Exercise: Atomistic Simulation of Biomolecular function, Part 1

Leonard Heinz

Tutorial adapted from Bert de Groot.

Contents

Introduction
Preparation of a typical MD simulation
Setup the simulation system
Carry out the simulation
Trajectory analysis
Optional exercises
References

Introduction

In this part of the exercise, we will set up a simulation of a biological macromolecule: a small protein.

Proteins are nature's universal machines. For example, they are used as building blocks (e.g. collagen in skin, bones and teeth), transporters (e.g. hemoglobin as oxygen transporter in the blood), as reaction catalysts (enzymes like lysozyme that catalyse the breakdown of sugars), and as nano-machines (like myosin that is at the basis of muscle contraction). The protein's structure or molecular architecture is sufficient for some of these functions (like for example in the case of collagen), but for most others the function is intimately linked to internal dynamics. In these cases, evolution has optimised and fine-tuned the protein to exhibit exactly that type of dynamics that is essential for its function. Therefore, if we want to understand protein function, we often first need to understand its dynamics (see references below).

Unfortunately, there are no experimental techniques available to study protein dynamics at the atomic resolution at the physiologically relevant time resolution (that can range from seconds or milliseconds down to nanoseconds or even picoseconds). Therefore, computer simulations are employed to numerically simulate protein dynamics.

We will use the GROMACS simulation package for this.

Today, we will simulate the dynamics of a small, typical protein domain: the B1 domain of protein G. B1 is one of the domains of protein G, a member of an important class of proteins, which form IgG binding receptors on the surface of certain Staphylococcal and Streptococcal strains. These proteins allow the pathogenic bacterium to evade the host immune response by coating the invading bacteria with host antibodies, thereby contributing significantly to the pathogenicity of these bacteria.


We will now follow a standard protocol to run a typical MD simulation of a protein in a box of water in gromacs. The individual steps are summarized in a flowchart on the right site.

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Preparation (A)

Before a simulation can be started, an initial structure of the protein is required. Fortunately, the structure of the B1 domain of protein G has been solved experimentally, both by x-ray crystallography and NMR. Experimentally solved protein structures are collected and distributed by the Protein Data Bank (PDB). Please open this link in a new browser window. To download the structure select "PDB File" under "Download Files". When prompted, select "save to disk", and save the file to save it in a new folder, e.g, gromacs_tutorial_p1 (click here if that does not work). To have a look at the contents of the file, on the unix prompt, type:

more 1PGB.pdb

The file starts with general information about the protein, about the structure, and about the experimental techniques used to determine the structure, as well as literature references where the structure is described in detail. (in "more", press the spacebar to scroll). The data file contains the atomic coordinates of our protein structure with one line per atom. (quit the "more" program by pressing "q"). Now we can have a look at the structure:

vmd 1PGB.pdb 

to visualise the structure. We now see a so-called wireframe representation of the protein structure: atoms (with different colors for the different chemical elements: cyan for carbon; red for oxygen and blue for nitrogen) are not shown directly, but the bonds between atoms are shown as lines. Under Graphics -> Representations -> Drawing Method, also try other representations such as "Licorice", "VDW" and "New Cartoon". Exit rasmol under File -> Quit.

Question: Why do we start our MD simulations from the experimentally determined 3D structure? Isn't it enough to know the protein's amino acid sequence?

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Setup (B)

We will now prepare the protein structure to be simulated in gromacs. Although we now have a starting structure for our protein, one might have noticed that hydrogen atoms (which would appear white) are still missing from the structure. This is because hydrogen atoms contain too few electrons to be observed by x-ray crystallography at moderate resolutions. Also, gromacs requires a molecular description (or topology) of the molecules to be simulated before we can start, containing information on e.g. which atoms are covalently bonded and other physical information. Both the generation of hydrogen atoms and writing of the topology can be done with the gromacs program pdb2gmx:

gromacs_2018
gmx pdb2gmx -f 1PGB.pdb -o conf.pdb

when prompted for the force-field to be used, choose the number corresponding to the OPLS-AA/L all-atom force field, and SPC/E for water. View the result with:

vmd conf.pdb 

See the added hydrogens? The topology file written by pdb2gmx is called "topol.top". Have a look at the contents of the file using:

 more topol.top 

you will see a list of all the atoms (with masses, charges), followed by bonds (covalent bonds connecting the atoms), angles, dihedral angles etc. Near the very end of the topology (in the "[molecules]" section) there is a summary of the simulation system, including the protein and 24 crystallographic water molecules.

The topology file thus contains all the physical information about all interactions between the atoms of the protein (bonds, angles, torsion angles, Lennard-Jones interactions and electrostatic interactions).

The next step in setting up the simulation system is to solvate the protein in a water box, to mimick a physiological environment. For that, we first need to define a simulation box. In this case we will generate a rectangular box with the box-edges at least 7 Angstroms apart from the protein surface:

gmx editconf -f conf.pdb -o box.pdb -d 0.7 

(note that gromacs uses units of nanometers). View the result with

vmd box.pdb

and, in the VMD terminal, type:

pbc box

Now, exit VMD and fill the simulation box with SPC water using gmx solvate:

gmx solvate -cp box.pdb -cs spc216 -o water.pdb -p topol.top

Again, view the output (water.pdb) with VMD. Now the simulation system is almost ready. Before we can start the dynamics, we must perform an energy minimisation.

Question: Why do we need an energy minimisation step? Wouldn't the crystal structure as it is be a good starting point for MD as it is?

