Canavan Task 9 - Normal Mode Analysis
Contents
Protocol
Further information can be found in the protocol.
Choosing structures
For human Aspartoacylase, there are four structures available in the PDB. For a closer description of the structures have a look at task 4.
One important difference between the structures is the conformation of a loop formed by residues 158 - 164. This loop represents the gate for the binding site, which can either be closed or open. 2O53 and 2O4H both represent the closed conformation, whereas 2I3C and 2Q51 represent the open conformation.
Therefore we thought it would be interesting to investigate the normal modes of a structure with the closed (2O53) and the open (2I3C) conformation.
Since we used the dimer of 2O53 and 2I3C as an input to Webnm@, we also wanted to analyse the internal motions of one monomer. Therefore we also analysed chain A of 2O53.
Normal mode analysis
<figure id="nm_timescale">
Timescale of protein motions taken from Bahar, Lezon, Bakan (2010)<ref name="nm_timescale"> Normal Mode Analysis of Biomolecular Structures: Functional Mechanisms of Membrane Proteins Ivet Bahar, Timothy R. Lezon, Ahmet Bakan, and Indira H. Shrivastava Chemical Reviews 2010 110 (3), 1463-1497</ref>
</figure>
Normal mode analysis aims at explaining the internal motions of a protein.
Molecular Dynamics simulations are only capable of simulating very short amount of times (pico seconds). They are very computationally demanding, since the motion of each atom is calculated with an energy function.
The native state of a protein actually represents an ensemble of microstates that are comprised of the overall fold and the same secondary structure elements, but differ in the local atomic coordinates. The microstates are thought to represent fluctuations around the well-defined equilibrium native structure. In this sense, large conformational changes of proteins can be monitored that occur within these defined microstates. These low level conformational changes take much longer (nano seconds) and thus are not accessible by standard molecular dynamics simulation. But they can be addressed by normal mode analysis, where only movements of backbone atoms are considered. The underlying assumption for the calculation of normal modes is, that the thermally induced fluctuations around the eqilibrium native structure can be approximated by a simple harmonic potential.
In order to calculate normal modes, one has to perform a diagonalization of the 3N × 3N Hessian matrix. The Hessian matrix is obtained from the second derivatives of the potential with respect to the coordinates of the native conformation.
The amount of normal modes depends on the available degrees of freedom of the molecule, that can be translational, rotational or vibrational degrees of freedom. A polymer chain of N atoms enjoys 3N – 6 internal degrees of freedom which corresponds to the amount of normal modes.
The PDB files for our protein contain 301 atoms per chain, which results in 897 normal modes for one chain and 1800 normal modes for the dimer.
Webnm@
Webnm@ <ref> Hollup SM, Sælensminde G, Reuter N. WEBnm@: a web application for normal mode analysis of proteins BMC Bioinformatics. 2005 Mar 11;6(1):52 </ref> claims on its website that they "provide users with simple and automated computation and analysis of low-frequency normal modes for proteins". For the calculation of the normal modes they use the Molecular Modelling Toolkit (MMTK package) <ref> Hinsen, Konrad, The molecular modeling toolkit: A new approach to molecular simulations, Journal of Computational Chemistry, 21:2:79-85 </ref> and a C-alpha force field <ref>Hinsen K, Petrescu AJ, Dellerue S, Bellissent-Funel MC, Kneller GR, "Harmonicity in slow protein dynamics", Chemical Physics, 261:25-37, 2000</ref>. In this force field only C-alpha atoms are used, to which the mass of the whole corresponding residue is assigned.
With Webnm@ the following properties can be analysed:
- Deformation Energies and Eigenvalue Plot:
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.
- Atomic Displacement Analysis:
Plots the displacement of each Calpha atom, i.e. highlights which parts of the protein are the most displaced for each mode.
- Correlation Matrix Analysis:
Plots the correlation of motions between all the Calphas in the protein structure.
- Mode Visualisation:
Webnm@ provides the possibility for an interactive visualization of the modes using vector field representation or vibrations (JMol applet or downloadable VMD files)
2O53
2O53 is a homodimer without bound substrate and is in the closed conformation. We used the PDB identifier 2O53 as an input to Webnm@.
Deformation Energies
The deformation energies in general increase with each mode. Only mode 11 represents an exception as the deformation energy for this mode is lower than for mode 10.
<figtable id="2o53_def_energy">
| Mode Index | Deformation Energy | Mode Index | Deformation Energy |
| 7 | 870.03 | 14 | 3740.78 |
| 8 | 976.54 | 15 | 4168.69 |
| 9 | 1562.41 | 16 | 5263.58 |
| 10 | 2800.99 | 17 | 5461.10 |
| 11 | 2798.65 | 18 | 5906.92 |
| 12 | 2954.75 | 19 | 6126.73 |
| 13 | 3448.49 | 20 | 6356.04 |
</figtable>
Eigenvalues Plot
The eigenvalues are inversely related to the amplitude of motion of the modes. Therefore mode 7 describes the highest amplitude of motion in the protein and the other modes describe a decreasing amplitude of motion.
