Trajectory analysis: titin domain extension

To use Timeline to identify events in a trajectory, we must choose which parameters to examine, perform the required analyses, and explore the resulting 2D data sets. We use as an example the titin I91 extension trajectory introduced above, and start with examining secondary structure, to get an overall sense of the architectural changes that take place during forced extension. Then we will look at geometric fluctuations during the trajectory, which will both illustrate how to use some of the Timeline tools and provide some hints as to when and where important events are taking place in the I91 extension. Then we will look at the hydrogen bond breaking between the $\beta$-strands of the domain's $\beta$-sheets, to get more insight into how the protein architecture handles applied force.

Secondary structure during titin domain extension

We examine how the secondary structure of the domain changes as the force extension takes place. We can see visually by animating the 3D trajectory that the domain begins as a $\beta$-sandwich then unravels as the force extension takes place, but there is more to the story; we can make a 2D data plot to examine the fate of each $\beta$-strand.

• Start a new VMD session. Launch VMD by:
  • Unix/Mac OS X Users: typing vmd in a Terminal window.

  • Windows Users: using the Start menu.

• Load in the PSF file for titin I91 domain. In the VMD Main window, select File $\rightarrow$ New Molecule, then in the Molecule File Browser window, with Load files for: New Molecule selected, navigate to the timeline-tutorial-files directory and select titin.psf.

• Load in the titin extension trajectory. In the Molecule File Browser window, with Load files for: 0: titin.psf selected, open titin.dcd, which is also in the timeline-tutorial-files directory. The trajectory shows a steered molecular dynamics extension of the I91 domain of the giant muscle protein titin, solvated in a water droplet with a non-periodic boundary.

• Adjust the VMD Main time slider to frame 0. In the VMD Main window, select Graphics $\rightarrow$ Representations... to display the Graphical Representations window. In the Graphical Representations window, edit the default all selection to not water. Set the Coloring Method to Secondary Structure and Drawing Method to New Cartoon.

• Open the Timeline plugin window. In the VMD Main window, select Extension $\rightarrow$ Analysis $\rightarrow$ Timeline.

• Display secondary structure for all frames, all residues in the trajectory. In the VMD Timeline window, select Calculate $\rightarrow$ Calc. Sec. Structure

• Scrub the cursor and explore the 2D data plot. With left mouse depressed move the 2D cursor around the 2D data plot. Note how the 3D highlight (a red Licorice representation) moves around the molecule, highlighting whatever is currently under the 2D cursor.

  Figure: Secondary structure for all residues of I27 for all frames of the loaded trajectory. The structure corresponding to the red highlight rectangle in the Timeline (left) data panel is shown in the 3D view (right panel). See Figure 9 for a magnified view of the color key.

  

• Get detailed information about the trajectory. Details about the residue beneath the 2D cursor are shown in the details box to left and below the box plot. The current residue number, residue name, chain, segment, and frame, as well as the data value for the selected residue, and the current analysis method. These change as you move the cursor.

• Zoom and scroll around the data plot. Right-mouse-click-and-drag to draw a green-outline box to define the area to zoom into. Right-click will zoom out. The three slider controls on the right side of the Timeline window also control zoom: the vertical slider zooms vertically, the horizontal slider zoom horizontally, the central zoom slider scales the whole data block at once. The fit all button scales both axes to fit within the standard size of the Timeline window. The every residue button changes the vertical scale to display numbering for every vertical element (residues or selections (covered below, in Section 4.3)).

  Figure 9: Color key for secondary structure plots.

  

• Examine color scale key: The color key for secondary structure attributes is labeled ``sec. structure'', and displays the one-letter structure codes used by STRIDE software. The one-letter code descriptions are listed in Help $\rightarrow$ Structure codes..., and in Figure 9. Most relevant here, `E' (yellow) corresponds to 'Extended conformation', the main component of beta sheets; `T'(aqua) corresponds to ``Turn'', another beta sheet component, and `C' (white) stands for ``Coil'' (random coil, no structure). Note that secondary structure is a special case for coloring; for all other cases of calculations, the color scale shows a numerical range.

