Task 10: Molecular Dynamics Analysis

In this task we are going to analyze the results of the molecular dynamics simulations of task 8. A detailed task description can be found here. The analysis focuses on this tutorial.

Native

A BRIEF CHECK OF RESULTS

In order to verify that our simulation ran successfully we used the command line tool gmxcheck. we executed it as follows for our .xtc file:

gmxcheck -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.xtc

How many frames are in the trajectory file and what is the time resolution?

We observed 2001 frames with a time resolution of 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?

The simulation ran 4h00:39 and had a simulation speed of 59.835 ns/day. To calculate 1 second we would need (1 / (59 * (10^(-9)))) / 365 = 46 436.0344 years

Which contribution to the potential energy accounts for most of the calculations?

• potential energy: -4.57312e+05 kJ/mol

VISUALIZATION OF RESULTS

We extracted 1000 frames from the trajectory (-dt 10), leaving out the water (selected Protein when asked for a selection). Moreover, we will remove the jumps over the boundaries and make a continuous trajectory (-pbc nojump):

trjconv -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.xtc -o protein.pdb -pbc nojump -dt 10

After that we opened the generated protein.pdb file with pymol. Here we changed the coloring to spectrum by typing the following to the pymol command line:

spectrum

In a next step we enabled the the visualization of the cell with this command:

show cell

In order to remove the tumbeling and wiggeling motion of our protein we used the command intra_fit since we are only interested in the internal motions of the protein:

intra_fit protein

The results of these actions can be seen in figure 1 and 2. Figure one shows our WT protein in line view which makes it able to see the motion of the side chains. Figure to shows the protein in cartoon view to see the overall movement of the secondary structure elements.

Figure 1: motion of protein in line view

Figure 2: motion of protein in cartoon view

QUALITY ASSURANCE

CONVERGENCE OF ENERGY TERMS

In this part of quality assurance we analyzed different metrics of our MD simulation by creating plots from our *.edr file. We created plots for the temperature, pressure, energy, volume, density, box, coulomb and van der waals values of our MD simulation by using the tool g_energy as follows:

//calculating temperature enter then "12 0" 
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/temperature.xvg

//calculating pressure enter then "13 0" 
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/pressure.xvg

//calculating energy (potential, kinetic and total) enter then "9\n10\n11 0" 
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/energy.xvg

//calculating volume enter then "18 0" 
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/volume.xvg

//calculating density enter then "19 0" 
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/density.xvg

//calculating box enter then "15\n16\n17 0" 
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/box.xvg

//calculating coulomb enter then "48\n50 0"
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/coulomb-inter.xvg

//calculating van der waals enter then "49\n51 0"
g_energy -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.edr -o ../../../Dropbox/Studium/3_semester/master_praktikum/task10/vanderwaals-inter.xvg

Temperature Over Time

Figure 3: Fluctuation of temperature over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Temperature"	297.886	0.007	1.57824	"-0.0105059 (K)"

In figure 3 we can see that the temperature stays quite the same over the whole simulation which might be interpreted as that our system has reached its stable temperature for simulation.

Pressure over Time

Figure 4: Fluctuation of pressure over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Pressure"	1.02313	0.023	133.659	"-0.0928554 (bar)"

Energy over Time

Figure 5: Potential, kinetic and total energy over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Potential"	-457312	61	640.502	" -423.792 (kJ/mol)"
"Kinetic En."	81855.1	1.9	433.677	" -2.88684 (kJ/mol)"
"Total Energy"	-375457	61	784.246	" -426.678 (kJ/mol)"

Volume over Time

Figure 6: Fluctuation of volume over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Volume"	356.629	0.041	0.397685	" -0.151337 (nm^3)"

Density over Time

Figure 7: Fluctuation of density over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Density"	1021.28	0.12	1.13884	"0.433467 (kg/m^3)"

Box over Time

Figure 8: box size over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Box-X"	7.95996	" 0.0003"	0.00295875	"-0.00112603 (nm)"
"Box-Y"	7.95996	" 0.0003"	0.00295875	"-0.00112603 (nm)"
"Box-Z"	5.62854	0.00021	0.00209216	"-0.000796226 (nm)"

Coulomb over Time

Figure 9: Fluctuation of coulomb energies over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"Coul-SR:Protein-non-Protein"	" -20429.9"	"110"	"425.888"	"-561.713 (kJ/mol)"
"Coul-14:Protein-non-Protein"	" 0"	" 0"	" 0"	" 0 (kJ/mol)"

Van der Waals over Time

Figure 10: Fluctuation of van der waals energies over time in WT

"Energy"	"Average"	"Err.Est."	"RMSD"	"Tot-Drift"
"LJ-SR:Protein-non-Protein"	"-2172.28"	"15"	"136.956"	"-103.12 (kJ/mol)"
"LJ-14:Protein-non-Protein"	" 0"	" 0"	" 0"	" 0 (kJ/mol)"

Questions

1. What is the average temperature and what is the heat capacity of the system?

The average temperature of our system is 297.886 K and the heat capacity ranges from 303 to 292. (values taken from figure 3).

2. What are the terms plotted in the files energy.xvg and box.xvg

In energy.xvg we plot the energy values of kinetic energy, potential energy and total energy over the time of our simulation.

In box.xvg we plot the size of the box around our protein which is given in nm.

3. Estimate the plateau values for the pressure, the volume and the density.

We consider the plateau value as two values, the upper and lower plateau. These plateaus represent the maximum and minimum values of our given plots.

