Normal Mode Analysis (PKU)

Short Task Description

This week, we will perform a normal mode analysis of our wildtype protein. We will calculate and visualize large coordinate movements to identify e.g. domains and try to watch ligand interaction. For this, we will use the webnm@ and elNemo webservers. See the task description for details, a journal of commands and scripts, if necessary, can be found here.

Normal Mode Analysis

In normal mode analysis (NMA) the protein is modeled as a harmonically oscillating system to e.g. describe conformational changes. Normal modes are much faster to calculate than a molecular dynamics simulation, especially as usually very few low-frequency modes suffice to describe a protein's motions.<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 Volume 32, Issue suppl 2</ref> Often, models do not include the sidechains of a protein so the effect of mutations can not be detected. Also, non-harmonic motions are not observable which limits the insights gained from NMA in comparison to the much more detailed molecular dynamics simulation.

There are 14 unmutated structures of human phenylalanine hydroxylase, some of them with different ligands e.g. the co-factor tetrahydrobiopterin, the co-factor and thienylalanine (thienylalanine is a receptor antagonist to the substrate phenylalanine) or the co-factor and norleucine. As can be seen from <xr id="tab:rmsd"/> of RMSD values below, unfortunately they are all in the same conformation. There are also phosphorylated and unphosphorylated structures of PheOH of rattus norvegicus (1PHZ and 2PHM in <xr id="tab:rmsd"/>) but they also are virtually identical with a RMSD of 0.330. When we submit 1J8U and e.g. 1MMT, the structures with the highest RMSD, we see very little contribution of the low frequency modes, but get an overlap of the high frequence modes and the 'conformational change' of over 0.82, which in this case means the change is indeed only a very small motion that does not fit to the larger changes possible in the protein (as shown by the low frequency normal modes). Therefore, the different structures are not of much value for the analysis, the structural changes are very small and limited to some displaced loops and we cannot compare different conformations. Instead we will use the 1J8U structure with and without ligand in the analysis.

<figtable id="tab:rmsd"> RMSD of human phenylalanine hydroxylase structures in PDB to the 1J8U reference structure

PDB ID	RMSD to 1J8U
1J8T	0.111
1DMW	0.150
1KWO	1.583
1LRM	0.167
1MMK	1.586
1MMT	1.640
1PAH	0.278
2PAH	0.590
3PAH	0.288
4PAH	0.283
5PAH	0.286
6PAH	0.280
4ANP	0.220
1PHZ (rattus n.)	0.380
2PHM (rattus n.)	0.409

</figtable>

WEBnm@

Mode 7

This mode shows a high atomic displacement for the start (residue 20-40) and parts of the end begining with residue 240-300 in <xr id="fig:mod7dis" /> this also can be seen in <xr id="fig:mode7" /> where the image of a beating heart comes to mind. We therefore classify this as a pumping motion which opens the protein to the substrate.

<figure id="fig:mode7">

Animation of mode 7 from WEBnm@. Original pdb-structure is colored green. BH4 is colored yellow and the Fe2+ ion is colored in red. The mesh represents the model gained from WEBnm@.

</figure>

<figure id="fig:mod7dis">

Atomicdisplacement per residue for mode 7 provided by WEBnm@

</figure>

Mode 8

Like in Mode 7 this mode opens the catalytic site which can be either to be able to bind, or to release the substrate or the product in respect. In difference to <xr id="fig:mod7dis" /> there is a rather small part (residue 25-40) of the molecule in this mode which is moving, as one can see in <xr id="fig:mod8dis" />. This is also easy to be seen in <xr id="fig:mode8" /> where only the lower left part of the protein is moving

<figure id="fig:mode8">

Animation of mode 8 from WEBnm@. Original pdb-structure is colored green. BH4 is colored yellow and the Fe2+ ion is colored in red. The mesh represents the model gained from WEBnm@.

