Embryonic nodal flow and the dynamics of nodal vesicular parcels

Cilia and Nodal Flow in Asymmetry: An Engineering Perspective

Over the past several years, cilia in the primitive node have become recognized more and more for their contribution to development, and more specifically, for their role in axis determination. Although many of the mechanisms behind their influence remain undocumented, it is known that their presence and motion in the primitive node of developing embryos is the determinant of the left-right axis. Studies on cilial mechanics and nodal fluid dynamics have provided clues as to how this asymmetry mechanism works, and more importantly, have shown that direct manipulation of the flow field in the node can directly influence physiology. Although relatively uncommon, cilial disorders have been shown to have a variety of impacts on individuals from chronic respiratory infections to infertility, as well as situs inversus which is linked to congenital heart disease. After first providing background information pertinent to understanding nodal flow and information on why this discussion is important, this paper aims to give a review of the history of nodal cilia investigations, an overview of cilia mechanics and nodal flow dynamics, as well as a review of research studies current and past that sought to understand the mechanisms behind nodal cilia's involvement in symmetry-breaking pathways through a biomedical engineering perspective. This discussion has the additional intention to compile interdisciplinary knowledge on asymmetry and development such that it may encourage more collaborative efforts between the sciences on this topic, as well as provide insight on potential paths forward in the field.

Quantum noise may limit the mechanosensory sensitivity of cilia in the left-right organizer of the vertebrate bodyplan

Could nature be harnessing quantum mechanics in cilia to optimize the sensitivity of the mechanism of left-right symmetry breaking during development in vertebrates? I evaluate whether mechanosensing - i.e., the detection of a left-right asymmetric signal through mechanical stimulation of sensory cilia, as opposed to biochemical signalling - might be functioning in the embryonic left-right organizer of the vertebrate bodyplan through quantum mechanics. I conclude that there is a possible role for quantum biology in mechanosensing in cilia. The system may not be limited by classical thermal noise, but instead by quantum noise, with an amplification process providing active cooling.

Cilia and centrosomes: Ultrastructural and mechanical perspectives

Cilia and centrosomes of eukaryotic cells play important roles in cell movement, fluid transport, extracellular sensing, and chromosome division. The physiological functions of cilia and centrosomes are generated by their dynamics, motions, and forces controlled by the physical, chemical, and biological environments. How an individual cilium achieves its beat pattern and induces fluid flow is governed by its ultrastructure as well as the coordination of associated molecular motors. Thus, a bottom-up understanding of the physiological functions of cilia and centrosomes from the molecular to tissue levels is required. Correlations between the structure and motion can be understood in terms of mechanics. This review first focuses on cilia and centrosomes at the molecular level, introducing their ultrastructure. We then shift to the organelle level and introduce the kinematics and mechanics of cilia and centrosomes. Next, at the tissue level, we introduce nodal ciliary dynamics and nodal flow, which play crucial roles in the organogenetic process of left-right asymmetry. We also introduce respiratory ciliary dynamics and mucous flow, which are critical for protecting the epithelium from drying and exposure to harmful particles and viruses, i.e., respiratory clearance function. Finally, we discuss the future research directions in this field.

Simulations of particle tracking in the oligociliated mouse node and implications for left-right symmetry-breaking mechanics

The concept of internal anatomical asymmetry is familiar-usually in humans the heart is on the left and the liver is on the right; however, how does the developing embryo know to produce this consistent laterality? Symmetry-breaking initiates with left-right asymmetric cilia-driven fluid mechanics in a small fluid-filled structure called the ventral node in mice. However, the question of what converts this flow into left-right asymmetric development remains unanswered. A leading hypothesis is that flow transports morphogen-containing vesicles within the node, the absorption of which results in asymmetrical gene expression. To investigate how vesicle transport might result in the situs patterns observe in wild-type and mutant experiments, we extend the open-source Stokes flow package, NEAREST, to consider the hydrodynamic and Brownian motion of particles in a mouse model with flow driven by one, two and 112 beating cilia. Three models for morphogen-containing particle released are simulated to assess their compatibility with observed results in oligociliated and wild-type mouse embryos: uniformly random release, localized cilium stress-induced release and localized release from motile cilia themselves. Only the uniformly random release model appears consistent with the data, with neither localized release model resulting in significant transport in the oligociliated embryo. This article is part of the Theo Murphy meeting issue 'Unity and diversity of cilia in locomotion and transport'.

