New method to obtain small parameter power series expansions of Mathieu radial and angular functions

Larsen, Todd M.; Erricolo, Danilo; Uslenghi, Piergiorgio L. E.

doi:10.1090/s0025-5718-08-02114-5

Cited by 3 publications

(1 citation statement)

References 26 publications

(41 reference statements)

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“…denotes a dimensionless parameter (not to be confused with a wavenumber!). For small q, analytical approximations of the Mathieu functions can be obtained 24,44,45 and matched with the eigenfunctions Ψ mem e;n and Ψ mem o;n at the boundary μ = μ 0 .…”

Section: Mass Conservationmentioning

confidence: 99%

Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

et al. 2020

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In the Caenorhabditis elegans zygote, PAR protein patterns, driven by mutual anatagonism, determine the anterior-posterior axis and facilitate the redistribution of proteins for the first cell division. Yet, the factors that determine the selection of the polarity axis remain unclear. We present a reaction-diffusion model in realistic cell geometry, based on biomolecular reactions and accounting for the coupling between membrane and cytosolic dynamics. We find that the kinetics of the phosphorylation-dephosphorylation cycle of PARs and the diffusive protein fluxes from the cytosol towards the membrane are crucial for the robust selection of the anterior-posterior axis for polarisation. The local ratio of membrane surface to cytosolic volume is the main geometric cue that initiates pattern formation, while the choice of the long-axis for polarisation is largely determined by the length of the aPAR-pPAR interface, and mediated by processes that minimise the diffusive fluxes of PAR proteins between cytosol and membrane.

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Section: Mass Conservationmentioning

confidence: 99%

Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

et al. 2020

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Highly Canalized MinD Transfer and MinE Sequestration Explain the Origin of Robust MinCDE-Protein Dynamics

Halatek¹,

Frey²

2012

Cell Reports

133

276

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Min-protein oscillations in Escherichia coli are characterized by the remarkable robustness with which spatial patterns dynamically adapt to variations of cell geometry. Moreover, adaption, and therefore proper cell division, is independent of temperature. These observations raise fundamental questions about the mechanisms establishing robust Min oscillations, and about the role of spatial cues, as they are at odds with present models. Here, we introduce a robust model based on experimental data, consistently explaining the mechanisms underlying pole-to-pole, striped, and circular patterns, as well as the observed temperature dependence of the oscillation period. Contrary to prior conjectures, the model predicts that MinD and cardiolipin domains are not colocalized. The transient sequestration of MinE and highly canalized transfer of MinD between polar zones are the key mechanisms underlying oscillations. MinD channeling enhances midcell localization and facilitates stripe formation, revealing the potential optimization process from which robust Min-oscillations originally arose.

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Mode analysis of a confocal elliptical dielectric nanowire coated with double-layer graphene

Cheng

Xue

Wei

et al. 2019

Optics Communications

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New method to obtain small parameter power series expansions of Mathieu radial and angular functions

Cited by 3 publications

References 26 publications

Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

Geometric cues stabilise long-axis polarisation of PAR protein patterns in C. elegans

Highly Canalized MinD Transfer and MinE Sequestration Explain the Origin of Robust MinCDE-Protein Dynamics

Mode analysis of a confocal elliptical dielectric nanowire coated with double-layer graphene

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