Mechanosensitive self-assembly of myosin II minifilaments

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate nonmuscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the cross-bridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds on a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching.

Figure 1

Assembly model. (a) Artistic three-dimensional rendering of a myosin minifilament that contracts actin fibers. (b) Schematic representation of a slice consisting of two antiparallel protofilaments with indicated lengths (minifilament length $L$, bare zone length $L_b$, parallel stagger $l_p$, antiparallel stagger $l_a$, and rod length $l_r$). (c) The graph on which the assembly occurs. The light red and the dark blue disks represent sites with opposing myosin heads. The solid red lines in the middle represent strong interactions between antiparallel myosin rods, the dotted blue lines represent interactions caused by a favorable parallel overlap of myosin rods and the dashed green lines represent weak antiparallel interactions. (d) Artistic representation of intermediates (right), with corresponding regions of the graph indicated (left). Top: Initial nucleation seed of two antiparallel molecules. Middle: Inner core of the minifilament containing three of the nucleation seeds. Bottom: One protofilament.

Figure 2

Parallel cluster model (PCM) for force generation. (a) The PCM considers the three most important states of the cross-bridge cycle. The reaction rates $k_{01}$ and $k_{10}$ are constant, while the rate $k_{20}$ depends on force as given in (2). The rates $k_{12},k_{21}$ are high compared to the other rates. (b) Mean dwell time of a single myosin head on actin assuming catch-slip bond (${\mathrm{\Delta }}_c=0.92$), a pure slip bond (${\mathrm{\Delta }}_c=0$), and a pure catch-bond (${\mathrm{\Delta }}_c=1$).

Figure 3

Assembly dynamics. (a) Time course of the mean minifilament size for dimensionless association rate $\kappa =0.018$ (black line) with standard deviation (gray area). (b) Mean number of assembled myosins as a function of $\kappa$. (c) Variance of $N$ as a function of $\kappa$. A peak at ${\kappa }_c\approx 0.018$ indicates the transition between partially and fully assembled minifilaments. (d) Relaxation time of the minifilament as a function of $\kappa$ as obtained from a saturating exponential fit to the mean size of an assembling cluster.

Figure 4

Equilibrium distribution $p$ and dissociation rates $\alpha$ as a function of association rate $\kappa$. (a) Equilibrium distribution $p\left(N\right)$ of the assembly model for different values of $\kappa$. (b) Resulting dissociation rates $\alpha (\langle N\rangle )$ [compare Eq. (5)] that are used in the mean-field model or in a coarse-grained model.

Figure 5

Steady states. (a) Mean values and variances of the full model for different forces $F$ and on-rate $k_{\mathrm{on}}$ ($k_{\mathrm{off}}^0=10{\mathrm{s}}^{-1}$). The red dashed line represents the critical on-rate $k_{\text{on}}$ for a cluster without actin, whereas the solid line represents the critical on-rate as a function of force. (b) Equilibrium distribution $p(i,N)$ (top row) and phase portrait (bottom row) in the three different regions. In the top row the solid white line depicts the nullcline of $i$, whereas the blue line depicts the nullcline of $N$. The dashed white line depicts the nullcline of $i$ at zero force. The red circles denote stable fixed points of the mean-field theory for the indicated force (middle) and zero force (right). The phase portraits (bottom row) illustrate how a change in force and on-rate affects the flow lines (blue) and the nullclines (red region $\langle \dot{i}\rangle <0$, blue region $\langle \dot{N}\rangle <0$).

Figure 6

(a) Time-dependent mean number of fluorescently labeled myosin proteins per minifilament starting from a nonfluorescent minifilament drawn from the equilibrium distribution at $k_{\text{on}}=0.4{\mathrm{s}}^{-1}$ for different forces and with the myosins heads blocked in the unbound state. The transparently colored regions denote the region of one standard deviation. (b) Results for fitting functions of type $N[1-exp(-t/\tau \left)\right]$ to the mean number of fluorescently labeled myosins for different on-rates and forces. The dashed lines indicate the fluorescence recovery if the motor cycle is turned off, which is always significantly faster, even at forces where the minifilament is not bound to actin on both sides but typically only on one. The dotted lines indicate the result when using pure catch-bonds.