Molecular Dynamics Simulations HEXA
Contents
- 1 Run the MD simulation
- 2 Detailed results
- 3 Comparison of the results
- 3.1 check the trajectory
- 3.2 Visualize in pymol
- 3.3 create a movie
- 3.4 energy calculations for pressure, temperature, potential and total energy
- 3.5 minimum distance between periodic boundary cells
- 3.6 RMSF for protein and C-alpha and Pymol analysis of average and bfactor
- 3.7 Radius of gyration
- 3.8 solvent accesible surface area
- 3.9 hydrogen-bonds between protein and protein / protein and water
- 3.10 Ramachandran plot
- 3.11 RMSD matrix
- 3.12 cluster analysis
- 3.13 internal RMSD
- 3.14 Comparison to Normal Mode Analysis
- 4 Discussion
Run the MD simulation
A detailed description of how to run the MD analysis software to get the same results as we did, can be found [here].
Detailed results
The detailed results and the discussion of the single results can be found for each run on their own page.
- [Wildtype]
- [Mutation 436]
- [Mutation 485]
Back to [top].
Back to [Tay-Sachs Disease].
Comparison of the results
In this section, we want to compare the different results of the MD analysis to look if there are differences between the wild type structure and the structures with the mutation. For more information about the single result analysis please look at the point Detailed results.
check the trajectory
| Wildtype | Mutation 436 | Mutation 485 | ||||||
| Item | #frames | Timesteps (ps) | Item | #frames | Timesteps (ps) | Item | #frames | Timesteps (ps) |
| Step | 2001 | 5 | Step | 2001 | 5 | Step | 2001 | 5 |
| Time | 2001 | 5 | Time | 2001 | 5 | Time | 2001 | 5 |
| Coords | 2001 | 5 | Coords | 2001 | 5 | Coords | 2001 | 5 |
As you can see in the table above, each simulation has the same number of frames on the different items. Therefore, the different results of the different MD simulation runs are comparable. We used the results of these runs for the following comparison of the different results.
Back to [top].
Back to [Tay-Sachs Disease].
Visualize in pymol
Next, we want to compare the pictures of the tertiary structure with pymol.
| wildtype | Mutation 436 | Mutation 485 |
In general, the structure of the different simulation results is equal (which can be seen in Figure 1, Figure 2 and Figure 3), which was expected, because we only mutated on amino acid in the complete system.
Back to [top].
Back to [Tay-Sachs Disease].
create a movie
The MD simulation gave the possibility to watch movies with the protein motions. Therefore, we created for each simulation result one movie in stick view and one movie in cartoon view, which can be see on Figure ?, Figure ? and Figure ?.
| wildtype | Mutation 436 | Mutation 485 |
The motion of the complete protein seems to be very similar (compare Figure 4 - Figure 9). Therefore, it is not possible to see a difference between them.
Therefore, we also want to have a closer look to the motion of the different residues.
The MD simulation simulates the motion of each residue. It is not an approximate model, because the motion of every residues was calculated. So it is possible to have a closer look to the single residues and to compare the motion of the original amino acid and the mutated amino acid. This comparions can be seen on Figure 10 - Figure 13.
- Mutation at position 436
| wildtype | Mutation 436 |
The amino acids seem to be very similar and also the motion of the amino acid is very similar, which can be seen on Figure 10 and Figure 11. Therefore, we suggest that there is no big difference between these two amino acids and the motion of the protein. Hence, we think, that the substitution of the amino acid may not change the function and the motion of the protein.
- Mutation at position 485
| wildtype | Mutation 485 |
First of all, we can see that the amino acids are totally different. Secondly, we can see that the original amino acid is more flexible than the mutated one, which can be seen on Figure 12 and Figure 13. The original amino acid shows more motion in the simulation than the mutated amino acid. Therefore, because of the different motion of the amino acids, we suggest that the mutated amino acid may change the function and locally the structure of the protein.
Back to [top].
Back to [Tay-Sachs Disease].
energy calculations for pressure, temperature, potential and total energy
In this section we compare the pressure, temperature, potential and total energy of the different runs.
Pressure
| Wildtype | Mutation 436 | Mutation 485 |
| Average (bar) | ||
| 1.00711 | 1.0066 | 0.998385 |
| Minimum (bar) | ||
| -217.3543 | -219.7197 | -230.0158 |
| Maximum (bar) | ||
| 231.9909 | 238.8288 | 243.7419 |
There are differences between the pressure of the different systems, but these differences are very low and therefore, it should not change the structure a lot. Therefore, we think, that such small differences between the three different structures do not explain why two of them do not function any longer, because of the mutation. Otherwise, there are big differences in the minimum and maximum values between these three systems. There is a difference of more than 10 bar in both peaks. If we have a look at Figure 14, Figure 15, and Figure 16, where we can see the distribution of the pressure over the simulation time which are very similar. So therefore, it is not possible to see big differences between the three different simulation results
temperature
| Wildtype | Mutation 436 | Mutation 485 |
| Average (in K) | ||
| 297.94 | 297.94 | 297.936 |
| Minimum (in K) | ||
| 294.82 | 294.63 | 294.99 |
| Maximum (in K) | ||
| 301.31 | 300.83 | 301.08 |
The temperature of the system is nearly the same, only the temperature of the Mutation 485 is little bit lower. But this difference is that low, so therefore, we can say, the three model have the same temperature. If we have a look at the different plots and the table of the temperatures over the simulation time, all three plots (Figure 17, Figure 18 and Figure 19) show nearly the same picture. There are in each plot some outliers to higher or lower degress, but in general almost the complete time the system has a temperature of about 298K.
