Cortical geometry may influence placement of interface between Par protein domains in early Caenorhabditis elegans embryos

Dawes, Adriana T.; Iron, David

doi:10.1016/j.jtbi.2013.04.024

Cited by 15 publications

(26 citation statements)

References 30 publications

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“…The model organizes Par proteins and actomyosin into functional modules, with cortical flow induced by local gradients of actomyosin making it an emergent property of the model. As discussed in earlier papers (Dawes and Munro 2011;Dawes and Iron 2013), bistable kinetics in the Par protein interactions are required for the observed dynamics.…”

Section: Discussionmentioning

confidence: 84%

“…Please see Dawes and Munro (2011), Dawes and Iron (2013) for a more detailed discussion. Briefly, we treat ParA, ParP and actomyosin as functional modules and do not explicitly model the individual proteins.…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…Here, we assume actomyosin assembly dynamics can be positively regulated by ParA, in addition to the negative assembly regulation by ParP used in our previous model (Dawes and Iron 2013). Based on theoretical analysis of cytokinetic rings (Carlsson 2006), we assume that tension due to actomyosin contractility is directly proportional to actomyosin density.…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…Based on theoretical analysis of cytokinetic rings (Carlsson 2006), we assume that tension due to actomyosin contractility is directly proportional to actomyosin density. Combining that with the standard constitutive relationship that holds that velocity is linearly proportional to the gradient of tension, we assume that advection is directly proportional to the local spatial gradient of actomyosin (Dawes and Iron 2013).…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…In this study, we are focusing only on the initial symmetry breaking event during the early establishment phase. In our previous study (Dawes and Iron 2013), we used a similar model but for the purposes of studying mechanisms of halting cortical flow, well after the initial symmetry breaking event. We use similar equations for the Par protein dynamics, but in this paper we have modified the form of the equations for actomyosin regulation.…”

mentioning

confidence: 99%

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Actomyosin Regulation and Symmetry Breaking in a Model of Polarization in the Early Caenorhabditis elegans Embryo

Kravtsova

Dawes

2014

Bull Math Biol

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Polarization, whereby a cell defines a spatial axis by segregating specific determinants to distinct regions, is an essential and highly conserved biological process. The process of polarization is initiated by a cue that breaks an initially symmetric distribution of determinants, allowing for a spatially asymmetric redistribution. The nature of this cue is currently not well understood. Utilizing the conservation of polarization process and its determinants, we theoretically investigate the nature of the cue and the regulation of contractility that enables the establishment of polarity in early embryos of the nematode worm Caenorhabditis elegans (C. elegans). Our biologically based model, which consists of coupled partial differential equations, suggests that a biochemical but not mechanical cue is sufficient for symmetry breaking, and inhibition of contractile elements by specific determinants is needed for sustained spatial redistribution.

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Section: Discussionmentioning

confidence: 84%

Section: The Mathematical Modelmentioning

confidence: 99%

Section: The Mathematical Modelmentioning

confidence: 99%

Section: The Mathematical Modelmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Actomyosin Regulation and Symmetry Breaking in a Model of Polarization in the Early Caenorhabditis elegans Embryo

Kravtsova

Dawes

2014

Bull Math Biol

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From Random Walks to Fully Anisotropic Diffusion Models for Cell and Animal Movement

Painter

Hillen

2018

Modeling and Simulation in Science, Engineering and Technology

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Long time behavior and stable patterns in high-dimensional polarity models of asymmetric cell division

Morita

Seirin-Lee

2021

J. Math. Biol.

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Asymmetric cell division is one of the fundamental processes to create cell diversity in the early stage of embryonic development. During this process, the polarity formation in the cell membrane has been considered as a key process by which the entire polarity formation in the cytosol is controlled, and it has been extensively studied in both experiments and mathematical models. Nonetheless, a mathematically rigorous analysis of the polarity formation in the asymmetric cell division has been little explored, particularly for bulk-surface models. In this article, we deal with polarity models proposed for describing the PAR polarity formation in the asymmetric cell division of a C. elegans embryo. Using a simpler but mathematically consistent model, we exhibit the long time behavior of the polarity formation of a bulk-surface cell. Moreover, we mathematically prove the existence of stable polarity solutions of the model equation in an arbitrary high-dimensional domain and analyse how the boundary position of polarity domain is determined. Our results propose that the existence and dynamics of the polarity in the asymmetric cell division can be understood universally in terms of basic mathematical structures.

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Cortical geometry may influence placement of interface between Par protein domains in early Caenorhabditis elegans embryos

Cited by 15 publications

References 30 publications

Actomyosin Regulation and Symmetry Breaking in a Model of Polarization in the Early Caenorhabditis elegans Embryo

Actomyosin Regulation and Symmetry Breaking in a Model of Polarization in the Early Caenorhabditis elegans Embryo

From Random Walks to Fully Anisotropic Diffusion Models for Cell and Animal Movement

Long time behavior and stable patterns in high-dimensional polarity models of asymmetric cell division

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