Molecular Dynamics Simulations Analysis of Glucocerebrosidase

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 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_wt_md.tpr -f 2NT0_wt_md.xtc -o protein.pdb -pbc nojump -dt 10

Figure 1: The protein with the spectrum

Figure 2: The protein with the box around it

Figure 3: The cartoon presentation after using the command dss

Figure 4: The active site

Figure 5: Molecular Dynamics Simulation of Glucocerebrosidase

In figure 5 you can see the protein in motion. Compared to the results in Normal Mode Analysis the motion is not as strong as we had seen it there and the parts that are moving are smaller. Here we can see the sidechains bouncing and little elements of the protein. But there are no attraction or repulsion moves as in the Normal Modes.

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_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

Temperature

Figure 6: Temperature of the Molecular Dynamics Simulation of the Wildtype

Energy	Average	Err.Est.	RMSD	Tot-Drift
Temperature	297.912	0.0062	1.08924	0.00616934 (K)

What is the average temperature and what is the heat capacity of the system?
297.912 K

In figure 6 you can see the plot for the temperature during the simulation. It fluctuates between 295 K and 301 K. So the temperature is very stable, the difference is only six Kelvin. That means that the system reached very soon a stable temperature.

Pressure

Figure 7: Pressure of the Molecular Dynamics Simulation of the Wildtype

Energy	Average	Err.Est.	RMSD	Tot-Drift
Pressure	1.00032	0.014	87.9016	0.0583997 (bar)

Estimate the plateau values for the pressure.
0 bar? 1.00032 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

Figure 8: Energies of the Molecular Dynamics Simulation of the Wildtype

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)

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

Figure 9: Volume of the Molecular Dynamics Simulation of the Wildtype

Energy	Average	Err.Est.	RMSD	Tot-Drift
Volume	735.655	0.042	0.552925	-0.0802412 (nm^3)

Estimate the plateau values for the volume.
735.655? 736?

In figure 9 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

Figure 10: Density of the Molecular Dynamics Simulation of the Wildtype

Energy	Average	Err.Est.	RMSD	Tot-Drift
Density	1009.64	0.058	0.75885	0.110104 (kg/m^3)

Estimate the plateau values for the density.
1009.64? 1010?

In figure 10 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

Figure 11: Boxes of the Molecular Dynamics Simulation of the Wildtype

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.

In figure 11 you can see the sizes of the box, the x-, the y- and the z-term. They are very constant with 10.1328, 10.1328 and 7.16498 nm.

Interaction Energy: Coulomb

Figure 12: Interaction energy of protein and solvent

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)

In figure 12 you can see the Coulomb Energy. It has its average at -24690.5 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 to 10000 is the equilibrium.

Interaction Energy: van der Waals

Figure 13: Interaction energy of protein and solvent

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

Figure 14: Minima periodic distance on the protein

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.

Figure 14: Minima periodic distance on the C-alpha group

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

Figure 15: RMSF fluctuation

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.

Figure 16: Colored structure according to b-factors and flexible regions

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

Figure 17a: RMSD: All atom versus all, against starting structure

Figure 17b: RMSD: All atom versus all, against average structure

Figure 18a: RMSD: Backbone, against starting structure

Figure 18b: RMSD: Backbone, against average structure

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.

Figure 19: Radius of gyration

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.

Figure 20: Solvent Accessable Surface

Figure 21: Atomic SAS

Figure 22: Residue SAS

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

Figure 23: Hydrogen bonds in the protein

Figure 24: Hydrogen bonds between protein and the surrounding solvent

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

still running

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

Figure 26: Ramachandran plot

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

Figure 27: RMSD Matrix

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

Figure 28: RMSD Distribution

In figure 28 you can see that most structures have a RMS lower than 0.1. 4 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

Figure 29: dRMSD

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

Figure 30: The protein with the spectrum

Figure 31: The protein with the box around it

Figure 32: The cartoon presentation after using the command dss

Figure 33: The active site

Figure 34: Molecular Dynamics Simulation of Glucocerebrosidase

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

Figure 35: Temperature of the Molecular Dynamics Simulation of Glucocerebrosidase with Mutation 7

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

Figure 36: Pressure of the Molecular Dynamics Simulation of Glucocerebrosidase with Mutation 7

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

Figure 37: Energies of the Molecular Dynamics Simulation of Glucocerebrosidase with Mutation 7

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

Figure 38: Volume of the Molecular Dynamics Simulation of Glucocerebrosidase with Mutation 7

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

Figure 39: Density of the Molecular Dynamics Simulation of Glucocerebrosidase with Mutation 7

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

Figure 40: Boxes of the Molecular Dynamics Simulation of Glucocerebrosidase with Mutation 7

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

Figure 41: Interaction energy of protein and solvent

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

Figure 42: Interaction energy of protein and solvent

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

Figure 43: Minima periodic distance on the protein

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.

Figure 44: Minima periodic distance on the C-alpha group

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

Figure 45: RMSF fluctuation

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.

Figure 46a: Colored structure according to flexible regions

Figure 46b: Colored structure according to b-factors

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_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

Figure 47a: RMSD: All atom versus all, against starting structure

Figure 47b: RMSD: All atom versus all, against average structure

Figure 48a: RMSD: Backbone, against starting structure

Figure 48b: RMSD: Backbone, against average structure

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.

Figure 49: Radius of gyration

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.

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

Figure x: The protein with the spectrum

Figure x: The protein with the box around it

Figure x: The cartoon presentation after using the command dss

Figure x: The active site

Figure x: Molecular Dynamics Simulation of Glucocerebrosidase

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

Figure x: Temperature of the Molecular Dynamics Simulation of the protein with Mutation 10

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

Figure x: Pressure of the Molecular Dynamics Simulation of the protein with mutation 10

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

Figure x: Energies of the Molecular Dynamics Simulation

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

Figure x: Volume of the Molecular Dynamics Simulation

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

Figure x: Density of the Molecular Dynamics Simulation

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

Figure x: Boxes of the Molecular Dynamics Simulation

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

Figure x: Interaction energy of protein and solvent

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

Figure x: Interaction energy of protein and solvent

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

Figure x: Minima periodic distance on the protein

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.

Figure x: Minima periodic distance on the C-alpha group

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

Figure x: RMSF fluctuation

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.

Figure x: Colored structure according to flexible regions

Figure x: Colored structure according to b-factors

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.