2017 

8.  Pintado, P; Sampaio, P; Tavares, B; MontenegroJohnson, T D; Smith, D J; Lopes, S S Dynamics of cilia length in leftright development Journal Article Royal Society Open Science, 4 (3), 2017. Abstract  BibTeX  Tags: Cilia, Symmetrybreaking flow, Zebrafish  Links: @article{pintado2016dynamics, title = {Dynamics of cilia length in leftright development}, author = {P. Pintado and P. Sampaio and B. Tavares and T. D. MontenegroJohnson and D. J. Smith and S. S. Lopes}, url = {http://tomonjon.com/wpcontent/uploads/2017/04/dynamics_of_cilia_LR_zebrafish.pdf}, doi = {10.1098/rsos.161102}, year = {2017}, date = {20170308}, journal = {Royal Society Open Science}, volume = {4}, number = {3}, abstract = {Reduction in the length of motile cilia in the zebrafish leftright organizer (LRO), also known as Kupffer's vesicle, has a large impact on leftright development. Here we demonstrate through genetic overexpression in zebrafish embryos and mathematical modelling that the impact of increased motile cilia length in embryonic LRO fluid flow is milder than that of short cilia. Through Arl13b overexpression, which increases cilia length without impacting cilia beat frequency, we show that the increase in cilium length is associated with a decrease in beat amplitude, resulting in similar flow strengths for Arl13b overexpression and wildtype (WT) embryos, which were not predicted by current theory. Longer cilia exhibit pronounced helical beat patterns and, consequently, lower beat amplitudes relative to WT, a result of an elastohydrodynamic shape transition. For long helical cilia, fluid dynamics modelling predicts a mild (approx. 12%) reduction in the torque exerted on the fluid relative to the WT, resulting in a proportional reduction in flow generation. This mild reduction is corroborated by experiments, providing a mechanism for the mild impact on organ situs.}, keywords = {Cilia, Symmetrybreaking flow, Zebrafish}, pubstate = {published}, tppubtype = {article} } Reduction in the length of motile cilia in the zebrafish leftright organizer (LRO), also known as Kupffer's vesicle, has a large impact on leftright development. Here we demonstrate through genetic overexpression in zebrafish embryos and mathematical modelling that the impact of increased motile cilia length in embryonic LRO fluid flow is milder than that of short cilia. Through Arl13b overexpression, which increases cilia length without impacting cilia beat frequency, we show that the increase in cilium length is associated with a decrease in beat amplitude, resulting in similar flow strengths for Arl13b overexpression and wildtype (WT) embryos, which were not predicted by current theory. Longer cilia exhibit pronounced helical beat patterns and, consequently, lower beat amplitudes relative to WT, a result of an elastohydrodynamic shape transition. For long helical cilia, fluid dynamics modelling predicts a mild (approx. 12%) reduction in the torque exerted on the fluid relative to the WT, resulting in a proportional reduction in flow generation. This mild reduction is corroborated by experiments, providing a mechanism for the mild impact on organ situs. 
2016 

7.  MontenegroJohnson, T D; Baker, D I; Smith, D J; Lopes, S S Threedimensional flow in Kupffer's Vesicle Journal Article Journal of Mathematical Biology, 73 (3), pp. 705  725, 2016, ISSN: 14321416. Abstract  BibTeX  Tags: Boundary Elements, Cilia, Symmetrybreaking flow, Zebrafish  Links: @article{montenegro2016three, title = {Threedimensional flow in Kupffer's Vesicle}, author = {T. D. MontenegroJohnson and D. I. Baker and D. J. Smith and S. S. Lopes}, url = {http://tomonjon.com/wpcontent/uploads/2016/11/zebrafish_jmbiol_arxiv1.pdf}, doi = {10.1007/s0028501609677}, issn = {14321416}, year = {2016}, date = {20160129}, journal = {Journal of Mathematical Biology}, volume = {73}, number = {3}, pages = {705  725}, abstract = {Whilst many vertebrates appear externally leftright symmetric, the arrangement of internal organs is asymmetric. In zebrafish, the breaking of leftright symmetry is organised by Kupffer's Vesicle (KV): an approximately spherical, fluidfilled structure that begins to form in the embryo 10 hours post fertilisation. A crucial component of zebrafish symmetry breaking is the establishment of a ciliadriven fluid flow within KV. However, it is still unclear (a) how dorsal, ventral and equatorial cilia contribute to the global vortical flow, and (b) if this flow breaks leftright symmetry through mechanical transduction or morphogen transport. Fully answering these questions requires knowledge of the threedimensional flow patterns within KV, which have not been quantified in previous work. In this study, we calculate and analyse the threedimensional flow in KV. We consider flow from both individual and groups of cilia, and (a) find anticlockwise flow can arise purely from excess of cilia on the dorsal roof over the ventral floor, showing how this vortical flow is stabilised by dorsal tilt of equatorial cilia, and (b) show that anterior clustering of dorsal cilia leads to around 40 {%} faster flow in the anterior over the posterior corner. We argue that these flow features are supportive of symmetry breaking through mechanosensory cilia, and suggest a novel experiment to test this hypothesis. From our new understanding of the flow, we propose a further experiment to reverse the flow within KV to potentially induce situs inversus.