Multiple pathways of the actin-myosin cycle in energy transduction and the release of orthophosphate in muscle

FIGURE 1. Cartoon representing the sarcomere and its shortening induced by the working stroke of myosin motors. Reciprocal sliding between the actin filaments (white), originating from the Z-line at the sarcomere extremities, and the myosin filaments (black), bound to the M-line at the sarcomere center and carrying two bipolar arrays of myosin motors (represented by their motor domains or sub-fragment 1 S1, red; all actin-attached for simplicity), is powered by the working stroke of the actin-attached myosin motor (red to green oval). The working stroke consists of inter-domain tilting of the lever arm about the catalytic domain, which remains firmly attached to the actin site (gray).

SCHEME 1. 5 step reaction scheme from Dantzig et al., 1992.

FIGURE 2. Schematic drawing of the subdomains within the myosin catalytic domain and their reciprocal structural changes accompanying the working stroke transition. The four subdomains identified by different colors are the N-terminal (black), the upper 50-kDa subdomain (blue), the lower 50-kDa subdomain (gray), and the converter (green). Two (yellow and red) of the structural elements joining the subdomains are visible. The α-helix constituting the lever arm is cyan. The structures are obtained from the scallop myosin: (A) S1 complexed with VO4 3-, representing the pre-working stroke state. (B) Nucleotide-free S1, representing the end-of-stroke state. The vertical arrows indicate the approximate direction of the actin filament axis. The orientation of the two structures is defined by conserving the orientation of the lower 50-kDa relative to actin. The release of Pi is indicated with the dashed arrow. The exit direction is an open question, and more recent evidence (Llinas et al., 2015) indicates that it is opposite (backdoor) to what is shown here. The direction of the movement of the subdomains in the transition between the two states is shown by the short continuous arrows. The ∼70°…

FIGURE 3. Force and velocity transients. (A) Early components of force transients (middle trace in each panel) elicited by a step release (upper trace) superimposed on the steady force of the isometric contraction (T 0) of a single fiber from frog skeletal muscle. Release amplitude per half-sarcomere (hs), 2.3 nm (upper panel) and 6.5 nm (lower panel). The lower horizontal line is the baseline for force. (B) Isotonic velocity transients following steps in force superimposed on the isometric force (T 0) of a single fiber from frog skeletal muscle. Upper trace, stepwise decrease to a force T = 0.5 T 0; middle trace, force baseline; lower traces, change in half-sarcomere length (L) corresponding to steps to the forces indicated by the figures on the right. The figures on the left of the 0.1 T 0 trace show the phases of the transient. Reproduced from Figure 1 of Piazzesi et al. (2002) with permission. (C) Comparison of L 1 (filled circles) and L 2 (filled diamonds) relations from velocity transients with T 1 (open circles) and T 2 (open diamonds) relations from force transients. Reproduced from Figure 4 of Piazzesi et al. (2002) with permission. (D) Rate of early force recovery (r 2) versus…

FIGURE 4. Relevant parameters of the kinetic model of the working stroke. (A) Free energy diagram of the myosin motor states (M1–M5) as a function of the relative position (x) between the myosin motor and the actin monomer. x is set to 0 for the minimum free energy of an attached motor in the state M1. The free energy minima of the various states are separated by a distance z (the step size) = 2.75 nm so that the working stroke of 11 nm is preserved with a number of structural transitions = 4. The thick line marks the axial distribution of motors during the isometric contraction. (B) Functions expressing the x-dependence of the forward (continuous lines) and backward (dashed lines) transitions. The figures indicate the order of the transition. (C) Fractional occupancy of the various states as a function of x during isometric contraction. (D) Sketch of the conformation of the five states (M1–M5) of the myosin motor characterized by orientations of the lever arm separated by angles corresponding to an axial displacement of 2.75 nm of the tip of the lever under zero force. The lower panel shows the fractional occupancy of the different states in isometric contraction. (E) Simulated velocity…

FIGURE 5. Motion of myosin motors during the velocity transient. (A) Force change normalized by isometric force T 0 and length change in nm/hs. (B) Axial X-ray intensity distribution in the region of the M3 reflection recorded at the BioCAT beamline of the APS Synchrotron (Argonne, United States). Colors denote X-ray exposure periods, as shown in (A) brown, L 0; orange, L 2s; magenta, L 2e; and cyan, L 3. (C) Structural organization of myosin motors in the muscle sarcomere at each X-ray exposure, as predicted by the M3 interference fine structure in (B). (A–C) From Figure 1 of Reconditi et al. (2004). (D) Superimposed half-sarcomere shortenings (left panel) following force decreases to three different values (identified by the color code in the inset) and intensity ratio (R M3, right panel) of the higher over the lower angle component of the M3 intensity distribution. From Figure 2A, B of Reconditi et al. (2004).