Pressure:

• upper plateau:450 bar
• lower plateau: -450 bar

Volume:

• upper plateau: 357.9 nm^3
• lower plateau: 355.8 nm^3

Density:

• upper plateau: 1026 kg/m^3
• lower plateau: 1017 kg/m^3

4. What are the terms plotted in the files coulomb-inter.xvg and vanderwaals-inter.xvg

The coloumb and van der waals energys of our WT over time.

MINIMUM DISTANCES BETWEEN PERIODIC IMAGES

We ran gromacs with the following command:

//when asked for group selection we selected group 1
g_mindist -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.xtc -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -od /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/minimal-periodic-distance.xvg -pi

And produced the plot seen in figure 11.

Figure 11: minimum periodic distance on the protein over time in WT

In a next step we produced a plot which only uses the C-alpha atoms to calculate the minimum distance between periodic images. For this we used the same command as before. Although, we selected group 3 this time. The result can be seen in figure 12.

Figure 12: minimum periodic distance on C-alpha atoms over time in WT

Questions

What was the minimal distance between periodic images and at what time did that occur?

The shortest periodic distance is 1.73442 (nm) at time 2720 (ps), between atoms 563 and 5314.

What happens if the minimal distance becomes shorter than the cut-off distance used for electrostatic interactions? Is it the case in your simulations?

If the distance would become shorter than the cut-off distance used for electrostatic interactions our energy would dramatically increase. This did not happen for our simulation so we can assume that our measured value of 1.73 nm is still higher than the cutoff.

Run now g_mindist on the C-alpha group, does it change the results? What does is mean for your system?

With C-alpha group we got a shortest periodic distance of 2.4249 (nm) at time 6805 (ps), between atoms 589 and 5297. This is an increase of the distance since we only consider C-alpha atoms and no side chains as in our previous calculation.

ROOT MEAN SQUARE FLUCTUATIONS

In this part of the analysis we are going to have a look at the root mean square fluctuations. By analyzing this value for our structure we might be able to figure out which parts of our protein are more flexible than others.

To do so we executed the following command:

g_rmsf -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.xtc -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -o  /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/rmsf-per-residue.xvg -ox  /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/average.pdb -oq  /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/bfactors.pdb -res

Which gives us three result files:

• rmsf-per-residue.xvg : this file contains a plot over the whole structure length of the RMSF values
• average.pdb : is the average conformation of the structure
• bfactors.pdb: assigned b factor values to the residues which gives us information about the flexibility

Figure 13: RMSF per residue in WT

Figure 14: B-factor in WT, front view

Figure 15: B-factor in WT, back view

Questions

Indicate the start and end residue for the most flexible regions and the maximum amplitudes.

The most flexible region in our structure is from position 131 to 152 which is a loop connecting two alpha-helices. This can be observed in the plot in figure 13 as well as in the 3D view of our protein in figure 14. In general we can say that most of the parts are rather rigid, especially the residues which are located within the core. We observe slightly more flexibility in some alpha-helices which are located at the surface of the protein. Such as the residues located at position 197, 208, 215 and 216. There are also some beta-sheets which contain slightly flexible residues such as residues at position 413 and 420.

CONVERGENCE OF RMSD

It is adviced in the tutorial to remove the jumps of our protein and bring it back to the middle. This is done with the following command:

trjconv -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.xtc -o 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md_nojump.xtc -pbc nojump

Then we calculated the RMSD for the whole protein and a second time only for the backbone with the following command:

//whole protein: select 1 and 1 again
g_rms -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md_nojump.xtc -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -o /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/rmsd-all-atom-vs-start.xvg

//backbone only: select 4 and 4 again
g_rms -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md_nojump.xtc -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -o /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/rmsd-backbone-vs-start.xvg

After that we calculated the RMSD for the average protein structure with the following commands, once for the whole protein and once for the backbone only:

trjconv -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md_nojump.xtc -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -o /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/protein.xtc

g_rms -f /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/protein.xtc -s /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/average.pdb -o /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/rmsd-all-atom-vs-average.xvg

g_rms -f /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/protein.xtc -s /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/average.pdb -o /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/rmsd-backbone-vs-average.xvg

We received then the following results:

Figure 16: RMSD all atom vs start in WT

Figure 17: RMSD backbone vs start in WT

Figure 18: RMSD all atom vs average in WT

Figure 19: RMSD backbone vs average in WT

Questions

If observed, at what time and value does the RMSD reach a plateau?

We observed in the figures (16-17, against start structure) that the plateau is reached after 5000ps with the following approximated values:

• All atom vs start: 0.225
• Backbone vs start: 0.175

For the average structures we observed that the plateau is reached earlier after 300ps with the following approximated values:

• All atom vs average: 0.16
• Backbone vs average: 0.125

Briefly discuss two differences between the graphs against the starting structure and against the average structure. Which is a better measure for convergence?

As we can see the plateau is reached earlier in the average structure than in the start structure. The reason for this might be that the average structure is closer to the equilibrium than the start structure. Hence, also the RMSD values are lower here.

Since the average structures converges earlier than the starting structure we think that this plots are the better ones to judge whether convergence has been reached or not.

CONVERGENCE OF RADIUS OF GYRATION

To calculate the radius of gyration we executed the following command:

g_gyrate -f 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.xtc -s 1J8U_nosol_after_SCWRL_no_h_merged_crystal_water_md.tpr -o /home/student/Dropbox/Studium/3_semester/master_praktikum/task10/radius-of-gyration.xvg

And received the following plot :

Figure 20: Radius of gyration in WT

Questions

At what time and value does the radius of gyration converge?

The radius of gyration fluctuates between 1.90 to 1.95 nm. The value for RGz is fluctuating between 1.55 to 1.70, RGx is fluctuating between 1.45 to 1.70 and RGy is fluctuating between 1.45 to 1.55.