Difference between revisions of "Canavan Task 9 - Normal Mode Analysis"

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(2O53 monomer)
(2O53)
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In the fluctuations plot averaged over all modes, it can be seen that the atomic movements are different for the two monomers.
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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.
   
 
<b>Correlation Matrix Analysis</b>
 
<b>Correlation Matrix Analysis</b>

Revision as of 16:50, 19 August 2012

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.

We also looked at 2O53 and 2O4H in order to examine if there are differences between the ligand bound (2O4H) and apo-structure (2O53).

Finally, we also wanted to analyse the internal motions of one monomer. Therefore we analysed chain A of 2O53.

Normal mode analysis

<figure id="nm_timescale">

<xr nolink 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 simulation very short amount of times (pico seconds). They are very compuationally 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 which contain 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

<figtable id="2o53_def_energy">



<xr nolink id="2o53_def_energy"/> Deformation energies for 2O53 calculated by webnm@
Mode Index Deformation Energy Mode Index Deformation Energy
7 870.03 143740.78
8976.54 154168.69
91562.41 165263.58
102800.99 175461.10
112798.65 185906.92
122954.75 196126.73
133448.49 206356.04

</figtable>


Eigenvalues Plot

The eigenvalues are inversely related to the 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 correalted motions, that are not very emphasized.


Plot

<figtable id="2o53_plots">

<figure id="2o53_eigenvaluesplot">
<xr nolink id="2o53_eigenvaluesplot"/>
The eigenvalues plot for 2O53. The eigenvalues increase almost lineraly with the modes.
</figure>
<figure id="2o53_fluctuationsplot">
<xr nolink id="2o53_fluctuationsplot"/>
The fluctuations plot for 2O4H. Interestingly the movements are different for the two monomers. ChainB starts about residue 300.
</figure>
<figure id="2o53_correlation_matrix">
<xr nolink id="2o53_correlation_matrix"/>
The correlation matrix for 2O53. There are correlated motions for residues 250-300 in chainA as well as in chainB.
</figure>

</figtable>

2O4H

In 2O4H an intermediate substrate has been cocrystallized and the enzyme is in the closed conformation. We uploaded a modified pdb file, where we changed the HETATM entry into ATOM, so that the ligand will be considered during normal mode analysis.

Deformation Energies

<figtable id="2o4h_def_energy">

<xr nolink id="2o4h_def_energy"/> Deformation energies for 2O4H calculated by webnm@
Mode Index Deformation Energy Mode Index Deformation Energy
7890.47 143813.56
81001.20 154209.21
91576.14 165299.13
102832.63 175374.76
112837.90 185750.94
122995.56 196278.71
133417.11 206396.79

</figtable>

Eigenvalues Plot

The eigenvalues are inversely related to the 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="2o4h_eigenvaluesplot"/>


Atomic Displacements

The plots for mode 7 to 12 are identical with the plots for 2O53. Therefore the ligand in the structure does not influence the movement of the protein at all. The atomic displacements for all modes can be seen her: [AD for modes 7 to 12]


The fluctuations plot averaged over all modes is also identical with the plot for 2o53. Even very small fluctuations are exactly the same.


Correlation Matrix Analysis

And again, the correlation matrix is also totally identical with the correlation matrix for 2O53.

Plot

<figtable id="2o4h_plots">

<figure id="2o4h_eigenvaluesplot">
<xr nolink id="2o4h_eigenvaluesplot"/>
The eigenvalues plot for 2O4H. The eigenvalues increase almost lineraly with the modes.
</figure>
<figure id="2o4h_fluctuationsplot">
<xr nolink id="2o4h_fluctuationsplot"/>
The fluctuations plot for 2O4H. The plot is identical to the plot for 2O53.
</figure>
<figure id="2o4h_correlation_matrix">
<xr nolink id="2o4h_correlation_matrix"/>
The correlation matrix for 2O4H. There are correlated motions for residues 250-300 in chainA as well as in chainB . The matrix is identical with the matrix for 2O53.
</figure>

</figtable>

2I3C

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.


Deformation Energies

<figtable id="2i3c_def_energy">

<xr nolink id="2i3c_def_energy"/> Deformation energies for 2I3C calculated by webnm@
Mode Index Deformation Energy Mode Index Deformation Energy
7819.58 143831.12
8897.71 154275.48
91423.78 165370.37
102661.79 175549.08
112485.43 185226.29
122576.98 196459.76
133362.10 205641.86

</figtable>


Eigenvalues Plot

The eigenvalue plot looks as for the proteins analysed before: almost linear increase in eigenvalue for the modes.

The eigenvalue plot can be seen in <xr id="2i3c_eigenvalues"/>


Atomic Displacements

The plots are very similar to the plots for 2O53 and 2O4H. The plots for atomic displacement for modes 7 to 12 can be seen here: [AD for modes 7 to 12]


Correlation Matrix analysis

As for the other proteins, the C-terminal domain shows correlated movements.