Potential
| Wildtype | Mutation 436 | Mutation 485 |
| Average (in kJ/mol) | ||
| -1.2815e+06 | -1.28165e+06 | -1.28176e+06 |
| Minimum (in kJ/mol) | ||
| -1.2853e+06 | -1.2852e+06 | -1.28513e+06 |
| Maximum (in kJ/mol) | ||
| -1.2778e+06 | -1.2771e+06 | -1.27769e+06 |
The average potential of the three different structures is very similar. Althoug there are very small differences between the wildtype structure and the structures with the mutation. The Wildtype has the highest potential energy, whereas Mutation 436 has a potential energy which is a little bit lower. The structure with a mutation at position 485 has the lowest potential. The values we can see on the tabel above, are only average values, therefore, we want to have a more detailed look to the plots of the potential energy distribtuion over time (Figure 20, Figure 21 and Figure 22). Especially if we compare Figure 20 and Figure 22, we can see that almost during the complete simulation, the potential is lower than on the wildtype. If we look at Figure 21, we can see the same picture, but not that clear than on Figure 22. Therefore, both mutations change the potential energy a little bit.
Total Energy
| Wildtype | Mutation 436 | Mutation 485 |
| Average (in kJ/mol) | ||
| -1.0517e+06 | -1.0519e+06 | -1.05203e+06 |
| Minimum (in kJ/mol) | ||
| -1.0559e+06 | -1.0557e+06 | -1.0569e+06 |
| Maximum (in kJ/mol) | ||
| -1.0472e+06 | -1.0463e+06 | -1.0468e+06 |
If we look at the total energy of our different systems, it is clearly to see, that the trend, we already observed by potential energy is more clear to see here. Therefore, the different mutations have an effect on the protein structure and energy. Also in this case, the change is not that much, but nevertheless, there is a change, and also only little changes in the energy of the protein can damage the function. The mutation at position 485 seems has significantly more effect on the energy of the system, than the mutation at position 436, but both mutations decrease the energy of the structure. Therefore, it is possible, that the structure become too rigid and can not bind to their targets as without the mutation.
If we look at the plots (Figure 23, Figure 24 and Figure 25) it is easy to see, that the distribution seems to be similar, but the average axis is lower on Figure 24 and Figure 25 than on the wildtype plot on Figure 23. This is the same result as we saw before on the analysis of the potential energy and it was expected, because the potential energy is a part of the total energy and therefore, if there are differences in the potential energy, there have to be changes in the total energy. In our case, the total energy shows more clearly that there is a energy difference between the wildtype structure and the mutation structures.
Back to [top].
Back to [Tay-Sachs Disease].
minimum distance between periodic boundary cells
Now we want to compare the calculations of the minimum distance between periodic boundary cells. First of all, the distance should not be 0, because than some parts of the protein will interact with itself, which should not occurr in a protein. So therefore, these minimum distance values should not be too low. Second, also small differences between the values of the different system could have big effects on the protein structure, because if some parts of the protein interact with itself, they could not interact with the original partner anylonger and therefore, the shape of the protein could be changed or destroy.
| Wildtype | Mutation 436 | Mutation 485 |
| Average (in nm) | ||
| 3.139 | 2.415 | 3.215 |
| Minimum (in nm) | ||
| 1.770 | 1.408 | 1.772 |
| Maximum (in nm) | ||
| 4.081 | 4.096 | 4.217 |
On the first view, we can see that Figure 26, Figure 27 and Figure 28 show totally different plots. First of all, it is important to keep in mind, that the MD simulation is a non-deterministic algorithm. Therefore, we can not compare the timeline itself, but we can compare the values and the distribution of the values. So therefore, we can see that on the wildtype plot the values are between 2 and 4. Most of the time the values are about 3.7, and only some values are lower than 3.
If we compare the wildtype to the plot of the structure with the mutation at position 346, we can see that almost all of the minimum distances during the simulation are lower then 3. Therefore, the distance between two interacting parts of the protein is signifiantly lower than on the wildtype (2.415 average for mutation 436, 3.139 average for wildtype). Because there is only one change in the complete sequence of the protein, we suggest, that the part with the mutation causes this changes. Therefore, the mutation lead to significantly different interaction in between the protein and therefore it probably change the shape of the protein.
If we compare the wildtype with the structure with a mutation at position 485, we can see that most of the distance is about 3. So in general, on the first view the two plots seems to be totally different. But if we have a closer look to the plots, these two plots are similar than the wildtype plot compared to the plot of mutation 436. Therefore, in this case the minimum distance increases a little bit (about 0.2 nm), but the difference is not that strong as we could observed by mutation 436. Nevertheless, also only small changes have influence of the function and the shape of the protein. Therefore, the interacting parts seems to be farther away than without the mutation.
Interesstingly, the two mutations have different effects on the interactions in the protein. Mutation 436 decrease the minimum distance between interacting atoms of the protein, whereas the Mutation at position 485 increase the minimum distance.
Nevertheless, if the minimum distance decrease or increase, in both cases the mutation changes the distances and therefore, we suggest that both mutations has an effect on the protein structure and function.
Back to [top].
Back to [Tay-Sachs Disease].