The eigenvalue plot can be seen in <xr id="2o53_eigenvaluesplot"/>
Atomic Displacements
In the lowest mode (7) there are quite random displacements. They are scattered all over the protein. The same can be said for mode 9. For mode 8, 10 and 12 there are peaks around residue 400, which is a long solvent exposed loop. For modes 8,10,11 there is a peak around residue 100 in chain A which corresponds to the peak for the residues around position 400 in chain B. For mode 11 and 12 there are two sharp peaks around residues 250 and 265. This regions are composed of many solvent exposed flexible loops of the C-terminal domain. [AD for modes 7 to 12]
The fluctuations plot (<xr id="2o53_fluctuationsplot"/>) shows the atomic displacements averaged over all modes. It can be seen that the atomic movements are different for the two monomers.
Correlation Matrix Analysis
From the correlation matrix it can be found, that the C-terminal domain (residue 211-311) shows correlated movements. In chain B this domain can be found starting at residue 520.
There are some other smaller correlated motions, that are not very emphasized.
Plot
<figtable id="2o53_plots">
| <figure id="2o53_eigenvaluesplot"></figure> | <figure id="2o53_fluctuationsplot"></figure> | <figure id="2o53_correlation_matrix"></figure> |
</figtable>
2I3C and Comparison to 2O53
This structure shows the binding site in an open conformation.
Some amino acids have been replaced by artificial amino acids and are not considered by webnm@ in the normal mode analysis.
Overlap Analysis
Overlap Analysis was not possible. Webnm@ throws a "General Error".
Deformation Energies
Again, the deformation energies increase with each mode, except for mode 11, that has a lower deformation energy that mode 10.
For mode 7 - 13, 2I3C has the lower deformation energies. Then it is almost vice.versa and 2O53 has lower deformation energies. This might hint to stronger movements of 2I3C. In <xr id="comp_def_ener"/> the deformation energies for both proteins are plotted.
<figtable id="2i3c_def_energy">
| Mode Index | Deformation Energy | Mode Index | Deformation Energy |
| 7 | 819.58 | 14 | 3831.12 |
| 8 | 897.71 | 15 | 4275.48 |
| 9 | 1423.78 | 16 | 5370.37 |
| 10 | 2661.79 | 17 | 5549.08 |
| 11 | 2485.43 | 18 | 5226.29 |
| 12 | 2576.98 | 19 | 6459.76 |
| 13 | 3362.10 | 20 | 5641.86 |
</figtable>
Eigenvalues Plot
The eigenvalue plot looks the same as for 2O53: almost linear increase in eigenvalue for the modes.
The eigenvalue plot can be seen in <xr id="2i3c_eigenvalues"/>
Atomic Displacements
The atomic displacements for 2O53 and 2I3C are very similar. The plotsfor modes 7 to 12 can be seen here: [AD for modes 7 to 12]
Yet, especially for the higher modes, there are some differences. First, the amplitude of some peaks is different for 2O53 and 2I3C. And second, there are some additional peaks in some modes for 2I3C, which represent different local felxibility.
Modes 11 and 12 deviate the most. 2O53 shows more and stronger peaks for these both modes, which indicates stronger low level movements. In <xr id="comparison 2o53_2i3c_mode11_12"/>these differences are illustrated.
Correlation Matrix analysis
As for 2O53, the C-terminal domain (residues 212-300) shows correlated movements. The correlation matrix is shown in <xr id="2i3c_correlation_matrix"/>.
Fluctuation
The fluctuation plot for 2I3C is presented in <xr id="2i3c_fluctuationsplot"/>.
As you can see in <xr id="comparison_2o53_2i3c_fluctuations"/>, the fluctuations for all modes for both proteins are identical. Since the fluctuation plot combines the motions from all modes, this indicates that the differences in the atomic displacement plots for both proteins are only minor ones.
Plots
<figtable id="comp_plots">
| <figure id="2i3c_eigenvalues"></figure> | <figure id="2i3c_fluctuationsplot"></figure> | <figure id="2i3c_correlation_matrix"></figure> |
| <figure id="comp_def_ener"></figure> | <figure id="comparison_2o53_2i3c_fluctuations"></figure> | <figure id="comparison 2o53_2i3c_mode11_12"></figure> |
</figtable>
Visualisation
When comparing the visualisation of the modes for both crystal structures, one can not identify significant differences. In the following the visualisation of the different modes for 2O53 and 2I3C is shown.
mode7
The movements according to mode 7 represent a sheering motion between the protein monomers. There are slight differences for both monomers, especially in the C-terminal region, as can be seen in <xr id="2I3C_ad_mode7"/>. Yet these differences can be observed for 2O53 as well as for 2I3C.
