

Mode 7

Mode 7 captured of WEBnm@. The PAH structure (pdb 1J8U) is shown in transparent green, the ligands in red (H4B: C₉H₁₅N₅O₃) and orange (Fe₂). The blue doted lines represent the movement of the structure.

</figure> <figure id="web_plot7">

Normalized squared displacement per residue for mode 7 to 12. The x-axis represent the residue number in the sequence, whereby 0 is the first of the structure sequence, which is residue 103 in the FASTA-sequence of P00439. The y-axis shows the normalized squared displacement.

</figure>

This mode seems to have a high movement as the blue dotted lines in <xr id="web_mode7"/> are relatively long. Furthermore, they seem to open and close on all sites the same, which gives the imagine of a pump and not a twist. We additionally looked at the movement provided by the webserver, where the "breathing" rhythm could be seen, too. This also can be viewed in <xr id="web_plot7"/>. Between residues 20 and 30 there is a high atomic displacement which also can be seen for residues 240 to 300.

Mode 8

Mode 8 captured of WEBnm@. The PAH structure (pdb 1J8U) is shown in transparent green, the ligands in red (H4B: C₉H₁₅N₅O₃) and orange (Fe₂). The blue doted lines represent the movement of the structure.

</figure> <figure id="web_plot8">

Normalized squared displacement per residue for mode 7 to 12. The x-axis represent the residue number in the sequence, whereby 0 is the first of the structure sequence, which is residue 103 in the FASTA-sequence of P00439. The y-axis shows the normalized squared displacement.

</figure>

Mode 8 of WEBnm@ shows a few differences to mode 7 as there seems to be only an atomic displacement at residues 20 to 50 (<xr id="web_plot8"/>). In <xr id="web_mode8"/> you can see that this is represented in the picture on the right site of the binding site. The animation looks like a hinge-movement. Maybe this helps the protein to bind or release a substrate.

Mode 9

Mode 9 captured of WEBnm@.The PAH structure (pdb 1J8U) is shown in transparent green, the ligands in red (H4B: C₉H₁₅N₅O₃) and orange (Fe₂). The blue doted lines represent the movement of the structure.

</figure> <figure id="web_plot9">

Normalized squared displacement per residue for mode 7 to 12. The x-axis represent the residue number in the sequence, whereby 0 is the first of the structure sequence, which is residue 103 in the FASTA-sequence of P00439. The y-axis shows the normalized squared displacement.

</figure>

Like in the mode before there is only a part of the protein showing a high atomic displacement. This part is between the residues 280 and 310 (<xr id="web_plot9"/>). However, there is also a small part in the beginning which shows atomic displacement of about two in the normalized value. Also you can see in <xr id="web_mode9"/> that there are two parts of the protein that have a high fluctuation, which is at the top of the picture and at the right. The vectors on the right seem to show a backward movement. With all parts moving on the same time, the binding site seems to be opened and closed by this movement.

Mode 10

Mode 10 captured of WEBnm@. The PAH structure (pdb 1J8U) is shown in transparent green, the ligands in red (H4B: C₉H₁₅N₅O₃) and orange (Fe₂). The blue doted lines represent the movement of the structure.

</figure> <figure id="web_plot10">

Normalized squared displacement per residue for mode 7 to 12. The x-axis represent the residue number in the sequence, whereby 0 is the first of the structure sequence, which is residue 103 in the FASTA-sequence of P00439. The y-axis shows the normalized squared displacement.

</figure>

Mode 10 shows a high atomic displacement in some parts of the protein. Especially in the beginning before residue 50 and again after residue 280 (<xr id="web_plot10"/>). However, in <xr id="web_mode10"/> there seems to be not that much movement. In this case the fluctuation seems to go in the direction of the binding site and thereby constricting this.

Mode 11

Mode 11 captured of WEBnm@. The PAH structure (pdb 1J8U) is shown in transparent green, the ligands in red (H4B: C₉H₁₅N₅O₃) and orange (Fe₂). The blue doted lines represent the movement of the structure.

</figure> <figure id="web_plot11">

Normalized squared displacement per residue for mode 7 to 12. The x-axis represent the residue number in the sequence, whereby 0 is the first of the structure sequence, which is residue 103 in the FASTA-sequence of P00439. The y-axis shows the normalized squared displacement.

