3. Results and Discussion
3.2. Molecular dynamic simulations of the CTLD of perlucin and MBP-‐A
3.2.5. Atomic positional fluctuations of residues and RMSd values of the CTLD of perlucin and MBP-‐A
3.2.5. Atomic positional fluctuations of residues and RMSd values of the
Fig. 3.2.15. Average backbone fluctuations per residue of the MD simulation series of perlucin.
The average, mass-‐weighted positional fluctuations of the backbone atoms per residue are given in Å for the three MD simulation series: with four calcium ions (red, crosses), with two calcium ions (blue, triangles) and without calcium ions (green, circles). For clarity the data points are connected with dashed lines in the corresponding colours. The average general helical and strand conformation of the residues of the simulations with four ions (run09) is indicated through violet or yellow bars at the bottom of the graph (see Fig. 3.2.5.). Additionally those residues that have oxygen atoms in close proximity (see section 3.2.4. and Fig. 3.2.14.) to calcium ions are indicated through markers: Ca-‐4 is represented by a triangle variant, Ca-‐3 by a hexagon, Ca-‐2 by a diamond and Ca-‐1 by a circle with cross.
Fig. 3.2.16. Average backbone fluctuations per residue of the MD simulation series of the CTLD of MBP-‐A. The average, mass-‐weighted positional fluctuations of the backbone atoms per residue are given in Å for the three MD simulation series: with three calcium ions (red, crosses), with one calcium ion (blue, triangles) and without calcium ions (green, circles). For clarity the data points are connected with dashed lines in the corresponding colours. The average general helical and strand conformation of the residues of the simulations with three ions (run07) is indicated through violet or yellow bars at the bottom of the graph (see Fig.
3.2.5.). Additionally the residues that have oxygen atoms in close proximity (see section 3.2.4.
and Fig. 3.2.14.) to calcium ions are indicated through markers: Ca-‐3 is represented by a hexagon, Ca-‐2 by a diamond and Ca-‐1 by a circle with cross.
Figs. 3.2.15. and 3.2.16. show the average backbone (Cα, C, N, O) positional fluctuations of the MD simulation series of perlucin and the CTLD of MBP-‐A. First of all the terminal residues show a high fluctuation since the can move relatively unconstrained. This is the case for the C-‐terminal region of perlucin and for N-‐terminal region of the CTLD of MBP-‐A. Note that only the residues up to Arg131 are shown for perlucin although the initial structure of the simulations with four ions (run09) has four more residues. As it is commented in the preceding sections the N-‐terminal region of MBP-‐A – up to the strand β1 – is artificially able to move freely due to the missing long α-‐helical coil. Note that the initial structure of the simulation series without calcium ions (green circles, run02) has five residues less at the N-‐terminus compared to the other simulation series.
But even if the fluctuations at the termini are not considered it is obvious that the fluctuations of the perlucin structures between α2 and β4 are considerably larger compared to MBP-‐A. Up to the C-‐terminal end of α2 and after the N-‐terminal end of β4 the fluctuations are of similar magnitude.
For the loop region of perlucin between α2 and β2 high fluctuations up to 3.4 Å are observed. They are most probably uncorrelated to the number of associated ions since no residue in this region has oxygen atoms in a close distance to calcium ions. It is supposed that the large fluctuations are caused by an incorrect modelling of this region due to a lack of an appropriate template (see section 3.1. and Fig. 3.1.4. as well as Fig.
3.2.5.). The loop region of MBP-‐A between α2 and β2 is considerably shorter an exhibits less fluctuations.
Consider the segments between β2 and β2’’ and the long loop region with calcium associated residues before β3. In these two regions with high fluctuations hints of a correlation between residue fluctuations associated calcium ions can be inferred for
perlucin. Between β2 and β2’’ the fluctuations are maximal (green, circles) for perlucin and MBP-‐A when no calcium ions are present in this region and minimal (red, crosses) when Ca-‐1 (circles with crosses) and Ca-‐3 (hexagons) are associated to residues in this region. If Ca-‐1 and Ca-‐3 are not included in the simulations (blue, circles) but Ca-‐2 (diamonds) – and Ca-‐4 (triangle variant) in the case of perlucin – then one could expect that the fluctuations arrive at the same level as in the case of the simulations without calcium ions. This happens indeed for MBP-‐A but for perlucin the fluctuations are between the two observed limiting cases.
In the next long loop segment with two residues associated to Ca-‐2 (diamonds) a similar tendency can be observed with the respect to the fluctuations. Without any calcium ions the fluctuations are higher for both perlucin and MBP-‐A compared to the simulations including Ca-‐2. If Ca-‐1 has a stabilizing effect in this region cannot be said definitely. The fluctuations obtained from the perlucin simulations could suggest such an effect but in MBP-‐A a similar observation cannot be made.
Concerning Ca-‐4 (triangle variant) in the perlucin model an ion at this characteristic site might have a stabilizing effect of the N-‐terminal end of α2. As it can be seen in Fig.
3.2.15. the structure without ions shows higher fluctuations at the N-‐terminal end of α2.
A refinement of the loop region behind the C-‐terminal end of α2 might lower the fluctuations in this region. One has to keep in mind that due to the small number of simulations performed for each initial protein-‐ion configuration these results might not reflect the ensemble average. Nonetheless the data suggest that calcium ions could have a stabilizing effect on the CTLD fold by reducing the fluctuations.
Fig. 3.2.17. Average backbone RMSd during the MD simulation series of perlucin. The RMSd values were calculated after the fit of the structures to the protein structures after minimization. For the fit the heavy backbone atoms (Cα, C, N, O) were used. The three RMSd graphs with the higher RMSd values were obtained with the residue range 1 to 131 for the fit.
