Molecular Dynamics Simulations Analysis of Glucocerebrosidase
Contents
- 1 Introduction
- 2 Wildtype
- 3 Mutation 7
- 4 Mutation 10
- 5 Discussion
- 6 References
Introduction
To analyze our Molecular Dynamics Simulations we followed the tutorial described here: http://md.chem.rug.nl/~mdcourse/analysis1.html
Wildtype
A brief check of results
- command:
gmxcheck -f 2NT0_wt_md.xtc
How many frames are in the trajectory file and what is the time resolution?
- 2001 frames
- timestep: 5ps
How long did the simulation run in real time (hours), what was the simulation speed (ns/day) and how many years would the simulation take to reach a second?
- Simulation run: 8h37:36
- Simulation speed: 27.821
- Time to reach a second: 1/0.000000028 = 35714285,714285714 days = 97847,358121331 years
Which contribution to the potential energy accounts for most of the calculations?
- -9.39801e+05 kJ/mol
Visualization of results
For visualization 1000 frames from the trajectory are extracted (-dt 10), only the protein without water is selected and the jumps over the boundaries are removed to make a continuous trajectory (-pbc nojump).
- command:
trjconv -s 2NT0_wt_md.tpr -f 2NT0_wt_md.xtc -o protein.pdb -pbc nojump -dt 10
In Figure 5 one can see the protein in motion. Compared to the results in Normal Mode Analysis the motion is not as strong and the parts that are moving are smaller than the moving ones of the Normal Mode Analysis. In this simulation mostly side chains and little elements of the protein are bouncing. Big movements like attraction or repulsion ,as seen in the Normal Mode Analysis, are not present.
Quality assurance
Convergence of energy terms
To assess the quality of the model, the convergence of thermodynamic parameters, such as the temperature, the pressure, the potential and the kinetic energy is investigated. Not converged values indicate, that the simulation has not reached a thermal equilibrium and should be extended further.
To investigate the convergance, files for temperature, pressure, energy, volume, density, box and interaction energies between protein and solvent (Coulomb and van der Waals) have been created with the following commands:
g_energy -f 2NT0_wt_md.edr -o temperature.xvg
g_energy -f 2NT0_wt_md.edr -o pressure.xvg
g_energy -f 2NT0_wt_md.edr -o energy.xvg
g_energy -f 2NT0_wt_md.edr -o volume.xvg
g_energy -f 2NT0_wt_md.edr -o density.xvg
g_energy -f 2NT0_wt_md.edr -o box.xvg
In the next steps, the files have been visualized with xmgrace.
Temperature
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Temperature | 297.912 | 0.0062 | 1.08924 | 0.00616934 (K) |
Figure 6 shows the plot for the temperature during the simulation. The temperature fluctuates between 295 K and 301 K and has an average of 297.912 K. The temperature of the system is therefore very stable, with a difference between minimal and maximal temperature of only six Kelvin. This indicates that the temperature of the system converged and reached a stable temperature very fast.
Pressure
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Pressure | 1.00032 | 0.014 | 87.9016 | 0.0583997 (bar) |
Estimate the plateau values for the pressure.
1.00032 bar
The pressure fluctuation, shown in Figure 7, lies within -300 and +300 bar. This results in a difference of 600 bar which is quite large. The system does not seem to have reached a stable pressure. It is hard to estimate when and at what point it would have converged, as no trend is observable during the simulation.
Energy
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Potential | -939801 | 85 | 924.013 | -583.172 (kJ/mol) |
| Kinetic En. | 170900 | 3.6 | 624.851 | 3.53909 (kJ/mol) |
| Total Energy | -768901 | 84 | 1128.21 | -579.63 (kJ/mol) |
In the energy file three different terms are plotted: potential, kinetic and total energy. The plot in Figure 8 shows that all three energy terms reached their plateau. It is hard to estimate the size of the fluctuations, as the scale is quite large. But as the energy terms converged, the simulation seems to have reached its optimum.
Volume
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Volume | 735.655 | 0.042 | 0.552925 | -0.0802412 (nm^3) |
The volume, shown in Figure 9, fluctuates between 734 nm³ and 737 nm³ and the average is 735 nm³. The small differences in volume indicate, that the volume has converged.
Density
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Density | 1009.64 | 0.058 | 0.75885 | 0.110104 (kg/m^3) |
Figure 10 shows the density fluctuating around 1010 kg/m³ with an average of 1009.64 kg/m³. The maximum differences are of only about 5 kg/m³ which indicates, that the density has converged as well.
Box
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Box-X | 10.1328 | 0.0002 | 0.00253864 | -0.000368389 (nm) |
| Box-Y | 10.1328 | 0.0002 | 0.00253864 | -0.000368389 (nm) |
| Box-Z | 7.16498 | 0.00014 | 0.00179508 | -0.000260487 (nm) |
What are the terms plotted in the file box.xvg?
The size of the box around the protein.
Figure 11 shows the plotted size of the box around the protein. The x-, y- and z-terms are very constant with values of 10.1328, 10.1328 and 7.16498 nm.
Interaction Energy: Coulomb
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Coul-SR:Protein-non-Protein | -24690.5 | 120 | 476.146 | -405.451 (kJ/mol) |
| Coul-14:Protein-non-Protein | 0 | 0 | 0 | 0 (kJ/mol) |
Figure 12 shows the Coulomb Energy with an average at -24690.5 kJ/mol. The energy fluctuates around that value in an interval of about 1000 kJ/mol. Near the end of the simulation the energy becomes more stable. As the equilibration takes longer for this term than for the others, the value present at the time 8000 to 10000 is the equilibrium.
