Spatiotemporal dynamics of a reaction-diffusion model of pollen tube tip growth

Learning Interactions in Reaction Diffusion Equations by Neural Networks

Partial differential equations are common models in biology for predicting and explaining complex behaviors. Nevertheless, deriving the equations and estimating the corresponding parameters remains challenging from data. In particular, the fine description of the interactions between species requires care for taking into account various regimes such as saturation effects. We apply a method based on neural networks to discover the underlying PDE systems, which involve fractional terms and may also contain integration terms based on observed data. Our proposed framework, called Frac-PDE-Net, adapts the PDE-Net 2.0 by adding layers that are designed to learn fractional and integration terms. The key technical challenge of this task is the identifiability issue. More precisely, one needs to identify the main terms and combine similar terms among a huge number of candidates in fractional form generated by the neural network scheme due to the division operation. In order to overcome this barrier, we set up certain assumptions according to realistic biological behavior. Additionally, we use an L2-norm based term selection criterion and the sparse regression to obtain a parsimonious model. It turns out that the method of Frac-PDE-Net is capable of recovering the main terms with accurate coefficients, allowing for effective long term prediction. We demonstrate the interest of the method on a biological PDE model proposed to study the pollen tube growth problem.

Electrifying rhythms in plant cells

Physiological oscillations (or rhythms) pervade all spatiotemporal scales of biological organization, either because they perform critical functions or simply because they can arise spontaneously and may be difficult to prevent. Regardless of the case, they reflect regulatory relationships between control points of a given system and offer insights as read-outs of the concerted regulation of a myriad of biological processes. Here we review recent advances in understanding ultradian oscillations (period < 24h) in plant cells, with a special focus on single-cell oscillations. Ion channels are at the center stage due to their involvement in electrical/excitabile phenomena associated with oscillations and cell-cell communication. We highlight the importance of quantitative approaches to measure oscillations in appropriate physiological conditions, which are essential strategies to deal with the complexity of biological rhythms. Future development of optogenetics techniques in plants will further boost research on the role of membrane potential in oscillations and waves across multiple cell types.

Constrained Nonlinear and Mixed Effects Integral Differential Equation Models for Dynamic Cell Polarity Signaling

Polar cell growth is a process that couples the establishment of cell polarity with growth and is extremely important in the growth, development, and reproduction of eukaryotic organisms, such as pollen tube growth during plant fertilization and neuronal axon growth in animals. Pollen tube growth requires dynamic but polarized distribution and activation of a signaling protein named ROP1 to the plasma membrane via three processes: positive feedback and negative feedback regulation of ROP1 activation and its lateral diffusion along the plasma membrane. In this paper, we introduce a mechanistic integro-differential equation (IDE) along with constrained semiparametric regression to quantitatively describe the interplay among these three processes that lead to the polar distribution of active ROP1 at a steady state. Moreover, we introduce a population variability by a constrained nonlinear mixed model. Our analysis of ROP1 activity distributions from multiple pollen tubes revealed that the equilibrium between the positive and negative feedbacks for pollen tubes with similar shapes are remarkably stable, permitting us to infer an inherent quantitative relationship between the positive and negative feedback loops that defines the tip growth of pollen tubes and the polarity of tip growth.

Fertilization in flowering plants: an odyssey of sperm cell delivery

In light of the available discoveries in the field, this review manuscript discusses on plant reproduction mechanism and molecular players involved in the process. Sperm cells in angiosperms are immotile and are physically distant to the female gametophytes (FG). To secure the production of the next generation, plants have devised a clever approach by which the two sperm cells in each pollen are safely delivered to the female gametophyte where two fertilization events occur (by each sperm cell fertilizing an egg cell and central cell) to give rise to embryo and endosperm. Each of the successfully fertilized ovules later develops into a seed. Sets of macromolecules play roles in pollen tube (PT) guidance, from the stigma, through the transmitting tract and funiculus to the micropylar end of the ovule. Other sets of genetic players are involved in PT reception and in its rupture after it enters the ovule, and yet other sets of genes function in gametic fusion. Angiosperms have come long way from primitive reproductive structure development to today's sophisticated, diverse, and in most cases flamboyant organ. In this review, we will be discussing on the intricate yet complex molecular mechanism of double fertilization and how it might have been shaped by the evolutionary forces focusing particularly on the model plant Arabidopsis.

Exocytosis and Endocytosis: Yin-Yang Crosstalk for Sculpting a Dynamic Growing Pollen Tube Tip

The growing pollen tube has become one of the most fascinating model cell systems for investigations into cell polarity and polar cell growth in plants. Rapidly growing pollen tubes achieve tip-focused cell expansion by vigorous anterograde exocytosis, through which various newly synthesized macromolecules are directionally transported and deposited at the cell apex. Meanwhile, active retrograde endocytosis counter balances the exocytosis at the tip which is believed to recycle the excessive exocytic components for multiple rounds of secretion. Therefore, apical exocytosis and endocytosis are the frontline cellular processes which drive the polar growth of pollen tubes, although they represent opposite vesicular trafficking events with distinct underpinning mechanisms. Nevertheless, the molecular basis governing the spatiotemporal crosstalk and counterbalance of exocytosis and endocytosis during pollen tube polarization and growth remains elusive. Here we discuss recent insight into exocytosis and endocytosis in sculpturing high rates of polarized pollen tube growth. In addition, we especially introduce the novel integration of mathematical modeling in uncovering the mysteries of cell polarity and polar cell growth.