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

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'.

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

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.

Wall stress enhanced exocytosis of extracellular vesicles as a possible mechanism of left-right symmetry-breaking in vertebrate development

In certain vertebrate species, the developing embryo breaks left-right symmetry in a transient organising structure: the "Left-Right Organiser" (LRO) known as the "node" in mice, and "Kupffer's vesicle" in fish. Directional cilia-driven flow is integral to this symmetry-breaking process, however the mechanism by which this flow is translated into an asymmetric signal remains contested; the principal theories are either flow transport of vesicles containing morphogens, or flow mechanosensing by cilia. Whilst some recent work favours the morphogen theory, other findings seem to support mechanosensing. In this study, we consider a hypothesis whereby the cilia themselves drive the release of morphogen-carrying extracellular vesicles (EVs) into the LRO; namely, that fluid stresses on the cell membrane induce/enhance exocytosis of EVs. Using a mathematical model, we calculate significant wall normal and shear stresses for a range of typical cilium parameter values comparable to levels capable of enhancing exocytosis. This mechanism may be able to reconcile the apparently conflicting experimental evidence.

Simulation of the nodal flow of mutant embryos with a small number of cilia: comparison of mechanosensing and vesicle transport hypotheses

Left-right (L-R) asymmetry in the body plan is determined by nodal flow in vertebrate embryos. Shinohara et al. (Shinohara K et al. 2012 Nat. Commun.3, 622 (doi:10.1038/ncomms1624)) used Dpcd and Rfx3 mutant mouse embryos and showed that only a few cilia were sufficient to achieve L-R asymmetry. However, the mechanism underlying the breaking of symmetry by such weak ciliary flow is unclear. Flow-mediated signals associated with the L-R asymmetric organogenesis have not been clarified, and two different hypotheses-vesicle transport and mechanosensing-are now debated in the research field of developmental biology. In this study, we developed a computational model of the node system reported by Shinohara et al. and examined the feasibilities of the two hypotheses with a small number of cilia. With the small number of rotating cilia, flow was induced locally and global strong flow was not observed in the node. Particles were then effectively transported only when they were close to the cilia, and particle transport was strongly dependent on the ciliary positions. Although the maximum wall shear rate was also influenced by ciliary position, the mean wall shear rate at the perinodal wall increased monotonically with the number of cilia. We also investigated the membrane tension of immotile cilia, which is relevant to the regulation of mechanotransduction. The results indicated that tension of about 0.1 μN m-1 was exerted at the base even when the fluid shear rate was applied at about 0.1 s-1. The area of high tension was also localized at the upstream side, and negative tension appeared at the downstream side. Such localization may be useful to sense the flow direction at the periphery, as time-averaged anticlockwise circulation was induced in the node by rotation of a few cilia. Our numerical results support the mechanosensing hypothesis, and we expect that our study will stimulate further experimental investigations of mechanotransduction in the near future.

Cilia in Left-Right Symmetry Breaking

Visceral organs of vertebrates show left-right (L-R) asymmetry with regard to their position and morphology. Cilia play essential role in generating L-R asymmetry. A number of genes required for L-R asymmetry have now been identified in vertebrates, including human, many of which contribute to the formation and motility of cilia. In the mouse embryo, breaking of L-R symmetry occurs in the ventral node, where two types of cilia (motile and immotile) are present. Motile cilia are located at the central region of the node, and generate a leftward fluid flow. These motile cilia at the node are unique in that they rotate in the clockwise direction, unlike other immotile cilia such as airway cilia that show planar beating. The second type of cilia essential for L-R asymmetry is immotile cilia that are peripherally located immotile cilia. They sense a flow-dependent signal, which is either chemical or mechanical in nature. Although Ca²⁺ signaling is implicated in flow sensing, the precise mechanism remains unknown.