</figure>

This mode seems to have some similarities with mode 10 in the atomic displacement as there is a high atomic displacement in the beginning and in the end of the protein (<xr id="web_plot11"/>). However, looking at <xr id="web_mode11"/> some differences can be viewed like in the bottom left of the picture, where you can see that the movement has another direction and may be indicate a small twist instead of the closing fluctuation.

Mode 12

Mode 12 captured of WEBnm@. The PAH structure (pdb 1J8U) is shown in transparent green, the ligands in red (H4B: C₉H₁₅N₅O₃) and orange (Fe₂). The blue doted lines represent the movement of the structure.

</figure> <figure id="web_plot12">

Normalized squared displacement per residue for mode 7 to 12. The x-axis represent the residue number in the sequence, whereby 0 is the first of the structure sequence, which is residue 103 in the FASTA-sequence of P00439. The y-axis shows the normalized squared displacement.

</figure>

The last mode in this task provided by WEBnm@ shows highest atomic displacement at residues 25 to 50 (<xr id="web_plot12"/>), but also in the rest of the protein, which also can be viewed in <xr id="web_mode12"/>. Nevertheless, in the upper part of the picture only small vectors are shown, which indicates only small motion, whereas on the lower part there seems to be a left to right movement in the foreground of the protein in this snapshot.

Correlation matrix of the protein PAH (pdb 1J8U) for the residues 103 to 427 of the FASTA sequence. Red color stands for positive correlations and blue for negative.

</figure> <xr id="correlation"/> represents the correlation of the residues of the protein. You can see in the fluctuations that the whole structures move as one and therefore indicate that there is only one domain. This coincides with the fact that PAH consists of two domains, where the second one starts at residue 119 and ends at residue 450. The first domain is not included in the different pdb structures of PAH as it goes from residue 35 to 100.

elNémo

ElNémo computes models for the given protein 1J8U. Thereby it calculates 100 lowest-frequency modes and provides a lot of information about the modes with different parameters and visualizations:

PDB-files with the conformations of the modes
animations of the modes of three different sites
CA-vari (calculates distance fluctuations between all C-alpha atoms)
R² residue mean square displacement of all C-alpha atoms
Frequency and collectivity of the modes

First five modes
Mode	Frequency	Collectivity
mode 7	1.00	0.5475
mode 8	1.02	0.4062
mode 9	1.36	0.2941
mode 10	1.43	0.0948
mode 11	1.60	0.3466

The five modes with lowest frequency for the protein PAH (pdb 1J8U). The first column represents the mode the second one the frequency and the third the collectivity. Mode 10 has a particularly low collectivity (marked in green).

</figtable>

B-factor analysis for the correlation between observed and normal-mode-derived atomi displacement parameters:
Correlation = 0.534 for 307 C-alpha atoms
RMSD: only if two structures are used

Theoretical every number of normal mode perturbed models can be generated. However, a high number would take a lot of time. Therefore, it calculates its 100 lowest frequency modes. On default animation and other parameters it is only computed for five normal modes and can be increased up to 25. Additionally more normal modes can be calculated after the run. The analyses of the five modes with lowest frequency normal modes are shown below. For the calculation of the models the Cα atoms are used. <ref name="elNémo"> Karsten Suhre and Yves-Henri Sanejouand (2004): "ElNémo: a normal mode web server for protein movement analysis and the generation of templates for molecular replacement". Nucl. Acids Res. 32 (2), W610-W614 doi:10.1093/nar/gkh368 </ref>

Mode7

Representation of the PAH (pdb 1J8U) movement calculated by elNémo.

</figure>

Matrix showing the maximal distance fluctuation of PAH (pdb 1J8U). If the distances decrease they are plotted in red, whereas increasing distances are shown in blue, but only if they are under the 10% strongest distance changes.

</figure>

Like mode 7 of WEBnm@ this mode of elNémo seems to have a pumping or "breathing" movement (<xr id="mode7_gif"/>). In principal the whole protein seems to be part of the fluctuation including the β-strand shown in red. The matrix in <xr id="mode7_matrix"/> also shows both increasing and decreasing distances spread over the whole protein.

Mode8

Representation of the PAH (pdb 1J8U) movement calculated by elNémo.