For the energy minimisation, we need a parameter file, specifying which type of minimisation should be carried out, the number of steps, etc. For your convenience a file called "em.mdp" has already been prepared and can be downloaded from here. View the file with "more" to see its contents. We use the gromacs preprocessor to prepare our energy minimisation:

gmx grompp -f em.mdp -c water.pdb -p topol.top -o em.tpr -maxwarn 2

This collects all the information from em.mdp, the coordinates from water.pdb and the topology from topol.top, checks if the contents are consistent and writes a unified output file: em.tpr, which will be used to carry out the minimisation:

gmx mdrun -v -s em.tpr -c em.pdb 

The output shows that already the initial energy was rather low, so in this case there were hardly any bad contacts. Having a look at "em.pdb" shows that the structure hardly changed during minimisation.


The careful user may have noticed that grompp gave a warning:

System has non-zero total charge: -4.

Before we continue with the dynamics, we should neutralise this net charge of the simulation system. This is to prevent artefacts that would arise as a side effect caused by the periodic boundary conditions used in the simulation. A net charge would result in an electrostatic repulsion between neighbouring periodic images. Therefore, 4 sodium ions will be added to the system:

gmx genion -s em.tpr -o ions.pdb -np 4 -p topol.top

Select the water group ("SOL"), and 4 water molecules will be replaced by sodium ions. The output (ions.pdb) can be checked with VMD. To better see the ions in VMD, select Graphics -> Representations, type "protein" in the "Select Atoms" field and confirm by pressing enter; then create a new representation, select the ions with "name NA", press enter and choose "VDW" as the drawing method. Go back to Contents

Simulation (C)

Just to be on the safe side, we repeat the energy minimisation, now with the ions included (remember to (re)run grompp to create a new run input file whenever changes to the topology, or coordinates have been made):

gmx grompp -f em.mdp -c ions.pdb -p topol.top -o em.tpr -maxwarn 2
gmx mdrun -v -s em.tpr -c em.pdb 

Now we have all that is required to start the dynamics. Again, a parameter file has been prepared for the simulation, and can be downloaded here. Please browse through the file "md.mdp" (using "more") to get an idea of the simulation parameters. The gromacs online manual describes all parameters in detail here. Please don't worry in this stage about all individual parameters, we've chosen common values typical for protein simulations. Again, we use the gromacs preprocessor to prepare the simulation:

gmx grompp -f md.mdp -c em.pdb -p topol.top -o md.tpr -maxwarn 2

and start the simulation!

gmx mdrun -v -s md.tpr -c md.pdb -nice 0

The simulation is running now, and depending on the speed and load of the computer, the simulation will run for a number of minutes.

Question: How do the parts of energy minimization and MD simulation differ (with reference to energy landscapes)?

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Analysis of a gromacs simulation (D)

If the simulation has finished, we can start analysing the results. Let us first see which kind of files have been written by the simulation (mdrun):

ls -lrt 

We see the following files: The first analysis step during or after a simulation is usually a visual inspection of the trajectory. For this we will use VMD.

vmd md.pdb traj_comp.xtc

Select a group of your interest using the "Representations"-menue. You can, e.g., use the keywords "protein", "water", "name NA" and the logical operators "and", "or", "not". Click the play-button in the main window to see the trajectory. We can see that the protein and its surroundings undergo thermal fluctuations, but overall, the protein structure is rather stable, as would be expected on such timescales.

For a more quantitative analysis on the protein fluctuations, we can view how fast and how far the protein deviates from the starting (experimental) structure:

gmx rms -s md.tpr -f traj_comp.xtc 

When prompted for groups to be analysed, type "1 1". gmx rms has written a file called "rmsd.xvg", which can be viewed with:

xmgrace rmsd.xvg 

We see the Root Mean Square Deviation (rmsd) from the starting structure, averaged over all protein atoms, as a function of time.

Question: Why is there an intial rise in the rmsd?

The simulation not only yields information on the structural properties of the simulation, but also on the energetics. With the program gmx energy the energies written by mdrun can be analysed:

gmx energy -f ener.edr 

Select "Potential" and end your selection by pressing enter twice, View the result with:

xmgrace energy.xvg

As can be seen, the total potential energy initially rises rapidly after which it relaxes again.

Question: Can you think of an explanation for this behaviour?

Please repeat the energy analysis for a number of different energy terms to obtain an impression of their behaviour.

Question: Do you think the length of our simulation is sufficient to provide a faithful picture of the protein's conformations at equillibrium?

You've probably noticed that in the simulation about only ten percent of the system that was simulated consisted of protein, the rest was water. As we are mainly interested in the protein's motions and not so much in the surrounding water, one could ask if we couldn't forget about the water and rather simulate the protein. That way, we could reach ten times longer simulations with the same computational effort!

Question: Why do you think that it is important to include explicit solvent in the simulation of a protein?

Continue with part 2.

Optional exercises

To check if your assumption is correct, repeat the simulation of protein G, this time without solvent (to observe the effect more clearly, increase the length of the simulation by changing "nsteps" in the file "md.mdp" by e.g. a factor of ten).

Question: What are the main differences to the protein's structure and dynamics as compared to the solvent simulation? (Hint: use programs like gmx rms and gmx gyrate to analyse both simulations).

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Further references:


For questions or feedback please contact Helmut Grubm├╝ller / hgrubmu@gwdg.de or Leonard Heinz / lheinz@gwdg.de