Left-Right Patterning: Breaking Symmetry to Asymmetric Morphogenesis

Vertebrates exhibit striking left-right (L-R) asymmetries in the structure and position of the internal organs. Symmetry is broken by motile cilia-generated asymmetric fluid flow, resulting in a signaling cascade - the Nodal-Pitx2 pathway - being robustly established within mesodermal tissue on the left side only. This pathway impinges upon various organ primordia to instruct their side-specific development. Recently, progress has been made in understanding both the breaking of embryonic L-R symmetry and how the Nodal-Pitx2 pathway controls lateralized cell differentiation, migration, and other aspects of cell behavior, as well as tissue-level mechanisms, that drive asymmetries in organ formation. Proper execution of asymmetric organogenesis is critical to health, making furthering our understanding of L-R development an important concern.

A computational model of dynein activation patterns that can explain nodal cilia rotation

Normal left-right patterning in vertebrates depends on the rotational movement of nodal cilia. In order to produce this ciliary motion, the activity of axonemal dyneins must be tightly regulated in a temporal and spatial manner; the specific activation pattern of the dynein motors in the nodal cilia has not been reported. Contemporary imaging techniques cannot directly assess dynein activity in a living cilium. In this study, we establish a three-dimensional model to mimic the ciliary ultrastructure and assume that the activation of dynein proteins is related to the interdoublet distance. By employing finite-element analysis and grid deformation techniques, we simulate the mechanical function of dyneins by pairs of point loads, investigate the time-variant interdoublet distance, and simulate the dynein-triggered ciliary motion. The computational results indicate that, to produce the rotational movement of nodal cilia, the dynein activity is transferred clockwise (looking from the tip) between the nine doublet microtubules, and along each microtubule, the dynein activation should occur faster at the basal region and slower when it is close to the ciliary tip. Moreover, the time cost by all the dyneins along one microtubule to be activated can be used to deduce the dynein activation pattern; it implies that, as an alternative method, measuring this time can indirectly reveal the dynein activity. The proposed protein-structure model can simulate the ciliary motion triggered by various dynein activation patterns explicitly and may contribute to furthering the studies on axonemal dynein activity.

Organized chaos in Kupffer's vesicle: how a heterogeneous structure achieves consistent left-right patterning

Successful establishment of left-right 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 left-right organizer of many other species. While swirling flow in KV is recognized as essential for left-right 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.

Chemosignalling, mechanotransduction and ciliary behaviour in the embryonic node: Computational evaluation of competing theories

Precise specification of left-right asymmetry is essential for patterning the internal organs of vertebrates. Within the embryonic node, posteriorly polarised cilia rotate, causing a leftward fluid flow (nodal flow) that establishes left-right asymmetry. The mechanism by which an embryo senses nodal flow remains uncertain. Existing hypotheses argue that either nodal flow carries morphogen(s) or lipid-bounded vesicles towards the left, thereby generating an asymmetric signal, and/or that mechano-sensory cilia sense this unidirectional flow, stimulating left-sided intracellular calcium signalling. To date, direct and definitive evidence supporting these hypotheses has been lacking. In this study, we conduct a multi-scale study to simulate the nodal cilia and the fluidic environment, analysing left-right signal transmission. By employing computational simulation techniques and solving the relevant three-dimensional unsteady transport equations, we study the flow pattern produced by the rotation of active cilia. By importing dilute species and particles into the computational domain, we investigate the transport of morphogens and nodal vesicular parcels, respectively. Furthermore, by extending the analysis to include the solid mechanics of passive deformable cilia and the coupling of their structural behaviour with the emerging fluid mechanics, we study the response of passive cilia to the nodal flow. Our results reproduce the unidirectional nodal flow, allowing us to evaluate the plausibility of both chemo- and mechano-sensing hypotheses. The quantitative measurements of the flow rate, the molecular transport and distribution provide guidance regarding the necessary morphogen molecular weights to break signalling symmetry. The passive sensory ciliary deformation gives indications regarding the plausibility of this mechano-signalling mechanism.