If certain loop regions were not included during the RMSd fit and calculation lower RMSd values were obtained. The RMSd graphs with the lower values were obtained when following regions were omitted: Tyr52 to Asn61 (run21: Arg50 to Asn61; run22: Arg50 to Tyr62), Asp68 to Trp75, Glu78 to Asn87, Pro90 to His101 and Arg106 to Leu113.
Fig. 3.2.18. Average backbone RMSd during the MD simulation series of MBP-‐A. The RMSd values were calculated after the fit of the structures to the protein structures after minimization. For the fit the heavy backbone atoms (Cα, C, N, O) of the full sequence were used.
Note that the sequence of the structure used in the simulation series without calcium ions was five residues shorter than the structure used in the other simulation series. Also keep in mind the artificial N-‐terminal conformation of the simulated CTLD structures due to the missing long α-‐helical coil. An exclusion of this region during the fit for the RMSd calculation could lead to lower RMSd values.
Figs. 3.2.17. and 3.2.18. show the average backbone RMSd values of perlucin and the CTLD of MBP-‐A respectively. The RMSd values of the perlucin structures calculated over the sequence length up to residue 131 range between 2.2 Å and 2.8 Å. There might be a tendency that the RMSd values are lower with associated calcium ions. The RMSd values of the structure without ions (green) are higher by trend than those of the structure with four calcium ions (red). The values from the structure with only two associated calcium ions (blue) seem to range between these two cases. If those loop regions with high fluctuations (see Fig. 3.2.15.) were excluded from the RMSd fit and calculation then the RMSd graphs with the lower values were obtained in Fig. 3.2.17.
Following regions were excluded: the segment between the N-‐terminal end of α2 and the beginning of β2 (run09: Tyr52 to Asn61, run21: Arg50 to Asn61, run22: Arg50 to Tyr62), the region between β2 and β2’’ (Asp68 to Trp75), the part from the N-‐terminal end of β2’’ and Trp88 (Glu78 to Asn87), Pro90 to His101 (Ser89 is buried and Cys102 is part of a disulphide bridge) and the segment between β3 and β4 (Arg106 to Leu113). Most of the residues in these segments are not classified as “buried” as it can be seen in Fig.
3.2.11. Consult also Fig. 3.2.15. for the fluctuations of the residues in these loop regions. The resulting RMSd values range between 1.4 Å and 1.8 Å and show no clear separation depending on the number of associated calcium ions.
The RMSd values obtained from the MD simulation series with MBP-‐A were calculated with the full residue range in every series. These RMSd values might be increased due to the artificial N-‐terminal conformation of the simulated CTLD structures due to the missing α-‐helical coil. This might explain why the RMSd of the MBP-‐A structure without calcium ions (green) is lower than the RMSd values from the other MD simulation series (red and blue): it has five N-‐terminal residues less than the MBP-‐A input structures from the remaining simulation series. Therefore the RMSd values obtained from the MD simulations of MBP-‐A without calcium ions should be regarded as an upper limit of the RMSd values that could be obtained for near optimal protein
structures – when protein crystal structures are regarded as the most stable ones – with the MD simulation protocol used in this thesis.
In this light the RMSd values obtained for all perlucin simulation series are considerably larger compared to the MBP-‐A simulation without calcium ions by trend.
Similar RMSd values (≈ 1.6 Å, MBP-‐A without calcium ions after 10.2 𝑛𝑛𝑛𝑛) can be obtained for perlucin if the contribution of loop regions is excluded. This shows that there is considerable motion of the residues in the loop regions whereas the remaining part of the perlucin protein structure has RMSd values similar to those obtained for simulated CTLD crystal structures of MBP-‐A including the artificial N-‐terminal region.
Fig. 3.2.19. Residues 1 to 131 of a perlucin structure of one MD simulation with four calcium ions after 10.2 𝑛𝑛𝑛𝑛 simulation time in two different orientations. In both images the segments that were excluded in the RMSd calculations in Fig. 3.2.17. are shown in orange and the remaining segments in blue. To facilitate the orientation two calcium ions are shown as red spheres and the disulphide bridges as bonds. Labels of the secondary structure elements are given according to Zelensky and Gready (Zelensky & Gready [2003]). The molecules are rendered with VMD (Humphrey et al. [1996] version 1.9.1) and labels are added with Inkscape (http://inkscape.org). The “New Cartoon” representation of the protein involves the STRIDE algorithm (Frishman & Argos [1995]).
Fig. 3.2.19. visualises the regions that were excluded during some RMSd calculations of perlucin (see also Fig. 3.2.17.). In this figure one exemplary perlucin structure from one MD simulation (after 10.2 𝑛𝑛𝑛𝑛) with four calcium ions is shown in two orientations (only two calcium ions are depicted for orientation purposes). The excluded segments are
shown in orange and the remaining ones in blue. As it can be seen in this exemplary structure the excluded segments comprised the LLR and some solvent exposed loops.
Many residues included in the RMSd calculations were part of the secondary structures of the CTLD fold.
One might now speculate that the RMSd values obtained without the segments from the LLR and other loop regions represent the evolution of the residues forming the
“central core” of perlucin. This would indicate that at least a reasonable model of those
“core residues” is present in the input perlucin models. As it is pointed out several times before the segment between α2 and the beginning of β2 of perlucin needs to be examined/remodelled in future studies.
Note that the total RMSd of the CTLD of MBP-‐A without calcium ions (Fig. 3.2.17. green graph) seems not to converge within the 10.2 𝑛𝑛𝑛𝑛. Since the N-‐terminal segment of the CTLD was shorter in this simulation series this could implicate that the system was not in equilibrium after 10 𝑛𝑛𝑛𝑛.
3.2.6. Backbone dihedral angles (Φ,Ψ) of the CTLD of perlucin and MBP-‐A