Figure 1.
Schematic representation of myofibril reorganization in a 2D myocyte.
(A) red: actin; blue: nucleus; green: FAs. The FAs can spread throughout the ECM island (outlined by solid black island). (B) Net force (F) exerted on bound integrins, as determined by the sum of all forces exerted by the anchoring premyofibril vectors, recruits free integrins and promotes growth of FAs. For the purposes of modeling the bound integrins connected to premyofibrils are labeled ρp(r). (C) Continued recruitment of free integrins to the growing FA at the cellular corners is associated with enhanced bundling of the premyofibrils and subsequently increased traction. (D) Built upon the premyofibrillar network, the nascent myofibrils align in parallel and develop into a fully organized bundle, further amplifying local force to result in FA maturation. For the purposes of modeling the bound integrins connected to nascent myofibrils are labeled as ρn(r). (E) Bound integrins with zero net force cannot recruit free integrin and are disassociated from the membrane, leading to release of the attached fiber (F). Consequently, contractile fibers on shorter axes (G) are less bundled than that following the longest diagonal of the cell. (H) Qualitative schematic of model implementation algorithm.
Figure 2.
Simulated dynamics of myofibril organization and immunostaining of actin alignment.
(A) Simulated results for the dynamic profile of myofibril organization in a stair-step-shaped myocyte. Red lines represent the myofibrils, with thicker lines representing regions of denser myofibrils. The grey color scale represents the amount of local parallel coupling of the nascent myofibrils; color values are in arbitrary units normalized to the highest values. As we start with a random distribution of free integrins, initially there were no fibers. The geometrical symmetry break in the stair-cell is so strong that for random initial conditions the fibers generally align with the major diagonal as soon as they are formed. However, nascent myofibrils become latterly coupled throughout the cell as evident by the diffuse grey shading at . As time elapsed, the nascent myofibrils reorganized and oriented themselves along the longest cellular diagonal, and coupled to each other greatly increasing parallel coupling. The steady state fiber organization matches the experimental results. (B) Immunostaining of the actin network from a myocyte with similar shape agrees with the numerical prediction; scale bar: 10 µm.
Figure 3.
Experimental images and model depictions of organization of actin and FAs.
First column: DIC images of micropatterned triangular (A), square (F), and circular (K) myocytes. Second column: Immunostained actin in triangular (B) and square (G) myocytes followed the longest cellular dimension, while actin fibers in the circular myocyte (L) primarily oriented on the 2 to 8 o'clock axis. Third column: Predicted myofibrillar pattern of triangular (C), square (H), and circular (M) myocytes agrees with experimental results. The steady state of the circular cell occurred slower than that of the triangular and square cells. The thickness of the lines is proportional to the myofibril density . The grey color scale represents myofibril bundling, i.e. degree of parallel coupling
. Fourth column: Immunostained vinculin of triangular (D) and square (I) myocytes was concentrated at cellular corners, while two opposing plaques of vinculin localized on the 2 to 8 o'clock axis in the circular (N) myocyte. Fifth column: Simulated FA density (
) at steady state in triangular (E), square (J), and circular (O) cells was consistent with experimental results. The FA distribution in a circular myocyte (O) was expected to break the symmetry. Color values in simulated results are in arbitrary units scaled from 0 to 1; scale bars are
.
Figure 4.
Sarcomeric structure, traction force at peak systole, and model predictions.
First column: Sarcomeric -actinin immunofluorescence delineates the Z-lines in triangular (A), square (F) and circular (K) myocytes. Z-line orientation indicated that the axis of contraction was parallel to the longest axis of the cell. In the circular myocyte, most of the Z-lines aligned on the 1 to 7 o'clock axis with the dominant axis of contraction expected to follow the 4 to 10 o'clock direction. Second column: DIC images of micropatterned triangular (B), square (G), and circular (L) myocytes at full relaxation. Third column: DIC images at full contraction of the triangular (C), square (H), and circular (M) myocytes show the cells shortened about 24%, 18%, and 14% along the longest cell dimension, respectively. Fourth column: The contractile traction map of the triangular (D) and square (I) myocytes displayed high traction stresses at the cellular corners. The contraction map of the circular myocyte (N) indicated that the cell broke radial symmetry, with the principal axis of contraction along the 3 to 9 o'clock axis. Fifth column: Numerical results of predicted traction (T) of triangular (E), square (J), and circular (O) myocytes replicated experimental results. In the fourth and fifth columns, the color scale and arrows represent the magnitude and direction of traction, respectively. Color values in simulated results are in arbitrary units; scale bars are
.
Figure 5.
Testing model assumptions in silico.
(A,B,D,E) Steady state results for different conditions tested in silico, where the red segments correspond to the direction of the all fibers, and the thickness of the red segments is proportional to the density of the fibers. The grey contour represents the degree of parallel coupling. Note that all the values were normalized by the maximum across all the conditions for ease of comparison between them. C) Plot of averaged (over the whole cell) degree of parallel coupling. Stair shape cell: fiber length-force independence, but mutual alignment –solid grey line; fiber length-force independence and no mutual alignment – dashed black line; fiber length-force dependence and mutual alignment - solid black line; no mutual alignment, but fiber length-force dependence - dash-dot grey line; the inset shows the difference in steady state values between the two latter cases. Triangle cell with both fiber length-force dependence and mutual alignment – grey line, triangular markers. Square cell with both fiber length-force dependence and mutual alignment – black line, square markers. Circular cell with fiber length-force dependence, with mutual aligment and no mutual aligment is shown as a black line with circular markers, and a grey line with empy circular markers, respectively. Comparing steady states for stair cells in (A) and (B) illustrates the necessity of fiber length-force dependence, while comparison of circular cells in (D) and (E) illustrates the necessity of mutual alignment of fibers.
Table 1.
Model variables.