Modeling myosin Va liposome transport through actin filament networks reveals a percolation threshold that modulates transport properties

FIGURE 1:. Schematic of the simulations. (A) A random mesh of actin filaments span a spherical region (partially cut away for visualization purposes) of radius 10 μm (magenta). Fluid liposomes, of 350 nm diameter, are transported (blue) by 10 myoVa motors, undergo tug-of-wars (red), or diffuse according to a coarse-grained model. 2–μm diameter spherical targets (gray) are distributed evenly over the surface of the sphere, and are hit (blue) if touched by a liposome. A simulation of 100 liposomes navigating a network of N = 25 actin filaments is shown (see Supplemental Movie S7 for a movie of the simulation). Actin filament thickness is exaggerated for visualization purposes; arrows indicate filament plus ends. (B) Schematic of state transitions in the model. Liposomes in the transport state (blue) have myoVa motors engaged with a single actin filament. If a motor engages with a second actin filament, a tug-of-war (red) is initiated. Tug-of-wars may be resolved with motors remaining engaged with the original filament (straight outcome), switching to the new filament (turn outcome), or detaching. In the latter case, the liposome enters the diffusion state (yellow). The coarse-grained model…

FIGURE 2:. Increasing actin network density causes a change in liposome motion. In each panel (A–C), to show the variability of liposome trajectories, three liposome trajectories are shown on the same actin network. Only actin filaments engaged by the liposome are pictured in panels B and C. A. Liposomes in the diffusion state (yellow spheres) describe a random walk. This is rarely observed in our simulations at any actin density. (B) Liposomes transported along a single actin filament (yellow arrow with arrow head indicating plus-end) adopt the transport state (blue spheres). This is observed in our simulations at low actin density. (C) At high actin density, liposomes transition between transport (blue spheres) and tug-of-war (red spheres) states, resulting in a random walk as they switch actin filaments once the tug-of-war is resolved. Actin filament thickness is exaggerated for visualization purposes (the magnification call-out in C shows actual size). Liposome position is shown at equally spaced intervals of Δt = 0.75s, and Gaussian random noise of SD σ =10 nm is added for visualization purposes. Small white arrows indicate liposome starting position.

FIGURE 3:. Actin network density triggers a shift in liposome state distribution. The average state of a simulated liposome shifts from being almost exclusively transport at low actin density to a mix of transport and tug-of-war at higher density. There is very little diffusion at any density. Inset shows a diagram of the model states and transitions. Error bars (SEM) are smaller than the symbols.

FIGURE 4:. A change in the number of actin filaments accessible for transport underlies a phase transition in myoVa-based transport with increasing actin density. Different quantities for liposome motion, i.e., liposome speed (A), MSD exponent (B), SD of MSD (C), and number of targets hit by liposomes at the network boundary (D) show a change in scaling as best described by two different power laws similarly to the change in scaling that occurs in the number of accessible actin, Nc ≈ 60 actin filaments (E) (see text for details). The blue-shaded region is where power law 1 applies, and the red-shaded region is where power law 2 applies for the accessible actin. Error bars show SEM. White circles show values for a single actin filament. Schematics of accessible actin (F), represented as the number of potential transport paths on a given actin network (left), and as a graph (right). Top shows a cartoon with 4 actin filaments as a demonstration. In this network, actin filaments 1 and 2 are within reach of a myoVa on the liposome surface, rB (i.e., distance from liposome center to the tip of myoVa on the liposome surface; see SM for details), at their nearest point, while actin filaments 1 and…

FIGURE 5:. A schematic of a percolation phase transition on a network with random connections. (A) A cartoon of N = 15 vertices (black circles), with an increasing number of edges, where an edge (line) connects two vertices. The giant component is the largest number of edge connected vertices (red circles and lines). z equals the average number of edges per vertex within the network. (B) Plot of the size of the giant component as a proportion of the total number of vertices versus z for networks with different numbers of vertices, N. As N approaches infinity, the size of the giant component becomes nonzero above a critical number of edges, the percolation threshold, and networks switch from being subcritical to supercritical.

FIGURE 6:. Percolation in accessible actin. (A–C) Histograms of the proportion of accessible actin within 10,000 networks for various network densities. On a subcritical network (A, N = 35), the histogram has a mode of 1. On a supercritical network (B and C, N = 70 and 125, respectively), the histogram is bimodal. (D) Plotting the mode(s) of the distribution as a function of the number of actin filaments shows the percolation threshold, Nc = 58, and the transition from subcritical to supercritical networks. Note that to calculate the accessible proportion of the actin network, we subtract 1 from accessible actin and divide by the total number of filaments.

FIGURE 7:. A fivefold increase in liposome size decreases the percolation threshold Nc, and the transition between scaling regimes, by a factor of five. (A) Histograms of accessible actin as a proportion of the total number of actin filaments within the network switch from being unimodal to bimodal at a critical network size of Nc = 11 filaments (see Figure 6). (B) The average state of a simulated liposome shifts from being almost exclusively transport to a mix of transport and tug-of-war as the number of actin filaments increases past Nc. Error bars (SEM) are smaller than the symbols. (C) Different quantities describing liposome motion (described in detail in main text) show a change in scaling similar to that which occurs in the number of accessible actin (bottom graph). White circles show predicted values for a single actin filament. Each transition occurs at a network size roughly fivefold less than for smaller liposomes (see Figure 6). Error bars show SEM. Power law fits in C are: power law 1, 350 N–0.06 (Speed), 1.2 N0 (MSD exponent), 0.28 N0.13 (SD MSD exponent), 0.88 N0.38 (Targets Hit),0.94 N0.32 (Accessible Actin); power law 2, 350–100(N–17)0.23 (Speed), 1.20–0.029 (N–22)0.45 (MSD…

FIGURE 8:. By varying actin density, cells can switch the functional role of the actin network to regulate intracellular transport.