Figure 1. A conceptual geometric model of microtubule self-organization.

(A) Drosophila epidermal cells elongate between stages 12 and 15 of embryonic development, during which the microtubules become more aligned. The scale bar is 10 µm. (B) Stretching a circular cell of radius 1 by a factor $b>1$ deforms the initially uniform microtubule angle distribution into the hairyball distribution, Equation 1. (C) The experimental microtubule angle distribution (green) from stage 12–15 Drosophila epidermal cells and the hairyball (dashed black) are in good agreement up to eccentricity 0.95 . For each eccentricity, the displayed experimental distribution is the mean distribution averaged across cells with the set eccentricity (±0.025 for $ecc=0.7-0.95$ and ±0.005 for $ecc=0.98$), and is produced as described in the Materials and methods. The number of cells per eccentricity ranged from 348 to 2748.