scholarly journals On the Necessary Conditions for Non-Equivalent Solutions of the Rotlet-Induced Stokes Flow in a Sphere: Towards a Minimal Model for Fluid Flow in the Kupffer’s Vesicle

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Yunay Hernández-Pereira ◽  
Adán O. Guerrero ◽  
Juan Manuel Rendón-Mancha ◽  
Idan Tuval
Keyword(s):  
Fluid Flow ◽  
Symmetry Breaking ◽  
Stokes Problem ◽  
Superposition Principle ◽  
Vortical Flow ◽  
Biophysical Model ◽  
Rigid Sphere ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle ◽  
General Conditions

The emergence of left–right (LR) asymmetry in vertebrates is a prime example of a highly conserved fundamental process in developmental biology. Details of how symmetry breaking is established in different organisms are, however, still not fully understood. In the zebrafish (Danio rerio), it is known that a cilia-mediated vortical flow exists within its LR organizer, the so-called Kupffer’s vesicle (KV), and that it is directly involved in early LR determination. However, the flow exhibits spatio-temporal complexity; moreover, its conversion to asymmetric development has proved difficult to resolve despite a number of recent experimental advances and numerical efforts. In this paper, we provide further theoretical insight into the essence of flow generation by putting together a minimal biophysical model which reduces to a set of singular solutions satisfying the imposed boundary conditions; one that is informed by our current understanding of the fluid flow in the KV, that satisfies the requirements for left–right symmetry breaking, but which is also amenable to extensive parametric analysis. Our work is a step forward in this direction. By finding the general conditions for the solution to the fluid mechanics of a singular rotlet within a rigid sphere, we have enlarged the set of available solutions in a way that can be easily extended to more complex configurations. These general conditions define a suitable set for which to apply the superposition principle to the linear Stokes problem and, hence, by which to construct a continuous set of solutions that correspond to spherically constrained vortical flows generated by arbitrarily displaced infinitesimal rotations around any three-dimensional axis.

scholarly journals Symmetry breaking cilia-driven flow in the zebrafish embryo

2012 ◽  
Vol 705 ◽  
pp. 26-45 ◽  
Author(s):  
Andrew A. Smith ◽  
Thomas D. Johnson ◽  
David J. Smith ◽  
John R. Blake
Keyword(s):  
Symmetry Breaking ◽  
Experimental Studies ◽  
Vital Role ◽  
Asymmetric Flow ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle ◽  
Posterior Tilt ◽  
Left Right Asymmetry ◽  
Internal Arrangement ◽  
Anterior Posterior

AbstractFluid mechanics plays a vital role in early vertebrate embryo development, an example being the establishment of left–right asymmetry. Following the dorsal–ventral and anterior–posterior axes, the left–right axis is the last to be established; in several species it has been shown that an important process involved with this is the production of a left–right asymmetric flow driven by ‘whirling’ cilia. It has previously been established in experimental and mathematical models of the mouse ventral node that the combination of a consistent rotational direction and posterior tilt creates left–right asymmetric flow. The zebrafish organizing structure, Kupffer’s vesicle, has a more complex internal arrangement of cilia than the mouse ventral node; experimental studies show that the flow exhibits an anticlockwise rotational motion when viewing the embryo from the dorsal roof, looking in the ventral direction. Reports of the arrangement and configuration of cilia suggest two possible mechanisms for the generation of this flow from existing axis information: (a) posterior tilt combined with increased cilia density on the dorsal roof; and (b) dorsal tilt of ‘equatorial’ cilia. We develop a mathematical model of symmetry breaking cilia-driven flow in Kupffer’s vesicle using the regularized Stokeslet boundary element method. Computations of the flow produced by tilted whirling cilia in an enclosed domain suggest that a possible mechanism capable of producing the flow field with qualitative and quantitative features closest to those observed experimentally is a combination of posteriorly tilted roof and floor cilia, and dorsally tilted equatorial cilia.

scholarly journals Chemosensing versus mechanosensing in nodal and Kupffer's vesicle cilia and in other left–right organizer organs

2019 ◽  
Vol 375 (1792) ◽  
pp. 20190566 ◽  
Author(s):  
Julyan H. E. Cartwright ◽  
Oreste Piro ◽  
Idan Tuval
Keyword(s):  
Fluid Flow ◽  
Chemical Species ◽  
Body Plan ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle ◽  
Left And Right

How is sensing carried out by cilia in the mouse node, zebrafish Kupffer's vesicle and similar left–right (LR) organizer organs in other species? Two possibilities have been put forward. In the former, cilia would detect some chemical species in the fluid; in the latter, they would detect fluid flow. In either case, the hypothesis is that an imbalance would be detected between this signalling coming from cilia on the left and right sides of the organizer, which would initiate a cascade of signals leading ultimately to the breaking of LR symmetry in the developing body plan of the organism. We review the evidence for both hypotheses. This article is part of the Theo Murphy meeting issue ‘Unity and diversity of cilia in locomotion and transport’.

Abstract 936: Inhibition of the Endoplasmic Reticulum Calcium ATP-ase Affects the Early Steps of Left-Right Patterning in Zebrafish Embryos.