Establishment of left-right asymmetry in vertebrate development: the node in mouse embryos

Establishment of vertebrate left-right asymmetry is a critical process for normal embryonic development. After the discovery of genes expressed asymmetrically along the left-right axis in chick embryos in the mid 1990s, the molecular mechanisms responsible for left-right patterning in vertebrate embryos have been studied extensively. In this review article, we discuss the mechanisms by which the initial symmetry along the left-right axis is broken in the mouse embryo. We focus on the role of primary cilia and molecular mechanisms of ciliogenesis at the node when symmetry is broken and left-right asymmetry is established. The node is considered a signaling center for early mouse embryonic development, and the results we review here have led to a better understanding of how the node functions and establishes left-right asymmetry.

Fluid flows and forces in development: functions, features and biophysical principles

Throughout morphogenesis, cells experience intracellular tensile and contractile forces on microscopic scales. Cells also experience extracellular forces, such as static forces mediated by the extracellular matrix and forces resulting from microscopic fluid flow. Although the biological ramifications of static forces have received much attention, little is known about the roles of fluid flows and forces during embryogenesis. Here, we focus on the microfluidic forces generated by cilia-driven fluid flow and heart-driven hemodynamics, as well as on the signaling pathways involved in flow sensing. We discuss recent studies that describe the functions and the biomechanical features of these fluid flows. These insights suggest that biological flow determines many aspects of cell behavior and identity through a specific set of physical stimuli and signaling pathways.

Two rotating cilia in the node cavity are sufficient to break left-right symmetry in the mouse embryo

Determination of left-right asymmetry in mouse embryos is achieved by a leftward fluid flow (nodal flow) in the node cavity that is generated by clockwise rotational movement of 200-300 cilia in the node. The precise action of nodal flow and how much flow input is required for the robust read-out of left-right determination remains unknown. Here we show that a local leftward flow generated by as few as two rotating cilia is sufficient to break left-right symmetry. Quantitative analysis of fluid flow and ciliary rotation in the node of mouse embryos shows that left-right asymmetry is already established within a few hours after the onset of rotation by a subset of nodal cilia. Examination of various ciliary mutant mice shows that two rotating cilia are sufficient to initiate left-right asymmetric gene expression. Our results suggest the existence of a highly sensitive system in the node that is able to sense an extremely weak unidirectional flow, and may favour a model in which the flow is sensed as a mechanical force.

The multiple roles of Notch signaling during left-right patterning

The establishment of left-right (LR) asymmetry is regulated by intricate signaling mechanisms during embryogenesis and this asymmetry is critical for morphogenesis as well as the positioning of internal organs within the organism. Recent progress including elucidation of ion transporters, leftward nodal flow, and regulation of asymmetric gene expression contributes to our understanding of how the breaking of the symmetry is initiated and how this laterality information is subsequently transmitted to the organ primordium. A number of developmental signaling pathways have been implicated in this complex process. In this review, we will focus on the roles of the Notch signaling pathway during development of LR asymmetry. The Notch signaling pathway is a short-range communication system between neighboring cells. While Notch signaling plays essential roles in regulating the morphogenesis of the node and left-specific expression of Nodal in the lateral plate mesoderm, a hallmark gene in LR patterning, Notch signaling also suppresses the expression of Pitx2 that is a direct downstream target of Nodal during later stages of development. This negative activity of Notch signaling towards left-specific activity was recently shown to be inhibited by the B cell lymphoma 6 (BCL6)/BCL6 co-repressor (BcoR) transcriptional repressor complex in a target-specific manner. The complex regulation of Notch-dependent gene expression for LR asymmetry will be highlighted in this review.