RMSF for protein and C-alpha and Pymol analysis of average and bfactor
Next we want to check if the mutations change the protein flexibility. Therefore, we calcualte the RMSF for the complete protein and the C-alpha atoms to have the possibility to differ between flexibility at the side chains and flexibility of the back bone. Furthermore, the program calcualted an average protein structure, which consists of all structures which are calculated during the simulation. The program also calculate the B-fact values on basis of the simulated structures. Furthermore, we want to visualise the most interessting results with pymol.
| original & average (protein) | original & B-Factors (protein) | average & B-Factors (protein) | original & average (c-alpha) | original & B-Factors (c-alpha) | average & B-Factors (c-alpha) | |
| Wildtype | ||||||
| 1.556 | 0.349 | 1.684 | 1.373 | 0.279 | - | |
| Mutation 436 | ||||||
| 1.525 | 0.348 | 1.671 | 1.324 | 0.277 | 1.334 | |
| Mutation 485 | ||||||
| 1.519 | 0.349 | 1.727 | 1.258 | 0.283 | 1.297 | |
First of all, we compare the RMSD between the different systems and second, we compare the RMSD between the different structures.
If we look at the RMSD values which are calculated if we align original and average structure, we can see that the RMSD value for the wildtype alignment is the highest value. The RMSDs of the mutations are similar, but the lowest RMSD value is the value for the structure with a mutation at position 485. A low RMSD value means, that there is less motion during the simluation. Therefore, our wildtype structure seems to move most during the simulation and therefore, this structures seems to be most flexible.
If we compare the RMSD values between original and B-factors, we can see, that the RMSD value is lower than by the alignment between original and average. Furthermore, there is no difference between the different systems. Therefore, the mutations do not change the flexibility of any residue. The wild type structure moves more than the structures with the mutations, but it seems ot be independent of the flexibility of the single residues. The alignments between the average structure and the B-factor structures gave higher RMSD values than the alignment between average and original. So the difference between the structure with the average B-factors and the average structure seems to be more different than the original and the average structure. Nevertheless, this fact is not that important.
It is more important to recognize, that the wildtype structure shows more motion than the mutated structures althought there is no difference in the flexibility of the different residues.
Next we want to look if the motions of the protein are high because of the motion of the different side chains or of the backbone. Therefore, we calculate the RMSF for the protein with only using the c-alpha atoms. Therefore, we do not regard the side chains anylonger.
If we look at the table we can see, that the RMSD values are lower. But the difference is not very high, therefore, most of the motion is because of the motion of the backbone and not of different positioning residues. The trend is the same as if we calculate the RMSD with side chains.
Therefore, the backbone of the wildtype structure shows the most motion, whereas the backbone of the mutated structures show a significantly lower motion.
Furthermore, we also got a plot were we can see the RMS flucation at the different positions within the protein. Residues with high RMS fluction have a high B-factor value and therefore are very flexible. We want to compare, if there are any changes in the flexible residues in the wildtype structure and the mutated structures.
In general, there are less peaks if we look at the RMS flucation calculated with the c-alpha atoms (which can be seen in the detailed results), but for the comparison of our results, we only look at the RMS flucation of the different residues calculated with the complete protein.
| Wildtype | Mutation 436 | Mutation 485 |
| Number of peaks (nm > 0.2) | ||
| 7 | 2 | 8 |
On the first look the plots (Figure 29, Figure 30 and Figure 31) are relatively similar. All three plots show the same distribution of peaks, although the height of the peak is very different. We decided to make a cutoff by 0.2nm to decide that this residue is flexible. Therefore, the wildtype has 7 very flexible residues, whereas mutation 436 has only 2 very flexible regions. Mutation 485 has 8 very flexible residues and is therefore very similar to the result of the wildtype.
In general, we distribution of the flexibility is similar for all three structures. But there are big differences in the height of the peaks and in the intensitiy of the flexibility. Therefore, we can see that especially mutation 436 change the flexibility of the different residues within the protein and therefore, the flexibility of the complete protein.
Back to [top].
Back to [Tay-Sachs Disease].
Radius of gyration
The Radius of gyration is the RMS distance of the protein parts from their centre. So therefore, it is possible to get a good insight into the shape of the protein during simulation, because if the radius is higher, this means the distance between the different protein parts and the protein centre is higher and therefore the protein has a bigger shape than before.
As result of the calculation we got a plot for each structure in which we can see the radius of gyration and also the components of the complete radius. The first component of the lot correspond to the longest axis of the molecule. Therefore, we not only know the radius of gyration, but also which axis are the main component of this radius.
| wildtype | Mutation 436 | Mutation 485 |
| Average (Rg in nm) | ||
| 2.407 | 2.408 | 2.416 |
| Minimum (Rg in nm) | ||
| 2.346 | 2.344 | 2.347 |
| Maximum (Rg in nm) | ||
| 2.440 | 2.436 | 2.339 |
First of all, the radius of gyration (on Figure 32, Figure 33 and Figure 34) seems to be very similar between the different structures. Therefore, all structures nee almost the same space, which was expected, because the structures has the same length and therefore they should approximilaty need the same space.
| Wildtype | Mutation 436 | Mutation 485 | Wildtype | Mutation 436 | Mutation 485 | Wildtype | Mutation 436 | Mutation 485 | |
| RgX (in nm) | RgY (in nm) | RgZ (in nm) | |||||||
| Average | 2.153 | 2.094 | 2.145 | 1.609 | 1.853 | 1.630 | 2.084 | 1.929 | 2.094 |
| Minimum | 2.012 | 1.986 | 1.992 | 1.423 | 1.581 | 1.444 | 1.945 | 1.618 | 1.809 |
| Maximum | 2.214 | 2.179 | 2.212 | 1.807 | 2.102 | 1.927 | 2.238 | 2.212 | 2.219 |
If we have a closer look at the different axis of the protein we can see that there are big differences. The x axis seems to be similar between the different structures. But the y and z axis differ extremly between the structures. On the wildtype, the value of the z axis is almost similar to the x axis value, whereas the value for the y axis is very low. The axis on the plot for mutation 436 are more flexible. There are some situation in which the value for the y and the z axis is almost the same, some situations in which the value of y is near by the value of x and some situations in which the value of z is near by the value of x. Therefore, this structures seems to pulsate in a way, because there are always changes in the radius of gyration for the y and the z axes. For the mutation 485, most of the time the z axis value is similar to the x axis value and the y axis value is very low. This is very similar to the wildtype. There are some situations in which the y and the z axis values are very similar. So therefore, again this structure seems to move more along the axes than the wildtype.
