Exercises: Coming Soon!

Determining a shape’s center of mass mathematically

In the main text, we noted that the center of some shapes can be computed mathematically. Consider the semicircular arc shown in the figure below, with endpoints (-1, 0) and (1, 0).

A semicircular arc with radius 1 corresponding to a circle whose center is at the origin.

Exercise: Determine the center of mass of the shape in the figure above. (Hint: finding the x-coordinate of the center of mass is easy, but finding the y-coordinate requires a little calculus for finding an average value.)

Exercise: Say that we connect (-1, 0) and (0, 1) to form a closed semicircle. What will be the center of mass of the resulting shape?

Calculating RMSD

Imagine that this plot depicts a 2D protein structure where each point represents an alpha carbon.

Simple 2D structure A.

Exercise: From what we have learned in this module about how to compare protein structures, calculate the center of mass of this protein structure.

Imagine that we have a second 2D protein structure and wanted to compare it with our first protein structure from the previous exercise.

Simple 2D structure B.

Exercise: Assume that we do not need to rotate either structure and calculate the RMSD between the two proteins. (Hint: calculate the center of mass and translate each point such that the new center of mass matches the center of mass of the previous protein. You can also translate both proteins such that their center of masss lie on the origin).

Ab initio and homology modeling

In this exercise, we will perform ab initio and homology structure prediction on a simple protein, the human hemoglobin subunit alpha we saw in part 1 of this module. First, go to the protein data bank and search for the protein “1SI4”. Download the PDB file by clicking on “Download Files” and then “PDB Format”. We will use this file for structure comparisons later. Next, go to the “Sequence” tab and click “Display Files” and then “FASTA Sequence”. Copy the first sequence corresponding to the alpha subunit and submit it to the ab initio structure prediction software, QUARK, and your choice of homology modeling software: SWISS-MODEL, Robetta, or GalaxyWEB. Once you get the results, use ProDy to calculate the RMSD between the predicted structures and the actual structure (1SI4).

Exercise: Which type of modeling resulted in the most accurate prediction? Is this what you expected? (Hint: Use “Chain A” to focus on subunit alpha)

Trying out AlphaFold

In the conclusion of part 1 of this module, we introduced AlphaFold from DeepMind that won the 14th CASP contest in 2020 by a wide margine. A simplified version of AlphaFold is available on Colab. This version currently does not work with the entire spike protein, so we will use the human hemoglobin subunit alpha once again. Following the directions from the previous exercise, grab the protein sequence of the alpha subunit. Next, open the simplified version of AlphaFold. Read the documentation and follow the directions in each step to generate the predicted structure.

Exercise: Use ProDy to calculate the RMSD between the predicted structure and the actual structure (1SI4). Did this simplified version of AlphaFold perform better than your Ab initio and homology modeling results from the previous exercise?

Qres Comparison

In part 2 of the module, we computed Qres between SARS and SARS-CoV-2 RBD to find local differences between the two structures. Here, we will try repeating this while using the hemoglobin subunit alpha protein. Using the PDB files of the human hemoglobin 1SI4 and mako shark hemoglobin 3MKB, upload the protein structures into VMD. Align the structures using “Multiseq” and visualize the structures using Qres as the coloring parameter.

Exercise: Use the visualizations to determine where the protein structures vary the most? Why do you think this makes sense?

Optional: Take the best performing predicted model from the previous exercise perform the Qres visual analysis with the actual human hemoglobin subunit alpha structure 1SI4. Where do the protein structures vary the most? Compare the predicted model with the mako shark hemoglobin 3MKB. Where do the structures vary the most, and are the results similar to the comparison between 1SI4 and 3MKB?

Calculating Interaction Energy with NAMD Energy

In this exercise, we will be performing a short analysis of SARS-CoV-2 Spike protein interaction energy with the human receptor ACE2 using NAMD. Go to the protein databank and download 6VW1.pdb. Upload the structure into VMD and go to Extension/Analysis/NAMD Energy. Calculate the energy types “VDW” and “Elec” using the following selections:

Selection 1 Selection 2
A protein and chain B protein and chain F and resid 482 to 486
B protein and chain B protein and chain F and resid 383 to 394

Exercise: How do the results of part A compare with that of part B? Can you justify the results? (Hint: Visualize the specific residues).

Visualizing Glycans with VMD

In the conclusion of part 2 of this module, we mentioned that the surface of the surface of viruses and host cells are “fuzzy” because they are covered by structures called glycans. As you may expect, SARS-CoV and SARS-CoV-2 are also covered by this “glycan shield”, where glycosylation of surface antigens allows the virus to hide from antibody detection. In this simple exercise, we will use VMD to visualize glycans on the spike protein of both viruses. First, we will need to download the protein sturctures of the SARS-CoV spike protein (PDB entry: 5xlr and the SARS-CoV-2 spike protein (PDB entry: 6vxx. Load each structure into VMD and go to Graphics>Representations. For VMD, there is no specific keyword to select glycans, so we will use a workaround using the keywords: “not protein and not water”. Create the representation and play around with the visualization. Assuming that all the non-proteins are glycans, which structure contains the most number of glycans? Do you think this supports SARS-CoV-2’s higher infectivity compared to SARS-CoV?