Left-right determination: involvement of molecular motor KIF3, cilia, and nodal flow

Mammalian left-right determination is a good example for how multiple cell biological processes coordinate in the formation of a basic body plan. The leftward movement of fluid at the ventral node, called nodal flow, is the central process in symmetry breaking on the left-right axis. Nodal flow is autonomously generated by the rotation of posteriorly tilted cilia that are built by transport via KIF3 motor on cells of the ventral node. How nodal flow is interpreted to create left-right asymmetry has been a matter of debate. Recent evidence suggests that the leftward movement of sheathed lipidic particles, called nodal vesicular parcels (NVPs), may result in the activation of the noncanonical hedgehog signaling pathway, an asymmetric elevation in intracellular Ca(2+) and changes in gene expression.

Biomimetic cilia arrays generate simultaneous pumping and mixing regimes

Living systems employ cilia to control and to sense the flow of fluids for many purposes, such as pumping, locomotion, feeding, and tissue morphogenesis. Beyond their use in biology, functional arrays of artificial cilia have been envisaged as a potential biomimetic strategy for inducing fluid flow and mixing in lab-on-a-chip devices. Here we report on fluid transport produced by magnetically actuated arrays of biomimetic cilia whose size approaches that of their biological counterparts, a scale at which advection and diffusion compete to determine mass transport. Our biomimetic cilia recreate the beat shape of embryonic nodal cilia, simultaneously generating two sharply segregated regimes of fluid flow: Above the cilia tips their motion causes directed, long-range fluid transport, whereas below the tips we show that the cilia beat generates an enhanced diffusivity capable of producing increased mixing rates. These two distinct types of flow occur simultaneously and are separated in space by less than 5 microm, approximately 20% of the biomimetic cilium length. While this suggests that our system may have applications as a versatile microfluidics device, we also focus on the biological implications of our findings. Our statistical analysis of particle transport identifying an enhanced diffusion regime provides novel evidence for the existence of mixing in ciliated systems, and we demonstrate that the directed transport regime is Poiseuille-Couette flow, the first analytical model consistent with biological measurements of fluid flow in the embryonic node.

Observation of nodal cilia movement and measurement of nodal flow

Mammalian left-right determination is a good example of how multiple cell biological processes coordinate in the formation of a basic body plan, but until recently its mechanism was totally elusive. In the past 10 years, molecular genetic studies of kinesin and dynein motor proteins, live-cell imaging techniques, and theoretical studies of fluid mechanics revealed unexpected mechanisms of left-right determination. The leftward movement of fluid at the ventral node, called nodal flow, is the central process in symmetry breaking on the left-right axis. Nodal flow is autonomously generated by the rotation of posteriorly tilted cilia that are built by transport via the KIF3 motor on cells of the ventral node. Recent evidence suggests that nodal flow transports sheathed lipidic particles, called nodal vesicular parcels (NVPs), to the left edge of the node, which results in the activation of the noncanonical Hedgehog signaling pathway, an asymmetric elevation in intracellular Ca(2+), and changes in gene expression. This chapter reviews techniques for the observation of nodal cilia movement and nodal flow in living vertebrate embryos.

Mathematical modelling of cilia-driven transport of biological fluids

Cilia-driven flow occurs in the airway surface liquid, in the female and male reproductive tracts and enables symmetry-breaking in the embryonic node. Viscoelastic rheology is found in healthy states in some systems, whereas in others may characterise disease, motivating the development of mathematical models that take this effect into account. We derive the fundamental solution for linear viscoelastic flow, which is subsequently used as a basis for slender-body theory. Our numerical algorithm allows efficient computation of three-dimensional time-dependent flow, bending moments, power and particle transport. We apply the model to the large-amplitude motion of a single cilium in a linear Maxwell liquid. A relatively short relaxation time of just 0.032 times the beat period significantly reduces forces, bending moments, power and particle transport, the last variable exhibiting exponential decay with relaxation time. A test particle is propelled approximately one-fifth as quickly along the direction of cilia beating for scaled relaxation time 0.032 as in the Newtonian case, and mean volume flow is abolished, emphasizing the sensitivity of cilia function to fluid rheology. These results may have implications for flow in the airways, where the transition from Newtonian to viscoelastic rheology in the peri-ciliary fluid may reduce clearance.