}, keywords = {Boundary Elements, Cilia, Symmetrybreaking flow, Zebrafish}, pubstate = {published}, tppubtype = {article} } Whilst many vertebrates appear externally leftright symmetric, the arrangement of internal organs is asymmetric. In zebrafish, the breaking of leftright symmetry is organised by Kupffer's Vesicle (KV): an approximately spherical, fluidfilled structure that begins to form in the embryo 10 hours post fertilisation. A crucial component of zebrafish symmetry breaking is the establishment of a ciliadriven fluid flow within KV. However, it is still unclear (a) how dorsal, ventral and equatorial cilia contribute to the global vortical flow, and (b) if this flow breaks leftright symmetry through mechanical transduction or morphogen transport. Fully answering these questions requires knowledge of the threedimensional flow patterns within KV, which have not been quantified in previous work. In this study, we calculate and analyse the threedimensional flow in KV. We consider flow from both individual and groups of cilia, and (a) find anticlockwise flow can arise purely from excess of cilia on the dorsal roof over the ventral floor, showing how this vortical flow is stabilised by dorsal tilt of equatorial cilia, and (b) show that anterior clustering of dorsal cilia leads to around 40 {%} faster flow in the anterior over the posterior corner. We argue that these flow features are supportive of symmetry breaking through mechanosensory cilia, and suggest a novel experiment to test this hypothesis. From our new understanding of the flow, we propose a further experiment to reverse the flow within KV to potentially induce situs inversus. 
2015 

6.  MontenegroJohnson, T D; Gadêlha, H; Smith, D J Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model Journal Article Open Science, 2 (3), 2015. Abstract  BibTeX  Tags: Elastohydrodynamics, Microscale propulsion, Sperm  Links: @article{montenegro2015spermatozoa, title = {Spermatozoa scattering by a microchannel feature: an elastohydrodynamic model}, author = {T. D. MontenegroJohnson and H. Gadêlha and D. J. Smith}, url = {http://tomonjon.com/wpcontent/uploads/2016/11/Spermatozoa_scattering_by_a_microchannel_feature.pdf}, doi = {10.1098/rsos.140475}, year = {2015}, date = {20150318}, journal = {Open Science}, volume = {2}, number = {3}, abstract = {Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for largeamplitude elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a ‘high viscosity’ parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5°–10°. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasizing the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature.}, keywords = {Elastohydrodynamics, Microscale propulsion, Sperm}, pubstate = {published}, tppubtype = {article} } Sperm traverse their microenvironment through viscous fluid by propagating flagellar waves; the waveform emerges as a consequence of elastic structure, internal active moments and low Reynolds number fluid dynamics. Engineered microchannels have recently been proposed as a method of sorting and manipulating motile cells; the interaction of cells with these artificial environments therefore warrants investigation. A numerical method is presented for largeamplitude elastohydrodynamic interaction of active swimmers with domain features. This method is employed to examine hydrodynamic scattering by a model microchannel backstep feature. Scattering is shown to depend on backstep height and the relative strength of viscous and elastic forces in the flagellum. In a ‘high viscosity’ parameter regime corresponding to human sperm in cervical mucus analogue, this hydrodynamic contribution to scattering is comparable in magnitude to recent data on contact effects, being of the order of 5°–10°. Scattering can be positive or negative depending on the relative strength of viscous and elastic effects, emphasizing the importance of viscosity on the interaction of sperm with their microenvironment. The modulation of scattering angle by viscosity is associated with variations in flagellar asymmetry induced by the elastohydrodynamic interaction with the boundary feature. 