</figure>

<figure id="fig:mod8dis">

Atomicdisplacement plot per residue for mode 8 provided by WEBnm@

</figure>

Mode 9

Like in Mode 8 only a small part (residue 290-300 in <xr id="fig:mod9dis" />) are moving a lot, but still the protein is in some kind of pumping dynamic (<xr id="fig:mode9" />) with mostly the lower right side moving. This creates the idea of compressing the room inside the protein, in order to rearrange or even retract the substrate.

<figure id="fig:mode9">

Animation of mode 9 from WEBnm@. Original pdb-structure is colored green. BH4 is colored yellow and the Fe2+ ion is colored in red. The mesh represents the model gained from WEBnm@.

</figure>

<figure id="fig:mod9dis">

Atomic displacement plot per residue for mode 9 provided by WEBnm@

</figure>

Mode 10

This mode is the first of the provided modes, we would not associate with a pumping or beating heart, but rather with a stretching motion, there is no clear tendency to be found for the protein which affects binding or catalytic domain (<xr id="fig:mode10" />). In difference to the structural changes, the displacement plot in <xr id="fig:mod10dis" /> shows a clear sign of strong movement in the beginning (residue 25-40) as well as in the end (residue 270-300) with a bit smaller movement shown by some peaks in the middle of the sequence.

<figure id="fig:mode10">

Animation of mode 10 from WEBnm@. Original pdb-structure is colored green. BH4 is colored yellow and the Fe2+ ion is colored in red. The mesh represents the model gained from WEBnm@.

</figure>

<figure id="fig:mod10dis">

Atomic displacement plot per residue for mode 10 provided by WEBnm@

</figure>

Mode 11

This mode again moves only the end and the beginning of the protein, with similar compartmentalization like the modes 7 to 10 (<xr id="fig:mod11dis" />), but this time, the movement classifies as a torsion of the protein, which shears along the diagonal of the protein in <xr id="fig:mode11" />. This could either be a random movement or the torsion, which splits the substrate into pieces.

<figure id="fig:mode11">

Animation of mode 11 from WEBnm@. Original pdb-structure is colored green. BH4 is colored yellow and the Fe2+ ion is colored in red. The mesh represents the model gained from WEBnm@.

</figure>

<figure id="fig:mod11dis">

Atomic displacement plot per residue for mode 11 provided by WEBnm@

</figure>

Mode 12

This mode unlike any other we had before offers a very small atomic displacement range (<xr id="fig:mod12dis" />) as the peak is only about 3 at residue 40, but the structure is moved quite a bit in this mode. This mode deforms the binding site in the center of the protein and also stretches the protein to the diagonal of the protein (<xr id="fig:mode12" />)

<figure id="fig:mode12">

Animation of mode 12 from WEBnm@. Original pdb-structure is colored green. BH4 is colored yellow and the Fe2+ ion is colored in red. The mesh represents the model gained from WEBnm@.

</figure>

<figure id="fig:mod12dis">

Atomic displacement plot per residue for mode 12 provided by WEBnm@

</figure>

Correlation plot

<figure id="fig:correleationWebnma">

Displayment of the correlation matrix provided by WEBnm@. This is a residue against residue plot, which shows the movement correlation of those two residues, where red indicates high correlation.

</figure>In this plot (<xr id="fig:correleationWebnma" />) one can see, that the correlated movements are very sparse in our protein. Only a few small correlations apart from the diagonal can be seen. One example is around residue 240 or 300. Apart from these two, there is no real correlation among the domains or intuitive way of finding or seperating domains from this plot alone.

elNemo

ElNemo computes ten perturbed models for the first five non-trivial normal modes of the input protein as a standard and perturbations for the lowest 25 modes on request in a separate queue. There is no fixed limit to the size or number of modes but too long running jobs will eventually be killed. The calculation uses a cutoff value to determine which atom-atom interactions are kept in the elastic network model and another parameter to determine how many residues are treated as rigid body to speed up calculation appropriately.

