Proteins move: superposing two states of adenylate kinase

A crystal structure looks like a fixed object, but most enzymes have to move to work. They open to let substrates (the molecules they act on) in, close around them so the chemistry can happen, and open again to release the products. If you only ever look at one structure, you miss half of the story.

Adenylate kinase is the classic example. It keeps a cell's energy balance by converting ATP + AMP into two ADP, and to do that, two of its three domains (compact, separately folded regions of the protein) swing shut over the substrates. Two crystal structures of the same E. coli enzyme, both entries in the Protein Data Bank (PDB, the public archive of solved 3D structures), capture both ends of that motion:

• PDB 4AKE: the open, empty enzyme (Müller et al., 1996; X-ray, 2.2 Å, the resolution: the finest detail the data can show, where smaller is sharper and one angstrom, Å, is 0.1 nanometres, about the width of an atom).
• PDB 1AKE: the closed enzyme holding Ap5A (Müller & Schulz, 1992). Ap5A is an inhibitor made of an ATP and an AMP joined by a chain of five phosphates, so it fills both substrate sites at once.

In this lesson you will lay one structure on top of the other (superposition), measure how different they are (RMSD, root-mean-square deviation: a kind of average distance between matching atoms), and find out why that one number depends entirely on which atoms you choose to align.

What you will make

Open and closed, superposed on the CORE domain (the large central domain that barely moves). Open apo (nothing bound) adenylate kinase (PDB 4AKE, chain A, one protein copy in the file, blue) and the closed enzyme (PDB 1AKE, chain A, rose) with the inhibitor Ap5A (orange sticks, bonds drawn as rods). The CORE regions overlap almost perfectly. The blue LID (the domain that closes over ATP; top) and NMP-binding domain (the domain that binds AMP, a nucleoside monophosphate or NMP; left) stand open, and in the closed structure they have folded in over Ap5A.

Colour by domain and the motion becomes obvious. The CORE (grey) barely changes between the two states. The LID (residues 122–159, top; a residue is one amino acid of the chain) and the NMP-binding domain (residues 30–59, left) move as rigid blocks, from their open positions (light blue) to closed positions (rose) that clamp down on Ap5A (orange). In our run the LID tip, Thr149 (threonine 149), moves 24.6 Å.

1. Open the open state Main chat

Start a new chat in RBAi:

Open PDB 4AKE as an interactive 3D structure. Tell me the chains, method and resolution. Do not change the structure.

What you should see: a 3D card, plus two chains (A and B, 214 residues each; both are copies of the same enzyme in the crystal) and X-ray diffraction, 2.2 Å (the atom positions are worked out from how a protein crystal scatters X-rays).

2. Superpose the closed state Edit with AI

Click Edit with AI on the 3D card to open Structure Studio, then:

Superpose PDB 1AKE onto this structure with super, matching 1AKE chain A onto chain A here. Report the RMSD and the number of aligned atoms.

RBAi fetches 1AKE in PyMOL (the molecular-graphics program the studio runs; super in the prompt is one of its superposition commands), superposes it and saves the overlay as a new version (Edit with AI keeps every change as a numbered version you can undo). It colours this structure blue and the overlay rose. In the overlay, 1AKE's chain A appears as chain C.

What you should see: in our run, RMSD 2.07 Å over 1,135 aligned atoms, after 5 cycles of outlier rejection. That sounds like the two structures are nearly the same, but they are not. Chain A has 1,656 atoms. PyMOL's super repeatedly throws out the atoms that fit worst, about a third of the chain here, and reports the RMSD of what is left. The atoms it rejected are the ones that moved.

3. Align on the CORE only and measure each domain Edit with AI

Undo that overlay. Then superpose 1AKE chain A onto chain A here again with super, but match only the CORE domain: residues 1-29, 60-121 and 160-214 (the NMP-binding domain is 30-59 and the LID is 122-159). Report the core RMSD and aligned atoms. Then, without fitting again, measure with PyMOL rms_cur the C-alpha RMSD between the two chain A copies for the CORE, the NMP-binding domain and the LID separately, and the largest C-alpha displacement and its residue.

What you should see, in our run (Cα, or C-alpha, is the central carbon of each amino acid, so a Cα RMSD uses one atom per residue):

• CORE fit: 1.36 Å over 920 aligned atoms
• Cα RMSD without refitting: CORE 2.05 Å, NMP-binding domain 11.21 Å, LID 16.24 Å
• Largest Cα displacement: 24.6 Å at Thr149, near the tip of the LID

Now the numbers tell the real story. Hold the CORE still, and the LID moves about 16 Å on average while the NMP-binding domain moves about 11 Å. We checked these values independently from the downloaded coordinates and got the same numbers.