2014 

5.  Smith, D J; MontenegroJohnson, T D; Lopes, S S Organized chaos in Kupffer's vesicle: how a heterogeneous structure achieves consistent leftright patterning Journal Article BioArchitecture, 4 (3), pp. 119125, 2014. Abstract  BibTeX  Tags: Cilia, Symmetrybreaking flow, Zebrafish  Links: @article{smith2014organised, title = {Organized chaos in Kupffer's vesicle: how a heterogeneous structure achieves consistent leftright patterning}, author = {D. J. Smith and T. D. MontenegroJohnson and S. S. Lopes }, url = {http://tomonjon.com/wpcontent/uploads/2016/11/smith2014organized.pdf}, doi = {10.4161/19490992.2014.956593}, year = {2014}, date = {20141106}, journal = {BioArchitecture}, volume = {4}, number = {3}, pages = {119125}, abstract = {Successful establishment of leftright asymmetry is crucial to healthy vertebrate development. In many species this process is initiated in a ciliated, enclosed cavity, for example Kupffer's vesicle (KV) in zebrafish. The microarchitecture of KV is more complex than that present in the leftright organizer of many other species. While swirling flow in KV is recognized as essential for leftright patterning, its generation, nature and conversion to asymmetric gene expression are only beginning to be fully understood. We recently [Sampaio, P et al. Dev Cell 29:716–728] combined imaging, genetics and fluid dynamics simulation to characterize normal and perturbed ciliary activity, and their correlation to asymmetric charon expression and embryonic organ fate. Randomness in cilia number and length have major implications for robust flow generation; even a modest change in mean cilia length has a major effect on flow speed to due to nonlinear scaling arising from fluid mechanics. Wildtype, and mutant embryos with normal liver laterality, exhibit stronger flow on the left prior to asymmetric inhibition of charon. Our discovery of immotile cilia, taken with data on morphant embryos with very few cilia, further support the role of mechanosensing in initiating and/or enhancing flow conversion into gene expression.}, keywords = {Cilia, Symmetrybreaking flow, Zebrafish}, pubstate = {published}, tppubtype = {article} } Successful establishment of leftright asymmetry is crucial to healthy vertebrate development. In many species this process is initiated in a ciliated, enclosed cavity, for example Kupffer's vesicle (KV) in zebrafish. The microarchitecture of KV is more complex than that present in the leftright organizer of many other species. While swirling flow in KV is recognized as essential for leftright patterning, its generation, nature and conversion to asymmetric gene expression are only beginning to be fully understood. We recently [Sampaio, P et al. Dev Cell 29:716–728] combined imaging, genetics and fluid dynamics simulation to characterize normal and perturbed ciliary activity, and their correlation to asymmetric charon expression and embryonic organ fate. Randomness in cilia number and length have major implications for robust flow generation; even a modest change in mean cilia length has a major effect on flow speed to due to nonlinear scaling arising from fluid mechanics. Wildtype, and mutant embryos with normal liver laterality, exhibit stronger flow on the left prior to asymmetric inhibition of charon. Our discovery of immotile cilia, taken with data on morphant embryos with very few cilia, further support the role of mechanosensing in initiating and/or enhancing flow conversion into gene expression. 
4.  Sampaio, P; Ferreira, R R; Guerrero, A; Pintado, P; Tavares, B; Amaro, J; Smith, A A; MontenegroJohnson, T D; Smith, D J; Lopes, S S LeftRight organizer flow dynamics: How much cilia activity reliably yields laterality? Journal Article Developmental Cell, 29 (6), pp. 716728, 2014. Abstract  BibTeX  Tags: Cilia, Symmetrybreaking flow, Zebrafish  Links: @article{sampaio2014left, title = {LeftRight organizer flow dynamics: How much cilia activity reliably yields laterality?}, author = {P. Sampaio and R. R. Ferreira and A. Guerrero and P. Pintado and B. Tavares and J. Amaro and A. A. Smith and T. D. MontenegroJohnson and D. J. Smith and S. S. Lopes }, url = {http://tomonjon.com/wpcontent/uploads/2016/11/sampaio2014left.pdf}, doi = {10.1016/j.devcel.2014.04.030}, year = {2014}, date = {20140612}, journal = {Developmental Cell}, volume = {29}, number = {6}, pages = {716728}, abstract = {Internal organs are asymmetrically positioned inside the body. Embryonic motile cilia play an essential role in this process by generating a directional fluid flow inside the vertebrate leftright organizer. Detailed characterization of how fluid flow dynamics modulates laterality is lacking. We used zebrafish genetics to experimentally generate a range of flow dynamics. By following the development of each embryo, we show that fluid flow in the leftright organizer is asymmetric and provides a good predictor of organ laterality. This was tested in mosaic organizers composed of motile and immotile cilia generated by dnah7 knockdowns. In parallel, we used simulations of fluid dynamics to analyze our experimental data. These revealed that fluid flow generated by 30 or more cilia predicts 90% situs solitus, similar to experimental observations. We conclude that cilia number, dorsal anterior motile cilia clustering, and left flow are critical to situs solitus via robust asymmetric charon expression.