Interaction Energy: van der Waals
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| LJ-SR:Protein-non-Protein | -3184.89 | 4.3 | 149.546 | -12.8142 (kJ/mol) |
| LJ-14:Protein-non-Protein | 0 | 0 | 0 | 0 (kJ/mol) |
In figure 13 you can see the van der Waals interaction energy. It has its average at -3184.89. The values are fluctuating in an interval of about 1000 kJ/mol. Also at the end of the time there is no equilibration recognisable. Maybe it always fluctuates in such a big interval or it needs more time to converge.
Minimum distances between periodic images
We used the following command: g_mindist -f 2NT0_wt_md.xtc -s 2NT0_wt_md.tpr -od minimal-periodic-distance.xvg -pi
What was the minimal distance between periodic images and at what time did that occur?
The shortest periodic distance is 1.97143 (nm) at time 5825 (ps), between atoms 960 and 2323.
What was the minimal distance between periodic images and at what time did that occur?
The shortest periodic distance is 2.43551 (nm) at time 5345 (ps), between atoms 952 and 2267.
What happens if the minimal distance becomes shorter than the cut-off distance used for electrostatic interactions? Is it the case in your simulations?
It is not the case in our simulation. The energy would "explode".
Run now g_mindist on the C-alpha group, does it change the results? What does is mean for your system?
It changes to a greater distance between two other atoms (952 and 2267). That means that it may be atoms of a side group that have this minimal distance. Also the fluctuation interval of the minimum distance becomes smaller.
Root mean square fluctuations
In the following we want to look at the RMSF, the root mean square fluctuations<ref>http://en.wikipedia.org/wiki/Root_mean_square_fluctuation</ref>.
Therefore we used the following command:
g_rmsf -f 2NT0_wt_md.xtc -s 2NT0_wt_md.tpr -o rmsf-per-residue.xvg -ox average.pdb -oq bfactors.pdb -res
Indicate the start and end residue for the most flexible regions and the maximum amplitudes.
In figure 15 you can see the RMSF fluctuation. With that you can recognise flexible regions. The most flexible region seems to be between residue 125 and residue 175. Other flexible regions are at the beginning of the protein between residue 20 and 50 and at the region about position 350.
In figure 16 you can see the protein colored according to b-factors and flexible regions. Blue means that the region is not flexible and red means that it is a very flexible region. You can see some loops that are flexible and parts of the alpha helices and beta sheets that are a bit more flexible. The most of the inner part of the protein is colored blue and therefore not flexible.
Convergence of RMSD
Now we want to calculate the RMSD. It is used as an indicator of convergence of the structure towards an equilibrium state.
We used the following commands:
trjconv -f 2NT0_wt_md.xtc -o traj_nojump.xtc -pbc nojump
g_rms -f traj_nojump.xtc -s 2NT0_wt_md.tpr -o rmsd-all-atom-vs-start.xvg
g_rms -f traj_nojump.xtc -s 2NT0_wt_md.tpr -o rmsd-backbone-vs-start.xvg
echo 1 | trjconv -f traj_nojump.xtc -s 2NT0_wt_md.tpr -o protein.xtc
g_rms -f protein.xtc -s average.pdb -o rmsd-all-atom-vs-average.xvg
g_rms -f protein.xtc -s average.pdb -o rmsd-backbone-vs-average.xvg
If observed, at what time and value does the RMSD reach a plateau?
If you compare the different methods (all atom/backbonde and against starting structure or average structure) as you can see in figure 17a, b and 18a, b there are different times when the RMSD reaches a plateau. For all atoms and backbone against the starting structure both reach their plateau at about 1500 ps with a value of 0.18 and a bit lower for backbone with about 0.17.
For the comparison to the average structure they reach a plateau later. At 3000 to 4000 ps. All atom versus all reaches a RMSD of about 0.2, the backbone of 0.06, which is very low.
Briefly discuss two differences between the graphs against the starting structure and against the average structure. Which is a better measure for convergence?
As already mentioned the convergence is reached later. The reason for that is that the average structure is nearer to the final structure. Another thing is that the RMSD for the average structures gets lower wheras it gets higher for the comparison to the starting structure. The starting structure is farer away from the final structure, so this is again the reason. It might be better to take the starting structure to recognise the convergence because you can see sooner that an equilibrian state is reached.
Convergence of radius of gyration
Now look at the radius of gyration<ref>http://en.wikipedia.org/wiki/Radius_of_gyration</ref>. Therefore we used the following command:
g_gyrate -f 2NT0_wt_md.xtc -s 2NT0_wt_md.tpr -o radius-of-gyration.xvg
The radius of gyration gives insight to the shape of the protein.
At what time and value does the radius of gyration converge?
The radius of gyration is always constant with about 2.3 nm. The RgX, RgY and RgZ fluctuate until the end and reach values between 1.8 and 1.9.
Structural analysis: properties derived from configurations
Solvent accessible surface area
With the Solvent accessible surface area (SASA)<ref>http://en.wikipedia.org/wiki/Accessible_Surface_Area</ref> we can see which parts of the protein are reachable by solvents.