Circulation ◽  
2007 ◽  
Vol 116 (suppl_16) ◽  
Author(s):  
Jil A Kreiling ◽  
Zaneta L Balantac ◽  
Andrew Crawford ◽  
Jamal Toure ◽  
Alper Celik ◽  
...  
Keyword(s):  
Endoplasmic Reticulum ◽  
Fluid Flow ◽  
Zebrafish Embryos ◽  
Calcium Signals ◽  
Subsequent Decrease ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle ◽  
Laterality Defects ◽  
Er Calcium

Vertebrates develop well defined and conserved left-right (L-R) asymmetries of the heart, gut and brain. Calcium signals play a role in the specification of L-R asymmetry, by translating cilia-dependent fluid flow into asymmetric patterns of gene expression. We aimed to determine the role of early calcium signals on the L-R patterning in zebrafish embryos. Calcium signals were manipulated in zebrafish embryos using thapsigargin, an inhibitor of the endoplasmic reticulum (ER) calcium ATP-ase pump. The embryos were treated with 0.5 μM thapsigargin during early gastrulation (4 – 6 hpf), mid-gastrulation (6 – 8 hpf), late gastrulation (8 –10 hpf) or early somitic stages (10 –12 hpf). The phenotype was analyzed with subtractive imaging, immunolabeling and in situ hybridization (ISH). At 30 hpf, the heart was centralized or reversed in 53% of the early thapsigargin-treated embryos (n=72) vs 5% of the DMSO-treated control embryos (n=75). The embryos were most sensitive to thapsigargin during early and mid-gastrulation with subsequent decrease in heart laterality defects. The incidence of heart laterality defects correlated with decreased or absent no tail expression in the dorsal forerunner cells and disruption of Kupffer’s vesicle formation in 73% of the early treated embryos (n=203), vs 2% of the control embryos (n=198) (p<0.01). Deviation from the normal morphological L-R asymmetry in the habenular nucleus of the diencephalon was found in 54% of the thapsigargin treated embryos (n=17) and in 88% of the embryos with L-looped heart (n=9) vs none control embryos. Analysis of the expression pattern of the “left-sided” marker pitx2 α in the dorsal diencephalon by ISH revealed this to be reversed or bilateral in 56% of the treated embryos (n=97) vs only 10% of the control embryos (p<0.05). In addition 47% of the thapsigargin treated embryo displayed reversed gut-looping (n=49) vs none control embryos. Our data suggest that inhibition of the ER calcium pump by thapsigargin during gastrulation impairs development of the Kupffer’s vesicle and disrupts the concordant heart, brain and gut L-R asymmetry. These results suggest an additional role of calcium in L-R asymmetry determination well before its previously recognized role in sensing fluid flow in the Kupffer’s vesicle.

scholarly journals Right-elevated expression of charon is regulated by fluid flow in medaka Kupffer's vesicle

2007 ◽  
Vol 49 (5) ◽  
pp. 395-405 ◽  
Author(s):  
Motoki Hojo ◽  
Shigeo Takashima ◽  
Daisuke Kobayashi ◽  
Akira Sumeragi ◽  
Atsuko Shimada ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle ◽  
Elevated Expression

scholarly journals Bardet–Biedl syndrome genes are important in retrograde intracellular trafficking and Kupffer's vesicle cilia function

2006 ◽  
Vol 15 (5) ◽  
pp. 667-677 ◽  
Author(s):  
Hsan-Jan Yen ◽  
Marwan K. Tayeh ◽  
Robert F. Mullins ◽  
Edwin M. Stone ◽  
Val C. Sheffield ◽  
...  
Keyword(s):  
Intracellular Trafficking ◽  
Bardet Biedl Syndrome ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle

scholarly journals Autoamplification and competition drive symmetry breaking: Initiation of centriole duplication by the PLK4-STIL network

2018 ◽  
Author(s):  
Marcin Leda ◽  
Andrew J. Holland ◽  
Andrew B. Goryachev
Keyword(s):  
Symmetry Breaking ◽  
Mammalian Cells ◽  
Molecular Mechanisms ◽  
Break Symmetry ◽  
Biophysical Model ◽  
Model Organisms ◽  
Centriole Duplication ◽  
Mother Centriole ◽  
Autocatalytic Activation

SummarySymmetry breaking, a central principle of physics, has been hailed as the driver of self-organization in biological systems in general and biogenesis of cellular organelles in particular, but the molecular mechanisms of symmetry breaking only begin to become understood. Centrioles, the structural cores of centrosomes and cilia, must duplicate every cell cycle to ensure their faithful inheritance through cellular divisions. Work in model organisms identified conserved proteins required for centriole duplication and found that altering their abundance affects centriole number. However, the biophysical principles that ensure that, under physiological conditions, only a single procentriole is produced on each mother centriole remain enigmatic. Here we propose a mechanistic biophysical model for the initiation of procentriole formation in mammalian cells. We posit that interactions between the master regulatory kinase PLK4 and its activator-substrate STIL form the basis of the procentriole initiation network. The model faithfully recapitulates the experimentally observed transition from PLK4 uniformly distributed around the mother centriole, the “ring”, to a unique PLK4 focus, the “spot”, that triggers the assembly of a new procentriole. This symmetry breaking requires a dual positive feedback based on autocatalytic activation of PLK4 and enhanced centriolar anchoring of PLK4-STIL complexes by phosphorylated STIL. We find that, contrary to previous proposals,in situdegradation of active PLK4 is insufficient to break symmetry. Instead, the model predicts that competition between transient PLK4 activity maxima for PLK4-STIL complexes explains both the instability of the PLK4 ring and formation of the unique PLK4 spot. In the model, strong competition at physiologically normal parameters robustly produces a single procentriole, while increasing overexpression of PLK4 and STIL weakens the competition and causes progressive addition of procentrioles in agreement with experimental observations.

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