So in general, we already know that our wildtye structure is very flexible and has a lot of motion. Nevertheless, this system seems not to slide along any axes, as the structures with the mutation do.
Back to [top].
Back to [Tay-Sachs Disease].
solvent accesible surface area
As a next step, we analyzed the solvent accesible surface area of the wildtyp and the two mutations for each residue of the protein and for all atoms of the protein. Furthermore, we looked at the solvent accesibility of the whole protein during the simulations. Therefore we received three plots for each mutation and two for the wildtyp which contains the solvent accesibility area with standard deviation for all residues (Figure 35-37), for all atoms (Figure 38-40) and for the whole protein (Figure 41-43). Furthermore, we calculated the minimum, the maximum and the average of those distributions which allows a detailed comparison.
| wildtype | Mutation 436 | Mutation 485 |
| Average (in nm²) | ||
| 0.537 | 0.553 | 0.542 |
| Minimum (in nm²) | ||
| 0.004 | 0.003 | 0.007 |
| Maximum (in nm²) | ||
| 2.058 | 2.005 | 2.014 |
First of all, we analyze the solvent accesibility of each residue. Looking at the table above, we can see that the values for the minimum, the maximum and the average agree mostly for wildtyp, muation 436 and mutation 484. The same can be seen by regarding the plots of the solvent accesibility of each residue. This indicates that both mutations do not change the solvent accesibility of the residues dramatically. Furthermore, the plots display that in all three cases the amplitude of the fluctation is not that high with some exceptions. Besides, the standard deviation is very low in all three plots which indicates that there are no extrem outliers in there. Both curves point out that there are mainly sparse moving residues during the complete simulation with some exceptions where the residues are very flexible. All in all, this suggest that the real movement which is sparse will not be strong influenced by the two mutations.
| wildtype | Mutation 436 | Mutation 485 |
| Average (in nm²) | ||
| 0.031 | 0.032 | 0.032 |
| Minimum (in nm²) | ||
| 0 | 0 | 0 |
| Maximum (in nm²) | ||
| 0.560 | 0.558 | 0.561 |
Next, we have a closer look at the solvent accesibility of each atom of the protein. The minimum, maximum and average values for the two mutations and the wildtype are very similar as well as the according solvent accesibility plots. This indicates that the muations do not cause extrem changes for the solvent accesibility which agrees with the conclusion for the residues. The amplitude of the fluctuations is most of the time low with some exceptions. This indicates that the protein movement is most of the time sparse. Finally, this this suggest that the real movement which is sparse will not be strong influenced by the two mutations.
| wildtype | Mutation 436 | Mutation 485 |
| Average (in nm²) | ||
| 135.036 | 138.727 | 135.452 |
| Minimum (in nm²) | ||
| 129.084 | 127.066 | 129.167 |
| Maximum (in nm²) | ||
| 142.218 | 146.571 | 142.977 |
Finally, we examine the solvent accesibility of the whole protein during the whole simulation. Looking at the minimum, the maximum and the average values, we can see that they are very similar von wildtyp, muation 436 and mutation 485. One exception ist mutation 436 where the values are a little bit higher. The plots which describes the solvent accesibility for different physiocochemical properties look very similar with no outstandig differences for mutation 436. This indicates that both mutations do not cause huge changes of the solvent accesibility of the whole protein. Only mutation 436 causes eventually some very small changes. The fluctation for all different physiocochemical properties is very constant with no outstanding outliers. Therefore, we suggest that the movement of the protein is sparse, because there exist no big changes which can be caused by structural change.
To sum up, all three differnt solvent accessibility analysis deliver same results. The mutation seem not to cause huge changes of the solvent accesibility. Furthermore the movement seem to be very sparse, because the fluctuations stay very constant during the whole simulation.
Back to [top].
Back to [Tay-Sachs Disease].
hydrogen-bonds between protein and protein / protein and water
Afterwards, we had a look at the hydrogen bonds where we differentiate between hydrogen bonds within a protein and hydrogen bonds between the protein and the surounding water. The following plots displays the number of the hydrogen bonds as well as possible pairs within 0.35nm during the simulation. Furthermore, we determine the minimum, maximum and average number of hydrogen bonds for a better comparison.
| wildtype | Mutation 436 | Mutation 485 |
The plots above show the number of hydrogens formed within a protein during the whole simulation. Looking only at the hydrogen bonds itself we can see a different development between the wildtype, mutation 436 and mutation 485. The number for the wildtyp (Figure 44) and mutation 436 (Figure 45) decrease during the simulation in some different ways. Contrary, muation 485 goes only a bit down and increases at the end again (Figure 46). The number stays for all three cases mostly between 300 and 350. Outstandig is, that the wildtyp has most of the time a higher number of hydrogen bonds. The reason therefore is probably that the mutations causes structural changes which influences the hydrogen bonds.