In figure 20 you can see the solvent accessable surface during the time, in figure 21 the atomic SAS and in figure 22 the residue SAS. It is very hard to say which residues are the most accessible to the solvent. But there might be some areas between residue 200 and 250 and 300 to 350, at residue 400 and also 450. Figure 20 shows that the solvation is almost the same all time.
Hydrogen bonds
As a next step we look at the hydrogen bonds in the protein and between the protein and the surrounding solvent. Therefore we use the following commands:
echo 1 1 | g_hbond -f traj_nojump.xtc -s 2NT0_wt_md.tpr -num hydrogen-bonds-intra-protein.xvg
echo 1 12 | g_hbond -f traj_nojump.xtc -s 2NT0_wt_md.tpr -num hydrogen-bonds-protein-water.xvg
Discuss the relation between the number of hydrogen bonds for both cases and the fluctuations in each.
In figure 23 you can see the hydrogen bonds internally, that means which are build between the protein itself, and in figure 24 you can see the hydrogen bonds that are build with the surrounding water. Internally there are less hydrogen bonds build (about 350), less than with the water (about 800), but there are more pairs within 0.35 nm (1700 compared to 1100). The fluctuation is larger with the solvent. Internally there is only little fluctuation in an interval of about 50 to 100.
Salt bridges
does not work
Ramachandran (phi/psi) plots
As a next step we plotted the Ramachandran plot with the following command:
g_rama -f traj_nojump.xtc -s 2NT0_wt_md.tpr -o ramachandran.xvg
Compared to standard Ramachandran plots<ref>http://en.wikipedia.org/wiki/Ramachandran_plot</ref> you can see that there are huge regions on the right side which normally do not occur. Looking at the Glycine Ramachandran plot at http://en.wikipedia.org/wiki/Ramachandran_plot there is more analogy than to the Ramachandran plot in general case. But Glycine is not overrepresented (6.8 per cent) in Glucocerebrosidase.
Analysis of dynamics and time-averaged properties
Root mean square deviations again
Now we want to compare the different structures during the trajectory. So we can find similar structures.
We therefore used the following commands:
g_rms -s 2NT0_wt_md.tpr -f traj_nojump.xtc -f2 traj_nojump.xtc -m rmsd-matrix.xpm -dt 10
xpm2ps -f rmsd-matrix.xpm -o rmsd-matrix.eps -rainbow blue
gv rmsd-matrix.eps
In figure 27 you can see some clusters that are colored green. The greatest one is at the end of the time, which seems to be the equilibration. It is also interesting that there is a cluster between 1500 and 4000 ps.
Cluster analysis
Now we want to find clusters of similar structures. Therefore we use the following commands:
g_cluster -h
echo 6 6 | g_cluster -s 2NT0_wt_md.tpr -f traj_nojump.xtc -dm rmsd-matrix.xpm -dist rmsd-distribution.xvg -o clusters.xpm -sz cluster-sizes.xvg -tr cluster-transitions.xpm -ntr cluster-transitions.xvg -clid cluster-id-over-time.xvg -cl clusters.pdb -cutoff 0.1 -method gromos -dt 10
In figure 28 you can see that most structures have a RMS lower than 0.1. Four clusters were found for the trajectory.
Executive: RMS = 0.656 (121 to 121 atoms)
But there are no notable differences between the clusters that can be seen by observing them in Pymol.
Distance RMSD
Now we want to see the interatomic distances by using the distance RMSD (dRMSD). Therefore we used the following command:
g_rmsdist -s 2NT0_wt_md.tpr -f traj_nojump.xtc -o distance-rmsd.xvg
At what time and value does the dRMSD converge and how does this graph compare to the standard RMSD?
It converges at the end at about 8000. So much time is needed until the protein reaches its equilibrium state. It looks very similar to figure 17a. It is only a bit more fluctuating but the values are quite the same.
Mutation 7
A brief check of results
- command:
gmxcheck -f 2NT0_mut7_md.xtc
How many frames are in the trajectory file and what is the time resolution?
- 2001 frames
- timestep: 5ps
How long did the simulation run in real time (hours), what was the simulation speed (ns/day) and how many years would the simulation take to reach a second?
- Simulation run: 8h47:42
- Simulation speed: 27.287
- Time to reach a second: 1/0.000000028 = 35714285,714285714 days = 97847,358121331 years
Which contribution to the potential energy accounts for most of the calculations?
- -9.39750e+05 kJ/mol
Visualization of results
For visualization we extract 1000 frames from the trajectory (-dt 10), only select the protein without the water and remove the jumps over the boundaries to make a continuous trajectory (-pbc nojump).
- command:
trjconv -s 2NT0_mut7_md.tpr -f 2NT0_mut7_md.xtc -o protein.pdb -pbc nojump -dt 10
Quality assurance
Convergence of energy terms
First we look at the energy terms. Therefore we look at the temperature, the pressure, the energy, the volume, the density, the box and the interaction energies between protein and solvent (Coulomb and van der Waals).
With the following commands we produced *.xvg files which were visualized with xmgrace.
g_energy -f 2NT0_mut7_md.edr -o temperature.xvg
g_energy -f 2NT0_mut7_md.edr -o pressure.xvg
g_energy -f 2NT0_mut7_md.edr -o energy.xvg
g_energy -f 2NT0_mut7_md.edr -o volume.xvg
g_energy -f 2NT0_mut7_md.edr -o density.xvg
g_energy -f 2NT0_mut7_md.edr -o box.xvg
Temperature
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Temperature | 297.909 | 0.0064 | 1.09154 | 0.00476588 (K) |
What is the average temperature and what is the heat capacity of the system?
