Contents

6.5. Exercises

6.5.1. Theory - Solvent Models in Molecular Dynamics

  1. Derive (6.6) from (6.3) by passing via the exponential form of the Poisson-Boltzmann equation (6.5). Give an appropriate expression for the equilibrium charge density \(\rho_\text{ext}(\mathbf{r})\) in the Poisson-Boltzmann approach.

  2. How may the solvent environment (especially in the case of a polar solvent, such as dimethylformamide (DMF), and a polar hydrogen-bonding solvent, such as water) influence the properties (conformation, reactivity) of the solute? Which solvent do you expect to be more difficult to mimick by an implicit model, DMF or water?

  3. In the context of the previous questions, explain possible advantages and pitfalls of using an implicit solvent compared to an explicit treatment.

  4. Bonus: How expensive is the computation of the pressure in (6.13), via the virial, in an MD and an MC algorithm, respectively?

  5. Bonus: Derive the ideal gas part of the virial in (6.12).

  6. A protein has the tendency to fold much quicker in implicit than in explicit solvent. Why is this? What are possible issues?

6.5.2. Results analysis - Protein Modelling

For all of the following questions, it is recommended to display structures using two separate representations in VMD. Once you have loaded a new protein structure or trajectory, create two new representations by going to Graphics→Representations and clicking Create Rep. Define one of these representations with Drawing Method set to Licorice and the other set to NewCartoon. You may also find it useful to differenciate between protein structures by modifying the Coloring Method to Molecule.

  1. Follow the instructions in Practical: TRP Cage using OpenMM and run the folding simulation. Calculate the correct number of steps for the simulations to run 50 ps of heating and 20 ns of dynamics and report those numbers in your report. Then download the trp_cage_gb.prmtop, trp_cage_gb.pdb,trp_cage_gb.nc files from Google Colab.

  2. Load the trp_cage_gb.pdb starting structure in VMD (either on your local machine or on vdi.epfl.ch). Include an image of this structure in your report. Are there any residues which would contribute to the instability of the starting structure in its current conformation, why?

  3. What type of structure is the final Trp-cage miniprotein? List the main components contributing to this structure, including the residues which are responsible for their formation.

  4. Load the .prmtop and then the .nc file into the same molecule in VMD. Explore the trajectory, and identify all important hydrogen bonds in the formation of any secondary structures you observe. Tabulate some of these hydrogen bonds in your report. Monitor an individual hydrogen bond involved in a secondary structure, and provide the graph of the hydrogen bond length over time. Can you infer at which interval (in nanoseconds) the secondary structure forms?

    Note: VMD always uses the first frame to determine secondary structure. If you want secondary structures elements to be correctly updated with the cartoon representation you need to go to Graphics , Representation click on the NewCartoon representation and then in the Trajectory tab you need to activate Update selection every frame.

  5. Perform a hydrogen bond analysis on the trajectory, and plot the moving average using Hbond moving average and RMSD. Include the moving-average graph in your report, and explain the observed trend with reference to the structural components of the Trp-cage miniprotein.

  6. Download the experimental structure as pdb file with PDB code: 1L2Y from the protein databank. Align the trajectory to the experimental structure using the RMSD fit described in Section 6.4.1. Graph the RMSD over the course of the trajectory and include it in your report, and explain the fluctuations in RMSD over the trajectory. Does the trajectory reach the same conformation as the experimental structure?

  7. Why is it useful to constrain bond lengths for larger MD simulations (typically with the SHAKE algorithm)? Which bonds would you typically constrain in such a scenario, and why?

  8. Bonus: Which properties do you need to take into account in order to select an appropriate timestep for your MD simulation? Are there any other reasons you might wish to reduce or increase this timestep? Why do you think did Simmerling et. al. use a different timestep for the heating and production phase of their simulations?

6.4. Hbond moving average and RMSD