1J8U (without ligand)

Mode 11 and especially mode 8 could show an opening of the catalytic subunit to allow access to the active site. Mode 8 is also the only one, where the termini of the sequence do not move. As the crystal structure is truncated on both ends, the strong movement other modes show there is probably arbitrary .

Mode 7

<figure id="fig:1J8U_nm7">

The crystal structure of 1J8U in transparent green and the normal mode 7 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U_nm7_fluc">

The relative fluctuations of the C alpha atoms of 1J8U computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 7.

</figure> This mode seems to correspond to mode 7 of Webnm@. It shows a strong squeezing of the whole protein. bending helices and sheets, that possibly opens and closes the binding pocket to the ligand or subtrate. The fluctuation matrix in <xr id="fig:1J8U_nm7_fluc"/> shows how the C-terminal parts of the protein move closer, while the parts at the start and middle move slightly apart.

Mode 8

<figure id="fig:1J8U_nm8">

The crystal structure of 1J8U in transparent green and the normal mode 8 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U_nm8_fluc">

The relative fluctuations of the C alpha atoms of 1J8U computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 8.

</figure> This mode seems to correspond to mode 8 of Webnm@. We see the same wide bending of the helix at the left in <xr id="fig:1J8U_nm8"/>. This could also open the binding pocket to the ligand or subtrate. The fluctuation matrix in <xr id="fig:1J8U_nm8_fluc"/> shows clearly how only small parts of the protein move very coordinated.

Mode 9

<figure id="fig:1J8U_nm9">

The crystal structure of 1J8U in transparent green and the normal mode 9 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U_nm9_fluc">

The relative fluctuations of the C alpha atoms of 1J8U computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 9.

</figure> The large displacement of the beta sheet at the bottom in <xr id="fig:1J8U_nm9"/> is similar to mode 9 of Webnm@. From the fluctuation matrix in <xr id="fig:1J8U_nm9_fluc"/> we see that only a small part of the protein near the N-terminus stays rigid while the rest seems to twitch.

Mode 10

<figure id="fig:1J8U_nm10">

The crystal structure of 1J8U in transparent green and the normal mode 10 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U_nm10_fluc">

The relative fluctuations of the C alpha atoms of 1J8U computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 10.

</figure> This mode seems to correspond rather to mode 11 of Webnm@. In the fluctation matrix <xr id="fig:1J8U_nm10_fluc"/> we see a lot of small parts moving, the protein in <xr id="fig:1J8U_nm10"/> appears to be twisted slightly.

Mode 11

<figure id="fig:1J8U_nm11">

The crystal structure of 1J8U in transparent green and the normal mode 11 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U_nm11_fluc">

The relative fluctuations of the C alpha atoms of 1J8U computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 11.

</figure> In this mode we see mostly movement at the borders of the fluctuation matrix in <xr id="fig:1J8U_nm11_fluc"/>, in <xr id="fig:1J8U_nm11"/> we see little total displacement but a small stretching and compressing of the binding pocket.

1J8U and BH4 ligand

We included the ligand tetrahydrobiopterin and the FE(II) molecule in the normal mode analysis. The webserver apparently changed the FE atom into a different representation for its models. Interestingly, except mode 9 the modes including the ligand appear to be inverted to the ones without ligand. The fluctuation matrices are almost identical but inversely colored, that means, 'opening' motions are now closing motions and vice versa. Modes 7 and 8 are additionally switched. As several crystal structures with different ligands are available (cf. our introduction), we know that different ligands influence the conformation only little. This applies for the wildtype protein at least, as there are disease causing mutations that respond to large doses of tetrahydrobiopterin with restored activity.

Inversion of Motions

<figure id="fig:1J8U+BH4_nm7+8">

The inverted movement of 1J8U of mode 7 with and mode 8 without the BH4 ligand in green and blue repectively.

</figure> <figure id="fig:1J8U+BH4_nm9+9">

The identical movement of mode 9 of 1J8U with and without the BH4 ligand in orange and blue repectively.

