Static versus stochastic heterogeneity of sarcomere motion.
(A) Concatenated contraction periods from a representative ROI in one beating cell on a 15 kPa substrate showing sarcomere length changes during activation, labeled as ΔSLi,k with sarcomere number i and contraction cycle number k. Each box is 0.6 s in width and −0.5 to 0.5 µm in height. Insets show correlation scatter plots from the ΔSLi,k-pairs marked in red (serial correlation) and blue (mutual correlation) respectively in A. The respective Pearson correlation coefficient r(i,j),(k,l) (see Eq. 1) is noted in the graphs. (B) (left column) Average serial correlation rsbetween ΔSL and V (i = j) of individual sarcomere from different contraction cycles (k ≠ l), quantifying the variability of motion patterns of individual sarcomere across contraction cycles. (Middle column) Average mutual correlation rmof ΔSL and V between all sarcomeres in a myofibril (i ≠ j) in each contraction cycle (k = l), quantifying the variability between motions of neighboring sarcomeres in each contraction cycle. (Right column) Ratio R between average mutual and serial correlation of sarcomere ΔSL and V respectively. R is a measure for the degree of stochasticity in the motions, purely stochastic when R = 1, or largely static when R ≪ 1. (C) Average Pearson correlation coefficients of ΔSL/Vi,k and ΔSL/Vj,l. The x-axis shows the mutual correlation of the motion of different sarcomeres (i ≠ j), the y-axis the serial correlation of the different cycles of one sarcomere (i = j), while (k ≠ l). The set of dashed lines mark regions of stochastic heterogeneity (right) and static heterogeneity (left). The yellow star marks data of the ROI in A. B,C show data of 2,062 ROIs (5 kPa: N = 134, 9 kPa: 442, 15 kPa: 339, 29 kPa: 393, 49 kPa: 449, 85 kPa: 305). Boxes show quartiles, red lines the median, green triangles the mean and whiskers the 5th and 95th percentile of the distribution per condition. Statistical analysis was performed using the Kruskal-Wallis and Dunn’s posthoc tests, with significance set at p < 0.01. All differences were significant. (D,E) Illustrative sketches of sarcomere length changes ΔSL in different contraction cycles, assuming purely static heterogeneity (D) and purely stochastic heterogeneity (E). Color maps denotes sarcomere contractile strength.