Figure 5.
Mathematical framework for FLS growth captures experimental FLS length distribution and growth dynamics.(A) Four smoothed, different example experimental FLS length trajectories (top) and their instantaneous growth velocities (bottom) in different colors. (B) Histogram of measured FLS growth velocities (n = 114,816) from tracked FLS trajectories with maximum likelihood estimation fit of a bi-exponential Laplace distribution. (C) Four randomly selected smoothed example trajectories (top) generated from our sum-product framework with their instantaneous velocities (bottom). We started simulations at random initiation points at 0–20 min. (D) FLS length distribution (blue circles; n = 3,193 observations) and corresponding data from simulating 10,000 trajectories (solid orange line; shaded area is the 95% confidence interval of the histogram bin means). The simulation data histogram was scaled by the ratio between the median FLS lengths larger than 5 µm and the median simulated FLS lengths larger than 5 µm to visualize agreement between theory and experiment. (E) Predicted persistence time distribution (top row, blue solid lines) and length distributions (bottom row, blue solid lines) agree with the experimental distributions (black dots) for the different values of M and N in Fig. 3 E. Values for θ are given in min−1. Persistence time distribution n = 20,679. (F) Comparison of the experimental normalized growth velocity distributions to the simulations for different combinations of number of sum terms M and number of product factors N, using the Kolmogorov-Smirnov goodness-of-fit statistic. Darker blue indicates a better fit. The best fit N for any given M is highlighted by a red dot and follows an approximate square root dependence. Colored squares correspond to the data shown in G. (G) Force/velocity distributions (vel. distrib.) for the five combinations highlighted by colored squares in F. The dashed line is the normalized experimental growth velocity. The inset shows an enlargement of the peak of the distributions indicated by the dashed rectangle. The data used to generate the graphs is available in the Supplemental data.

Mathematical framework for FLS growth captures experimental FLS length distribution and growth dynamics. (A) Four smoothed, different example experimental FLS length trajectories (top) and their instantaneous growth velocities (bottom) in different colors. (B) Histogram of measured FLS growth velocities (n = 114,816) from tracked FLS trajectories with maximum likelihood estimation fit of a bi-exponential Laplace distribution. (C) Four randomly selected smoothed example trajectories (top) generated from our sum-product framework with their instantaneous velocities (bottom). We started simulations at random initiation points at 0–20 min. (D) FLS length distribution (blue circles; n = 3,193 observations) and corresponding data from simulating 10,000 trajectories (solid orange line; shaded area is the 95% confidence interval of the histogram bin means). The simulation data histogram was scaled by the ratio between the median FLS lengths larger than 5 µm and the median simulated FLS lengths larger than 5 µm to visualize agreement between theory and experiment. (E) Predicted persistence time distribution (top row, blue solid lines) and length distributions (bottom row, blue solid lines) agree with the experimental distributions (black dots) for the different values of M and N in Fig. 3 E. Values for θ are given in min−1. Persistence time distribution n = 20,679. (F) Comparison of the experimental normalized growth velocity distributions to the simulations for different combinations of number of sum terms M and number of product factors N, using the Kolmogorov-Smirnov goodness-of-fit statistic. Darker blue indicates a better fit. The best fit N for any given M is highlighted by a red dot and follows an approximate square root dependence. Colored squares correspond to the data shown in G. (G) Force/velocity distributions (vel. distrib.) for the five combinations highlighted by colored squares in F. The dashed line is the normalized experimental growth velocity. The inset shows an enlargement of the peak of the distributions indicated by the dashed rectangle. The data used to generate the graphs is available in the Supplemental data.

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