FIGURE 6. Effect of [Pi] on the isotonic velocity transient. (A) Superimposed isotonic velocity transients following a force step to 0.5 T 0 in control (black) and 10 mM Pi (green). (B) Superimposed phase 2 of the velocity transients in control (black) and in 10 mM Pi (green), which were obtained after subtracting phase-1 and phase-3 shortenings. (C) Relation between the shortening accounted for by the working stroke (L T) and the force expressed in relative units T/T 0 in control (black) and 10 mM Pi (green). (D) Dependence of the rate constant of the working stroke (r 2) on T/T 0 in control (black) and 10 mM Pi (green). (E) Dependence of the rate of phase 3 (r 3) on T/T 0 in control (black) and 10 mM Pi (green). Reproduced from Figures 2, 3 of Caremani et al. (2013) with permission.

FIGURE 7. Effects of [Pi] on the isometric force, ATPase rate, and rate of force change during initial force increase and following a Pi jump. (A) Pi-dependence of isometric force (relative to the force in the control solution, 1 mM Pi). Filled circles, data from Figures 1F, 6A of Caremani et al. (2008). Model predictions: blue line, Scheme 1; red line, Scheme 2. (B) Pi-dependence of the ATPase rate: filled circles, pooled data from Bowater and Sleep (1988), Potma et al. (1995) and Potma and Stienen (1996). Model predictions: blue line, Scheme 1; red line, Scheme 2. Values relative to those in the control solution. (C) Pi-dependences of k TR (the rate of force redevelopment from a large release bringing the force to 0) and k Pi (the rate of force decrease following a Pi jump). Filled circles, observed k TR relation from Figure 6C of Caremani et al. (2008). Model prediction: blue continuous line, Scheme 1; red continuous line, Scheme 2. Open squares, observed k Pi relation from Figure 6 of Dantzig et al. (1992). Model prediction: blue dashed line, Scheme 1; red dashed line, Scheme 2. Modified from Linari et al. (2010).

SCHEME 2. 5 step reaction scheme integrated by a branched pathway accounting for the detachment from a strong bound AM'ADPPi state followed by release of hydrolysis products.

FIGURE 8. Pi transients in isometric contraction and during isovelocity shortening. (A) Force responses to Pi jump (points) imposed in isometric contraction and during shortening at the velocities (ML/s means fiber length/s) indicated on the traces. Records were interpolated by the sum of an exponential and a straight line (continuous line). (B) Relation of k Pi versus shortening velocity. (C) Relation between k Pi and final Pi concentration in isometric contraction (open circles) and during shortening at 0.1 fiber length/s (filled circles). Dashed lines interpolated to data. Continuous lines in (B–C) are the predictions of the model reported in Scheme 1 (reproduced from Figures 3, 4, 8 in Homsher et al. (1997) with permission).

FIGURE 9. Force transient elicited by a step release imposed at different times following a conditioning step. (A) Superimposed records of force responses (lower traces) to (a) a single step release of 7 nm per half-sarcomere (upper traces) and to (b) a step of 2 nm delivered 2 ms after a conditioning step of 5 nm. (B) Superimposed records of force responses to test steps of 2 nm delivered 2, 4, 8, and 15 ms after the conditioning step of 5 nm. Single muscle fiber from Rana esculenta tetanically stimulated at 2.1 μm sarcomere length and 4 °C. Half-sarcomere length changes measured in a selected fiber segment measuring ∼1 mm in length. From Figure 1 in Lombardi et al. (1992).

FIGURE 10. Simplified model with myosin slipping (Reaction Scheme 3). Kinetic scheme with three states of the myosin motor (blue): D, detached state; A1 and A2, low- and high-force states, respectively, attached to an actin monomer (brown). During shortening, the motor attached in the A2 state can slip to the next actin monomer farther from the center of the sarcomere (red) within the same ATPase cycle. The probability of a second slipping to the pink monomer is limited to 1/10 of that of the first slipping. From Figure 4 of Pertici et al. (2018).