</figure> <figure id="mode8_matrix">

Matrix showing the maximal distance fluctuation of PAH (pdb 1J8U). If the distances decrease they are plotted in red, whereas increasing distances are shown in blue, but only if they are under the 10% strongest distance changes.

</figure>

In <xr id="mode8_gif"/> you can see that the protein opens and closes at the binding site, whereby it looks like an opening and closing mouth. So this mode shows a hinge-movement for our protein PAH. The β-strand (red) does not move much. Additionally in the correlation matrix (<xr id="mode8_matrix"/>) only small parts of the protein seem to move at all and the distances hardly increase, but decrease. In WEBnm@ a similar movement can be seen in mode 8 with just a few residues moving.

Mode9

Representation of the PAH (pdb 1J8U) movement calculated by elNémo.

</figure> <figure id="mode9_matrix">

Matrix showing the maximal distance fluctuation of PAH (pdb 1J8U). If the distances decrease they are plotted in red, whereas increasing distances are shown in blue, but only if they are under the 10% strongest distance changes.

</figure>

In this mode first you can see that the β-strand (red) moves a lot (<xr id="mode9_gif"/>). Like in mode 7 it looks like "breathing", just in a stronger way. In the matrix (<xr id="mode9_matrix"/>) you can see that the residues in the beginning seem to get higher distances to the other residues, whereas from residue 70 a smaller distance to the last 20 residues can be viewed. So with this two parts it has some similarities with mode 9 of WEBnm@.

Mode10

Representation of the PAH (pdb 1J8U) movement calculated by elNémo.

</figure> <figure id="mode10_matrix">

Matrix showing the maximal distance fluctuation of PAH (pdb 1J8U). If the distances decrease they are plotted in red, whereas increasing distances are shown in blue, but only if they are under the 10% strongest distance changes.

</figure>

Mode 10 (<xr id="mode10_gif"/>) has some similarities with mode 8 showing a hinge-movement. Also the β-strand on the right shows nearly no fluctuation. <xr id="mode10_matrix"/> shows some movements on different parts of the protein. In comparison with the modes found with WEBnm@ this mode has some resemblances with both mode 10 and 11.

Mode11

Representation of the PAH (pdb 1J8U) movement calculated by elNémo.

</figure> <figure id="mode11_matrix">

Matrix showing the maximal distance fluctuation of PAH (pdb 1J8U). If the distances decrease they are plotted in red, whereas increasing distances are shown in blue, but only if they are under the 10% strongest distance changes.

</figure>

The fluctuation of mode 11 of PAH (<xr id="mode11_gif"/>) looks very similar to mode 9 (<xr id="mode9_gif"/>) with a "breathing" movement. Additionally the matrices have some resemblances. However, in this case (<xr id="mode11_matrix"/>) there are more increasing distances and only at residue 180 the decreasing distance to the last 20 residues can be seen. This one seems to have no corresponding mode in WEBnm@.

Including Ligands

Remarkably the modes do not change for our protein as we included the ligands Fe₂ and H4B to the molecule. Only mode 7 and 8 are exchanged, which can be seen in the animations of the modes with ligand below.

</figure> </figure> </figure> </figure> </figure>

Mode 7 calculated with elNémo for the PAH protein using pdb structure 1J8U. Thereby the ligands H4B (C₉H₁₅N₅O₃) and Fe₂ are included by changing HETATM to ATOM in the pdb file. This mode is associated to mode 8 without ligand .
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Discussion

A problem with the normal mode analysis (NMA) is that they only look at the backbone of the protein. Changes in the side chains are not considered. However, comparing to MD analysis hardly any previous knowledge is necessary for NMAs and therefore can be used as a starting study of the movement of proteins. Furthermore MD analyses need longer calculation time. Nevertheless, MD is able to look at unharmonic movements. Comparing the two NMA tools WEBnm@ and elNémo, we see that WEBnm@ is faster than elNémo and more user-friendly. However, the calculations are similar with both using the Cα atoms. Therefore, for our protein both tools provided similar outcomes as most modes of the one tool have associations to the modes of the other tool. Additionally you can see that the protein structures of PAH either show a breathing or a hinge-moving, but seldom a twist. In most cases the whole structure is affected of a movement, which coincides with the fact that only one domain is included in the structure.

References

Normal mode analysis (Phenylketonuria)

Contents

Summary