Figures and data
Sarcomere tracking in genetically engineered Z-line labeled iPSC-derived cardiomyocytes on micropatterned soft gels.
(A) Sketch of a human cardiomyocyte (CM) adhering to a micro-patterned gel (top) and sarcomere structure in relaxed and contracted state (bottom). (B) ACTN2-Citrine cardiomyocytes (culture day 20) on a polyacrylamide gel substrate (Young’s modulus: 15 kPa), patterned with rectangular stripes of Synthemax (70 × 10 µm). More than 50% of the stripes were typically occupied by single cardiomyocytes. Inset: zoomed-in view. (C) Tracking of sarcomere motion: (Top) blend of high-speed confocal movie of a CM adherent to a 15 kPa substrate (left) and deep-learning (3D U-Net)-based segmentation of sarcomere Z-bands (right) with line of interest (yellow). (Bottom) Intensity extracted along line of interest (LOI). Inset shows representative section of the Z-band intensity profile. (D-E) Confocal images of representative ACTN2-Citrine-labeled CMs with corresponding Z-band segmentation and LOIs (red lines). (G-I) Z-band trajectories tracked along the LOI. (J-0) Overlay plots of single sarcomere length change ΔSL(t) for all tracked sarcomeres in the marked LOIs (first 5 seconds in J-L, zoomed in M-0). Colored lines are individual sarcomere length changes; black lines display average length changes. Contraction intervals are marked by a blue background. Sarcomere popping events are marked with asterisks. Conditions (substrate stiffness): 5 kPa (D,G,J,M); 15 kPa (physiological): (E,H,K,N); 85 kPa (F,I,L,0).
Analysis of sarcomere length change dynamics.
(A-C) Phase-space plots of sarcomere length change ΔSL vs. velocity V for three representative LOIs from CMs on substrates of increasing stiffness (same LOIs as in Fig. 1). Gray lines show individual sarcomere dynamics, black lines average dynamics. Colored dots mark maximal and minimal values of ΔSL and V for individual sarcomere trajectories, with colors corresponding to data in E and G. (D) Box plot of maximal average contractions 
Static versus stochastic heterogeneity in the popping dynamics.
(A) Representative time-series of sarcomere length changes ΔSL of a myofibril in one representative cardiomyocyte on a 30 kPa substrate. Popping events, defined as sarcomere elongations beyond 0.25 µm within one contraction cycle, are marked in red. Contraction intervals are marked with a blue background. (B) Correlation analysis showing mutual correlation (rm) versus serial correlation (rs). The x-axis shows the mutual correlation of motion between different sarcomeres (i ≠ j), the y-axis shows the serial correlation of different cycles of one sarcomere (i = j, k ≠ l). Dashed lines delineate regions of static heterogeneity (left) and stochastic heterogeneity (right). Data points are colored by substrate stiffness (5-85 kPa). (C) Ratio R between average mutual and serial correlation of ΔSL, serving as a measure for the degree of stochasticity in motions, for different substrate stiffnesses. (D,E) Illustrative computer-generated sketches of sarcomere length changes ΔSL in different contraction cycles for purely static heterogeneity (D) and purely stochastic heterogeneity (E). Color bar denotes sarcomere contractile strength. (F) Zoomed view of consecutive experimentally observed contraction cycles showing popping events (red shaded regions) where sarcomeres elongated beyond the threshold of 0.25 µm during contraction. (G) Overall popping frequencies for different substrate conditions. (H) Popping frequency as a function of sarcomere equilibrium length SL0. Lines show averages for different substrate stiffnesses, with underlying distribution of equilibrium lengths shown below in gray. (I,J) Probability density distributions of time lag (I) and distance (J) between popping events for single LOI compared with corresponding geometric distributions (red lines). Data and statistics: Panels B,C,G-J show data from 2,321 LOIs (5 kPa: 184, 9 kPa: 580, 15 kPa: 392, 29 kPa: 319, 49 kPa: 503, 85 kPa: 343). Box plots show quartiles, mean (triangle) and median (line), with whiskers representing the 5th and 95th percentiles. Statistical analysis was performed using Kruskal-Wallis and Dunn’s post hoc tests, with significance set at p < 0.05. All differences were significant.
Mesoscopic model of coupled sarcomeres with non-monotonic force-velocity dynamics and comparison with data.
(A) Schematic of the myofibril model where each sarcomere comprises three parallel components: an active force generator, creating force Fa, a viscous element creating force Fd, and passive elastic element, creating force Fs. Sarcomeres are mechanically coupled in series; such that an external force Fm generated by elastic substrate deformation is transmitted uniformly through all sarcomeres in the chain. (B) Activation imposes a time-dependent modulation of the active force throughout the contraction cycles, with a waveform c(t). (C) Smooth curves: Activation-dependent force-velocity curves showing an S-shaped non-monotonic relationship with two stable branches and an unstable region with a negative-slope; the force-velocity relations are color-coded by activation level. Superimposed trajectories (gray) are trajectories of 20 individual sarcomeres, generated by Eq. 2. The black trajectory is the myofibril average, and one sarcomere is highlighted in red. (D-F) Experimental recordings and corresponding model outputs for cells on soft (5 kPa), intermediate (15 kPa), and stiff (85 kPa) substrates showing timeseries of ΔSL/length x with blue-shaded contraction intervals (experiment) or c(t) (model), together with the associated v-x trajectories in phase space; colored traces depict individual sarcomeres, and black traces denote cycle averages. (G-H) Extrema (maximum and minimum) of length x and velocity v per contraction cycle for individual sarcomeres and for the myofibril average as a function of substrate stiffness kl; dashed lines indicate the average, solid lines show individual-sarcomere values, colored shaded regions denote the standard deviation, and points with error bars display the experimental data median and inter-quantile range.
Simulation of static and stochastic heterogeneity in sarcomere dynamics.
(A-D) Top panels: overlaid timeseries of individual sarcomere length changes (colored curves) and the ensemble average (thick black curve). Bottom panels: trajectories in phase space (length change vs. velocity) of individual sarcomeres (gray) and ensemble average (black). (A) Uniform ensemble (no noise, no force variability). (B) Stochastic heterogeneity driven by noise only. (C) Static heterogeneity driven by intrinsic force variability (σa) only. (D) Mixed, static and stochastic heterogeneity with both noise and force variability. (E) Serial correlation rsversus mutual correlation rm across load levels and force variability; marker size encodes the dimensionless simulated substrate stiffness kl, and color shade indicates the standard deviation of the multiplicative factor modulating each sarcomere’s active force. Dashed lines mark the transition from purely static heterogeneity (R = 0) to purely stochastic heterogeneity (R = 1). Circles denote simulations with noise/stochastic fluctuations, and crosses denote deterministic simulations without noise/stochastic fluctuations.