The other plots (Figure 47-49) which contain additional the number of pairs within 0.35nm look almost similar. This is probably because of the scale. However, this shows that the difference is not that huge compared to the possible hydrogen bonds that could be formed.
| Wildtype | Mutation 436 | Mutation 485 | ||||
| bonds in the protein | possible bonds in the protein | bonds in the protein | possible bonds in the protein | bonds in the protein | possible bonds in the protein | |
| Average | 328.758 | 1537.77 | 319.787 | 1534.866 | 323.337 | 1543.024 |
| Minimum | 294 | 1486 | 292 | 1483 | 300 | 1491 |
| Maximum | 361 | 1587 | 356 | 1584 | 354 | 1602 |
The table above contains the minimum, maximum and average number of hydrogen bonds formed within a protein for the wildtyp and the both mutations. Comparing this values, we can see that there is noch big difference between the wildtyp and the mutations. This indicates that even if the fluctuation development differs, that the number of formed hydrogen is very similar. Furthermore, this shows that the result for the wildtyp is by closer look not outstanding higher.
| wildtype | Mutation 436 | Mutation 485 |
The plots above show the number of hydrogens formed between the protein and the surrounding water during the whole simulation. Looking only at the hydrogen bonds itself we can see a different development between the wildtype, mutation 436 and mutation 485. The number of hydrogen bonds of wildtyp(Figure 50) as well as mutation 436 (Figure 51) increases during the simulation whereas the number of hydrogen bonds of mutation 485 stays almost constant (Figure 52). Besides, the slop of the wildtyp seems to be more extreme. The number of formed hydrogen between the protein and the surrounding water ist for all three cases between 800 and 900.
The other plots (Figure 53-55) which contain additional the number of pairs within 0.35nm look almost similar. This is probably because of the scale. However, this shows that the difference is not that huge compared to the possible hydrogen bonds that could be formed.
| Wildtype | Mutation 436 | Mutation 485 | ||||
| bonds in the protein | possible bonds in the protein | bonds in the protein | possible bonds in the protein | bonds in the protein | possible bonds in the protein | |
| Average | 836.94 | 981.18 | 853.403 | 999.847 | 847.965 | 999.310 |
| Minimum | 768 | 853 | 778 | 905 | 783 | 882 |
| Maximum | 916 | 1091 | 907 | 1106 | 912 | 1126 |
The table above contains the minimum, maximum and average number of hydrogen bonds formed between the protein and the surrounding water for the wildtyp and the both mutations. Comparing this values, we can see that there is noch big difference between the wildtyp and the mutations. A outstanding difference exists only between the different average values, where the wildtyp has a smaller value. This indicates that the mutation probably changes the protein structure in way that less hydrogen bonds with the surrounding water were formed.
To sum up, the number of the hydrogen bonds within a protein and between the protein and the surrounding water is very similar. Having a closer look, we can see that the wildtyp differs a bit which indicates that the mutation cause small structural changes which cause a different number of formed hydrogenbonds. Furthermore, looking at the bonds formed within, we see that the wildtyp seems to form more hydrogen bonds where as between the protein and the surrounding water it seems to form less hydrogen bonds. Therefore, it could be possible that the mutated proteins form more bonds with the surrounding water instead of forming them within the protein.
Back to [top].
Back to [Tay-Sachs Disease].
Ramachandran plot
Next, we analysed the resulting Ramachandran Plots for the wildtyp, mutation 436 and mutation 485. Besides we compared them with a typical Ramachandran Plot. This plot displays which group of points stand for a certain secondary structure element.
| wildtype | Mutation 436 | Mutation 485 | Typical Ramachandran Plot |
 Figure 47:Typical Ramachandran Plot (Source: [wikipedia]) |
The Ramachandran plots which were created during our simulations contain a lot of points. This points bouild no clear regions like in the typical ramachandran plot. Here one regions goes over in another one. The only clear boundry exist in the vertical. On the left site are the typical secondary structure elements. For all three cases this regions looks very smeared whereas mutation 485 differes a bit, because it contains not this white region at the bottom where no points are. The right half contains in the middle the left-handed helices which were presented a lot in all three plots. In this regions the three plots differ as well, whereby the wildtyp has the clearest contours and mutation 485 displays the most blurred region. The rest of the point on both sides display some kind of other secondary structure. The high number of dots and smeared look can be explained by the fact that this ramachandran plots were created during the whole simulation. Therefore, every movement and structure change causes different secondary structures. Ramachandran Plot displays clear differences between the wildtyp, mutation 436 and mutation 485. This indicates that both mutations causes structural changes as well as they influence the movement of the protein. The Ramachandran Plot of mutation 485 deviates most which indicates that this mutation has the greates effect on the structure and its movement.
Back to [top].
Back to [Tay-Sachs Disease].
RMSD matrix
As an next step, we compared the resultion RMSD matrices of the wildtyp, mutation 436 and mutation485.
| wildtype | Mutation 436 | Mutation 485 |
The RMSD matrices display some differences between the different types. The first RMSD matrix, the wildtyp RMSD matrix, has the smallest RMSDs around the diagonal. Contrary, the RMSD matrix of mutation 436 contains a square around the diagonal which contains the lowest RMSDs. Having a closer look, this difference is not extreme which means that protein with mutation 436 differs only a bit compared to the wildtyp. The highest variation from the wildtyp displays the RMSD matrix for mutation 485 where a square at the right top contains really low RMSD scores. It is the only RMSD matrix which contains light blue colored regions far away from the diagonal. This different RMSD matrices indicates that the protein with the mutation 485 has most reagions with higher density. Mutation 436 causes some density changes as well, but they are probably harmful. Consequentially, mutation 485 causes highest density changes which probably influences the movement capability a lot. We suggest that the protein with this mutation will probably be more rigid and moves less.
Back to [top].