297.909 K
In figure 35 you can see the plot for the temperature during the simulation. It fluctuates between 295 K and 305 K. So the temperature is stable, the difference is ten Kelvin. That means that the system reached very soon a stable temperature.
Pressure
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Pressure | 1.00557 | 0.019 | 87.8392 | -0.0608909 (bar) |
Estimate the plateau values for the pressure.
0 bar? 1.00557 bar?
The pressure fluctuates around -300 bar and +300 bar. That is a difference of 600 bar which is very large. The system seems not to have reached its plateau. So it is also hard to estimate such a value because no trend is observable.
Energy
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Potential | -939750 | 81 | 924.746 | -485.89 (kJ/mol) |
| Kinetic En. | 170902 | 3.7 | 626.184 | 2.73516 (kJ/mol) |
| Total Energy | -768848 | 81 | 1132.31 | -483.155 (kJ/mol) |
What are the terms plotted in the file energy.xvg?
potential, kinetic and total energy
In the plot you can see that all three energy terms reached a plateau. It is hard to say how large the fluctuations are, because the scale is too large. But as they converged the simulation seems to have reached its optimum.
Volume
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Volume | 735.625 | 0.041 | 0.555533 | 0.00591744 (nm^3) |
Estimate the plateau values for the volume.
735.625?
In figure 38 you can see the volume fluctuating between 734 nm³ and 737 nm³. The difference is only three nm³. So the colume also converged to a an interval.
Density
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Density | 1009.66 | 0.057 | 0.762479 | -0.0081254 (kg/m^3) |
Estimate the plateau values for the density.
1009.66? 1010?
In figure 39 you can see the density fluctuating around 1010 kg/m³. The difference seems to be about 5 kg/m³. So the density also converged.
Box
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Box-X | 10.1327 | 0.00019 | 0.00255068 | 2.71821e-05 (nm) |
| Box-Y | 10.1327 | 0.00019 | 0.00255068 | 2.71821e-05 (nm) |
| Box-Z | 7.16488 | 0.00013 | 0.0018036 | 1.92236e-05 (nm) |
What are the terms plotted in the file box.xvg?
The size of the box around the protein.
In figure 40 you can see the sizes of the box, the x-, the y- and the z-term. They are very constant with 10.1327, 10.1327 and 7.16488 nm.
Interaction Energy: Coulomb
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Coul-SR:Protein-Protein | -23734.3 | 28 | 191.785 | 24.8598 (kJ/mol) |
| Coul-14:Protein-Protein | 95624.1 | 46 | 212.282 | 278.389 (kJ/mol) |
In figure 41 you can see the Coulomb Energy. It has its average at -23734.3 kJ/mol and 95624.1 kJ/mol. It fluctuates around that value in an interval of about 1000 kJ/mol. At the end it is more stable. As the equilibration takes longer for this term it may be that the value at the time 8000/-17000 to 10000/-19000 is the equilibrium.
Interaction Energy: van der Waals
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| LJ-SR:Protein-Protein | -16410.5 | 27 | 128.606 | 140.393 (kJ/mol) |
| LJ-14:Protein-Protein | 8533.35 | 2.4 | 61.2867 | 12.2783 (kJ/mol) |
In figure 13 you can see the van der Waals interaction energy. It has its average at -16410.5 kJ/mol and 8533.35 kJ/mol. The values are fluctuating in an interval of about 1000 kJ/mol.
Minimum distances between periodic images
We used the following command: g_mindist -f 2NT0_mut7_md.xtc -s 2NT0_mut7_md.tpr -od minimal-periodic-distance.xvg -pi
What was the minimal distance between periodic images and at what time did that occur?
The shortest periodic distance is 2.366 (nm) at time 135 (ps), between atoms 930 and 2377. This is a larger minimum distance than in the wildtype.
What was the minimal distance between periodic images and at what time did that occur?
The shortest periodic distance is 2.95133 (nm) at time 240 (ps), between atoms 921 and 2237. This is also larger than in the wildtype.
What happens if the minimal distance becomes shorter than the cut-off distance used for electrostatic interactions? Is it the case in your simulations?
It is not the case in our simulation. The energy would "explode".
Run now g_mindist on the C-alpha group, does it change the results? What does is mean for your system?
It changes to a greater distance between two other atoms (921 and 2237). That means that it may be atoms of a side group that have this minimal distance. Also the fluctuation interval of the minimum distance becomes smaller.
Root mean square fluctuations
In the following we want to look at the RMSF, the root mean square fluctuations<ref>http://en.wikipedia.org/wiki/Root_mean_square_fluctuation</ref>.
Therefore we used the following command:
g_rmsf -f 2NT0_mut7_md.xtc -s 2NT0_mut7_md.tpr -o rmsf-per-residue.xvg -ox average.pdb -oq bfactors.pdb -res
Indicate the start and end residue for the most flexible regions and the maximum amplitudes.
In figure 45 you can see the RMSF fluctuation. With that you can recognise flexible regions. The most flexible region seems to be around residue 350. This differs a lot from the wildtype where the most flexible regions was between 125 and residue 175 and the whole protein was more flexible.
In figure 46a you can see the protein colored according flexible regions. The b-factors are shown in figure 46b. Blue means that the region is not flexible and red means that it is a very flexible region. You can see one loop that is very flexible and parts of the alpha helices and beta sheets that are a bit flexible. The most of the inner part of the protein is colored blue and therefore not flexible. Compared to the wildtype the protein lost some flexibility.