}, keywords = {Cilia, Symmetrybreaking flow, Zebrafish}, pubstate = {published}, tppubtype = {article} } Internal organs are asymmetrically positioned inside the body. Embryonic motile cilia play an essential role in this process by generating a directional fluid flow inside the vertebrate leftright organizer. Detailed characterization of how fluid flow dynamics modulates laterality is lacking. We used zebrafish genetics to experimentally generate a range of flow dynamics. By following the development of each embryo, we show that fluid flow in the leftright organizer is asymmetric and provides a good predictor of organ laterality. This was tested in mosaic organizers composed of motile and immotile cilia generated by dnah7 knockdowns. In parallel, we used simulations of fluid dynamics to analyze our experimental data. These revealed that fluid flow generated by 30 or more cilia predicts 90% situs solitus, similar to experimental observations. We conclude that cilia number, dorsal anterior motile cilia clustering, and left flow are critical to situs solitus via robust asymmetric charon expression. 
2013 

3.  MontenegroJohnson, T D; Smith, D J; Loghin, D Physics of rheologically enhanced propulsion: different strokes in generalized Stokes Journal Article Physics of Fluids, 25 (8), pp. 081903, 2013, (Highlighted in the Journal Club for Condensed Matter Physics with a commentary by Prof. Thomas R. Powers.). Abstract  BibTeX  Tags: Complex fluid, Finite elements, Microscale propulsion  Links: @article{montenegro2013physics, title = {Physics of rheologically enhanced propulsion: different strokes in generalized Stokes}, author = {T. D. MontenegroJohnson and D. J. Smith and D. Loghin }, url = {http://tomonjon.com/wpcontent/uploads/2016/11/DifferentstrokesingeneralizedStokes.pdf}, doi = {10.1063/1.4818640}, year = {2013}, date = {20130821}, journal = {Physics of Fluids}, volume = {25}, number = {8}, pages = {081903}, abstract = {Shearthinning is an important rheological property of many biological fluids, such as mucus, whereby the apparent viscosity of the fluid decreases with shear. Certain microscopic swimmers have been shown to progress more rapidly through shearthinning fluids, but is this behavior generic to all microscopic swimmers, and what are the physics through which shearthinning rheology affects a swimmer's propulsion? We examine swimmers employing prescribed stroke kinematics in twodimensional, inertialess Carreau fluid: shearthinning “generalized Stokes” flow. Swimmers are modeled, using the method of femlets, by a set of immersed, regularized forces. The equations governing the fluid dynamics are then discretized over a bodyfitted mesh and solved with the finite element method. We analyze the locomotion of three distinct classes of microswimmer: (1) conceptual swimmers comprising sliding spheres employing both one and twodimensional strokes, (2) slipvelocity envelope models of ciliates commonly referred to as “squirmers,” and (3) monoflagellate pushers, such as sperm. We find that morphologically identical swimmers with different strokes may swim either faster or slower in shearthinning fluids than in Newtonian fluids. We explain this kinematic sensitivity by considering differences in the viscosity of the fluid surrounding propulsive and payload elements of the swimmer, and using this insight suggest two reciprocal sliding sphere swimmers which violate Purcell's Scallop theorem in shearthinning fluids. We also show that an increased flow decay rate arising from shearthinning rheology is associated with a reduction in the swimming speed of slipvelocity squirmers. For spermlike swimmers, a gradient of thick to thin fluid along the flagellum alters the force it exerts upon the fluid, flattening trajectories and increasing instantaneous swimming speed.}, note = {Highlighted in the Journal Club for Condensed Matter Physics with a commentary by Prof. Thomas R. Powers.