• Identify the time frames when each of the individual $\beta$-strands begins to lose secondary structure, and when it has completely lost secondary structure.

Thresholding and changing appearance: examining RMSF

There are two related ways to help examine how the values of a data set are distributed: first, by using the Threshold Count tool; second, by changing the color scaling range of the 2D plot. The Threshold Count tool adds up, for each frame, the number of residues or selections that fall within a given range, then plots these numbers for all frames. The plot is dynamically updated as the Threshold Min and Max values are changed. Here we review how to do this for the Root Mean Square Fluctuation data set examined in Figure 4, then use the results from this to set the color scaling range, in order to identify which structures are involved in the fluctuation events.

• Display root mean square fluctuation for all frames, all residues in the trajectory. In the VMD Timeline window, select Calculate $\rightarrow$ Calc. RMSF

• Use the thresholding tools. Adjust the Threshold Plot by changing the Threshold Min and Threshold Max bounds sliders. (Type in values here with select Threshold $\rightarrow$ Set bounds... Set them to 4.48 and 6.67 and note the repeating pattern of peaks. This thresholding can change much more quickly than we can adjust the 2D plot (especially for a large plot) and can track changes hard to total up by eye. The Threshold plot updates as the range is changed, to allow quick exploration of the plots. Now apply the threshold bounds values we set to the coloring of the whole 2D plot: select Appearance$\rightarrow$ Set scaling... and enter 4.48 and 6.67 as bottom and top values. The result should resemble Figure 4c. Scrub the highlight cursor over the transitions in the resultant plot to see what structures are involved in the fluctuation increases.

More on changing appearance.

Perform other changes to the Timeline plot, to see features that may be helpful when working with different data sets or different structures:

• Toggle display of one letter vs. three letter residue codes in the vertical plot labels by selecting Appearance $\rightarrow$ Show 1-letter codes .

• With the Analysis Selection set to all, or to any interesting sub-selection, make an RMSF plot as before with Calculate $\rightarrow$ Calc. RMSF. Change the 2D Plot color scale with Appearance $\rightarrow$ Color scale $\rightarrow$ Rainbow and Appearance $\rightarrow$ Color scale $\rightarrow$ Grayscale.

• For more experimentation with this specific trajectory, source a TCL script to load the example system in the state shown in Figures 2 and 3, with cartoon representation and coloring showing native secondary structure. To this, start a new VMD session, change directory using the VMD Tk terminal to timeline-tutorial-files, then enter into the VMD Tk terminal source start-titin.vmd. Note that this file sources titin-struct.vmd in the same directory. The latter Tcl script imposes the known native secondary structure of the published structure, in order to show more accurate beta-strands at trajectory start compared to that determined from the built-in secondary structure algorithm (STRIDE).

Examine backbone hydrogen bonds during titin extension

Figure 10: Exploring hydrogen bonds during titin I91 extension. The top panel shows hydrogen bond for all residues of I91 for all frames of the loaded trajectory. In the middle and bottom rows, structure corresponding to the red highlight rectangle in the zoomed-in Timeline 2D data plot (left panel) is shown in the 3D view (right panel). Hydrogen bonds are plotted as white when formed, and black when broken. The middle row shows highlighted a single, unbroken backbone hydrogen bond. The bottom row shows highlighted the same backbone hydrogen bond, now broken, at a later time frame.

Now we will look at the hydrogen bond breaking pattern during the I91 extension trajectory. Since we are looking at the protein architecture, we will examine the bonds between the partner $\beta$-strands that make up the two $\beta$-sheets which form the I91 domain $\beta$-sandwich.

• Change the Analysis Selection from all to name N HN O C, to select only the atoms involved in inter-$\beta$-stand hydrogen bonds.