Convergence of RMSD
Now we want to calculate the RMSD. It is used as an indicator of convergence of the structure towards an equilibrium state.
We used the following commands:
trjconv -f 2NT0_mut7_md.xtc -o traj_nojump.xtc -pbc nojump
g_rms -f traj_nojump.xtc -s 2NT0_mut7_md.tpr -o rmsd-all-atom-vs-start.xvg
g_rms -f traj_nojump.xtc -s 2NT0_mut7_md.tpr -o rmsd-backbone-vs-start.xvg
echo 1 | trjconv -f traj_nojump.xtc -s 2NT0_mut7_md.tpr -o protein.xtc
g_rms -f protein.xtc -s average.pdb -o rmsd-all-atom-vs-average.xvg
g_rms -f protein.xtc -s average.pdb -o rmsd-backbone-vs-average.xvg
If observed, at what time and value does the RMSD reach a plateau?
If you compare the different methods (all atom/backbonde and against starting structure or average structure) as you can see in figure 47a, b and 48a, b there are different times when the RMSD reaches a plateau. For all atoms and backbone against the starting structure both reach their plateau at about 2000 ps with a value of 0.17 and a bit higher for backbone with about 0.18.
For the comparison to the average structure they reach a plateau later. At 4000 to 5000 ps. All atom versus all reaches a RMSD of about 0.16, which is lower than in the wildtype, the backbone of 0.06, which is very low and almost the same as in the wildtype.
Briefly discuss two differences between the graphs against the starting structure and against the average structure. Which is a better measure for convergence?
As already mentioned the convergence is reached later. The reason for that is that the average structure is nearer to the final structure. Another thing is that the RMSD for the average structures gets lower wheras it gets higher for the comparison to the starting structure. The starting structure is farer away from the final structure, so this is again the reason. It might be better to take the starting structure to recognise the convergence because you can see sooner that an equilibrian state is reached.
Convergence of radius of gyration
Now look at the radius of gyration<ref>http://en.wikipedia.org/wiki/Radius_of_gyration</ref>. Therefore we used the following command:
g_gyrate -f 2NT0_mut7_md.xtc -s 2NT0_mut7_md.tpr -o radius-of-gyration.xvg
The radius of gyration gives insight to the shape of the protein.
At what time and value does the radius of gyration converge?
The radius of gyration is always constant with about 2.3 nm. The RgX, RgY and RgZ fluctuate until the end. RgX and RgY reach the value 2.1. RgZ is much lower and reaches a value of 1.5. This differs a lot from the wildtype Molecular Dynamics simulation.
Structural analysis: properties derived from configurations
Solvent accessible surface area
With the Solvent accessible surface area (SASA)<ref>http://en.wikipedia.org/wiki/Accessible_Surface_Area</ref> we can see which parts of the protein are reachable by solvents.
In figure 50 you can see the solvent accessable surface during the time, in figure 51 the atomic SAS and in figure 52 the residue SAS. It is very hard to say which residues are the most accessible to the solvent. But there might be some areas between residue 225, 250 and 300, at residue 350, 400 and also 450. Figure 50 shows that the solvation is almost the same all time.
Hydrogen bonds
As a next step we look at the hydrogen bonds in the protein and between the protein and the surrounding solvent. Therefore we use the following commands:
echo 1 1 | g_hbond -f traj_nojump.xtc -s 2NT0_mut7_md.tpr -num hydrogen-bonds-intra-protein.xvg
echo 1 12 | g_hbond -f traj_nojump.xtc -s 2NT0_mut7_md.tpr -num hydrogen-bonds-protein-water.xvg
Discuss the relation between the number of hydrogen bonds for both cases and the fluctuations in each.
In figure 53 you can see the hydrogen bonds internally, that means which are build between the protein itself, and in figure 54 you can see the hydrogen bonds that are build with the surrounding water. Internally there are less hydrogen bonds build (about 350), less than with the water (about 800), but there are more pairs within 0.35 nm (1700 compared to 1100). The fluctuation is larger with the solvent. Internally there is only little fluctuation in an interval of about 50 to 100. That's exactly the same as in the wildtype.
Salt bridges
does not work
Ramachandran (phi/psi) plots
As a next step we plotted the Ramachandran plot with the following command:
g_rama -f traj_nojump.xtc -s 2NT0_mut7_md.tpr -o ramachandran.xvg
Compared to standard Ramachandran plots<ref>http://en.wikipedia.org/wiki/Ramachandran_plot</ref> you can see that there are huge regions on the right side which normally do not occur. Looking at the Glycine Ramachandran plot at http://en.wikipedia.org/wiki/Ramachandran_plot there is more analogy than to the Ramachandran plot in general case. But Glycine is not overrepresented (6.8 per cent) in Glucocerebrosidase. That is the same as in the wildtype. But there is also one difference. If you compare Psi -50 ans Phi 150 to the wildtype Ramachandran plot you can see that there are some points missing. It is the same for Psi 150 and Phi 125. Although only one residue mutated there is a change in the Phi/Psi-angles.
Analysis of dynamics and time-averaged properties
Root mean square deviations again
Now we want to compare the different structures during the trajectory. So we can find similar structures.