<figtable id="comp_mode7">
| <figure id="2I3C_ad_mode7"></figure> | <figure id="2o53_ad_mode7"></figure> |
| <figure id="2I3C_vis_mode7"></figure> | <figure id="2o53_vis_mode7"></figure> |
</figtable>
mode8
Compared to mode 7, the movements of mode 8 have higher amplitudes as can be seen in <xr id="2o53_ad_mode8"/>. Again there also are small differences between chain A and chain B. In the visualization one can again see the movement of the two monomers. Compared to mode 7, the monomers move in the orthogonal direction.
The normal mode 8 is similar to mode 7 in that the two monomers move independent from another. In contrast to mode 7, the monomers move into a different direction. Furthermore, there are slight differences between the motions for both monomers as can be seen in <xr id="2I3C_ad_mode8"/>. There is a peak around residue 70, that is much higher for chain A, than for chain B. Yet this peak only represents a local movement.
<figtable id="comp_mode8">
| <figure id="2I3C_ad_mode8"></figure> | <figure id="2o53_ad_mode8"></figure> |
| <figure id="2I3C_vis_mode8"></figure> | <figure id="2o53_vis_mode8"></figure> |
</figtable>
mode9
There are hardly any differences in the atomic displacements for chain A and B for mode 9 (see <xr id="2o53_ad_mode9"/>). The two monomers move against each other in a very similar way as for mode 8. Yet the axis of the movement is different.
Mode 9 again is very similar to mode 7 and 8: the monomers move against each other, only on a different axis than for the other two modes.
<figtable id="comp_mode9">
| <figure id="2I3C_ad_mode9"></figure> | <figure id="2o53_ad_mode9"></figure> |
| <figure id="2I3C_vis_mode9"></figure> | <figure id="2o53_vis_mode9"></figure> |
</figtable>
mode10
The motions of mode 10 are different to the other modes. Here, the movement can be described as a "breathing" motion. The monomers become larger and smaller.
As for 2O53, this mode represents a different protein movement, that can be described as "breathing". Both monomers increase in their volume and dicrease again. In the atomid displacement plot (<xr id="2I3C_ad_mode10"/>) one can observe some differences for both monomers.
<figtable id="comp_mode10">
| <figure id="2I3C_ad_mode10"></figure> | <figure id="2o53_ad_mode10"></figure> |
| <figure id="2I3C_vis_mode10"></figure> | <figure id="2o53_vis_mode10"></figure> |
</figtable>
mode11 - 12
Modes 11 and 12 show similar movements compared to mode 7 - 9 or combinations of those.
<figtable id="comp_mode11to12">
| <figure id="2I3C_vis_mode11"></figure> | <figure id="2o53_vis_mode11"></figure> |
| <figure id="2I3C_vis_mode12"></figure> | <figure id="2o53_vis_mode12"></figure> |
</figtable>
Conclusion
We wanted to analyse the differences in the normal modes for 2O53 and 2I3C, that show Aspartoacylase in an open and a closed conformation repectively.
For the loop region formed by residues 158-164, that distinguishes both structures, no differences could be observed. Both loops are part of a bigger sheering motion, but the loop does not move independently as can be seen in <xr id="comp_mode7"/>.
<figure id="comp_mode7">
</figure>
2O53 monomer
The normal modes for the Aspartoacylase dimers analysed so far, mainly comprise motions of the two monomers against each other. We now wanted to find out whether there are also significant motions within an Aspartoacylase monomer and took a look at chain A of 2O53.
Deformation Energies
As can be seen in <xr id="2o53_mono_def_energy"/>, the energies are almost twice as high as for the dimer structure. Therefore we expect to see rather high frequent motions and less general conformational changes.
<figtable id="2o53_mono_def_energy">
| Mode Index | Deformation Energy | Mode Index | Deformation Energy |
| 7 | 1346.97 | 14 | 6275.60 |
| 8 | 1715.72 | 15 | 6763.95 |
| 9 | 2534.48 | 16 | 8447.56 |
| 10 | 3533.33 | 17 | 8956.73 |
| 11 | 4406.67 | 18 | 8843.26 |
| 12 | 5272.49 | 19 | 10358.79 |
| 13 | 6159.00 | 20 | 11875.58 |
</figtable>
Plots
The Eigenvalues Plot in <xr id="2o53_monomer_eigenvalues"/> shows a linear increase of the eigenvalues of each mode which means a linear increase in the frequency of the motions.
