Figure 1.
Structure of S1 of myosin II obtained by fitting the EM data[7].
S1 comprises a heavy chain, an essential light chain (ELC, blue thin line), and a regulatory light chain (RLC, dark yellow thin line). The heavy chain is composed of the lever-arm domain (red thick line) and the motor domain. In the motor domain, the N-terminal subdomain (pink), the upper 50 kDa subdomain (orange), and the lower 50 kDa subdomain (purple) are drawn with thick lines. The 50 kDa cleft is the interspace between the upper and lower 50 kDa subdomains. The nucleotide binding pocket lies between the upper 50 kDa subdomain and the N-terminal subdomain. The actin-binding interface of myosin includes the region around the 50 kDa cleft, loop 2, loop 3, and other loops.
Figure 2.
The kinetic network among actomyosin states considered in the present simulation.
Each state is defined by the nucleotide state and the myosin conformation, and and
are rates of transitions between actomyosin states.
Figure 3.
The setup for the Langevin molecular dynamics simulations of actomyosin.
An S1 of myosin II (red) with an essential light chain (ELC, blue) and a regulatory light chain (RLC, yellow) is placed on an actin filament (green), which lies along the direction.
s of the actin filament are connected to spatially fixed points by springs, and the lever-arm tip of myosin is constrained to move along a line that runs parallel to the actin filament. The angle around the
-axis is denoted by
.
Figure 4.
Free-energy landscapes of actin-myosin interactions.
Two-dimensional free-energy landscapes are drawn in the plane of the coordinate of the center of mass of the myosin head as contour maps in units of
(right), and one-dimensional free-energy landscapes on the coordinate
(left). Landscapes in A. Mpre.ADP.Pi (top), A.Mpost.ADP (middle), and A.Mclosed (bottom).
Figure 5.
One-dimensional free-energy landscapes in different actomyosin states.
Free-energy landscapes (A) in A.M.ADP.Pi with M being Mpre (dotted) and Mpost (dashed), (B) in A.M.ADP with M being Mpre (dotted), Mpost (dashed), and Mclosed (solid), and (C) in A.M with M being Mpost (dashed) and Mclosed (solid).
Figure 6.
Monte Carlo simulation of a combined process of diffusion of myosin head along landscapes and transitions among landscapes.
(A) Two example trajectories of myosin movement. Trajectories starting from the A.Mpre.ADP.Pi state and ending in the A. Mrigor state (left), and their close-up from A.Mclosed to A.Mrigor (right). Horizontal mesh lines are drawn every 5.5 nm. (B) The distribution of displacement of myosin head after the system reaches the A.Mclosed state. 8,000 trajectories starting from random positions in the A.Mpre.ADP.Pi state were used to calculate the distribution.
Figure 7.
Contribution of lever-arm swing to the net displacement.
(A) Position near the lever-arm tip and position of the center of mass of the myosin motor domain
are illustrated. (B) Free-energy landscapes drawn in the plane of
in the A.Mpre.ADP.Pi state (left) and in the A.Mclosed state (right). The diagonal line of
is drawn to emphasize that free-energy minima are located at
.
Figure 8.
Importance of conformational flexibility and electrostatic interactions for the global gradient of the landscape.
(A) Simulated free-energy landscapes in the A.Mclosed state assuming the structurally fluctuating parts of myosin and the N-terminus of actin to be disordered without guidance of the Gō-like potentials (black solid), assuming the structurally fluctuating parts of myosin to be disordered but the N-terminus of actin to fluctuate around the estimated conformation by following the Gō-like potential (black dashed), assuming myosin to fluctuate around the estimated conformation and the N-terminus of actin to be disordered (red solid), and assuming loop 2 and loop 3 of myosin and the N-terminus of actin to be disordered with other parts fluctuating around the estimated conformation by following the Gō-like potential (red dashed). (B) Simulated free-energy landscapes in the A.Mclosed state for 25 mM KCl solution (Debye length 1.9 nm, black line) and for 100 mM KCl solution (Debye length 0.95 nm, red line).
Figure 9.
Illustration of a cycle of the suggested myosin II movement.
The myosin structure is schematically represented as a composite of S2 (green) and S1, which is further composed of motor domain (black oval) and lever arm (blue). Black lines represent the free-energy landscapes for the myosin motor domain. (A) Myosin with ADP and Pi binds weakly to actin at around . (B) After the release of ADP and Pi, myosin begins to move along the actin filament, showing the biased Brownian motion. (C) Myosin reaches the strong binding site at
and turns into the rigor state. (D) After binding ATP, myosin detaches from the actin filament and goes through the recovery stroke, which should change the orientation of the motor domain. (E) The myosin searches for the next binding site on the actin filament through the swinging motion of S1 and S2. (F) Because of the tilted orientation of the motor domain, myosin tends to bind to the next binding site at
. In this way, the recovery stroke shown in D plays a positive role in generating the net displacement of myosin via cycles of ATP reactions.