We therefore used the following commands:
g_rms -s 2NT0_mut7_md.tpr -f traj_nojump.xtc -f2 traj_nojump.xtc -m rmsd-matrix.xpm -dt 10
xpm2ps -f rmsd-matrix.xpm -o rmsd-matrix.eps -rainbow blue
gv rmsd-matrix.eps
In figure 57 you can see some clusters that are colored blue and green. There are four clusters which are colored green and blue. This is different to the wildtype. There you also can see such clusters but not as clear as in figure 57. The huge cluster between 1500 and 4000 ps appears again but the smaller clusters in that region are stronger now.
Cluster analysis
Now we want to find clusters of similar structures. Therefore we use the following commands:
g_cluster -h
echo 6 6 | g_cluster -s 2NT0_mut7_md.tpr -f traj_nojump.xtc -dm rmsd-matrix.xpm -dist rmsd-distribution.xvg -o clusters.xpm -sz cluster-sizes.xvg -tr cluster-transitions.xpm -ntr cluster-transitions.xvg -clid cluster-id-over-time.xvg -cl clusters.pdb -cutoff 0.1 -method gromos -dt 10
In figure 58 you can see that most structures have a RMS lower than 0.1. Six clusters were found for the trajectory. The RMSD ranges from 0.0545 to 0.18 nm, the average RMSD is 0.102969.
But there are no notable differences between the clusters that can be seen by observing them in Pymol. Only some loops look a little different.
Distance RMSD
Now we want to see the interatomic distances by using the distance RMSD (dRMSD). Therefore we used the following command:
g_rmsdist -s 2NT0_mut7_md.tpr -f traj_nojump.xtc -o distance-rmsd.xvg
At what time and value does the dRMSD converge and how does this graph compare to the standard RMSD?
It converges at the end at about 7000. So much time is needed until the protein reaches its equilibrium state. There it reaches a RMSD of almost 0.25 nm.
Mutation 10
A brief check of results
- command:
gmxcheck -f 2NT0_mut10_md.xtc
How many frames are in the trajectory file and what is the time resolution?
- 2001 frames
- timestep: 5ps
How long did the simulation run in real time (hours), what was the simulation speed (ns/day) and how many years would the simulation take to reach a second?
- Simulation run: 8h39:07
- Simulation speed: 27.739
- Time to reach a second: 1/0.000000028 = 35714285,714285714 days = 97847,358121331 years
Which contribution to the potential energy accounts for most of the calculations?
- -9.39855e+05 kJ/mol
Visualization of results
For visualization we extract 1000 frames from the trajectory (-dt 10), only select the protein without the water and remove the jumps over the boundaries to make a continuous trajectory (-pbc nojump).
- command:
trjconv -s 2NT0_mut10_md.tpr -f 2NT0_mut10_md.xtc -o protein.pdb -pbc nojump -dt 10
Quality assurance
Convergence of energy terms
First we look at the energy terms. Therefore we look at the temperature, the pressure, the energy, the volume, the density, the box and the interaction energies between protein and solvent (Coulomb and van der Waals).
With the following commands we produced *.xvg files which were visualized with xmgrace.
g_energy -f 2NT0_mut10_md.edr -o temperature.xvg
g_energy -f 2NT0_mut10_md.edr -o pressure.xvg
g_energy -f 2NT0_mut10_md.edr -o energy.xvg
g_energy -f 2NT0_mut10_md.edr -o volume.xvg
g_energy -f 2NT0_mut10_md.edr -o density.xvg
g_energy -f 2NT0_mut10_md.edr -o box.xvg
Temperature
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Temperature | 297.907 | 0.007 | 1.09216 | 0.00537584 (K) |
What is the average temperature and what is the heat capacity of the system?
297.907 K
In figure x you can see the plot for the temperature during the simulation. It fluctuates between 294 K and 302 K. So the temperature is stable, the difference is only eight Kelvin. That means that the system reached very soon a stable temperature.
Pressure
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Pressure | 0.995622 | 0.016 | 87.7623 | -0.0375739 (bar) |
Estimate the plateau values for the pressure.
0 bar? 0.995622 bar? higher?
The pressure fluctuates around -300 bar and +300 bar. That is a difference of 600 bar which is very large. The system seems not to have reached its plateau. So it is also hard to estimate such a value because no trend is observable.
Energy
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Potential | -939855 | 120 | 936.926 | -807.027 (kJ/mol) |
| Kinetic En. | 170899 | 4 | 626.533 | 3.08393 (kJ/mol) |
| Total Energy | -768957 | 120 | 1142.33 | -803.943 (kJ/mol) |
What are the terms plotted in the file energy.xvg?
potential, kinetic and total energy
In the plot you can see that all three energy terms reached a plateau. It is hard to say how large the fluctuations are, because the scale is too large. But as they converged the simulation seems to have reached its optimum.
Volume
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Volume | 735.529 | 0.058 | 0.543357 | -0.382496 (nm^3) |
Estimate the plateau values for the volume.
735.529? 736?
In figure x you can see the volume fluctuating between 734 nm³ and 737 nm³. The difference is only three nm³. So the colume also converged to a an interval.
Density
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Density | 1009.82 | 0.08 | 0.745989 | 0.525138 (kg/m^3) |
Estimate the plateau values for the density.
1009.82? 1010?
In figure x you can see the density fluctuating around 1010 kg/m³. The difference seems to be about 5 kg/m³. So the density also converged.
