## 8. Using a Ramachandran Plot

Begin with the complete model 1HEW.pdb centered, displayed, and selected. (If you just completed section 7 of this tutorial, you will need first to put away your modified (I98Q) model (File: Close), and then open the file 1HEW.pdb.)

Color the model (backbone and sidechains) by residue type.

Wind: Ramachandran Plot
Move the Ramachandran Plot window to the lower right of the screen, so that you can see the graphics window. If needed, you can make it smaller by grabbing and dragging its lower left corner. Shorten the Control Panel, so that no part of it is hidden behind the Ramachandran Plot. For each selected residue (all should be selected) the Ramachandran diagram contains one small dot (actually a small square for glycines and a small plus sign for all others). Dots are colored according to the current color scheme.

Most of the peptide bonds in a protein are locked in the trans conformation. For each residue in a protein, two torsional angles phi and psi determine the backbone conformation of the protein. Phi for residue n is is the dihedral angle formed by four atoms: the carbonyl carbon (designated C in a PDB file) of residue n-1, and atoms N, CA, and C of residue n. Psi is the dihedral angle formed by atoms N, CA, and C of residue n, and atom N of residue n+1. Another way to say it: phi defines rotation about the CA-N bond of the residue, and psi defines rotation about the CA-C bond of the same residue. A Ramachandran plot is a graph of phi versus psi, with a dot (or small symbol) for each residue at the position corresponding the residue's phi and psi. The following exercises will improve your understanding of conformational angles in proteins.

Click on the Rama Plot to make it active, and place the pointer on a dot (do not click). The residue name and number appears in the upper left corner of the window. Notice again that the dots are colored by the same scheme as the model (currently, by type). When you place the pointer in a crowd of dots, several residue labels will appear.

Certain combinations of phi and psi are "forbidden" because they result in steric hindrance, or clashes, between atoms. The remainder of the plot corresponds to "allowed" conformations. DeepView shows the allowed regions bounded by curves in yellow (no clashing) and blue (modest, but frequently observed, contact). Notice that most of the dots fall in allowed regions. Find dots in forbidden regions and identify them by putting the pointer on them. Why do you think that glycine can adopt conformations that are forbidden for other residues?

> #### Are Ramachandran Plots Useful?

> During the last stages of structure determination of proteins by any method -- x-ray crystallography, NMR, or homology modeling -- structural biologists use a variety of tools, including Ramachandran plots, to call their attention to unrealistic conformations in their models. A Rama plot plainly signals residues that need further work before the entire model can be declared chemically realistic.

In addition to showing phi and psi, the Rama Plot window in DeepView allows you to change conformational angles, which can be very useful in model building. As mentioned earlier, you should realize that you can produce unrealistic models in this manner. The following operations are only to demonstrate features of DeepView.

With the Rama Plot window at the bottom right of the screen, out of the way of the graphics window, hide side chains, color the model CPK, and then select strands of beta structure (Select: Secondary Structure: Strands). Center the model. Compute H-bonds. How many strands of beta sheet are present in lysozyme? Scroll down the Control Panel list to see how many sections are selected, or just press <return> to eliminate unselected residues from the display. Count the strands. Then restore all of the mainchain to the screen without changing the selection (shift-click in any empty space of the "show" column on the control panel).

Look at the Ramachandran Plot, and notice that fewer dots are present -- only those representing the selected residues are shown (selection, not display, determines the contents of the plot). Also note that the majority of the dots lie in the yellow region at the upper left of the diagram. Angles corresponding to beta conformations lie in this region.

Select and display helices, and center the model. How many helices are present in lysozyme? What region of the Rama Plot contains phi and psi values corresponding to alpha helix?

Select, display, and center any three adjacent residues. Label the residues and display their side chains (just click the label and side headings in the Control Panel). Finally, color them CPK. On the Rama Plot, find the dot for the center residue. Click and drag the dot around on the diagram while watching the model (stereo recommended). You are changing phi when you drag it horizontally, and psi when you drag it vertically. This allows you to adjust backbone conformations during model building. You can undo a single change with Edit: Undo. To modify phi only, hold down the 9 key while dragging; to modify psi only, hold down 0 (the number zero) while dragging.

