Changes in morphogen kinetics and pollen grain size are potential mechanisms of aberrant pollen aperture patterning in previously observed and novel mutants of <i>Arabidopsis thaliana</i>

Pollen provides an excellent system to study pattern formation at the single-cell level. Pollen surface is covered by the pollen wall exine, whose deposition is excluded from certain surface areas, the apertures, which vary between the species in their numbers, positions, and morphology. What determines aperture patterns is not understood. Arabidopsis thaliana normally develops three apertures, equally spaced along the pollen equator. However, Arabidopsis mutants whose pollen has higher ploidy and larger volume develop four or more apertures. To explore possible mechanisms responsible for aperture patterning, we developed a mathematical model based on the Gierer-Meinhardt system of equations. This model was able to recapitulate aperture patterns observed in the wild-type and higher-ploidy pollen. We then used this model to further explore geometric and kinetic factors that may influence aperture patterns and found that pollen size, as well as certain kinetic parameters, like diffusion and decay of morphogens, could play a role in formation of aperture patterns. In conjunction with mathematical modeling, we also performed a forward genetic screen in Arabidopsis and discovered two mutants with aperture patterns that had not been previously observed in this species but were predicted by our model. The macaron mutant develops a single ring-like aperture, matching the unusual ring-like pattern produced by the model. The doughnut mutant forms two pore-like apertures at the poles of the pollen grain. Further tests on these novel mutants, motivated by the modeling results, suggested the existence of an area of inhibition around apertures that prevents formation of additional apertures in their vicinity. This work demonstrates the ability of the theoretical model to help focus experimental efforts and to provide fundamental insights into an important biological process.花粉是研究单细胞水平模式形成的极佳模型系统。花粉表面覆盖有花粉外壁（pollen wall exine），其沉积过程会被特定的表面区域——萌发孔（apertures）——阻断；不同物种的萌发孔在数量、位置与形态上均存在显著差异。目前学界尚未明确调控萌发孔模式形成的核心决定因素。 拟南芥（Arabidopsis thaliana）的野生型花粉通常会形成3个沿花粉赤道均匀分布的萌发孔。然而，倍性更高、体积更大的拟南芥突变体花粉，其萌发孔数量可达4个甚至更多。为探索调控萌发孔模式形成的潜在机制，我们基于吉尔勒-迈因哈特（Gierer-Meinhardt）方程组构建了数学模型。该模型能够复现野生型及高倍性拟南芥花粉的萌发孔模式。 随后我们利用该模型进一步探究了可能影响萌发孔模式的几何与动力学因素，发现花粉尺寸以及形态发生素（morphogens）的扩散、降解等部分动力学参数，可能在萌发孔模式形成中发挥关键作用。结合数学建模工作，我们还在拟南芥中开展了正向遗传筛选（forward genetic screen），发现了两种此前未在该物种中被观测到、但被我们的模型预测存在的萌发孔模式突变体。其中macaron突变体可形成单个环状萌发孔，与模型预测的特殊环状模式高度匹配；doughnut突变体则会在花粉粒两极形成两个孔隙状萌发孔。 基于建模结果对这两种新型突变体开展的进一步实验表明，萌发孔周围存在一个抑制区域，可阻止其附近形成额外的萌发孔。本研究证明，理论模型能够助力聚焦实验研究方向，并为解析这一重要生物学过程提供基础性见解。