Box
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Box-X | 10.1322 | 0.00027 | 0.002495 | -0.0017563 (nm) |
| Box-Y | 10.1322 | 0.00027 | 0.002495 | -0.0017563 (nm) |
| Box-Z | 7.16457 | 0.00019 | 0.00176423 | -0.00124195 (nm) |
What are the terms plotted in the file box.xvg?
The size of the box around the protein.
In figure x you can see the sizes of the box, the x-, the y- and the z-term. They are very constant with 10.1322, 10.1322 and 7.16457 nm.
Interaction Energy: Coulomb
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| Coul-SR:Protein-Protein | -23792.5 | 35 | 192.508 | -46.3472 (kJ/mol) |
| Coul-14:Protein-Protein | 95298 | 89 | 249.16 | 613.217 (kJ/mol) |
In figure x you can see the Coulomb Energy. It has its average at -23792.5 kJ/mol and 95298 kJ/mol. It fluctuates around that value in an interval of about 1000 kJ/mol. At the end it is more stable. As the equilibration takes longer for this term it may be that the value at the time 8000/-15500 to 10000/-16500 is the equilibrium.
Interaction Energy: van der Waals
| Energy | Average | Err.Est. | RMSD | Tot-Drift |
| LJ-SR:Protein-Protein | -16508.3 | 18 | 117.895 | 88.1434 (kJ/mol) |
| LJ-14:Protein-Protein | 8509.66 | 5.3 | 61.7179 | -36.3349 (kJ/mol) |
In figure x you can see the van der Waals interaction energy. It has its average at -16508.3/8509.66 kJ/mol. The values are fluctuating in an interval of about 1000 kJ/mol. Also at the end of the time there is no equilibration recognisable. Maybe it always fluctuates in such a big interval or it needs more time to converge.
Minimum distances between periodic images
We used the following command: g_mindist -f 2NT0_wt_md.xtc -s 2NT0_wt_md.tpr -od minimal-periodic-distance.xvg -pi
What was the minimal distance between periodic images and at what time did that occur?
The shortest periodic distance is 1.90705 (nm) at time 1485 (ps), between atoms 965 and 2274 (different to the wildtype), which is smaller than in the wildtype.
What was the minimal distance between periodic images and at what time did that occur?
The shortest periodic distance is 2.37553 (nm) at time 1485 (ps), between atoms 952 and 2267. This is again smaller than in the wildtype although these are the same atoms.
What happens if the minimal distance becomes shorter than the cut-off distance used for electrostatic interactions? Is it the case in your simulations?
It is not the case in our simulation. The energy would "explode".
Run now g_mindist on the C-alpha group, does it change the results? What does is mean for your system?
It changes to a greater distance between two other atoms (952 and 2267). That means that it may be atoms of a side group that have this minimal distance. Also the fluctuation interval of the minimum distance becomes smaller.
Root mean square fluctuations
In the following we want to look at the RMSF, the root mean square fluctuations<ref>http://en.wikipedia.org/wiki/Root_mean_square_fluctuation</ref>.
Therefore we used the following command:
g_rmsf -f 2NT0_mut10_md.xtc -s 2NT0_mut10_md.tpr -o rmsf-per-residue.xvg -ox average.pdb -oq bfactors.pdb -res
Indicate the start and end residue for the most flexible regions and the maximum amplitudes.
In figure x you can see the RMSF fluctuation. With that you can recognise flexible regions. The most flexible region seems to be around residue 50. There are many other flexible regions all over the protein. But there is no huge peak. This differs from the wildtype.
In figure x you can see the protein colored according to b-factors and flexible regions. Blue means that the region is not flexible and red means that it is a very flexible region. You can see some loops that are flexible and parts of the alpha helices and beta sheets that are a bit more flexible. The most of the inner part of the protein is colored blue and therefore not flexible. It differs again from the wildtype. Other regions are colored red and therefore the most flexible and also the flexibility of the alpha helices and the beta sheets differs.
Convergence of RMSD
Now we want to calculate the RMSD. It is used as an indicator of convergence of the structure towards an equilibrium state.
We used the following commands:
trjconv -f 2NT0_mut10_md.xtc -o traj_nojump.xtc -pbc nojump
g_rms -f traj_nojump.xtc -s 2NT0_mut10_md.tpr -o rmsd-all-atom-vs-start.xvg
g_rms -f traj_nojump.xtc -s 2NT0_mut10_md.tpr -o rmsd-backbone-vs-start.xvg
echo 1 | trjconv -f traj_nojump.xtc -s 2NT0_mut10_md.tpr -o protein.xtc
g_rms -f protein.xtc -s average.pdb -o rmsd-all-atom-vs-average.xvg
g_rms -f protein.xtc -s average.pdb -o rmsd-backbone-vs-average.xvg
If observed, at what time and value does the RMSD reach a plateau?
If you compare the different methods (all atom/backbonde and against starting structure or average structure) there are different times when the RMSD reaches a plateau. For all atoms and backbone against the starting structure both reach their plateau at about 3000 ps with a value of 0.2 and lower for backbone with about 0.07. These are lower values than in the wildtype although the equilibration is reached later.
For the comparison to the average structure they reach a plateau later. At 4000 to 5000 ps. Both reach a value of about 0.15, which is very high for the backbone compared to the wildtype simulations.
Briefly discuss two differences between the graphs against the starting structure and against the average structure. Which is a better measure for convergence?
As already mentioned the convergence is reached later. The reason for that is that the average structure is nearer to the final structure. Another thing is that the RMSD for the average structures gets lower wheras it gets higher for the comparison to the starting structure. The starting structure is farer away from the final structure, so this is again the reason. It might be better to take the starting structure to recognise the convergence because you can see sooner that an equilibrian state is reached.
