Figure 1.
Crystal structures of E. coli AK.
(A) Open conformation without ligand (PDBid: 4ake). The position of P-loop is indicated. (b) Closed conformation with Ap5A represented by sticks (PDBid: 1ake). The ATP and AMP moieties are encircled. Three relatively rigid domains, designated CORE, AMPbd, and LID, are colored by green, cyan, and magenta, respectively.
Figure 2.
PMF along the strings and the corresponding domain motions.
(Top) PMFs along the snapshots of the strings for (A) apo and (B) holo-AK at t = 0 (initial path), 2, 4, 6, 8, 10, 12 (MFEP) ns. The indices of string images are numbered from the open (PDBid: 4ake) to closed crystal structures (PDBid: 1ake). Partially-closed state of apo-AK and a substantial PMF barrier of holo-AK are encircled. (Bottom) Projections of MFEP onto the space defined by the distances of mass centers between the LID-CORE and AMPbd-CORE domains, for (C) apo and (D) holo-AK. The black curves indicate the initial paths (t = 0), and the red curves are the MFEPs (t = 12 ns). The PMF is visualized by the colored contour lines (delineating regions of low energy (blue) to regions of high energy (red)).
Figure 3.
PMFs of the domain motions and the RMSF along the MFEP.
(Top) PMF along the MFEP as a function of the inter-domain distances between (A) the LID-CORE and (B) AMPbd-CORE domains. The blue and red curves illustrate the results for apo-AK and holo-AK, respectively. The error bars are the statistical uncertainties relative to the PMF minimum. Note that the uncertainties are small because the domains were restricted to the regions around the MFEP. (Bottom) The RMSF of the atoms along the MFEP is shown as a function of the MFEP images for (C) apo and (D) holo-AK. The “cracked” regions with large RMSF values, around the LID-CORE hinge and P-loop, are encircled.
Figure 4.
Two-dimensional PMF surface of the motion of the ligand along the MFEP.
(A) PMF is projected onto the MFEP images and onto the 1st PC of the xyz-coordinates of the mass center of the AMP adenine. The PMF is represented by the colored contour lines. (B) Tens of the MD snapshots are superimposed at (left image), and 4 snapshots shows the misbinding between the AMP ribose and Asp84 at
(right image). The hydrogen bonds are indicated by the dashed yellow lines.
Figure 5.
Committor tests characterizing the TSE.
(A) The binned distributions of the final structures after 10 ns unrestrained MD simulations (blue bars), assigned by index of the nearest MFEP image (i.e., classified by the Voronoi tessellation). The MD simulations were executed from different initial distributions (red bars) at , 33, and 34. (B) The average structures of the MFEP images at
(before the TSE), and 34 (after the TSE). The ligand and the residues of Thr31, Lys57, Arg88, Gly85, and Gln92 are represented by sticks. The hydrogen bonds are indicated by the dashed yellow lines.
Figure 6.
Dehydration of an occluded water around the P-loop.
The isosurface representation of the 3D distribution function of water oxygen (red) and hydrogen (white) around the P-loop at (A) , (B) 41, and (C) 42. The surfaces show the areas in which the atoms are distributed four times as probably as in the bulk phase. For comparison, the oxygens of crystal waters are shown for (D) the open (PDBid: 4ake) and (E) closed conformations (PDBid: 1ake). An occluded water molecule at
and the corresponding crystal water of the open form are indicated by the circles. (F) Two-dimensional PMF surface as a function of the MFEP images and the distances of the LID-CORE domains. The PMF is represented by the colored contour lines. Regions of physical events (AMP-binding and dehydration) are encircled.