</figure>

The addition of the ligand does in fact not change the movement of the mode at all. The exception is the switch between mode 7 and 8 that are very close in frequency. <xr id="fig:1J8U+BH4_nm7+8"/> shows the overlay of mode 7 without and mode 8 with ligand in the model. The motions are harmonic and identical, but start in the opposite direction. The same applies for the modes 8 without and 7 with ligand and the modes 11 and 11 with ligand (not shown). The modes 9 and 10 do not even start in different directions (cf. <xr id="fig:1J8U+BH4_nm9+9" /> depicting mode 9). The addition of the ligand to the model therefore does not influence the model's movements at all and the inversion in the matrices is just a minor, but reproducable, feature in the model.

Mode 7

<figure id="fig:1J8U+BH4_nm7">

The crystal structure of 1J8U with the BH4 ligand in transparent green and the normal mode 7 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U+BH4_nm7_fluc">

The relative fluctuations of the C alpha atoms of 1J8U with the BH4 ligand computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 7.

</figure> This mode is reversed to mode 8 without ligand.

Mode 8

<figure id="fig:1J8U+BH4_nm8">

The crystal structure of 1J8U with the BH4 ligand in transparent green and the normal mode 8 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U+BH4_nm8_fluc">

The relative fluctuations of the C alpha atoms of 1J8U with the BH4 ligand computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 8.

</figure> This mode is reversed to mode 7 without ligand.

Mode 9

<figure id="fig:1J8U+BH4_nm9">

The crystal structure of 1J8U with the BH4 ligand in transparent green and the normal mode 9 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U+BH4_nm9_fluc">

The relative fluctuations of the C alpha atoms of 1J8U with the BH4 ligand computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 9.

</figure> This mode is identical to mode 9 without ligand, but the fluctuation matrix is inversely colored.

Mode 10

<figure id="fig:1J8U+BH4_nm10">

The crystal structure of 1J8U with the BH4 ligand in transparent green and the normal mode 10 movement computed by ElNemo in blue.

</figure> <figure id="fig:1J8U+BH4_nm10_fluc">

The relative fluctuations of the C alpha atoms of 1J8U with the BH4 ligand computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 10.

</figure> This mode is identical to mode 10 without ligand, but the fluctuation matrix is inversely colored.

Mode 11

<figure id="fig:1J8U+BH4_nm11">

The crystal structure of 1J8U with the BH4 ligand in transparent green and the normal mode 11 movement computed by ElNemo in blue.

This mode is reversed to mode 11 without ligand. </figure> <figure id="fig:1J8U+BH4_nm11_fluc">

The relative fluctuations of the C alpha atoms of 1J8U with the BH4 ligand computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 11.

</figure>

Independent domain movement

<figure id="fig:1PHZ_nm7_fluc">

The relative fluctuations of the C alpha atoms of 1PHZ computed by ElNemo. Red or blue dots indicate those residues for which the distance significantly increases or decreases respectively in movement related to mode 7. The smaller C-terminal binding domain is found in the upper left quadrant, the larger catalytic domain in the lower right quadrant.

</figure>

<figure id="fig:1PHZ_nm7">

The first normal mode of the structure 1PHZ containing the binding and the catalytic domain.

</figure> To see if independent movement of the domains is observable, we submitted another structure that contains the catalytic domain and the binding domain of phenylalanine hydroxylase, 1PHZ. Indeed show the matrices of fluctuation of the C alpha backbone of the low frequency modes almost exclusively the movement of the domains as unit and little intra-domain movement. In <xr id="fig:1PHZ_nm7_fluc"/> the large uncolored area in the nine lower right squares indicates how the catalytic domain moves collectively as rigid unit, the smaller mostly uncolored area in the upper left square shows the less rigid but still coordinated binding domain. See the animation in <xr id="fig:1PHZ_nm7"/> for a nice visualization.

References

<references/>