Back to [Tay-Sachs Disease].
cluster analysis
Afterwards, we regard the 231 different clusters for the wildtyp, mutation 436 and mutation 485. Therefore, we compared the visualized cluster and the distribution of the RMSD value over the different clusters. At last, we aligned some certain structures from the cluster, calculate the RMSD and compared them as well.
| wildtype | Mutation 436 | Mutation 485 |
The first pictures display the clusters for the wildtyp, mutation 436 and mutation 485. In this pictures it very difficult to extract small difference, because of the scale. It is possible to see that they look similar in general. The distributions of the RMSD values is more comparable where we can directly see some differences. The highest difference exists for the courve shape. The wildtpye increases slow and has a fast decrease. Contrary, the RMSD distribution for both mutations acts contrary. This means that it increases fast and decreases very slow with one break within. Mutation 485 differs most and contains a groove. This displays the influence of both mutations on the cluster and the associatend structure or movement.
| Cluster 1 | Cluster 2 | RMSD for the Wildtyp | RMSD for Mutation 436 | RMSD for Mutation 485 |
| cluster 1 | cluster 2 | 0.654 | 0.880 | 0.790 |
| cluster 1 | cluster 5 | 0.899 | 0.068 | 0.755 |
Comparing the build alignment of certain structures out of the clusters, we can see that the RMSD does not differ dramatically. For cluster 1 and 2 the smalles RMSD is achieved by the structure of the wildtyp cluster. Contrary the smallest RMSD value for cluster 1 and 5 is reached by the structure of mutation 436 which is outstandig small. This two examples show that the mutations have influence on the structure and the associated movement of the protein. With this to samples it is not possible to determine the influence strength of the mutations.
To sum up, we can see that both mutations have some influence on the protein structure and associated movement whereas mutation 485 will cause the strongest damage.
Back to [top].
Back to [Tay-Sachs Disease].
internal RMSD
Finally, we analyzed the internal RMSD. The internal RMSD describes the distances between the single atoms within protein, which helps to obtain the structure of the protein.The following plots display the internal RMSD during the whole simulation for the wildtyp, mutation 436 and mutation 485. Additional we extract the minimal, maximal and average internal RMSDs.
| Wildtype | Mutation 436 | Mutation 485 |
| Average (RMSD in nm) | ||
| 0.238 | 0.242 | 0.243 |
| Minimum (RMSD in nm) | ||
| 4.89e-7 | 0.141 | 4.906e-07 |
| Maximum (RMSD in nm) | ||
| 0.312 | 0.409 | 0.289 |
Looking at the internal RMSD plots, we can see that there exist only some small differences between the wildtyp and the two mutations. All three plots increase very fast at the beginning till they reach some kind of stagnation where the internal RMSD arise slow. They reach all about 0.3nm their stagnation. The only small difference between the wildtyp and both mutations is, the slop of the wildype which is stronger from the point where stagnation begins. Looking at the average value, we can see that the three curves are really similar. The minimum and maximum values are the only one which display some differences. The mutation seems to influence the internal RMSD only less which indicates that he mutations have no huge influence on the protein structure.
Back to [top].
Back to [Tay-Sachs Disease].
Comparison to Normal Mode Analysis
The comparison of Molecular Dynamics to the the Normal Mode Analysis can be found on the [Normal Mode Analysis site].
Discussion
In this section we want to discuss if the MD simulation could give us hints, that the mutations are bad for the protein. Sadly, we analysed in this case two mutations which are effective, but if the mutation has no effect on the protein function we suggest, that the values in the analysis are very similar. If this is not the case we suggest, that the mutation is effectiv.
In the following table we want to list if there are any differences between the wildtype and the mutation.
By the visualisation in pymol we can see, that there is a difference in the motion of the residues of the wildtype and the mutated structure at position 485, but there is no difference between wildtype and mutation 436.
| protein motion | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| Difference | no | yes |
Now we want to compare the energy calculations for the different structures. By analysing Pressure there is a difference, if the deflection is more than 0.001 in average. By the minimum and maximum comparison there we count a difference by a deflection of more than -3.
By the temperature there has to be a difference of more than 1 K.
By comparison the potential and the total energy, we count a difference, if there is a deflection of more than 20 kJ/mol.
| energy calculations | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| Pressure | |||
| Average (bar) | 1.00711 | 1.0066 | 0.998385 |
| Minimum (bar) | -217.3543 | -219.7197 | -230.0158 |
| Maximum (bar) | 231.9909 | 238.8288 | 243.7419 |
| Temperatur | |||
| Average (K) | 297.94 | 297.94 | 297.936 |
| Minimum (K) | 294.82 | 294.63 | 294.99 |
| Maximum (K) | 301.31 | 300.83 | 301.08 |
| Potential | |||
| Average (kJ/mol) | -1.2815e+06 | -1.28165e+06 | -1.28176e+06 |
| Minimum (kJ/mol) | -1.2853e+06 | -1.2852e+06 | -1.28513e+06 |
| Maximum (kJ/mol) | -1.2778e+06 | -1.2771e+06 | -1.27769e+06 |
| Total energy | |||
| Average (kJ/mol) | -1.05177e+06 | -1.0519e+06 | -1.05203e+06 |
| Minimum (kJ/mol) | -1.05599e+06 | -1.0557e+06 | -1.05687e+06 |
| Maximum (kJ/mol) | -1.04718e+06 | -1.0463e+06 | -1.04680e+06 |
| energy calculations | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| Pressure | ||
| Average | no | no |
| Minimum | no | yes |
| Maximum | yes | yes |
| Temperatur | ||
| Average | no | no |
| Minimum | no | no |
| Maximum | no | no |
| Potential energy | ||
| Average | no | yes |
| Minimum | no | no |
| Maximum | no | no |
| Total energy | ||
| Average | no | no |
| Minimum | yes | yes |
| Maximum | yes | yes |
There is no difference in the pressure of the different systems. There are some differences in the minimum and maximum value, but the average value is nearly the same, so therefore, we count differences in pressures as no. There is also no difference in the temperatur if we compare the different systems. If we have a look to the potential energy of the different structures, we can see, that there are differences in average. The minimum and maximum values are nearly the same, but the average value differs. The difference is more significant at the second mutation, so therefore, we counted this as a difference. Differences in the potential engery are very important for function, because if the protein has a difference in energy, the function could change. If we look at the total energy of the protein, we can see that the differences are very small and therefore, we decided that there is no difference in average, although there are differences in the minimum and maximum values.