The fluctuation plot (<xr id="2o53_monomer_fluctuationsplot"/>) shows only one strong peak for the residues around position 230. The averaged atomic displacement in this region is as high as 12, which is much stronger than for the analysed dimers. There also are some smaller fluctuations around 2 for residues around position 70 and for residues between position 250 and 270. The correlation matrix shown in <xr id="2o53_monomer_correlation_matrix"/> resembles the monomeric part of the correlation matrix for the analysed dimers. There are correlated motions between the regions around position 200-250 and position 250-300, and also for the small region formed by residues 20-30 and 40-50.
<figtable id="2o53_monomer_plots">
| <figure id="2o53_monomer_eigenvalues"></figure> | <figure id="2o53_monomer_fluctuationsplot"></figure> | <figure id="2o53_monomer_correlation_matrix"></figure> |
</figtable>
Visualisation
In the following, a visualisation for each mode is shown. The N-terminal and C-terminal domain are colored differently as well as the loop gating the active site. Chain A of 2O53 is also shown as a cartoon and used as a reference in the visualisations, to be able to estimate the relative movements in the modes.
<figtable id="2o53_monomer_mode7_8">
| mode7 | mode8 |
| Mode 7 represents a movement of the two domains against each other. As can be seen in the visualisation, the blue C-terminal domain shows the largest movements against the N-terminal domain. | Mode 8 also represents a movement of the C-terminal domain against the N-terminal domain. In comparison to mode 7, the movement of the C-terminal domain against the N-terminal domain has a different directionality. |
| <figure id="2o53_monomer_vis_mode7"></figure> | <figure id="2o53_monomer_vis_mode8"></figure> |
</figtable>
<figtable id="2o53_monomer_mode9">
| mode 9 | mode 10 |
| Mode 9 represents again a movement of the two domains against each other in a third different direction. | Mode 10 includes movements of loops in the N- and C-terminal domain. Especially, the two bottommost loops in the visualisation move enormously. |
| <figure id="2o53_monomer_vis_mode9"></figure> | <figure id="2o53_monomer_vis_mode10"></figure> |
</figtable>
<figtable id="2o53_monomer_mode11_12">
| mode 11 | mode 12 |
| Mode 11 represents relatively unspecific movements of different parts of the protein that move in different ways and different directions. In contrast to the movements of the lower modes, even the gating loop that is colored yellow shows some motion. | Mode 12 also shows rather unspecific movements that are very similar to those of mode 11. Again, the gating loop moves as well and moves towards the active center that is represented by the red colored Zn ion. |
| <figure id="2o53_monomer_vis_mode11"></figure> | <figure id="2o53_monomer_vis_mode12"></figure> |
</figtable>
ElNemo
ElNemo is a webserver which is available since 2004 wich employs elastic network models. It computes ten models (animations) for the first five non-trivial normal modes for a given protein structure. Their results include, amongst others, the following:
- properties of the normal mode; i.e., collectivity (which indicates how many of the atoms in the Protein are affected by the motion of a specific mode) and frequency, the amplitude, and the normalized mean square displacement
- B-factors
- distance fluctuations of Calpha atoms, given in a map
- an animation foreach computed mode.
In order for ElNemo to accept our proteins, we had to modify the pdf files. We eliminated all records except for the ATOM records. We then ran the calculation for our protein 2O53 with default parameters and chose the 6 lowest models which can be compared to the modes of WEBnm
2O53
Normal Mode Analysis for ID 12070820013211761
<figtable id="elnemo_2o53">
</figtable>
Correlation= 0.322 for 604 C-alpha atoms.
<R2> frequency collectivity mode 7 1.00 0.6719 mode 8 1.26 0.6285 mode 9 1.76 0.7056 mode 10 2.16 0.7016 mode 11 2.31 0.5394 mode 12 2.39 0.6059 mode 13 2.46 0.4075 mode 14 2.66 0.6475 mode 15 2.75 0.4065 mode 16 3.06 0.3493 mode 17 3.08 0.4132 mode 18 3.19 0.4097 mode 19 3.26 0.3425 mode 20 3.37 0.2945
References
<references/>
| Mode__ | Collectivity__ | Frequency__ | Animation__ | Comment | Distance Fluctuations of Calpha atoms |
|---|---|---|---|---|---|
| 7 | 0.67 | 1.00 | In mode 7, one can observe a shearing motion of the two domains. In the gif animation, the two domains are shown 'on top' of each other. If you look at the loops on the left side, you can see a significant increase in distance, while opposite residues on the right move closer together. | ||
| 8 | 0.63 | 1.26 | Mode 8 appears more of a rotation of the two domains against each other. | ||
| 9 | 0.71 | 1.76 | Mode 9 description | ||
| 10 | 0.70 | 2.16 | Mode 10 could be described as a breathing motion where the domains slightly twist with each breath. | ||
| 11 | 0.54 | 2.31 | Mode 11 description |
