Micro- and Macroscale Patterns of Petal Morphogenesis in Nigella damascena (Ranunculaceae) Revealed by Geometric Morphometrics and Cellular Analyses

Petals, the inner organs in a differentiated perianth, generally play an important role in pollinator attraction. As such they exhibit an extraordinary diversity of shapes, sizes, and colors. Being involved in pollinator attraction and reward, they are privileged targets of evolution. The corolla of the Ranunculaceae species Nigella damascena consists of elaborate nectariferous petals, made of a stalk, upper, and lower lips forming a nectar pouch, shiny pseudonectaries, and pilose ears. While the main events of petal development are properly described, a few is known about the pattern of organ size and shape covariation and the cellular dynamics during development. In this study, we investigated the relationships between morphogenesis and growth of N. damascena petals using geometric morphometrics coupled with the study of cell characteristics. First, we found that petal shape and size dynamics are allometric during development and that their covariation suggests that petal shape change dynamics are exponentially slower than growth. We then found that cell proliferation is the major driver of shape patterning during development, while petal size dynamics are mostly driven by cell expansion. Our analyses provide a quantitative basis to characterize the relationships between shape, size, and cell characteristics during the development of an elaborate floral structure. Such studies lay the ground for future evo-devo investigations of the large morphological diversity observed in nectariferous structures, in Ranunculaceae and beyond.

Certain Subclasses of Analytic Multivalent Functions Associated with Petal-Shape Domain

In this article, we introduce a new class of multivalent analytic functions associated with petal-shape region. Furthermore, some useful properties, such as the Fekete–Szegö inequality, and their consequences for some special cases are discussed. For some specific value of function f, we obtain sufficient conditions for multivalent starlike functions connected with petal-shape domain. Finally, in the concluding section, we draw the attention of the interested readers toward the prospect of studying the basic or quantum (or q-) generalizations of the results, which are presented in this paper. However, the (p,q)-variations of the suggested q-results will provide a relatively minor and inconsequential development because the additional (rather forced-in) parameter p is obviously redundant.

Effect of the Quasi-Petal Heat Transfer Tube on the Melting Process of the Nano-Enhanced Phase Change Substance in a Thermal Energy Storage Unit

The melting heat transfer of nano-enhanced phase change materials was addressed in a thermal energy storage unit. A heated U-shape tube was placed in a cylindrical shell. The cross-section of the tube is a petal-shape, which can have different amplitudes and wave numbers. The shell is filled with capric acid with a fusion temperature of 32 °C. The copper (Cu)/graphene oxide (GO) type nanoparticles were added to capric acid to improve its heat transfer properties. The enthalpy-porosity approach was used to model the phase change heat transfer in the presence of natural convection heat transfer effects. A novel mesh adaptation method was used to track the phase change melting front and produce high-quality mesh at the phase change region. The impacts of the volume fraction of nanoparticles, the amplitude and number of petals, the distance between tubes, and the angle of tube placements were investigated on the thermal energy rate and melting-time in the thermal energy storage unit. An average charging power can be raised by up to 45% by using petal shape tubes compared to a plain tube. The nanoadditives could improve the heat transfer by 7% for Cu and 11% for GO nanoparticles compared to the pure phase change material.

Combination of transcriptome sequencing and iTRAQ proteome reveals the molecular mechanisms determining petal shape in herbaceous peony (Paeonia lactiflora Pall.)

The molecular mechanisms controlling petal shape in a herbaceous peony, Paeonia lactiflora Pall., a popular high-grade cut flower worldwide, remain unclear. Here, we selected inner and outer petals from P. lactiflora ‘ZiFengyu’ with an anemone type as the study object. Using transcriptome sequencing and isobaric tags for relative and absolute quantitation proteome, 979 differentially expressed genes and 266 differentially expressed proteins were detected within the inner and outer petals. Of these, the present study identified a key gene APETALA2 that regulates flower shape development. In addition, we obtained a 1935 bp full-length cDNA sequence of APETALA2 by rapid amplification of cDNA ends amplification. Through further validation using quantitative real-time polymerase chain reaction and Western blot analysis, APETALA2 showed a markedly higher expression in outer than that in inner petals. Therefore, the present study indicates that the increased expression of APETALA2 contributes to the formation of petals in P. lactiflora.