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

Tian, Chenwei; Shi, Qingyan; Cui, Xinping; Guo, Jingzhe; Yang, Zhenbiao; Shi, Junping

doi:10.1007/s00285-019-01396-7

Cited by 14 publications

(18 citation statements)

References 49 publications

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“…The generation of theoretical models by mathematical analysis has been employed as a useful tool in biological studies to better understand the molecular basis of cells. More importantly, it helps to develop a testable hypothesis, apply the modeling on broader similar biological systems and stimulate new experiments ( Marco et al, 2007 ; Altschuler et al, 2008 ; Brannmark et al, 2017 ; Luo et al, 2017 ; Tian et al, 2019 ).…”

Section: Mathematical Modeling Of Exocytosis and Endocytosis During Pmentioning

confidence: 99%

“…The model then is employed to reproduce the connection between pollen tube polarity switch during growth guidance and exocytic parameters of the tip growth. The stimulating results from the modeling reveal a central role of exocytosis in coordinating pollen tube tip growth and guidance ( Luo et al, 2017 ; Tian et al, 2019 ). Nevertheless, the model is only a simplified framework without considering endocytosis, calcium, pH, phosphoinositides and so forth which are also critical for pollen tube growth and guidance.…”

Section: Mathematical Modeling Of Exocytosis and Endocytosis During Pmentioning

confidence: 99%

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

2020

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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.

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Section: Mathematical Modeling Of Exocytosis and Endocytosis During Pmentioning

confidence: 99%

Section: Mathematical Modeling Of Exocytosis and Endocytosis During Pmentioning

confidence: 99%

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

2020

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“…By using Fourier series, we have the following results regarding the eigenvalues of linearized systems (3.1) and (3.3). The proof is similar to the one of [45,Lemma 4.1], thus we omit the proof here.…”

Section: Pattern Formation In Scalar Modelsmentioning

confidence: 89%

“…The integral form also appears as nonlocal competition for the resource or a nonlocal crowding effect in a scalar model of bacteria colonies [4,14,15,43], and further studies have been conducted for diffusive competition model [34] or predator-prey model with nonlocal crowding effect in prey population [8,30]. Another reaction-diffusion model with effect of spatial average was proposed in [1] where the integral term represents the total amount of cytoplasmic molecules in a feedback loop, see also [45] for a more recent study.…”

Section: Introductionmentioning

confidence: 99%

Effect of spatial average on the spatiotemporal pattern formation of reaction-diffusion systems

Shi

Song

2020

Preprint

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Some quantities in the reaction-diffusion models from cellular biology or ecology depend on the spatial average of density functions instead of local density functions. We show that such nonlocal spatial average can induce instability of constant steady state, which is different from classical Turing instability. For a general scalar equation with spatial average, the occurrence of the steady state bifurcation is rigorously proved, and the formula to determine the bifurcation direction and the stability of the bifurcating steady state is given. For the two-species model, spatially non-homogeneous time-periodic orbits could arise due to spatially non-homogeneous Hopf bifurcation from the constant equilibrium. Examples from a nonlocal cooperative Lotka-Volterra model and a nonlocal Rosenzweig-MacArthur predator-prey model are used to demonstrate the bifurcation of spatially non-homogeneous patterns.

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“…The study of vegetation system in arid and semi-arid area is helpful for us to better understand the internal mechanism of evolution of vegetation system, to a certain extent, which can provide a certain indicative role for vegetation protection, so as to provide a certain reference value for the study of ecosystem robustness. Mathematical models, especially partial differential equation models [3,25,28,5,9,14,11], have been proven to be a very useful tool in explaining the evolution mechanisms of biological system including vegetation ecosystem.…”

mentioning

confidence: 99%

Interactions of time delay and spatial diffusion induce the periodic oscillation of the vegetation system

Sun

Jin

2022

DCDS-B

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Empirical data exhibit a common phenomenon that vegetation biomass fluctuates periodically over time in ecosystem, but the corresponding internal driving mechanism is still unclear. Simultaneously, considering that the conversion of soil water absorbed by roots of the vegetation into vegetation biomass needs a period time, we thus introduce the conversion time into Klausmeier model, then a spatiotemporal vegetation model with time delay is established. Through theoretical analysis, we not only give the occurence conditions of stability switches for system without and with diffusion at the vegetation-existence equilibrium, but also derive the existence conditions of saddle-node-Hopf bifurcation of non-spatial system and Hopf bifurcation of spatial system at the coincidence equilibrium. Our results reveal that the conversion delay induces the interaction between the vegetation and soil water in the form of periodic oscillation when conversion delay increases to the critical value. By comparing the results of system without and with diffusion, we find that the critical value decreases with the increases of spatial diffusion factors, which is more conducive to emergence of periodic oscillation phenomenon, while spatial diffusion factors have no effects on the amplitude of periodic oscillation. These results provide a theoretical basis for understanding the spatiotemporal evolution behaviors of vegetation system.

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

Cited by 14 publications

References 49 publications

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

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

Effect of spatial average on the spatiotemporal pattern formation of reaction-diffusion systems

Interactions of time delay and spatial diffusion induce the periodic oscillation of the vegetation system

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