A mechanistic motor-clutch model that explains cell shape dynamics to cyclic stretch

FIGURE 1:. Cellular morphological response to applied mechanical cyclic stretch. (A) In vitro HUVEC exposed to no stretch control (top) and 10% stretch conditions (bottom). Representative images show overall culture perpendicular realignment (left) and individual cell actin fiber realignment (right, yellow circle). (B) Three general processes by which changes in the actin cytoskeleton (actin fibers) can result in reogranization of cells in response to cyclic stretch. Fibers may lengthen or shorten due to polymerization or depolymerization, based on their orientation with respect to the direction of applied stretch. Fibers may rotate as a function of applied strain. Fibers may disassemble in directions where applied strain is greatest and reassemble in directions where strain is reduced.

FIGURE 2:. Experimental application of mechanical cyclic stretch to cultured cells. (A) Schematic of custom mechanical stretch device capable of applying cyclic strain to cell cultures. Device consists of two clamps attached to a motorized stage, where one clamp moves cyclically to stretch a PDMS slab. The PDMS slab contains wells in which cells are seeded. (B) Graphical representation of cyclic stretch waveform. Cultures are stretched from initial length L0 to final length Lε according to a sine function with period t.

FIGURE 3:. (A) The motor-clutch model of Chan and Odde (2008) was adapted to incorporate the effects of cyclic stretch on actin bundle dynamics. The original model of Chan and Odde is shown in black and consists of an F-actin bundle, molecular clutches, and myosin motors. Myosin motors pull on the actin bundle, which moves at a velocity Vactin. In the diagram, only one of the 50 clutches is shown for simplicity. Clutches can bind from the substrate to the actin bundle with a probability of kon. One end of each clutch originates from the current location of the substrate (Xsub), and other end of each clutch binds to the actin bundle at X(i). At the moment of binding, there is no load on the clutch, so Xsub = X(i). Owing to the relative motion of the substrate and actin, after bonding the clutch can be stretched (i.e., Xsub ≠ X(i)) and the clutch applies forces to the actin bundle and substrate. In the adapted model used here, the substrate anchor is moved sinusoidally to introduce stretch (shown in red). (B) Illustration of three forms of cyclic stretch: purely uniaxial, simple elongation, and equibiaxial.

FIGURE 4:. In vitro cellular morphology changes as a function of applied cyclic stretch. (A) Representative images of HUVEC exposed to no stretch control and 10% stretch conditions. (B–D) Cellular morphological measurements collected as a function of applied cyclic stretch. From left to right, visual descriptions of each measurement collected, average measurements (* denotes statistical significance with p value < 0.0125 according to Bonferroni multiple comparisons correction; bars on data points represent SEM), and representative frequency distribution histograms from no stretch control and 10% stretch conditions, n = 50–100 cells for each condition.

FIGURE 5:. Experimentally measured actin fiber and/or cell orientation compared with our simulation results. Angle is relative to the direction of applied stretch. Because different stretch amplitudes or durations can yield different fiber orientations, the maximum value of the average fiber orientation reported in a study was used. (A) Actin fiber and/or cell orientation following exposure to simple elongation cyclic stretch. (B) Actin fiber and/or cell orientation following exposure to purely uniaxial cyclic stretch.

FIGURE 6:. Simulated actin bundle reorientation as a function of cyclic stretch type, amplitude, and substrate stiffness. Bundles with initial orientations ranging from 0 to 90° are grouped into cells to create a single figure representing a whole cell. Single bundles in each cell represent the average final orientation and length of 10 simulated bundles (n = 10). Individual bundles were modeled using the adapted motor-clutch model with an initial length of 5000 nm, orientation ranging from 0 to 90°, and on substrate stiffnesses ranging from 0.1 to 10 kPa. Modeled actin bundles were then exposed to simulated simple substrate elongation (A), purely uniaxial cyclic stretch (B–D), or equibiaxial cyclic stretch (E) with frequency of 1 Hz and variable amplitude, following which bundle length and final orientation were collected. Red circles around bundles represent average size of bundles under no stretch control condition for each substrate stiffness.

FIGURE 7:. Actin bundle reorientation as a function of cyclic stretch frequency. Actin bundles are modeled with 10% simple elongation cyclic stretch for 24 h on a substrate stiffness of 10 kPa. (A) Reorien­tation over time with variable cyclic stretch frequency (top) and resultant characteristic time required for reorientation, or time required for a bundle to reach an orientation that is equal to 98% of its steady state orientation (bottom). (B) Reorientation as a function of number of cyclic stretch cycles with variable stretch frequency (top) and resultant characteristic number of cycles required for reorientation, or number of cycles required for a bundle to reach 98% of its steady state orientation (bottom).

FIGURE 8:. Simulated actin bundle reorientation as a function of motor-clutch model myosin motor function. (A) Actin bundle final orientation as a function of cyclic stretch and myosin motor stall force, Fm. (B) Average final bundle orientation as a function of stretch amplitude and myosin motor stall force, Fm.

FIGURE 9:. Timing of clutch bond failure influences direction of fiber alignment. A clutch unbinds as the substrate is stretching (A), allowing the substrate to move relative to the fiber (B). The clutch bond reforms (C), allowing the fiber and substrate to move together, where (D) the final position of the fiber has rotated relative to its initial position (dotted line).

FIGURE 10:. Proposed mechanism for changes in actin bundle orientation following exposure to cyclic stretch. (A–C. top row) Detachment events, moments where the actin bundle is completely detached from the substrate (i.e., no bound clutches), are counted during both the stretching and relaxing phase of the cyclic stretch regime for bundles with initial orientations over the initial 1000 s. (D–F, middle row) Relative differences in stretching-phase detachment events and relaxing-phase detachment events are plotted; differences > 0 predict perpendicular reorientation and differences <0 predict parallel reorientation. (G–I, bottom row) Simultaneously, actin bundle reorientation is tracked over a course of 24 h of cyclic stretch. (A, D, G, left column) Perpendicular realignment of all actin bundles on stiff substrates (10 kPa). Detachment events are significantly increased during the stretching phase compared with the relaxing phase, which corresponds to rapid perpendicular realignment. (B, E, H, middle column) Parallel realignment of actin bundles on soft substrates (0.1 kPa). For many bundles, detachment events are increased during the relaxing phase of stretching, which corresponds to…