• Calculate the hydrogen bonds that can be formed with the current selection, in Calculate $\rightarrow$ Calc. H-bonds.... Enter a Bond distance cutoff of 3.5 and an Angle cutoff (deg) of 45, then click the Calculate button . The result should resemble Figure 10.

• The value of data in the 2D plot is either 0 or 1. Set the Threshold Plot range from 0 to 1 to see the number of formed hydrogen bonds in each frame. (Although the auto-ranging is already set from 0 to 1, you must still adjust the threshold minimum control once to display the Threshold Plot).

• Zoom in the plot to examine individual hydrogen bonds. Click on the atoms in the 3D view to display the names and numbers of the residues involved.

• Use the hydrogen bond plot, and the fit all button, to look for overall patterns of hydrogen bonds breaking. Look for H-bond breaking -- the end of a white horizontal line -- clustered around the same time, and check the associated structures. While using a copy of a secondary structure plot such as Figure 8 for reference, note which $\beta$-strands the bond breakings are associated with, and how they relate to the beginning/ending times of secondary structure loss (unraveling) of individual $\beta$-strands.

  Figure 11: Clustered bond breaking during I91 extension. a) Force-extension curve of I91 extension, early force peak is marked with an arrow b) Before clustered bond breaking c) After clustered bond breaking. In b) and c) , structure corresponding to the red highlight rectangle in the zoomed-in Timeline 2D data plot (left panel) is shown in the 3D view (right panel). Hydrogen bonds are plotted as white when formed, and black when broken. The selected hydrogen bond is highlighted in green in the 3D plots.

  

• Load in a version of the I91 extension trajectory with four times as many frames (four times the temporal detail):
  navigate to to the examples directory and load titin-big.dcd

• We will examine a set of inter-$\beta$-strand hydrogen bonds that are stable during equilibration of I91. Change directory to the examples directory and type
  source stable-titin-backbone-hbonds.tcl in the Tk console. This will add two vmd atom macros: backboneHSel and backboneOSel.

• Change the analysis selection to backboneHSel or backboneOSel.

• Select Calculate $\rightarrow$ Calc. H-bonds... and click the Calculate button.

• Scrub through the trajectory with the highlight cursor, using the Threshold count tool to note how the hydrogen bond count has the largest drop between frames 11 and 18. Note where these breaking H-bonds are in the 2D view, as in the previous example.

• Add both CPK and Hbond graphic representations as for selection backboneHSel or backboneOSel. Note the hydrogen bonds ending in the 2D graph between frames 11 and 18, and how they correspond to the hydrogen breaking in the 3D view, as shown in Figure 11. These simultaneous hydrogen bond breaking seen in Figure 11c is what is responsible for the extension force peak seen in Figure 11a. Under forced extension, I91 architecture cannot allow further unraveling until these bonds are broken.

Using Data Files and Data Collections

These features help with saving and loading completed calculations (so you won't have to spend time calculating them again), and with creating and browsing sets of pre-computed calculations.

• Export and Import the calculated data. Select File $\rightarrow$ Write Data File... and save as test-rmsf.tml. Clear the plot with Calculate $\rightarrow$ Clear data, then read the data file back in with File $\rightarrow$ Load Data File..., and specify the test-rmsf.tml you just saved.

• Use a data collection: With the titin trajectory loaded, select Data $\rightarrow$ Set Data Collection directory... and select titin-data-coll in the dialog box, which is in the timeline-tutorial-files directory.
• The Data menu is now populated with the .tml files in that directory, select each to load that calculation data. Select Data $\rightarrow$ titin-strand-contacts.tml, then Data $\rightarrow$ titin-h-bonds.tml, etc. Loading each data set will reset the coloring range of the 2D plot to the full range of each loaded set.
• Try making a new directory, save two or more .tml files to it, then display the contents via the Data menu.