• Good exercise: find center of mass of a given shape.

• exercise: compute RMSD.

• Good exercise later: compute Q scores for the protein structure comparison that we performed at the end of part 1.

• Good exercise: compute Qres for very simple proteins

• Exercise based on following excellent observation: In the case of RMSD, I believe that they assign the RMSD of an alignment between a residue and gap to be 0, effectively ignoring it. I believe this is how it is ensured that the two sets have the same number of points (alpha carbons) and also one of the shortcomings of using RMSD. I think for prody, you can set a gap penalty during chain matching,

“Thus, gap-filled alignments focusing on low RMSDs, while accurate and useful for superposition of structures, are sub-optimal for machine learning as the features of many potentially relevant residues are discarded due to a lack of data in those positions. In most cases, positions with over a certain percentage of aligned residues are considered, with gaps replaced by zeros or by the average of the feature values in that position [22].”

• (RMSD with gap. Also included a jupyter notebook of this exercise with the necessary files to the email.) In this exercise, we will see what can happen to RMSD calculations when there is a gap in sequence alignment between two proteins. Let’s use our homology modeling result robetta4 (single chain of SARS-CoV-2 Spike) and the associated SARS-CoV-2 Spike model 6vxx from the PDB.

First, calculate the RMSD between the two models by following the RMSD tutorial and using the chain A to chain A matching (matches[0][0] & matches[0][1]). You should get a RMSD of about 2.5853.

If you followed the tutorial, robetta4 should be under the variable struct1. We will create a new variable, struct3, by taking the sequence of robetta4 and deleting a large selection. We can create the variable by using:

struct3 = struct1.select(‘resid 1 to 400 or resid 601 to 20000’)

We use a large value ‘20000’ to ensure that the rest of the protein is captured. Variable struct3 will represent the robetta4 model that has a gap/deletion at residue 400 to 600 (a 200 residue gap). Now we will repeat the RMSD calculation using struct3 instead of struct1. You should get a RMSD of about 2.1927. Is this what you expected?

(There are less residues to compare and deviations to consider, which may have attributed to the decreased RMSD score.)

• Why are contact maps and cross-correlation maps “symmetric” about the main diagonal?

• Something on identifying a dynamics difference from a contact map or better cross-correlation in similar proteins.

• If you have not already done so, try modeling the SARS-CoV-2 S protein or RBD using SWISS-MODEL, Robetta, or GalaxyWEB using the steps inHomology Structure Prediction Tutorial. Then, use ProDy to calculate the RMSD between your models and the PDB entries 6vxx for the S protein and 6lzg for the RBD. Did your models perform better than our models?

• Visualize your best performing model(s) and the corresponding PDB entry in VMD. If the models are sufficiently similar, try performing a structural alignment using Multiseq and see where in the the structure your predicted models did well.

• Using VMD, model the SARS-CoV-2 S (6vxx) protein and SARS S (5x58) protein. Create the graphical representation of glycans and compare the number of glycans between the two proteins. Are they any different? Could this possibly be another reason why SARS-CoV-2 is more infectious than SARS?

• In our GNM tutorial, we created the contact map using the threshold of 20Å. Try making the contact map of one of the chains of SARS-CoV-2 S protein 6vxx with different thresholds. Do the maps look different?

• In this module, we only used homology modeling for large molecules such as the SARS-CoV-2 S protein and the RBD. It would be interesting to directly compare the accuracy of homology modeling and ab initio modeling. Try using one of the three homology modeling softwares to predict the structure of the human hemoglobin subunit (sequence). After you get your predicted models, try calculating the RMSD using the PDB entry 1si4. How do they compare to the RMSD from our ab inito (QUARK) models?

Glycans

Here, we will show how to visualize glycans in VMD. Be sure to have installed VMD and know how to load molecules into the program. If you need a refresher, go to the VMD and Multiseq Tutorial. In the Visualizing Regions and Residues Tutorial, we went over how to change the visualizations of molecules and proteins in VMD. Please visit that tutorial first if you have not done so already.

We will use the PDB entry of the SARS-CoV-2 Spike protein, 6vyb.

First, download and load 6vyb into VMD and go to Graphics>Representations. For VMD, there is no specific keyword to select glycans. A workaround is to use the keywords: “not protein and not water”. To recreate the basic VMD visualizations of the glycans in the module, use the following representations. (For the protein chains, use Glass3 for Material).

The end result should look like this:

In the visualization you just created, the three chains in the S protein are in dark green, dark orange, and dark yellow. The presumed glycans are shown in red. Notice how they are all over the S protein! You may have noticed that one of the chains appear to be different in that part of it is sticking out from the rest of the protein. This is because this the PDB entry 6vyb contains the structure of the SARS-CoV-2 S protein in its open conformation. Let’s return to the main text to see what that means.