Proteins are complex mechanical objects that often must undergo
structural changes to achieve their function. The best example is
the quaternary transition of hemoglobin upon binding
oxygen. The path between the T (deoxy) and R (oxy)
using the Conjugate Peak Refinement(CPR)
yielding a minimum energy path of a quaternary transition.
The result is a continuous "movie" of the T --> R transition at
atomic level of detail.
Many changes occur as originally predicted
by Perutz in 1970. However, the path reveals important aspects of
the transition mechanics that could not have been predicted from the
end-states. The overall T-->R transition can be divided into three
phases of tertiary
change, separated by two major
The quaternary motions are organized as consecutive rotations around
two distinct sets of helices:
First a simultaneous 3 degree rotation of each Alpha-unit around its G-helix, followed by a simultaneous 6 degree rotation of each Alpha/Beta-dimer around its Alpha-H-helix. The resultant of these two sets of rotations is the 15 degree rotation-axis that is often used to relate the two end-states, but is inappropriate to describe the actual motion.
In all movies shown below, the motion is
shown forward and back once (to facilitate viewing in “auto-replay” mode).
The subunit colors are as in the paper (Alpha1 in yellow, Alpha2 in red, Beta1 in blue, Beta2 in green).
The hemes are shown in licorice.
The first quaternary event.
The first major quaternary transition is characterized by a shrinking of the entrance to the central cavity on the Alpha-side. This motions is organized as a 3 degree rotation of each Alpha-unit around its Alpha-G-helix (indicated by a dotted line in this figure).
Relative to its position in the T-state (shown here in color), each
alpha-subunit pivots towards the other, resulting in an intermediate state half-way along
(in grey). In this state, the central channel is closed only
between the alpha-units
(the view here is down
the central channel, along the C2-symmetry axis = purple X).
This motion is shown in Movie1:
The two Alpha-subunits counter-rotate 3 degree around their respective G helices (shown as grey cylinders in the movie), while the Beta-subunits remain stationary. Some tertiary motion (mostly of the N- and C-termini of the Alpha-subunits) accompanies this quaternary event. The view is the same as the figure above, i.e., down the C2-axis (shown as a purple dot).
Similar movie, but looking down the rotation axes, i.e., down the 2 Alpha-G-helices (shown as grey coils in the movie), which thus appear nearly stationary. The view is orthogonal to the C2-axis (shown as a purple rod).
The Beta-subunits do not undergo much change. This rotation brings the Alpha-H-helices into a position where they will be able to serve as axes during the second major quaternary change later in the path (see right panel).
Another view shows the closing of the cavity between the two Alpha-subunits, while the cavity between the b-subunits remain open. The view is the same as in the figure 4A of the paper, down the C2-axis (shown as purple dot).
The second quaternary event.
The second major quaternary event is an abrupt change involving rotation of 6 degrees by each dimer about its Alpha-H-helix (indicated by a dotted line in this figure).
Relative to the intermediate halfway along the path, here in color
the grey one in the left panel), each alpha/beta dimer rotates into the
R-state (shown in grey). The view is orthogonal to the C2-axis (shown
as a purple rod).
This motion is shown in Movie2:
The a1b1 and a2b2 dimers counter-rotate 6 degrees around their respective alpha-H helices (shown as grey cylinders in the movie). Some tertiary motion (a small shift in helices alpha-C as they glide past the beta-FG loop at the "switch" interface) accompanies this quaternary event. The view is the same as the figure above.
Similar movie, but looking down the Alpha1-H-helix (shown as grey coil in the movie), which thus appears nearly stationary while the a1b1 dimer rotates around that helix.
Another view shows the closing of the cavity between the two Beta-subunits, while the cavity between the Alpha-subunits is already closed. The view is the same as in the figure 4B of the paper, down the C2-axis shown as purple dot).
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