Molecular Dynamics Simulations HEXA

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]

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.

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
Figure ?: Pressure distribution of the wildtype.	Figure ?: Pressure distribution of the Mutation 436.	Figure ?: Pressure distribution of the Mutation 485.

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. If we have a look at Figure ?, Figure ?, and Figure ?, 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
Error Estimation
0.0029	0.0029	0.0045
Temperature distribution of the Wildtype.	Temperature distribution of Mutation 436.	Temperature distribution of Mutation 485.

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 of the temperatures over the simulation time, all three plots (Figure ?, Figure ? and Figure ?) 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
Figure : Potential energy distribution of the Wildtype.	Figure : Potential energy distribution of Mutation 436.	Figure : Potential energy distribution of the Mutation 485.

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 ?, Figure? and Figure ?). Especially if we compare Figure ? and Figure ?+2, we can see that almost during the complete simulation, the potential is lower than on the wildtype. If we look at Figure ?+1, we can see the same picture, but not that clear than on Figure ?+2. Therefore, both mutations change the potential energy a little bit.

Total Energy

Wildtype	Mutation 436	Mutation 485
Average (in kJ/mol)
-1.05177e+06	-1.0519e+06	-1.05203e+06
Figure ?: Total energy distribution of the Wildtype.	Figure ?: Total energy distribution of Mutation 436.	Figure ?: Total energy distribution of Mutation 485.

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 ?, Figure ? and Figure ?) it is easy to see, that the distribution seems to be similar, but the average axis is lower on Figure ? and Figure ? than on the wildtype plot on Figure ?. 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.

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
Figure ?: Plot of the minimum distance between periodic boundary cells of the wildtype.	Figure ?: Plot of the minimum distance between periodic boundary cells of mutation 436.	Figure ?: Plot of the minimum distance between periodic boundary cells of mutation 485.

On the first view, we can see that Figure ?, Figure ? and Figure ? 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. 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 4. 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 seems to increase a little bit, 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.

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
Figure ?: Plot of the RMSF values over the whole protein of the wildtype.	Figure ?: Plot of the RMSF values over the whole protein of mutation 436.	Figure ?: Plot of the RMSF values over the whole protein of mutation 485.
Number of peaks (nm > 0.2)
7	2	8

On the first look the plots (Figure ?, Figure ? and Figure ?) 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.

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
Figure ?: Distribution of the radius of gyration over time of the wildtype	Figure ?: Distribution of the radius of gyration over time for of Mutation 436	Figure ?: Distribution of the radius of gyration over time of Mutation 485

First of all, the radius of gyration (on Figure ?, Figure ? and Figure ?) 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.
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.

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.