Now review the definitions of phi and psi (above), and use the Rama plot to confirm that the torsional angles you are changing correspond to those described in the definitions. What is the relationship -- cis or trans -- between the first and last atoms defined by each angle when the value of the angle is zero? When the angle is 180? For either phi or psi, set the angle near zero. Look along the bond that rotates when you move the dot, with the fixed end pointing toward you and the moving end pointed away (looking toward the C-terminus, or toward higher numbered residues). What direction of rotation of the moving end corresponds to a positive rotation? Answers below.

When you change backbone angles, the N-terminal part of the model is fixed, and the C-terminal end moves. You can allow the N-terminal part to move instead by clicking the small C in the upper left corner of the Ramachandran Plot window, just the below the Help (?) button. Try it. Clicking changes C to N. When N is showing, the N-terminal end moves and the C-terminal end is fixed.

DeepView provides other means to change phi/psi angles. Again select, display, and center three adjacent residues. Look at their conformation, as well as the position of their Rama dots, before proceeding.

Tools: Set Omega/Phi/Psi: Other...
On the dialog, enter 0 (zero) for both phi and psi. Click OK. Notice the change in your model. You can set phi and psi for one or many residues at once. Repeat, setting phi and psi to 180 degrees. This shows the backbone in its most extended form.

Now select, display, and center all residues, leaving side chains hidden. Your model probably doesn't look much like lysozyme any more. Even small changes in backbone angles in an intact model will create many clashes. These exercises are for demonstration purposes only, and to help you understand the meaning of the Rama Plot. If you were making backbone torsional changes in a model, you would disconnect the parts you want to change from the rest of the model (using Build: Break Backbone), and then reconnect afterward (Build: Ligate Backbone).

Tools: Set Omega/Phi/Psi: Helix
Center the model. The entire backbone model has been rebuilt as one long alpha helix. Poor tri-NAG is left out in the cold. The helix is not perfectly straight, due to very tiny deviations from ideal helical angles.

The command Tools: Set Omega/Phi/Psi: Strand rebuilds all selected residues in beta conformation. Try it.

File: Quit
DeepView stops and returns you to the desktop.

### Review

> - Use the Ramachandran (Wind: Ramachandran Plot) plot to judge the quality of a model by finding residues that are in unlikely or high-energy conformations.
> - DeepView represents each residue of the model in the Rama plot as either a small square (glycine) or "+" (all other residues).
> - The two-dimensional coordinates (phi, psi) of a residue's symbol correspond to the phi (C-N-CA-C) and psi (N-CA-C-N) conformational angles (dihedral angles) on each side of CA for that residue.
> - Regions of the plot enclosed by yellow polygons represent fully allowed conformations of the model backbone. Regions enclosed by blue polygons represent conformations that result in contacts or mild clashes (forbidden with hard-sphere models, but frequently observed in high-quality models).
> - The Rama plot displays selected residues only, with colors corresponding to the current model element (backbone, sidechain, ribbon) that is selected for coloring (Color:Act on...).
> - Dragging a residue's symbol on the Rama plot changes the phi/psi angles of the residue. This action usually makes a real mess of a model (and only the last change is undoable), but is very useful for reviewing the definitions and sign conventions associated with conformational angles.
> - To modify phi only, hold down the 9 key while dragging; to modify psi only, hold down 0 (the number zero) while dragging.
> - The command Tools: Set Phi/Psi/Omega... allows you to set conformational angles of selected residues, which might be useful in building peptide models from scratch.

Take time to PLAY with the tools introduced in this section.

#### Answers to Questions About Phi and Psi

The first and last atoms are cis when the angle is zero degrees, and trans when the angle is 180 degrees. With atoms arranged as instructed, positive rotations are clockwise.

Next Section: 9. Judging the Quality of Models

To The Molecular Level