Convergence of radius of gyration
Now look at the radius of gyration<ref>http://en.wikipedia.org/wiki/Radius_of_gyration</ref>. Therefore we used the following command:
g_gyrate -f 2NT0_mut10_md.xtc -s 2NT0_mut10_md.tpr -o radius-of-gyration.xvg
The radius of gyration gives insight to the shape of the protein.
At what time and value does the radius of gyration converge?
The radius of gyration is always constant with about 2.3 nm. The RgX, RgY and RgZ fluctuate until the end, only RgY has relatively small fluctuating intervals. RgY reaches about 1.05 nm, RgX about 1.9 nm and RgZ about 1.75 nm. This again differs compared to the wildtype simulation.
Structural analysis: properties derived from configurations
Solvent accessible surface area
With the Solvent accessible surface area (SASA)<ref>http://en.wikipedia.org/wiki/Accessible_Surface_Area</ref> we can see which parts of the protein are reachable by solvents.
In figure x you can see the solvent accessable surface during the time, in figure x the atomic SAS and in figure x the residue SAS. It is very hard to say which residues are the most accessible to the solvent. But there might be some areas between residue 200 and 250 and 300 to 350, at residue 400 and also 450. Figure x shows that the solvation is almost the same all time.
Hydrogen bonds
As a next step we look at the hydrogen bonds in the protein and between the protein and the surrounding solvent. Therefore we use the following commands:
echo 1 1 | g_hbond -f traj_nojump.xtc -s 2NT0_mut10_md.tpr -num hydrogen-bonds-intra-protein.xvg
echo 1 12 | g_hbond -f traj_nojump.xtc -s 2NT0_mut10_md.tpr -num hydrogen-bonds-protein-water.xvg
Discuss the relation between the number of hydrogen bonds for both cases and the fluctuations in each.
In figure x you can see the hydrogen bonds internally, that means which are build between the protein itself, and in figure x you can see the hydrogen bonds that are build with the surrounding water. Internally there are less hydrogen bonds build (about 350), less than with the water (about 800), but there are more pairs within 0.35 nm (1700 compared to 1100). The fluctuation is larger with the solvent. Internally there is only little fluctuation in an interval of about 50 to 100. That is the same as in the wildtype. Only the fluctuation seems to be larger at the end.
Salt bridges
does not work
Ramachandran (phi/psi) plots
As a next step we plotted the Ramachandran plot with the following command:
g_rama -f traj_nojump.xtc -s 2NT0_mut10_md.tpr -o ramachandran.xvg
Compared to standard Ramachandran plots<ref>http://en.wikipedia.org/wiki/Ramachandran_plot</ref> you can see that there are huge regions on the right side which normally do not occur. Looking at the Glycine Ramachandran plot at http://en.wikipedia.org/wiki/Ramachandran_plot there is more analogy than to the Ramachandran plot in general case. But Glycine is not overrepresented (6.8 per cent) in Glucocerebrosidase. It looks similar to the Ramachandran plot of the wildtype, but there are also some differences. The region around Psi 50 and Phi 100 is smaller than in the wildtype. If you look at Psi -100 and Phi -150 you can see that there are more points. Here again the change of only one amino acid changes the Ramachandran plot.
Analysis of dynamics and time-averaged properties
Root mean square deviations again
Now we want to compare the different structures during the trajectory. So we can find similar structures.
We therefore used the following commands:
g_rms -s 2NT0_mut10_md.tpr -f traj_nojump.xtc -f2 traj_nojump.xtc -m rmsd-matrix.xpm -dt 10
xpm2ps -f rmsd-matrix.xpm -o rmsd-matrix.eps -rainbow blue
gv rmsd-matrix.eps
In figure x you can see some clusters that are colored blue and green. Conspicuous is the blue one from 3000 to 9000. The structures must be very similar in this interval. At the end there must be some change again. The wildtype simulation does not show this.
Cluster analysis
Now we want to find clusters of similar structures. Therefore we use the following commands:
g_cluster -h
echo 6 6 | g_cluster -s 2NT0_mut10_md.tpr -f traj_nojump.xtc -dm rmsd-matrix.xpm -dist rmsd-distribution.xvg -o clusters.xpm -sz cluster-sizes.xvg -tr cluster-transitions.xpm -ntr cluster-transitions.xvg -clid cluster-id-over-time.xvg -cl clusters.pdb -cutoff 0.1 -method gromos -dt 10
In figure x you can see that half of the structures have a RMS lower than 0.1, half of them higher than 0.1. Compared to the wildtype you can see that the clusters are more different. We could also see this in the previous section. The RMSD ranges from 0.0551 to 0.198 nm, the average RMSD is 0.100617. Seven clusters were found for the trajectory.
Anyway there are again no notable differences between the clusters that can be seen by observing them in Pymol. Only some loops look a little different.
Distance RMSD
Now we want to see the interatomic distances by using the distance RMSD (dRMSD). Therefore we used the following command:
g_rmsdist -s 2NT0_mut10_md.tpr -f traj_nojump.xtc -o distance-rmsd.xvg
At what time and value does the dRMSD converge and how does this graph compare to the standard RMSD?
It converges at the end at about 6000. So much time is needed until the protein reaches its equilibrium state. It reaches a RMSD of 0.175.