}, keywords = {Complex fluid, Finite elements, Microscale propulsion}, pubstate = {published}, tppubtype = {article} } Shearthinning is an important rheological property of many biological fluids, such as mucus, whereby the apparent viscosity of the fluid decreases with shear. Certain microscopic swimmers have been shown to progress more rapidly through shearthinning fluids, but is this behavior generic to all microscopic swimmers, and what are the physics through which shearthinning rheology affects a swimmer's propulsion? We examine swimmers employing prescribed stroke kinematics in twodimensional, inertialess Carreau fluid: shearthinning “generalized Stokes” flow. Swimmers are modeled, using the method of femlets, by a set of immersed, regularized forces. The equations governing the fluid dynamics are then discretized over a bodyfitted mesh and solved with the finite element method. We analyze the locomotion of three distinct classes of microswimmer: (1) conceptual swimmers comprising sliding spheres employing both one and twodimensional strokes, (2) slipvelocity envelope models of ciliates commonly referred to as “squirmers,” and (3) monoflagellate pushers, such as sperm. We find that morphologically identical swimmers with different strokes may swim either faster or slower in shearthinning fluids than in Newtonian fluids. We explain this kinematic sensitivity by considering differences in the viscosity of the fluid surrounding propulsive and payload elements of the swimmer, and using this insight suggest two reciprocal sliding sphere swimmers which violate Purcell's Scallop theorem in shearthinning fluids. We also show that an increased flow decay rate arising from shearthinning rheology is associated with a reduction in the swimming speed of slipvelocity squirmers. For spermlike swimmers, a gradient of thick to thin fluid along the flagellum alters the force it exerts upon the fluid, flattening trajectories and increasing instantaneous swimming speed. 
2012 

2.  MontenegroJohnson, T D; Smith, A A; Smith, D J; Loghin, D; Blake, J R Modelling the fluid mechanics of cilia and flagella in reproduction and development Journal Article European Physical Journal E, 35 (10), pp. 111, 2012, ISSN: 1292895X. Abstract  BibTeX  Tags: Cilia, Complex fluid, Microscale propulsion, Symmetrybreaking flow  Links: @article{montenegro2012modelling, title = {Modelling the fluid mechanics of cilia and flagella in reproduction and development}, author = {T. D. MontenegroJohnson and A. A. Smith and D. J. Smith and D. Loghin and J. R. Blake}, url = {http://tomonjon.com/wpcontent/uploads/2016/11/Modellingthefluidmechanicsofciliaandflagellainreproductionanddevelopment.pdf}, doi = {10.1140/epje/i2012121111}, issn = {1292895X}, year = {2012}, date = {20121029}, journal = {European Physical Journal E}, volume = {35}, number = {10}, pages = {111}, abstract = {Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscousdominated microscale flow, including timereversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higherorder multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: 1) leftright symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and 2) motility of microswimmers through nonNewtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a bodyconforming finiteelement framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a threesphere model swimmer and a model sperm are similarly affected by shearthinning; in both cases swimming due to a prescribed beat is enhanced by shearthinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shearthickening hindering cell progress.}, keywords = {Cilia, Complex fluid, Microscale propulsion, Symmetrybreaking flow}, pubstate = {published}, tppubtype = {article} } Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscousdominated microscale flow, including timereversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higherorder multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: 1) leftright symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and 2) motility of microswimmers through nonNewtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a bodyconforming finiteelement framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a threesphere model swimmer and a model sperm are similarly affected by shearthinning; in both cases swimming due to a prescribed beat is enhanced by shearthinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shearthickening hindering cell progress. 
1.  Smith, A A; MontenegroJohnson, T D; Smith, D J; Blake, J R Symmetrybreaking ciliadriven flow in the zebrafish embryo Journal Article Journal of Fluid Mechanics, 705 , pp. 26  45, 2012, (joint first author). Abstract  BibTeX  Tags: Cilia, Symmetrybreaking flow, Zebrafish  Links: @article{smith2012symmetry, title = {Symmetrybreaking ciliadriven flow in the zebrafish embryo}, author = {A. A. Smith and T. D. MontenegroJohnson and D. J. Smith and J. R. Blake}, url = {http://tomonjon.com/wpcontent/uploads/2016/11/Symmetrybreakingciliadrivenflowinthezebrafishembryo.pdf}, doi = {10.1017/jfm.2012.117}, year = {2012}, date = {20120413}, journal = {Journal of Fluid Mechanics}, volume = {705}, pages = {26  45}, abstract = {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 ciliadriven 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.}, note = {joint first author}, keywords = {Cilia, Symmetrybreaking flow, Zebrafish}, pubstate = {published}, tppubtype = {article} } 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 ciliadriven 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. 
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