4. Make the figures Edit with AI

Two figures, white background, nothing clipped, no labels. Hide chain B of 4AKE and the second chain of 1AKE so only the two chain A copies show. Figure 1: open 4AKE chain A as a blue cartoon and closed 1AKE chain A (chain C) as a rose cartoon, with the Ap5A inhibitor (resn AP5) of 1AKE as orange sticks; orient so the LID (122-159) is at the top and the NMP-binding domain (30-59) at the left, looking into the cleft. Figure 2, same orientation: colour both copies by domain, CORE grey80 on both, LID and NMP-binding domain of open 4AKE in light blue and of closed 1AKE in rose, Ap5A orange sticks, so the two domains swinging shut over Ap5A are obvious.

These are the two figures above, both ray-traced (rendered with realistic light and shadow) in PyMOL from this one request; cartoon draws each chain as a ribbon. Rotate the live view as well: from the side you can see the LID close down like a lid on a box.

The ideas behind the picture

• Domains move as rigid bodies. The LID and NMP-binding domain hardly change shape inside themselves. They swing on hinges relative to the CORE. Closing them shuts water out of the active site and brings the phosphates of ATP and AMP together, so the phosphate can transfer.
• Superposition finds the rotation and translation that bring one structure as close as possible to another, for the atoms you tell it to match.
• RMSD is only meaningful with its atom set. The same pair of structures gave 2.07 Å (whole chain, with outlier rejection), 1.36 Å (CORE fit) and 16.24 Å (LID, measured after the CORE fit). None of them is "the" RMSD. When you report an RMSD, say which atoms you fitted, which you measured and whether outliers were rejected.
• Fit on what doesn't move, measure what does. Aligning on a stable core and then measuring the rest, without refitting, is how structural biologists describe domain motions.

What the picture shows, and what it doesn't

• These are two end points, not a movie. The figures don't show the path between open and closed, how fast the enzyme moves, or the intermediate states it passes through in solution.
• Crystal packing (how neighbouring molecules press together in the crystal) can favour one state. Each structure is one snapshot under one set of crystal conditions.
• Ap5A is an inhibitor that mimics both substrates at once. The closed structure is a model of the transition state (the reaction's short-lived halfway point), not a picture of real ATP and AMP mid-reaction.
• The domain boundaries we used (CORE 1–29, 60–121 and 160–214; NMP 30–59; LID 122–159) are the standard definitions for this enzyme. Shifting a boundary by a few residues changes the numbers slightly, not the conclusion.

Going further: which state does AlphaFold predict?

AlphaFold (an AI program that predicts a protein's 3D structure from its amino-acid sequence) predicts one structure per sequence. For an enzyme that moves, which state does it pick? We asked in the same studio (Edit with AI), naming the enzyme by its UniProt entry (UniProt is the main public protein-sequence database):

Also superpose the AlphaFold model of E. coli adenylate kinase (UniProt P69441) onto chain A here with super, matching only the CORE residues 1-29, 60-121 and 160-214. Then, without fitting again, measure with PyMOL rms_cur the C-alpha RMSD of the AlphaFold model's LID (122-159) and NMP-binding domain (30-59) against open 4AKE chain A and against closed 1AKE (chain C). Which state does the AlphaFold model resemble more?

In our run the CORE fit was 1.29 Å over 900 atoms. The model's LID was 15.71 Å from open 4AKE but only 1.11 Å from closed 1AKE. Its NMP-binding domain was 12.13 Å from open and 1.71 Å from closed. The AlphaFold model is closed, even though the prediction contains no ligand. It is a reminder that a predicted structure is one state, not the protein's whole range of shapes.

Your turn

Think like a researcher. Before you ask RBAi, predict: if you superposed 4AKE on 1AKE using only the LID (residues 122–159), what would happen to the CORE RMSD, and why? Then run it in Edit with AI and compare. Next, decide which single number you would put in a paper's abstract to describe this motion, and write one sentence that states it honestly: atoms fitted, atoms measured, value.

Try it

Open RBAi and superpose the two states yourself, starting with step 1. Try cealign or align (two other PyMOL superposition commands) instead of super as well, and see how much the reported RMSD changes for the same two structures.