Figure 1. Model. (A) Schematic illustration of the geometry showing an actin filament with subunits (monomers) along two right-handed protofilament helices and two-headed myosin motor domains extending from the thick filament backbone. Target zones for myosin head binding indicated by darker monomers. A one-site model with one myosin-binding site per target zone on top and a three-site model with three binding sites per target zone on the bottom is shown. The figure is approximately to scale longitudinally, but the interfilament distance is greatly exaggerated compared with the longitudinal scale. (B) Kinetic scheme for the actin–myosin interaction at the central site of a target zone shown in black (compare Eqs. 4, 5, 6, 7, 8, 9, 10, 11, and 12). Connections of the kinetic schemes to nearest neighbor sites at 5.5 nm on either side of the central site indicated by gray or green arrows and with states and rate functions indexed by superscript p for the site closer to the actin filament plus end (dark gray) and superscript m for the site closer to the minus end (green). A, actin; D, ADP; M, myosin; P/Pi, inorganic phosphate; T, ATP. The symbols ki, k+i, and k-i represent rate constants, whereas KI represents the equilibrium constant for fast equilibria. If an argument (x) is included, this indicates strain dependence. The states MT, MDP, and AMDP are common for all sites in a target zone. The AMDPT state is a transient intermediate and therefore not included in the free energy diagrams in C or in calculations of force or other contractile variables. (C) Free energy diagrams for model with three sites giving three identical sets of diagrams but displaced relative each other along the x axis. Dashed, dotted, and dashed-dotted colored lines represent free energies for the case with nonlinear cross-bridge elasticity (compare Fig. S1 and Eq. 10). Note that the site at the most positive x-value is toward the actin filament minus end. (D) Transition rate functions from state AMDP to AMDL (k+P; Eq. 4) and the reverse rate (k-P; Eq. 5) for the central site shown for linear (full lines) and nonlinear (dashed lines) cross-bridge elasticity. Transition rate functions for peripheral sites have identical shape but are shifted 5.5 nm along the x axis in the positive direction (m-site) or the negative direction (p-site). The stepwise change in rate functions at x = −2.8 nm reflect limitation of the attachment range assumed in the model (compare Månsson et al., 2019). (E) Other rate functions than those shown in D for transitions between states for the central site (Eqs. 7, 8, 9, 10, and 11). Rate functions for linear and nonlinear cross-bridge elasticity shown by full and dashed lines, respectively.
Figure 1.

Model. (A) Schematic illustration of the geometry showing an actin filament with subunits (monomers) along two right-handed protofilament helices and two-headed myosin motor domains extending from the thick filament backbone. Target zones for myosin head binding indicated by darker monomers. A one-site model with one myosin-binding site per target zone on top and a three-site model with three binding sites per target zone on the bottom is shown. The figure is approximately to scale longitudinally, but the interfilament distance is greatly exaggerated compared with the longitudinal scale. (B) Kinetic scheme for the actin–myosin interaction at the central site of a target zone shown in black (compare Eqs. 4, 5, 6, 7, 8, 9, 10, 11, and 12). Connections of the kinetic schemes to nearest neighbor sites at 5.5 nm on either side of the central site indicated by gray or green arrows and with states and rate functions indexed by superscript p for the site closer to the actin filament plus end (dark gray) and superscript m for the site closer to the minus end (green). A, actin; D, ADP; M, myosin; P/Pi, inorganic phosphate; T, ATP. The symbols ki, k+i, and k-i represent rate constants, whereas KI represents the equilibrium constant for fast equilibria. If an argument (x) is included, this indicates strain dependence. The states MT, MDP, and AMDP are common for all sites in a target zone. The AMDPT state is a transient intermediate and therefore not included in the free energy diagrams in C or in calculations of force or other contractile variables. (C) Free energy diagrams for model with three sites giving three identical sets of diagrams but displaced relative each other along the x axis. Dashed, dotted, and dashed-dotted colored lines represent free energies for the case with nonlinear cross-bridge elasticity (compare Fig. S1 and Eq. 10). Note that the site at the most positive x-value is toward the actin filament minus end. (D) Transition rate functions from state AMDP to AMDL (k+P; Eq. 4) and the reverse rate (k-P; Eq. 5) for the central site shown for linear (full lines) and nonlinear (dashed lines) cross-bridge elasticity. Transition rate functions for peripheral sites have identical shape but are shifted 5.5 nm along the x axis in the positive direction (m-site) or the negative direction (p-site). The stepwise change in rate functions at x = −2.8 nm reflect limitation of the attachment range assumed in the model (compare Månsson et al., 2019). (E) Other rate functions than those shown in D for transitions between states for the central site (Eqs. 7, 8, 9, 10, and 11). Rate functions for linear and nonlinear cross-bridge elasticity shown by full and dashed lines, respectively.

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