Department of Chemistry, University of Washington, Seattle, Washington.
Pacific Northwest National Laboratory, EMSL, Richland, Washington.
Biophys J. 2022 Jun 21;121(12):2389-2397. doi: 10.1016/j.bpj.2022.05.018. Epub 2022 May 21.
Ripples arise at edges of petals of blooming Lilium casablanca flowers and at edges of torn plastic sheets. In both systems, ripples are a consequence of excess length along the edge of a sheet. Through the use of time-lapse videos of blooming lilies and published images of torn plastic sheets, we find that ripples in both systems are well described by the scaling relationship a∝w(L-w), where a is amplitude, w is wavelength, and L is arc length. A phenomenological relationship previously reported for self-similar ripple patterns, namely ⟨a⟩∝⟨w⟩, can be recovered by assuming that buckling stress is constant. Excess length along petal edges can also influence their overall Gaussian curvature, such that petals invert from a cup shape to a saddle shape upon blooming. Previous simulations of these shape changes have assumed that petal thickness decreases at least quadratically. Here, we evaluate tomograms of several varieties of lily buds and find that this assumption is valid along the short axis of the buds, but not the long axis. A challenge of employing traditional tomography methods to measure petal thickness is that the sample is destroyed; a single bud cannot be followed through the entire blooming process. To address this challenge, we provide proof of principle that the nondestructive, label-free method of x-ray tomography produces high-contrast three-dimensional scans on time scales short enough to follow lily blooming.
盛开的卡萨布兰卡百合花的花瓣边缘和撕裂的塑料片边缘会产生波纹。在这两种系统中，波纹都是由于沿片材边缘的多余长度引起的。通过使用盛开的百合花的延时视频和已发布的撕裂塑料片的图像，我们发现这两种系统中的波纹都可以很好地用标度关系 a∝w(L-w) 来描述，其中 a 是振幅，w 是波长，L 是弧长。先前报道的自相似波纹图案的唯象关系 ⟨a⟩∝⟨w⟩可以通过假设屈曲应力是常数来恢复。花瓣边缘的多余长度也会影响它们的整体高斯曲率，使得花瓣在开花时从杯形变为鞍形。这些形状变化的先前模拟假设花瓣厚度至少按二次方减小。在这里，我们评估了几种百合花芽的断层扫描图像，发现这个假设在芽的短轴方向上是有效的，但在长轴方向上则不然。采用传统断层扫描方法测量花瓣厚度的一个挑战是样本被破坏；单个芽不能在整个开花过程中被跟踪。为了解决这个挑战，我们提供了一个原理证明，即非破坏性的、无标记的 X 射线断层扫描方法可以在足够短的时间尺度上产生高对比度的三维扫描，足以跟踪百合花的开放过程。
