Pollen wall patterns as a model for biological self-assembly.

We are still far from being able to predict organisms' shapes purely from their genetic codes. While it is imperative to identify which encoded macromolecules contribute to a phenotype, determining how macromolecules self-assemble independently of the genetic code may be equally crucial for understanding shape development. Pollen grains are typically single-celled microgametophytes that have decorated walls of various shapes and patterns. The accumulation of morphological data and a comprehensive understanding of the wall development makes this system ripe for mathematical and physical modeling. Therefore, pollen walls are an excellent system for identifying both the genetic products and the physical processes that result in a huge diversity of extracellular morphologies. In this piece, I highlight the current understanding of pollen wall biology relevant for quantification studies and enumerate the modellable aspects of pollen wall patterning and specific approaches that one may take to elucidate how pollen grains build their beautifully patterned walls.

Mimicry of a biophysical pathway leads to diverse pollen-like surface patterns.

A ubiquitous structural feature in biological systems is texture in extracellular matrix that gains functions when hardened, for example, cell walls, insect scales, and diatom tests. Here, we develop patterned liquid crystal elastomer (LCE) particles by recapitulating the biophysical patterning mechanism that forms pollen grain surfaces. In pollen grains, a phase separation of extracellular material into a pattern of condensed and fluid-like phases induces undulations in the underlying elastic cell membrane to form patterns on the cell surface. In this work, LCE particles with variable surface patterns were created through a phase separation of liquid crystal oligomers (LCOs) droplet coupled to homeotropic anchoring at the droplet interface, analogously to the pollen grain wall formation. Specifically, nematically ordered polydisperse LCOs and isotropic organic solvent (dichloromethane) phase-separate at the surface of oil-in-water droplets, while, different LCO chain lengths segregate to different surface curvatures simultaneously. This phase separation, which creates a distortion in the director field, is in competition with homeotropic anchoring induced by sodium dodecyl sulfate (SDS). By tuning the polymer chemistry of the system, we are able to influence this separation process and tune the types of surface patterns in these pollen-like microparticles. Our study reveals that the energetically favorable biological mechanism can be leveraged to offer simple yet versatile approaches to synthesize microparticles for mechanosensing, tissue engineering, drug delivery, energy storage, and displays.

Pollen Cell Wall Patterns Form from Modulated Phases.

The ornately geometric walls of pollen grains have inspired scientists for decades. We show that the evolved diversity of these patterns is entirely recapitulated by a biophysical model in which an initially uniform polysaccharide layer in the extracellular space, mechanically coupled to the cell membrane, phase separates to a spatially modulated state. Experiments reveal this process occurring in living cells. We observe that in ∼10% of extant species, this phase separation reaches equilibrium during development such that individual pollen grains are identical and perfectly reproducible. About 90% of species undergo an arrest of this process prior to equilibrium such that individual grains are similar but inexact copies. Equilibrium patterns have appeared multiple times during the evolution of seed plants, but selection does not favor these states. This framework for pattern development provides a route to rationalizing the surface textures of other secreted structures, such as cell walls and insect cuticle.

First-order patterning transitions on a sphere as a route to cell morphology.

We propose a general theory for surface patterning in many different biological systems, including mite and insect cuticles, pollen grains, fungal spores, and insect eggs. The patterns of interest are often intricate and diverse, yet an individual pattern is robustly reproducible by a single species and a similar set of developmental stages produces a variety of patterns. We argue that the pattern diversity and reproducibility may be explained by interpreting the pattern development as a first-order phase transition to a spatially modulated phase. Brazovskii showed that for such transitions on a flat, infinite sheet, the patterns are uniform striped or hexagonal. Biological objects, however, have finite extent and offer different topologies, such as the spherical surfaces of pollen grains. We consider Brazovskii transitions on spheres and show that the patterns have a richer phenomenology than simple stripes or hexagons. We calculate the free energy difference between the unpatterned state and the many possible patterned phases, taking into account fluctuations and the system's finite size. The proliferation of variety on a sphere may be understood as a consequence of topology, which forces defects into perfectly ordered phases. The defects are then accommodated in different ways. We also argue that the first-order character of the transition is responsible for the reproducibility and robustness of the pattern formation.