Now we compare the minimum distance between periodic boundary cells of the different structures.
We decided to see a difference between the two structures if the defluction between the two values is more than 0.1nm.
| minimum distance between periodic boundary cells | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| Average (nm) | 3.139 | 2.415 | 3.215 |
| Minimum (nm) | 1.770 | 1.408 | 1.772 |
| Maximum (nm) | 4.081 | 4.096 | 4.217 |
| minimum distance between periodic boundary cells | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| Average | yes | no |
| Minimum | yes | no |
| Maximum | no | yes |
In this case there is a difference between wildtype and mutation 436 in average and minimum and the maximum value of the wildtype and mutation 485. So in this case, the mutation at position 436 seems to change the structure more than the mutation at position 485.
By the comparions of the RMSF calclation of the different structure, we count only the significant peaks with more than 0.2. If the number is not the same we count this as difference.
| RMSF calculation | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| RMSF for protein | |||
| #high B-factor regions | 7 | 2 | 8 |
| RMSF for c-alpha | |||
| #high B-factor regions | 3 | 1 | 3 |
| RMSF calculation | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| RMSF for protein | ||
| #high B-factor regions | yes | yes |
| RMSF for c-alpha | ||
| #high B-factor regions | yes | no |
As we can see in the table above, there is always a difference in the number of peaks if we calculate the RMSF for the wohle protein. Nevertheless, the difference between wildtype and mutation 436 is a way more significant than the difference between wildtype and mutation 485. Furthermore, if we only compare the c-alpha atoms, the number of peaks of the wildtype and mutation 485 is equal. Therefore, the mutation at position 436 seems to change the protein more than the mutation at position 485.
Now, we want to compare the Radius of gyration between the different structures. In this case, we mark a difference is there is a defluction of 0.01 nm.
| Radius of gyration | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| Rg | |||
| Average (nm) | 2.407 | 2.408 | 2.416 |
| Minimum (nm) | 2.346 | 2.344 | 2.347 |
| Maximum (nm) | 2.440 | 2.436 | 2.449 |
| RgX | |||
| Average (nm) | 2.153 | 2.094 | 2.145 |
| Minimum (nm) | 2.012 | 1.986 | 1.992 |
| Maximum (nm) | 2.214 | 2.179 | 2.212 |
| RgY | |||
| Average (nm) | 1.609 | 1.853 | 1.630 |
| Minimum (nm) | 1.423 | 1.581 | 1.444 |
| Maximum (nm) | 1.807 | 2.102 | 1.927 |
| RgZ | |||
| Average (nm) | 2.084 | 1.929 | 2.094 |
| Minimum (nm) | 1.945 | 1.618 | 1.809 |
| Maximum (nm) | 2.238 | 2.212 | 2.219 |
| Radius of gyration | |||
| Difference wt - mut 436 | Difference wt - mut 485 | ||
| Rg | |||
| Average | no | yes | |
| Minimum | no | no | |
| Maximum | yes | no | |
| RgX | |||
| Average | yes | yes | |
| Minimum | yes | yes | |
| Maximum | yes | no | |
| RgY | |||
| Average | yes | yes | |
| Minimum | yes | yes | |
| Maximum | yes | yes | |
| RgZ | |||
| Average | yes | yes | |
| Minimum | yes | yes | |
| Maximum | yes | yes | |
In this case, most of the time, there is a difference between wildtype and mutation. In average, there is only a difference between Mutation 485 and wildtype, if we look at the complete radius of gyration. But if we have a closer look and compare how the average value of the complete radius is composed, we can see that there are significant differences. There is always a difference between the wildtype and the mutated structures.
Another very important properity of each protein is the area which is accessible to the surface. By comparions of the solvent accessible surface area of each residue and each atom, there is a difference if there is a deflection of 0.01 nm². The last comparison is an average value for the complete protein over time and therefore, we only counted a difference, the defluction is more than 1 nm².
| solvent accessible surface area | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| Solvent accessible area of each residue | |||
| Average (in nm²) | 0.537 | 0.553 | 0.542 |
| Minimum (in nm²) | 0.004 | 0.003 | 0.007 |
| Maximum (in nm²) | 2.058 | 2.005 | 2.014 |
| Solvent accessible area of each atom | |||
| Average (in nm²) | 0.031 | 0.032 | 0.032 |
| Minimum (in nm²) | 0 | 0 | 0 |
| Maximum (in nm²) | 0.560 | 0.558 | 0.561 |
| Solvent accessible area of the protein over time | |||
| Average (in nm²) | 135.036 | 138.727 | 135.452 |
| Minimum (in nm²) | 129.084 | 127.066 | 129.167 |
| Maximum (in nm²) | 142.218 | 146.571 | 142.977 |
| Solvent accessible surface area | |||
| Difference wt - mut 436 | Difference wt - mut 485 | ||
| Solvent accessible area of each residue | |||
| Average | yes | no | |
| Minimum | no | no | |
| Maximum | yes | yes | |
| Solvent accessible area of each atom | |||
| Average | no | no | |
| Minimum | no | no | |
| Maximum | no | no | |
| Solvent accessible area of the protein over time | |||
| Average | yes | no | |
| Minimum | yes | no | |
| Maximum | yes | no | |
There is a difference of the solvent accessible area of each residue between wildtype and the mutations, but the solvent accessible area of each atom is equal in average. More important is the solvent accessible surface area of the whole protein over time and there we can see, is only a difference between wildtype and mutation 436. The area of the wildtype and the mutation at position 485 is nearly the same.
