Catch-slip bonds can be dispensable for motor force regulation during skeletal muscle contraction

It is intriguing how multiple molecular motors can perform coordinated and synchronous functions, which is essential in various cellular processes. Recent studies on skeletal muscle might have shed light on this issue, where rather precise motor force regulation was partly attributed to the specific stochastic features of a single attached myosin motor. Though attached motors can randomly detach from actin filaments either through an adenosine triphosphate (ATP) hydrolysis cycle or through “catch-slip bond” breaking, their respective contribution in motor force regulation has not been clarified. Here, through simulating a mechanical model of sarcomere with a coupled Monte Carlo method and finite element method, we find that the stochastic features of an ATP hydrolysis cycle can be sufficient while those of catch-slip bonds can be dispensable for motor force regulation.

Figure 1

(a) Mechanical model of a sarcomere: the thin filament (green) is modeled as an elastic rod with axial rigidity, EA, the thick filament (gray) is considered as rigid, and motors (blue) are modeled as elastic springs [5]. The thin filament slides toward the M band at velocity $V$, upon filament load $P$. (b) Myosin motors are assigned with three states within a chemomechanical cycle. (c) Force-stretch relation for a myosin motor. $x$ is the stretch on the motor. A detached motor behaves like a linear spring given by the line $oa$, which is at $x=0$ without force. An attached motor bound with ADP behaves as a bilinear spring given by the curve $b-c-d$, which is at the isometric state when $x=0$. When the ADP is stochastically released, for example, at $f$, the bound motor without ADP behaves as a linear spring given by the dashed line $ef$. The elastic stretch on a motor is zero at $b, -5.6\mathrm{nm}$ at $c$, and $-7\mathrm{nm}$ at $d$, respectively. The shaded area corresponds to the released elastic energy of a bound motor with ADP, $\mathrm{\Delta }\phi$, at a force of $F_r$. (d) Variation of the ADP release rate, $k_{\mathrm{ADP}}$, with motor force $F$ based on Eq. (3).

Figure 2

Variation of the number of attached motors, $N_{\mathrm{on}}$, vs time $t$ at four different filament loads. In the simulation, the total number of motors is fixed, which are all initially attached to the thin filament. Case 1: motors detach from the thin filament either through the ATP hydrolysis cycle or as catch-slip bonds. Case 2: motors detach from the thin filament only through the ATP hydrolysis cycle. Case 3: motors detach from the thin filament only through catch-slip bond breaking. Case 4: motors can detach from the thin filament either through ATP hydrolysis or as a slip bond.

Figure 3

(a) Average number of attached myosin motors vs the filament load, (b) shortening velocity of the thin filament vs the filament load, and (c) motor forces vs the filament load, with diamonds for Case 1, circles for Case 2, squares for Case 3, and triangles for Case 4. (d) Motor forces vs the filament loads at different $\xi$ when motors can detach from thin filaments only as catch-slip bonds. The dashed line in (a) is a linear fit to the data points of Cases 1, 2, and 4. The dashed curve in (b) fits to the data points of Cases 1, 2, and 4 with the Hill's law [37]. Error bars represent the standard error of the mean (SEM).

Figure 4

(a) Percentage of closed bonds and (b) force per closed bond vs external loads at different $\xi$. Inset: The schematics of a cluster of catch-slip bonds under load, $P_N$.

Figure 5

Effects of breaking rates of slip bonds: (a) Average number of attached myosin motors vs the filament load; (b) Shortening velocity of the thin filament vs the filament load. Error bars represent the standard of the mean (SEM).

Figure 6

Flow chart of the simulation scheme of a coupled Monte Carlo method and finite element method.