Fluid dynamics in zebrafish Kupffer's vesicle

Work in mouse has implicated cilia motility and leftward nodal flow as the mechanism for breaking left-right symmetry. In zebrafish, it is assumed that Kupffer's vesicle is analogous to the mouse node. However, its architecture is different and the fluid dynamics inside Kupffer's vesicle is not completely understood. We show that cells lining both the dorsal roof and the ventral floor of Kupffer's vesicle possess posteriorly pointed cilia that rotate clockwise when viewed apically. Analysis of bead movements within Kupffer's vesicle shows a net circular flow but the local flow differs in direction depending on the location within the vesicle. Histological analysis suggests that the orientation of the cells at anterior-dorsal region likely direct net flow in the vesicle. Our data suggest that the plane of the circular net flow is tilted with respect to the D-V axis, which may be converted to a local leftward flow in the anterior-dorsal region of the vesicle.

Fluid dynamics in developmental biology: moving fluids that shape ontogeny

Human conception, indeed fertilization in general, takes place in a fluid, but what role does fluid dynamics have during the subsequent development of an organism? It is becoming increasingly clear that the number of genes in the genome of a typical organism is not sufficient to specify the minutiae of all features of its ontogeny. Instead, genetics often acts as a choreographer, guiding development but leaving some aspects to be controlled by physical and chemical means. Fluids are ubiquitous in biological systems, so it is not surprising that fluid dynamics should play an important role in the physical and chemical processes shaping ontogeny. However, only in a few cases have the strands been teased apart to see exactly how fluid forces operate to guide development. Here, we review instances in which the hand of fluid dynamics in developmental biology is acknowledged, both in human development and within a wider biological context, together with some in which fluid dynamics is notable but whose workings have yet to be understood, and we provide a fluid dynamicist's perspective on possible avenues for future research.

Designing synthetic, pumping cilia that switch the flow direction in microchannels

Using computational modeling, we simulate the 3D movement of actuated cilia in a fluid-filled microchannel. The cilia are modeled as deformable, elastic filaments, and the simulations capture the complex fluid-structure interactions among these filaments, the channel walls, and the surrounding solution. The cilia are tilted with respect to the surface and are actuated by a sinusoidal force that is applied at the free ends. We find that these cilia give rise to a unidirectional flow in the system and by simply altering the frequency of the applied force we can controllably switch the direction of the net flow. The findings indicate that beating, synthetic cilia could be harnessed to regulate the fluid streams in microfluidic devices.

Fluid dynamics of establishing left-right patterning in development

How does the clockwise motion of tens of monocilia drive a leftward flow in the node? And, as the observed flow is leftward, how is the fluid recirculating within the node, as it must, because the node is a closed structure? How does the nodal flow lead to left-right symmetry breaking in the embryo? These questions are within the realm of fluid physics, whose application to the problem of left-right symmetry breaking in vertebrates has led to important advances in the field.

Fluid mechanics of nodal flow due to embryonic primary cilia

Breaking of left-right symmetry is crucial in vertebrate development. The role of cilia-driven flow has been the subject of many recent publications, but the underlying mechanisms remain controversial. At approximately 8 days post-fertilization, after the establishment of the dorsal-ventral and anterior-posterior axes, a depressed structure is found on the ventral side of mouse embryos, termed the ventral node. Within the node, 'whirling' primary cilia, tilted towards the posterior, drive a flow implicated in the initial left-right signalling asymmetry. However, the underlying fluid mechanics have not been fully and correctly explained until recently and accurate characterization is required in determining how the flow triggers the downstream signalling cascades. Using the approximation of resistive force theory, we show how the flow is produced and calculate the optimal configuration to cause maximum flow, showing excellent agreement with in vitro measurements and numerical simulation, and paralleling recent analogue experiments. By calculating numerical solutions of the slender body theory equations, we present time-dependent physically based fluid dynamics simulations of particle pathlines in flows generated by large arrays of beating cilia, showing the far-field radial streamlines predicted by the theory.