Another very important characteristic for the stability of a protein is the number of hydrogen bonds in the protein and between the protein and the water. If there is a difference of more than 5 hydrogen bonds we decided to count them as not similar.
| hydrogen-bonds | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| bonds within the protein | |||
| real occurring bonds | |||
| Average | 328.758 | 319.787 | 323.337 |
| Minimum | 294 | 292 | 300 |
| Maximum | 361 | 356 | 354 |
| possible bonds | |||
| Average | 1537.77 | 1534.866 | 1543.024 |
| Minimum | 1468 | 1483 | 1491 |
| Maximum | 1587 | 1584 | 1602 |
| bonds between protein and water | |||
| real occurring bonds | |||
| Average | 836.94 | 853.403 | 847.965 |
| Minimum | 768 | 778 | 783 |
| Maximum | 916 | 907 | 982 |
| possible bonds | |||
| Average | 981.18 | 999.847 | 999.310 |
| Minimum | 853 | 905 | 882 |
| Maximum | 1091 | 1106 | 1126 |
| Hydrogen-bonds | |||
| Difference wt - mut 436 | Difference wt - mut 485 | ||
| bonds within the protein | |||
| real occurring bonds | |||
| Average | yes | yes | |
| Minimum | no | yes | |
| Maximum | yes | yes | |
| possible bonds | |||
| Average | yes | yes | |
| Minimum | yes | yes | |
| Maximum | no | yes | |
| bonds between protein and water | |||
| real occurring bonds | |||
| Average | yes | yes | |
| Minimum | yes | yes | |
| Maximum | yes | yes | |
| possible bonds | |||
| Average | yes | yes | |
| Minimum | yes | yes | |
| Maximum | yes | yes | |
There is almost at every comparions a difference between wildtype and mutation. The number of real occurring hydrogen-bonds as well as the number of possible hydrogen bonds differ between them. Therefore, the structure of the mutated proteins seems to change dramatically.
Now we want to compare the Ramachandran plots of the different structures. Here we only do a visuale comparison.
| Ramachandran Plot | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| Difference | no | yes |
The Ramachandran plots for the wildtype and mutation 436 are quite equal, whereas there a big differences between the wildtype and the mutation 485 ramachandran plot.
Furthermore, we want to compare the RMSD matrices of the different structures, which is also done visualy.
| RMSD matrix | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| Difference | no | yes |
The RMSD matrices of the wildtype and mutation 436 are quite similar. There are differences, but in general the color of the plots are relatively equal, whereas, the plot of mutation 485 is much darker and therefore different.
Now we want to have a look to the number of the different clusters. If there is a difference of more than 5 clusters, we count it as not equal.
| Cluster analysis | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| #Clusters | 225 | 231 | 225 |
| Cluster analysis | ||
| Difference wt - mut 436 | Difference wt - mut 485 | |
| Difference | yes | no |
The algorithm found 225 different clusters for the wildtype and mutation 485, but it found 231 clusters for mutation 436.
As last point we compared the internal RMSD of the proteins. If there is a difference of more than 0.01 the structures are counted as different.
| Internal RMSD | |||
| Wildtype | Mutation 436 | Mutation 485 | |
| Average | 0.238 | 0.242 | 0.243 |
| Minimum | 4.89e-7 | 0.141 | 4.906e-07 |
| Maximum | 0.312 | 0.409 | 0.289 |
| Internal RMSD | |||
| Difference wt - mut 436 | Difference wt - mut 485 | ||
| Average | no | no | |
| Minimum | yes | no | |
| Maximum | yes | no | |
In this analysis we can see, that the internal RMSD between the wildtype structure and the mutated structures is almost the same and therefore, there is no difference in the internal RMSD values.
No we want to decide if the mutations are silent or non-silent. Therefore, we count how often is there a difference between the average values of the wildtype and the mutated structures.
| Wildtype vs. Mutation 436 | Wildtype vs. Mutation 485 | |
| #Differences | 13 | 13 |
| Ratio | 56% | 56% |
| Conclusion | non-silent | non-silent |
| correctness | wrong | right |
Both mutations have the same number of differences between it and the wildtype. Therefore 56% of the criteria are different from the wildtype. We predicted both mutations as non-silent.
This is wrong. Only one mutation is non-silent. Mutation 436 indeed is silent. There are hints, that this mutation is silent, because there is no difference in the motion of the mutated amino acid and in the energy values. But there are a lot of difference in other analysis.
Therefore, we have a prediction correctness of 50% which is really bad. So we can see, Molecular Dynamics could be very helpful by analysing a mutation, but it can also fail.
MD is a very time-consuminig analyse procedure and therefore, in our case, it was not very helpful, with a prediction correctness of 50%. Therefore, we think, it is useful to analyse the mutations first with other methods and only in special cases or cases of doubt it is useful to use the MD simulation.
Back to [top].
Back to [Tay-Sachs Disease].