Plot

<figtable id="2i3c_plots">

<figure id="2i3c_eigenvalues">
<xr nolink id="2i3c_eigenvalues"/>
The eigenvalues plot for 2I3C. The eigenvalues increase almost lineraly with the modes.
</figure>
<figure id="2i3c_fluctuationsplot">
<xr nolink id="2i3c_fluctuationsplot"/>
The fluctuations plot for 2I3C. The plot is almost identical to the plot for 2O53.
</figure>
<figure id="2i3c_correlation_matrix">
<xr nolink id="2i3c_correlation_matrix"/>
.
</figure>

</figtable>


Comparison 2I3C and 2O53

Overlap Analysis

Overlap Analysis was not possible. Webnm@ throws a "General Error".


Deformation Energy

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.


Atomic Displacements

The atomic displacements for 2O53 and 2I3C are very similar. 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.


Fluctuation

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="comp_def_ener">
<xr nolink id="comp_def_ener"/>
The deformation energies for modes 7 to 20 are shown for 2O53 and 2I3C. For mode 7 to 13, 2I3C has lower energies and respective stronger movements in these modes. For modes 14 to 20 it is almost vice versa.
</figure>
<figure id="comparison_2o53_2i3c_fluctuations">
<xr nolink id="comparison_2o53_2i3c_fluctuations"/>
Normalized squared fluctuations for 2O53 and 2I3C. The fluctuations are almost identical for both proteins
</figure>
<figure id="comparison 2o53_2i3c_mode11_12">
<xr nolink id="comparison 2o53_2i3c_mode11_12"/>
In red, the atomic replacement for 2O53 is shown and in blue for 2I3C. One can identify some additional peaks for 2O53.
</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. Yet these differences can be observed for 2O53 as well as for 2I3C.


mode7

The movements according to mode 7 represent a sheering motion between the protein monomers. There are slight differences for both monmers, especially in the C-terminal region, as can be seen in <xr id="2I3C_ad_mode7"/>.

<figtable id="comp_mode7">

<figure id="2I3C_ad_mode7">
<xr nolink id="2I3C_ad_mode7"/>
Atomic displacement plot for mode7 of 2I3C. There are slight differences for chain A and B.
</figure>
<figure id="2o53_ad_mode7">
<xr nolink id="2o53_ad_mode7"/>
Atomic displacement plot for mode7 of 2O53. There are slight differences for chain A and B.
</figure>
<figure id="2I3C_vis_mode7">
<xr nolink id="2I3C_vis_mode7"/>
Visualization of the movements according to mode 7 for 2I3C. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2o53_vis_mode7">
<xr nolink id="2o53_vis_mode7"/>
Visualization of the movements according to mode 7 for 2O53. Chain A is colored green, chain B is colored blue.
</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">
<xr nolink id="2I3C_ad_mode8"/>
Atomic displacement plot for mode7 of 2I3C. There are slight differences for chain A and B.
</figure>
<figure id="2o53_ad_mode8">
<xr nolink id="2o53_ad_mode8"/>
Atomic displacement plot for mode8 of 2O53. There are slight differences for chain A and B.
</figure>
<figure id="2I3C_vis_mode8">
<xr nolink id="2I3C_vis_mode8"/>
Visualization of the movements according to mode 8 for 2I3C. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2o53_vis_mode8">
<xr nolink id="2o53_vis_mode8"/>
Visualization of the movements according to mode 8 for 2O53. Chain A is colored green, chain B is colored blue.
</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">
<xr nolink id="2I3C_ad_mode9"/>
Atomic displacement plot for mode7 of 2I3C. There are slight differences for chain A and B.
</figure>
<figure id="2o53_ad_mode9">
<xr nolink id="2o53_ad_mode9"/>
Atomic displacement plot for mode9 of 2O53. There are slight differences for chain A and B.
</figure>
<figure id="2I3C_vis_mode9">
<xr nolink id="2I3C_vis_mode9"/>
Visualization of the movements according to mode 9 for 2I3C. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2o53_vis_mode9">
<xr nolink id="2o53_vis_mode9"/>
Visualization of the movements according to mode 9 for 2O53. Chain A is colored green, chain B is colored blue.
</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">
<xr nolink id="2I3C_ad_mode10"/>
Atomic displacement plot for mode 10 of 2I3C. There are slight differences for chain A and B.
</figure>
<figure id="2o53_ad_mode10">
<xr nolink id="2o53_ad_mode10"/>
Atomic displacement plot for mode9 of 2O53. There are slight differences for chain A and B.
</figure>
<figure id="2I3C_vis_mode10">
<xr nolink id="2I3C_vis_mode10"/>
Visualization of the movements according to mode 10 for 2I3C. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2o53_vis_mode10">
<xr nolink id="2o53_vis_mode10"/>
Visualization of the movements according to mode 10 for 2O53. Chain A is colored green, chain B is colored blue.
</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">
<xr nolink id="2I3C_vis_mode11"/>
Visualization of the movements according to mode 11 for 2I3C. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2o53_vis_mode11">
<xr nolink id="2o53_vis_mode11"/>
Visualization of the movements according to mode 11 for 2O53. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2I3C_vis_mode12">
<xr nolink id="2I3C_vis_mode12"/>
Visualization of the movements according to mode 12 for 2I3C. Chain A is colored green, chain B is colored blue.
</figure>
<figure id="2o53_vis_mode12">
<xr nolink id="2o53_vis_mode12"/>
Visualization of the movements according to mode 12 for 2O53. Chain A is colored green, chain B is colored blue.
</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">

<xr nolink id="comp_mode7"/>
Superposition of mode 7 for 2O53 and 2I3C. In green, the gating loop of 2O53 is shown and in blue for 2I3C.

</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">


<xr nolink id="2o53_mono_def_energy"/> Deformation energies for chain A of 2O53 calculated by webnm@
Mode Index Deformation Energy Mode Index Deformation Energy
7 1346.97 146275.60
81715.72 156763.95
92534.48 168447.56
103533.33 178956.73
114406.67 188843.26
125272.49 1910358.79
136159.00 2011875.58

</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.


<figtable id="2o53_monomer_plots">

<figure id="2o53_monomer_eigenvalues">
<xr nolink id="2o53_monomer_eigenvalues"/>
The eigenvalues plot for 2I3C. The eigenvalues increase almost lineraly with the modes.
</figure>
<figure id="2o53_monomer_fluctuationsplot">
<xr nolink id="2o53_monomer_fluctuationsplot"/>
The fluctuations plot for 2O53 monomer. The plot is almost identical to the plot for 2O53.
</figure>
<figure id="2o53_monomer_correlation_matrix">
<xr nolink id="2o53_monomer_correlation_matrix"/>
.
</figure>

</figtable>

Visualisation

mode7


<figtable id="2o53_monomer_mode7">

<figure id="2o53_monomer_vis_mode7">
<xr nolink id="2o53_monomer_vis_mode7"/>
Visualization of the movements of the 2O53 monomer according to mode 7. The N-terminal domain is colored green, the C-terminal domain is colored blue. The closed loop gating the binding site is colored yellow. The Zn ion of the bindig site is shown in red.
</figure>

</figtable>

mode8


<figtable id="2o53_monomer_mode8">

<figure id="2o53_monomer_vis_mode8">
<xr nolink id="2o53_monomer_vis_mode8"/>
Visualization of the movements of the 2O53 monomer according to mode 8. The N-terminal domain is colored green, the C-terminal domain is colored blue. The closed loop gating the binding site is colored yellow. The Zn ion of the bindig site is shown in red.
</figure>

</figtable>


mode9


<figtable id="2o53_monomer_mode9">

<figure id="2o53_monomer_vis_mode9">
<xr nolink id="2o53_monomer_vis_mode9"/>
Visualization of the movements of the 2O53 monomer according to mode 9. The N-terminal domain is colored green, the C-terminal domain is colored blue. The closed loop gating the binding site is colored yellow. The Zn ion of the bindig site is shown in red.
</figure>

</figtable>


mode10


<figtable id="2o53_monomer_mode10">

<figure id="2o53_monomer_vis_mode10">
<xr nolink id="2o53_monomer_vis_mode10"/>
Visualization of the movements of the 2O53 monomer according to mode 10. The N-terminal domain is colored green, the C-terminal domain is colored blue. The closed loop gating the binding site is colored yellow. The Zn ion of the bindig site is shown in red.
</figure>

</figtable>

mode11


<figtable id="2o53_monomer_mode11">

<figure id="2o53_monomer_vis_mode11">
<xr nolink id="2o53_monomer_vis_mode11"/>
Visualization of the movements of the 2O53 monomer according to mode 11. The N-terminal domain is colored green, the C-terminal domain is colored blue. The closed loop gating the binding site is colored yellow. The Zn ion of the bindig site is shown in red.
</figure>

</figtable>


mode12


<figtable id="2o53_monomer_mode12">

<figure id="2o53_monomer_vis_mode12">
<xr nolink id="2o53_monomer_vis_mode12"/>
Visualization of the movements of the 2O53 monomer according to mode 12. The N-terminal domain is colored green, the C-terminal domain is colored blue. The closed loop gating the binding site is colored yellow. The Zn ion of the bindig site is shown in red.
</figure>

</figtable>

ElNemo

In order for ElNemo to accept our proteins, we had to modify the pdf files. We eliminated all records except for the ATOM records.

2O53

Normal Mode Analysis for ID 12070820013211761

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/>